43.002/43.002 YES 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR vNonEmpty:S x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 ) 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Inlining of Conditions Processor [STERN17]: 43.002/43.002 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR vNonEmpty:S x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 ) 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Clean CTRS Processor: 43.002/43.002 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 ) 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 CRule InfChecker Info: 43.002/43.002 a -> b 43.002/43.002 Rule remains 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 CRule InfChecker Info: 43.002/43.002 c -> k(f(a)) 43.002/43.002 Rule remains 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 CRule InfChecker Info: 43.002/43.002 c -> k(g(b)) 43.002/43.002 Rule remains 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 CRule InfChecker Info: 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 Rule remains 43.002/43.002 Proof: 43.002/43.002 NO 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Infeasibility Problem: 43.002/43.002 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S:S) -> g(x:S:S) | h(f(x:S:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S:S) -> k(x:S:S) 43.002/43.002 )] 43.002/43.002 43.002/43.002 Infeasibility Conditions: 43.002/43.002 h(f(x:S:S)) ->* k(g(b)) 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Obtaining a proof using Prover9: 43.002/43.002 43.002/43.002 -> Prover9 Output: 43.002/43.002 ============================== Prover9 =============================== 43.002/43.002 Prover9 (64) version 2009-11A, November 2009. 43.002/43.002 Process 120339 was started by ubuntu on ubuntu, 43.002/43.002 Fri Jul 16 15:38:35 2021 43.002/43.002 The command was "./prover9 -f /tmp/prover9120330-0.in". 43.002/43.002 ============================== end of head =========================== 43.002/43.002 43.002/43.002 ============================== INPUT ================================= 43.002/43.002 43.002/43.002 % Reading from file /tmp/prover9120330-0.in 43.002/43.002 43.002/43.002 assign(max_seconds,20). 43.002/43.002 43.002/43.002 formulas(assumptions). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). 43.002/43.002 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 43.002/43.002 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 43.002/43.002 ->_s0(a,b) # label(replacement). 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). 43.002/43.002 ->*_s0(h(f(x2)),k(g(b))) -> ->_s0(f(x2),g(x2)) # label(replacement). 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). 43.002/43.002 ->_s0(h(x2),k(x2)) # label(replacement). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(goals). 43.002/43.002 (exists x2 ->*_s0(h(f(x2)),k(g(b)))) # label(goal). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of input ========================== 43.002/43.002 43.002/43.002 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 43.002/43.002 43.002/43.002 % Formulas that are not ordinary clauses: 43.002/43.002 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 4 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 5 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->*_s0(h(f(x2)),k(g(b))) -> ->_s0(f(x2),g(x2)) # label(replacement) # label(non_clause). [assumption]. 43.002/43.002 7 (exists x2 ->*_s0(h(f(x2)),k(g(b)))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 43.002/43.002 ============================== end of process non-clausal formulas === 43.002/43.002 43.002/43.002 ============================== PROCESS INITIAL CLAUSES =============== 43.002/43.002 43.002/43.002 % Clauses before input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 -->*_s0(h(f(x)),k(g(b))) | ->_s0(f(x),g(x)) # label(replacement). [clausify(6)]. 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 -->*_s0(h(f(x)),k(g(b))) # label(goal). [deny(7)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== PREDICATE ELIMINATION ================= 43.002/43.002 43.002/43.002 No predicates eliminated. 43.002/43.002 43.002/43.002 ============================== end predicate elimination ============= 43.002/43.002 43.002/43.002 Auto_denials: 43.002/43.002 % copying label goal to answer in negative clause 43.002/43.002 43.002/43.002 Term ordering decisions: 43.002/43.002 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 43.002/43.002 Function symbol precedence: function_order([ a, c, b, f, k, h, g ]). 43.002/43.002 After inverse_order: (no changes). 43.002/43.002 Unfolding symbols: (none). 43.002/43.002 43.002/43.002 Auto_inference settings: 43.002/43.002 % set(neg_binary_resolution). % (HNE depth_diff=-3) 43.002/43.002 % clear(ordered_res). % (HNE depth_diff=-3) 43.002/43.002 % set(ur_resolution). % (HNE depth_diff=-3) 43.002/43.002 % set(ur_resolution) -> set(pos_ur_resolution). 43.002/43.002 % set(ur_resolution) -> set(neg_ur_resolution). 43.002/43.002 43.002/43.002 Auto_process settings: (no changes). 43.002/43.002 43.002/43.002 kept: 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 kept: 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 kept: 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 kept: 11 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 kept: 12 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 kept: 13 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 kept: 14 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 kept: 15 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 kept: 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 kept: 17 -->*_s0(h(f(x)),k(g(b))) | ->_s0(f(x),g(x)) # label(replacement). [clausify(6)]. 43.002/43.002 kept: 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 kept: 19 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 20 -->*_s0(h(f(x)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 43.002/43.002 ============================== end of process initial clauses ======== 43.002/43.002 43.002/43.002 ============================== CLAUSES FOR SEARCH ==================== 43.002/43.002 43.002/43.002 % Clauses after input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 12 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 13 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 14 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 15 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 20 -->*_s0(h(f(x)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of clauses for search ============= 43.002/43.002 43.002/43.002 ============================== SEARCH ================================ 43.002/43.002 43.002/43.002 % Starting search at 0.00 seconds. 43.002/43.002 43.002/43.002 given #1 (I,wt=3): 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 43.002/43.002 given #2 (I,wt=9): 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 43.002/43.002 given #3 (I,wt=8): 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 43.002/43.002 given #4 (I,wt=8): 11 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 43.002/43.002 given #5 (I,wt=8): 12 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 43.002/43.002 given #6 (I,wt=8): 13 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 43.002/43.002 given #7 (I,wt=3): 14 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #8 (I,wt=5): 15 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #9 (I,wt=5): 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #10 (I,wt=5): 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #11 (I,wt=5): 19 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #12 (I,wt=7): 20 -->*_s0(h(f(x)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 43.002/43.002 ============================== PROOF ================================= 43.002/43.002 43.002/43.002 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 43.002/43.002 % Length of proof is 10. 43.002/43.002 % Level of proof is 3. 43.002/43.002 % Maximum clause weight is 9.000. 43.002/43.002 % Given clauses 12. 43.002/43.002 43.002/43.002 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 7 (exists x2 ->*_s0(h(f(x2)),k(g(b)))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 20 -->*_s0(h(f(x)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 35 ->*_s0(c,k(g(b))). [ur(9,a,16,a,b,8,a)]. 43.002/43.002 49 -->*_s0(c,k(g(b))) # answer(goal). [ur(9,a,18,a,c,20,a)]. 43.002/43.002 50 $F # answer(goal). [resolve(49,a,35,a)]. 43.002/43.002 43.002/43.002 ============================== end of proof ========================== 43.002/43.002 43.002/43.002 ============================== STATISTICS ============================ 43.002/43.002 43.002/43.002 Given=12. Generated=42. Kept=42. proofs=1. 43.002/43.002 Usable=12. Sos=25. Demods=0. Limbo=3, Disabled=14. Hints=0. 43.002/43.002 Kept_by_rule=0, Deleted_by_rule=0. 43.002/43.002 Forward_subsumed=0. Back_subsumed=1. 43.002/43.002 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 43.002/43.002 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 43.002/43.002 Demod_attempts=0. Demod_rewrites=0. 43.002/43.002 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 43.002/43.002 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=8. 43.002/43.002 Megabytes=0.10. 43.002/43.002 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 43.002/43.002 43.002/43.002 ============================== end of statistics ===================== 43.002/43.002 43.002/43.002 ============================== end of search ========================= 43.002/43.002 43.002/43.002 THEOREM PROVED 43.002/43.002 43.002/43.002 Exiting with 1 proof. 43.002/43.002 43.002/43.002 Process 120339 exit (max_proofs) Fri Jul 16 15:38:35 2021 43.002/43.002 43.002/43.002 43.002/43.002 The problem is feasible. 43.002/43.002 43.002/43.002 43.002/43.002 CRule InfChecker Info: 43.002/43.002 h(f(a)) -> c 43.002/43.002 Rule remains 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 CRule InfChecker Info: 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 Rule remains 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 ) 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 Critical Pairs Processor: 43.002/43.002 -> Rules: 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 -> Vars: 43.002/43.002 "x", "x" 43.002/43.002 -> FVars: 43.002/43.002 "x2", "x3" 43.002/43.002 -> PVars: 43.002/43.002 "x": ["x2", "x3"] 43.002/43.002 43.002/43.002 -> Rlps: 43.002/43.002 crule: a -> b, id: 1, possubterms: a-> [] 43.002/43.002 crule: c -> k(f(a)), id: 2, possubterms: c-> [] 43.002/43.002 crule: c -> k(g(b)), id: 3, possubterms: c-> [] 43.002/43.002 crule: f(x2:S) -> g(x2:S) | h(f(x2:S)) ->* k(g(b)), id: 4, possubterms: f(x2:S)-> [] 43.002/43.002 crule: h(f(a)) -> c, id: 5, possubterms: h(f(a))-> [], f(a)-> [1], a-> [1,1] 43.002/43.002 crule: h(x3:S) -> k(x3:S), id: 6, possubterms: h(x3:S)-> [] 43.002/43.002 43.002/43.002 -> Unifications: 43.002/43.002 R3 unifies with R2 at p: [], l: c, lp: c, conds: {}, sig: {}, l': c, r: k(g(b)), r': k(f(a)) 43.002/43.002 R5 unifies with R4 at p: [1], l: h(f(a)), lp: f(a), conds: {h(f(x:S)) ->* k(g(b))}, sig: {x:S -> a}, l': f(x:S), r: c, r': g(x:S) 43.002/43.002 R5 unifies with R1 at p: [1,1], l: h(f(a)), lp: a, conds: {}, sig: {}, l': a, r: c, r': b 43.002/43.002 R6 unifies with R5 at p: [], l: h(x3:S), lp: h(x3:S), conds: {}, sig: {x3:S -> f(a)}, l': h(f(a)), r: k(x3:S), r': c 43.002/43.002 43.002/43.002 -> Critical pairs info: 43.002/43.002 => Not trivial, Overlay, N1 43.002/43.002 => Not trivial, Not overlay, N2 43.002/43.002 | h(f(a)) ->* k(g(b)) => Not trivial, Not overlay, N3 43.002/43.002 => Not trivial, Overlay, N4 43.002/43.002 43.002/43.002 -> Problem conclusions: 43.002/43.002 Left linear, Right linear, Linear 43.002/43.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 43.002/43.002 CTRS Type: 1 43.002/43.002 Deterministic, Strongly deterministic 43.002/43.002 Oriented CTRS, Properly oriented CTRS, Not join CTRS 43.002/43.002 Maybe right-stable CTRS, Not overlay CTRS 43.002/43.002 Maybe normal CTRS, Maybe almost normal CTRS 43.002/43.002 Maybe terminating CTRS, Maybe joinable CCPs 43.002/43.002 Maybe level confluent 43.002/43.002 Maybe confluent 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 Clean Infeasible CCPs Processor: 43.002/43.002 Num of CPIs: 4 43.002/43.002 Timeout: 30 43.002/43.002 Timeout for each infeasibility problem: 30 s 43.002/43.002 => Not trivial, Overlay, N1 43.002/43.002 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 43.002/43.002 43.002/43.002 => Not trivial, Not overlay, N2 43.002/43.002 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 43.002/43.002 43.002/43.002 | h(f(a)) ->* k(g(b)) => Not trivial, Not overlay, Feasible conditions, N3 43.002/43.002 (PROBLEM INFEASIBILITY) 43.002/43.002 (VAR x) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x) -> g(x) | h(f(x)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x) -> k(x)) 43.002/43.002 (CONDITION h(f(a)) ->* k(g(b))) 43.002/43.002 43.002/43.002 Proof: 43.002/43.002 NO 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Infeasibility Problem: 43.002/43.002 [(VAR vNonEmpty:S x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 )] 43.002/43.002 43.002/43.002 Infeasibility Conditions: 43.002/43.002 h(f(a)) ->* k(g(b)) 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Obtaining a proof using Prover9: 43.002/43.002 43.002/43.002 -> Prover9 Output: 43.002/43.002 ============================== Prover9 =============================== 43.002/43.002 Prover9 (64) version 2009-11A, November 2009. 43.002/43.002 Process 120575 was started by ubuntu on ubuntu, 43.002/43.002 Fri Jul 16 15:38:36 2021 43.002/43.002 The command was "./prover9 -f /tmp/prover9120542-0.in". 43.002/43.002 ============================== end of head =========================== 43.002/43.002 43.002/43.002 ============================== INPUT ================================= 43.002/43.002 43.002/43.002 % Reading from file /tmp/prover9120542-0.in 43.002/43.002 43.002/43.002 assign(max_seconds,20). 43.002/43.002 43.002/43.002 formulas(assumptions). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). 43.002/43.002 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 43.002/43.002 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 43.002/43.002 ->_s0(a,b) # label(replacement). 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). 43.002/43.002 ->*_s0(h(f(x1)),k(g(b))) -> ->_s0(f(x1),g(x1)) # label(replacement). 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). 43.002/43.002 ->_s0(h(x1),k(x1)) # label(replacement). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(goals). 43.002/43.002 ->*_s0(h(f(a)),k(g(b))) # label(goal). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of input ========================== 43.002/43.002 43.002/43.002 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 43.002/43.002 43.002/43.002 % Formulas that are not ordinary clauses: 43.002/43.002 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 4 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 5 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->*_s0(h(f(x1)),k(g(b))) -> ->_s0(f(x1),g(x1)) # label(replacement) # label(non_clause). [assumption]. 43.002/43.002 7 ->*_s0(h(f(a)),k(g(b))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 43.002/43.002 ============================== end of process non-clausal formulas === 43.002/43.002 43.002/43.002 ============================== PROCESS INITIAL CLAUSES =============== 43.002/43.002 43.002/43.002 % Clauses before input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 -->*_s0(h(f(x)),k(g(b))) | ->_s0(f(x),g(x)) # label(replacement). [clausify(6)]. 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 -->*_s0(h(f(a)),k(g(b))) # label(goal). [deny(7)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== PREDICATE ELIMINATION ================= 43.002/43.002 43.002/43.002 No predicates eliminated. 43.002/43.002 43.002/43.002 ============================== end predicate elimination ============= 43.002/43.002 43.002/43.002 Auto_denials: 43.002/43.002 % copying label goal to answer in negative clause 43.002/43.002 43.002/43.002 Term ordering decisions: 43.002/43.002 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 43.002/43.002 Function symbol precedence: function_order([ a, c, b, f, k, h, g ]). 43.002/43.002 After inverse_order: (no changes). 43.002/43.002 Unfolding symbols: (none). 43.002/43.002 43.002/43.002 Auto_inference settings: 43.002/43.002 % set(neg_binary_resolution). % (HNE depth_diff=-3) 43.002/43.002 % clear(ordered_res). % (HNE depth_diff=-3) 43.002/43.002 % set(ur_resolution). % (HNE depth_diff=-3) 43.002/43.002 % set(ur_resolution) -> set(pos_ur_resolution). 43.002/43.002 % set(ur_resolution) -> set(neg_ur_resolution). 43.002/43.002 43.002/43.002 Auto_process settings: (no changes). 43.002/43.002 43.002/43.002 kept: 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 kept: 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 kept: 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 kept: 11 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 kept: 12 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 kept: 13 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 kept: 14 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 kept: 15 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 kept: 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 kept: 17 -->*_s0(h(f(x)),k(g(b))) | ->_s0(f(x),g(x)) # label(replacement). [clausify(6)]. 43.002/43.002 kept: 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 kept: 19 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 20 -->*_s0(h(f(a)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 43.002/43.002 ============================== end of process initial clauses ======== 43.002/43.002 43.002/43.002 ============================== CLAUSES FOR SEARCH ==================== 43.002/43.002 43.002/43.002 % Clauses after input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 12 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 13 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 14 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 15 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 17 -->*_s0(h(f(x)),k(g(b))) | ->_s0(f(x),g(x)) # label(replacement). [clausify(6)]. 43.002/43.002 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 20 -->*_s0(h(f(a)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of clauses for search ============= 43.002/43.002 43.002/43.002 ============================== SEARCH ================================ 43.002/43.002 43.002/43.002 % Starting search at 0.00 seconds. 43.002/43.002 43.002/43.002 given #1 (I,wt=3): 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 43.002/43.002 given #2 (I,wt=9): 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 43.002/43.002 given #3 (I,wt=8): 10 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 43.002/43.002 43.002/43.002 given #4 (I,wt=8): 11 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(3)]. 43.002/43.002 43.002/43.002 given #5 (I,wt=8): 12 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(4)]. 43.002/43.002 43.002/43.002 given #6 (I,wt=8): 13 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(5)]. 43.002/43.002 43.002/43.002 given #7 (I,wt=3): 14 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #8 (I,wt=5): 15 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #9 (I,wt=5): 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #10 (I,wt=12): 17 -->*_s0(h(f(x)),k(g(b))) | ->_s0(f(x),g(x)) # label(replacement). [clausify(6)]. 43.002/43.002 43.002/43.002 given #11 (I,wt=5): 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #12 (I,wt=5): 19 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #13 (I,wt=7): 20 -->*_s0(h(f(a)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 43.002/43.002 ============================== PROOF ================================= 43.002/43.002 43.002/43.002 % Proof 1 at 0.01 (+ 0.00) seconds: goal. 43.002/43.002 % Length of proof is 10. 43.002/43.002 % Level of proof is 3. 43.002/43.002 % Maximum clause weight is 9.000. 43.002/43.002 % Given clauses 13. 43.002/43.002 43.002/43.002 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 7 ->*_s0(h(f(a)),k(g(b))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 8 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 9 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 43.002/43.002 16 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 20 -->*_s0(h(f(a)),k(g(b))) # label(goal) # answer(goal). [deny(7)]. 43.002/43.002 35 ->*_s0(c,k(g(b))). [ur(9,a,16,a,b,8,a)]. 43.002/43.002 49 -->*_s0(c,k(g(b))) # answer(goal). [ur(9,a,18,a,c,20,a)]. 43.002/43.002 50 $F # answer(goal). [resolve(49,a,35,a)]. 43.002/43.002 43.002/43.002 ============================== end of proof ========================== 43.002/43.002 43.002/43.002 ============================== STATISTICS ============================ 43.002/43.002 43.002/43.002 Given=13. Generated=42. Kept=42. proofs=1. 43.002/43.002 Usable=13. Sos=25. Demods=0. Limbo=3, Disabled=13. Hints=0. 43.002/43.002 Kept_by_rule=0, Deleted_by_rule=0. 43.002/43.002 Forward_subsumed=0. Back_subsumed=0. 43.002/43.002 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 43.002/43.002 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 43.002/43.002 Demod_attempts=0. Demod_rewrites=0. 43.002/43.002 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 43.002/43.002 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=7. 43.002/43.002 Megabytes=0.10. 43.002/43.002 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. 43.002/43.002 43.002/43.002 ============================== end of statistics ===================== 43.002/43.002 43.002/43.002 ============================== end of search ========================= 43.002/43.002 43.002/43.002 THEOREM PROVED 43.002/43.002 43.002/43.002 Exiting with 1 proof. 43.002/43.002 43.002/43.002 Process 120575 exit (max_proofs) Fri Jul 16 15:38:36 2021 43.002/43.002 43.002/43.002 43.002/43.002 The problem is feasible. 43.002/43.002 43.002/43.002 43.002/43.002 43.002/43.002 43.002/43.002 => Not trivial, Overlay, N4 43.002/43.002 43.002/43.002 Proof: 43.002/43.002 NO_CONDS 43.002/43.002 43.002/43.002 43.002/43.002 43.002/43.002 -> Problem conclusions: 43.002/43.002 Left linear, Right linear, Linear 43.002/43.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 43.002/43.002 CTRS Type: 1 43.002/43.002 Deterministic, Strongly deterministic 43.002/43.002 Oriented CTRS, Properly oriented CTRS, Not join CTRS 43.002/43.002 Maybe right-stable CTRS, Not overlay CTRS 43.002/43.002 Maybe normal CTRS, Maybe almost normal CTRS 43.002/43.002 Maybe terminating CTRS, Maybe joinable CCPs 43.002/43.002 Maybe level confluent 43.002/43.002 Maybe confluent 43.002/43.002 43.002/43.002 Resulting CCPs: 43.002/43.002 => Not trivial, Overlay, N1 43.002/43.002 => Not trivial, Not overlay, N2 43.002/43.002 | h(f(a)) ->* k(g(b)) => Not trivial, Not overlay, Feasible conditions, N3 43.002/43.002 => Not trivial, Overlay, N4 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 Underlying TRS Termination Processor: 43.002/43.002 43.002/43.002 Resulting Underlying TRS: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 ) 43.002/43.002 Underlying TRS terminating? 43.002/43.002 YES 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 (VAR vu95NonEmpty:S xu58S:S) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(xu58S:S) -> g(xu58S:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(xu58S:S) -> k(xu58S:S) 43.002/43.002 ) 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Dependency Pairs Processor: 43.002/43.002 -> Pairs: 43.002/43.002 C -> A 43.002/43.002 C -> F(a) 43.002/43.002 H(f(a)) -> C 43.002/43.002 -> Rules: 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(xu58S:S) -> g(xu58S:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(xu58S:S) -> k(xu58S:S) 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 SCC Processor: 43.002/43.002 -> Pairs: 43.002/43.002 C -> A 43.002/43.002 C -> F(a) 43.002/43.002 H(f(a)) -> C 43.002/43.002 -> Rules: 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(xu58S:S) -> g(xu58S:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(xu58S:S) -> k(xu58S:S) 43.002/43.002 ->Strongly Connected Components: 43.002/43.002 There is no strongly connected component 43.002/43.002 43.002/43.002 The problem is finite. 43.002/43.002 43.002/43.002 43.002/43.002 -> Problem conclusions: 43.002/43.002 Left linear, Right linear, Linear 43.002/43.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 43.002/43.002 CTRS Type: 1 43.002/43.002 Deterministic, Strongly deterministic 43.002/43.002 Oriented CTRS, Properly oriented CTRS, Not join CTRS 43.002/43.002 Maybe right-stable CTRS, Not overlay CTRS 43.002/43.002 Maybe normal CTRS, Maybe almost normal CTRS 43.002/43.002 Terminating CTRS, Maybe joinable CCPs 43.002/43.002 Maybe level confluent 43.002/43.002 Maybe confluent 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Transform CTRS Processor: 43.002/43.002 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> g(x:S) | h(f(x:S)) ->* k(g(b)) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 ) 43.002/43.002 Critical Pairs: 43.002/43.002 => Not trivial, Overlay, N1 43.002/43.002 => Not trivial, Not overlay, N2 43.002/43.002 | h(f(a)) ->* k(g(b)) => Not trivial, Not overlay, Feasible conditions, N3 43.002/43.002 => Not trivial, Overlay, N4 43.002/43.002 Terminating:YES 43.002/43.002 43.002/43.002 -> Problem conclusions: 43.002/43.002 Left linear, Right linear, Linear 43.002/43.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 43.002/43.002 CTRS Type: 1 43.002/43.002 Deterministic, Strongly deterministic 43.002/43.002 Oriented CTRS, Properly oriented CTRS, Not join CTRS 43.002/43.002 Maybe right-stable CTRS, Not overlay CTRS 43.002/43.002 Maybe normal CTRS, Maybe almost normal CTRS 43.002/43.002 Terminating CTRS, Maybe joinable CCPs 43.002/43.002 Maybe level confluent 43.002/43.002 Maybe confluent 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Resulting U(R): 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1 2) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 CSR Converter From Canonical u-Replacement Map Processor [CSUR20]: 43.002/43.002 43.002/43.002 Original Replacement Map: 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1 2) 43.002/43.002 43.002/43.002 New Replacement Map: 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 43.002/43.002 New problem: 43.002/43.002 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 Terminating:"YES" 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 Terminating:"YES" 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 Huet Levy Processor: 43.002/43.002 -> Rules: 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 -> Vars: 43.002/43.002 x, x, x 43.002/43.002 -> UVars: 43.002/43.002 (UV-RuleId: 1, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 (UV-RuleId: 2, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 (UV-RuleId: 3, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 (UV-RuleId: 4, UV-LActive: [x], UV-RActive: [x], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 (UV-RuleId: 5, UV-LActive: [], UV-RActive: [], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 (UV-RuleId: 6, UV-LActive: [x], UV-RActive: [x], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 (UV-RuleId: 7, UV-LActive: [x], UV-RActive: [x], UV-LFrozen: [], UV-RFrozen: []) 43.002/43.002 -> FVars: 43.002/43.002 x2, x3, x4 43.002/43.002 -> PVars: 43.002/43.002 x: [x2, x3, x4] 43.002/43.002 43.002/43.002 -> Rlps: 43.002/43.002 (rule: a -> b, id: 1, possubterms: a->[]) 43.002/43.002 (rule: c -> k(f(a)), id: 2, possubterms: c->[]) 43.002/43.002 (rule: c -> k(g(b)), id: 3, possubterms: c->[]) 43.002/43.002 (rule: f(x2:S) -> U9_1(h(f(x2:S)),x2:S), id: 4, possubterms: f(x2:S)->[]) 43.002/43.002 (rule: h(f(a)) -> c, id: 5, possubterms: h(f(a))->[], f(a)->[1], a->[1, 1]) 43.002/43.002 (rule: h(x3:S) -> k(x3:S), id: 6, possubterms: h(x3:S)->[]) 43.002/43.002 (rule: U9_1(k(g(b)),x4:S) -> g(x4:S), id: 7, possubterms: U9_1(k(g(b)),x4:S)->[], k(g(b))->[1], g(b)->[1, 1], b->[1, 1, 1]) 43.002/43.002 43.002/43.002 -> Unifications: 43.002/43.002 (R3 unifies with R2 at p: [], l: c, lp: c, sig: {}, l': c, r: k(g(b)), r': k(f(a))) 43.002/43.002 (R5 unifies with R4 at p: [1], l: h(f(a)), lp: f(a), sig: {x:S -> a}, l': f(x:S), r: c, r': U9_1(h(f(x:S)),x:S)) 43.002/43.002 (R5 unifies with R1 at p: [1,1], l: h(f(a)), lp: a, sig: {}, l': a, r: c, r': b) 43.002/43.002 (R6 unifies with R5 at p: [], l: h(x3:S), lp: h(x3:S), sig: {x3:S -> f(a)}, l': h(f(a)), r: k(x3:S), r': c) 43.002/43.002 43.002/43.002 -> Critical pairs info: 43.002/43.002 => Not trivial, Overlay, N1 43.002/43.002 => Not trivial, Not overlay, N2 43.002/43.002 => Not trivial, Not overlay, N3 43.002/43.002 => Not trivial, Overlay, N4 43.002/43.002 43.002/43.002 -> Problem conclusions: 43.002/43.002 Left linear, Not right linear, Not linear 43.002/43.002 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 43.002/43.002 Not Huet-Levy confluent, Not Newman confluent 43.002/43.002 R is a CS-TRS, Left-homogeneous u-replacing variables 43.002/43.002 43.002/43.002 43.002/43.002 43.002/43.002 The problem is decomposed in 4 subproblems. 43.002/43.002 43.002/43.002 Problem 1.1: 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 Critical Pairs: 43.002/43.002 => Not trivial, Overlay, N1 43.002/43.002 Terminating:"YES" 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 Huet InfChecker Processor: 43.002/43.002 Infeasible convergence? 43.002/43.002 NO 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Infeasibility Problem: 43.002/43.002 [(VAR vNonEmpty:S x:S z:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (U91 1 2) 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 U91(k(g(b)),x:S) -> g(x:S) 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U91(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 )] 43.002/43.002 Infeasibility Conditions: 43.002/43.002 k(f(a)) ->* z:S, k(g(b)) ->* z:S 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Obtaining a proof using Prover9: 43.002/43.002 43.002/43.002 -> Prover9 Output: 43.002/43.002 ============================== Prover9 =============================== 43.002/43.002 Prover9 (64) version 2009-11A, November 2009. 43.002/43.002 Process 120701 was started by ubuntu on ubuntu, 43.002/43.002 Fri Jul 16 15:38:59 2021 43.002/43.002 The command was "./prover9 -f /tmp/prover9120692-0.in". 43.002/43.002 ============================== end of head =========================== 43.002/43.002 43.002/43.002 ============================== INPUT ================================= 43.002/43.002 43.002/43.002 % Reading from file /tmp/prover9120692-0.in 43.002/43.002 43.002/43.002 assign(max_seconds,20). 43.002/43.002 43.002/43.002 formulas(assumptions). 43.002/43.002 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence). 43.002/43.002 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 43.002/43.002 ->_s0(U91(k(g(b)),x1),g(x1)) # label(replacement). 43.002/43.002 ->_s0(a,b) # label(replacement). 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). 43.002/43.002 ->_s0(f(x1),U91(h(f(x1)),x1)) # label(replacement). 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). 43.002/43.002 ->_s0(h(x1),k(x1)) # label(replacement). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). 43.002/43.002 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(goals). 43.002/43.002 (exists x2 (->*_s0(k(f(a)),x2) & ->*_s0(k(g(b)),x2))) # label(goal). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of input ========================== 43.002/43.002 43.002/43.002 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 43.002/43.002 43.002/43.002 % Formulas that are not ordinary clauses: 43.002/43.002 1 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 4 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 5 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(k(f(a)),x2) & ->*_s0(k(g(b)),x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 43.002/43.002 ============================== end of process non-clausal formulas === 43.002/43.002 43.002/43.002 ============================== PROCESS INITIAL CLAUSES =============== 43.002/43.002 43.002/43.002 % Clauses before input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 -->*_s0(k(f(a)),x) | -->*_s0(k(g(b)),x) # label(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== PREDICATE ELIMINATION ================= 43.002/43.002 43.002/43.002 No predicates eliminated. 43.002/43.002 43.002/43.002 ============================== end predicate elimination ============= 43.002/43.002 43.002/43.002 Auto_denials: 43.002/43.002 % copying label goal to answer in negative clause 43.002/43.002 43.002/43.002 Term ordering decisions: 43.002/43.002 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 43.002/43.002 Function symbol precedence: function_order([ a, c, b, U91, k, f, h, g ]). 43.002/43.002 After inverse_order: (no changes). 43.002/43.002 Unfolding symbols: (none). 43.002/43.002 43.002/43.002 Auto_inference settings: 43.002/43.002 % set(neg_binary_resolution). % (HNE depth_diff=-6) 43.002/43.002 % clear(ordered_res). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution) -> set(pos_ur_resolution). 43.002/43.002 % set(ur_resolution) -> set(neg_ur_resolution). 43.002/43.002 43.002/43.002 Auto_process settings: 43.002/43.002 % set(unit_deletion). % (Horn set with negative nonunits) 43.002/43.002 43.002/43.002 kept: 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 kept: 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 kept: 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 kept: 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 kept: 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 kept: 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 kept: 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 kept: 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 kept: 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 kept: 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 kept: 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 kept: 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 kept: 24 -->*_s0(k(f(a)),x) | -->*_s0(k(g(b)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 ============================== end of process initial clauses ======== 43.002/43.002 43.002/43.002 ============================== CLAUSES FOR SEARCH ==================== 43.002/43.002 43.002/43.002 % Clauses after input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(k(f(a)),x) | -->*_s0(k(g(b)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of clauses for search ============= 43.002/43.002 43.002/43.002 ============================== SEARCH ================================ 43.002/43.002 43.002/43.002 % Starting search at 0.00 seconds. 43.002/43.002 43.002/43.002 given #1 (I,wt=10): 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 43.002/43.002 given #2 (I,wt=10): 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 43.002/43.002 given #3 (I,wt=8): 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 43.002/43.002 given #4 (I,wt=8): 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 43.002/43.002 given #5 (I,wt=8): 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 43.002/43.002 given #6 (I,wt=8): 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 43.002/43.002 given #7 (I,wt=8): 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #8 (I,wt=3): 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #9 (I,wt=5): 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #10 (I,wt=5): 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #11 (I,wt=8): 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #12 (I,wt=5): 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #13 (I,wt=5): 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #14 (I,wt=3): 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 43.002/43.002 given #15 (I,wt=9): 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 43.002/43.002 given #16 (I,wt=10): 24 -->*_s0(k(f(a)),x) | -->*_s0(k(g(b)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 given #17 (A,wt=10): 25 ->_s0(k(U91(k(g(b)),x)),k(g(x))). [ur(14,a,15,a)]. 43.002/43.002 43.002/43.002 given #18 (F,wt=7): 75 -->*_s0(k(g(b)),k(f(a))) # answer(goal). [resolve(24,a,22,a)]. 43.002/43.002 43.002/43.002 given #19 (F,wt=7): 77 -->*_s0(k(f(a)),k(g(b))) # answer(goal). [resolve(24,b,22,a)]. 43.002/43.002 43.002/43.002 given #20 (F,wt=7): 86 -->_s0(k(g(b)),k(f(a))) # answer(goal). [ur(23,b,22,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #21 (F,wt=5): 89 -->_s0(g(b),f(a)) # answer(goal). [resolve(86,a,14,b)]. 43.002/43.002 43.002/43.002 given #22 (T,wt=3): 72 ->*_s0(a,b). [ur(23,a,16,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #23 (T,wt=5): 31 ->_s0(k(a),k(b)). [ur(14,a,16,a)]. 43.002/43.002 43.002/43.002 given #24 (T,wt=5): 32 ->_s0(g(a),g(b)). [ur(13,a,16,a)]. 43.002/43.002 43.002/43.002 given #25 (T,wt=5): 33 ->_s0(h(a),h(b)). [ur(12,a,16,a)]. 43.002/43.002 43.002/43.002 given #26 (A,wt=10): 26 ->_s0(g(U91(k(g(b)),x)),g(g(x))). [ur(13,a,15,a)]. 43.002/43.002 43.002/43.002 given #27 (F,wt=7): 88 -->_s0(k(f(a)),k(g(b))) # answer(goal). [ur(23,b,22,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #28 (F,wt=5): 118 -->_s0(f(a),g(b)) # answer(goal). [resolve(88,a,14,b)]. 43.002/43.002 43.002/43.002 given #29 (F,wt=10): 85 -->_s0(k(g(b)),x) | -->*_s0(x,k(f(a))) # answer(goal). [resolve(75,a,23,c)]. 43.002/43.002 43.002/43.002 given #30 (F,wt=10): 87 -->_s0(k(f(a)),x) | -->*_s0(x,k(g(b))) # answer(goal). [resolve(77,a,23,c)]. 43.002/43.002 43.002/43.002 given #31 (T,wt=5): 34 ->_s0(f(a),f(b)). [ur(11,a,16,a)]. 43.002/43.002 43.002/43.002 given #32 (T,wt=5): 67 ->*_s0(h(x),k(x)). [ur(23,a,21,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #33 (T,wt=5): 68 ->*_s0(h(f(a)),c). [ur(23,a,20,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #34 (T,wt=5): 70 ->*_s0(c,k(g(b))). [ur(23,a,18,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #35 (A,wt=10): 27 ->_s0(h(U91(k(g(b)),x)),h(g(x))). [ur(12,a,15,a)]. 43.002/43.002 43.002/43.002 given #36 (F,wt=5): 133 -->_s0(k(f(a)),c) # answer(goal). [resolve(70,a,87,b)]. 43.002/43.002 43.002/43.002 given #37 (F,wt=7): 130 -->_s0(k(f(a)),h(g(b))) # answer(goal). [resolve(67,a,87,b)]. 43.002/43.002 43.002/43.002 given #38 (F,wt=7): 131 -->_s0(k(g(b)),h(f(a))) # answer(goal). [resolve(67,a,85,b)]. 43.002/43.002 43.002/43.002 given #39 (F,wt=10): 119 -->*_s0(k(x),k(f(a))) | -->_s0(g(b),x) # answer(goal). [resolve(85,a,14,b)]. 43.002/43.002 43.002/43.002 given #40 (T,wt=5): 71 ->*_s0(c,k(f(a))). [ur(23,a,17,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #41 (T,wt=5): 90 ->*_s0(k(a),k(b)). [ur(23,a,31,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #42 (T,wt=5): 97 ->*_s0(g(a),g(b)). [ur(23,a,32,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #43 (T,wt=5): 104 ->*_s0(h(a),h(b)). [ur(23,a,33,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #44 (A,wt=10): 28 ->_s0(f(U91(k(g(b)),x)),f(g(x))). [ur(11,a,15,a)]. 43.002/43.002 43.002/43.002 given #45 (F,wt=5): 145 -->_s0(k(g(b)),c) # answer(goal). [resolve(71,a,85,b)]. 43.002/43.002 43.002/43.002 given #46 (F,wt=10): 121 -->*_s0(k(x),k(g(b))) | -->_s0(f(a),x) # answer(goal). [resolve(87,a,14,b)]. 43.002/43.002 43.002/43.002 given #47 (F,wt=7): 155 -->*_s0(k(f(b)),k(g(b))) # answer(goal). [resolve(121,b,34,a)]. 43.002/43.002 43.002/43.002 given #48 (F,wt=5): 159 -->_s0(k(f(b)),c) # answer(goal). [ur(23,b,70,a,c,155,a)]. 43.002/43.002 43.002/43.002 given #49 (T,wt=5): 123 ->*_s0(f(a),f(b)). [ur(23,a,34,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #50 (T,wt=5): 132 ->*_s0(h(a),k(b)). [ur(23,a,33,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #51 (T,wt=7): 35 ->_s0(U91(x,a),U91(x,b)). [ur(10,a,16,a)]. 43.002/43.002 43.002/43.002 given #52 (T,wt=7): 36 ->_s0(U91(a,x),U91(b,x)). [ur(9,a,16,a)]. 43.002/43.002 43.002/43.002 given #53 (A,wt=12): 29 ->_s0(U91(x,U91(k(g(b)),y)),U91(x,g(y))). [ur(10,a,15,a)]. 43.002/43.002 43.002/43.002 given #54 (F,wt=7): 160 -->_s0(k(f(b)),h(g(b))) # answer(goal). [ur(23,b,67,a,c,155,a)]. 43.002/43.002 43.002/43.002 given #55 (F,wt=7): 161 -->_s0(k(f(b)),k(g(b))) # answer(goal). [ur(23,b,22,a,c,155,a)]. 43.002/43.002 43.002/43.002 given #56 (F,wt=5): 183 -->_s0(f(b),g(b)) # answer(goal). [resolve(161,a,14,b)]. 43.002/43.002 43.002/43.002 given #57 (F,wt=10): 144 -->*_s0(k(g(x)),k(f(a))) | -->_s0(b,x) # answer(goal). [resolve(119,b,13,b)]. 43.002/43.002 43.002/43.002 given #58 (T,wt=7): 37 ->_s0(k(c),k(k(f(a)))). [ur(14,a,17,a)]. 43.002/43.002 43.002/43.002 given #59 (T,wt=7): 38 ->_s0(g(c),g(k(f(a)))). [ur(13,a,17,a)]. 43.002/43.002 43.002/43.002 given #60 (T,wt=7): 39 ->_s0(h(c),h(k(f(a)))). [ur(12,a,17,a)]. 43.002/43.002 43.002/43.002 given #61 (T,wt=7): 40 ->_s0(f(c),f(k(f(a)))). [ur(11,a,17,a)]. 43.002/43.002 43.002/43.002 given #62 (A,wt=12): 30 ->_s0(U91(U91(k(g(b)),x),y),U91(g(x),y)). [ur(9,a,15,a)]. 43.002/43.002 43.002/43.002 given #63 (F,wt=10): 156 -->*_s0(k(U91(h(f(a)),a)),k(g(b))) # answer(goal). [resolve(121,b,19,a)]. 43.002/43.002 43.002/43.002 given #64 (F,wt=8): 222 -->_s0(k(U91(h(f(a)),a)),c) # answer(goal). [ur(23,b,70,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #65 (F,wt=10): 157 -->*_s0(k(f(x)),k(g(b))) | -->_s0(a,x) # answer(goal). [resolve(121,b,11,b)]. 43.002/43.002 43.002/43.002 given #66 (F,wt=10): 158 -->_s0(k(f(b)),x) | -->*_s0(x,k(g(b))) # answer(goal). [resolve(155,a,23,c)]. 43.002/43.002 43.002/43.002 given #67 (T,wt=7): 43 ->_s0(k(c),k(k(g(b)))). [ur(14,a,18,a)]. 43.002/43.002 43.002/43.002 given #68 (T,wt=7): 44 ->_s0(g(c),g(k(g(b)))). [ur(13,a,18,a)]. 43.002/43.002 43.002/43.002 given #69 (T,wt=7): 45 ->_s0(h(c),h(k(g(b)))). [ur(12,a,18,a)]. 43.002/43.002 43.002/43.002 given #70 (T,wt=7): 46 ->_s0(f(c),f(k(g(b)))). [ur(11,a,18,a)]. 43.002/43.002 43.002/43.002 given #71 (A,wt=9): 41 ->_s0(U91(x,c),U91(x,k(f(a)))). [ur(10,a,17,a)]. 43.002/43.002 43.002/43.002 given #72 (F,wt=10): 223 -->_s0(k(U91(h(f(a)),a)),h(g(b))) # answer(goal). [ur(23,b,67,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #73 (F,wt=10): 224 -->_s0(k(U91(h(f(a)),a)),k(g(b))) # answer(goal). [ur(23,b,22,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #74 (F,wt=8): 264 -->_s0(U91(h(f(a)),a),g(b)) # answer(goal). [resolve(224,a,14,b)]. 43.002/43.002 43.002/43.002 given #75 (F,wt=10): 226 -->*_s0(k(x),k(g(b))) | -->_s0(f(b),x) # answer(goal). [resolve(158,a,14,b)]. 43.002/43.002 43.002/43.002 given #76 (T,wt=7): 55 ->_s0(k(h(f(a))),k(c)). [ur(14,a,20,a)]. 43.002/43.002 43.002/43.002 given #77 (T,wt=7): 56 ->_s0(g(h(f(a))),g(c)). [ur(13,a,20,a)]. 43.002/43.002 43.002/43.002 given #78 (T,wt=7): 57 ->_s0(h(h(f(a))),h(c)). [ur(12,a,20,a)]. 43.002/43.002 43.002/43.002 given #79 (T,wt=7): 58 ->_s0(f(h(f(a))),f(c)). [ur(11,a,20,a)]. 43.002/43.002 43.002/43.002 given #80 (A,wt=9): 42 ->_s0(U91(c,x),U91(k(f(a)),x)). [ur(9,a,17,a)]. 43.002/43.002 43.002/43.002 given #81 (F,wt=10): 266 -->*_s0(k(U91(h(f(b)),b)),k(g(b))) # answer(goal). [resolve(226,b,19,a)]. 43.002/43.002 43.002/43.002 given #82 (F,wt=8): 305 -->_s0(k(U91(h(f(b)),b)),c) # answer(goal). [ur(23,b,70,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #83 (F,wt=10): 267 -->*_s0(k(f(x)),k(g(b))) | -->_s0(b,x) # answer(goal). [resolve(226,b,11,b)]. 43.002/43.002 43.002/43.002 given #84 (F,wt=10): 306 -->_s0(k(U91(h(f(b)),b)),h(g(b))) # answer(goal). [ur(23,b,67,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #85 (T,wt=7): 61 ->_s0(k(h(x)),k(k(x))). [ur(14,a,21,a)]. 43.002/43.002 43.002/43.002 given #86 (T,wt=7): 62 ->_s0(g(h(x)),g(k(x))). [ur(13,a,21,a)]. 43.002/43.002 43.002/43.002 given #87 (T,wt=7): 63 ->_s0(h(h(x)),h(k(x))). [ur(12,a,21,a)]. 43.002/43.002 43.002/43.002 given #88 (T,wt=7): 64 ->_s0(f(h(x)),f(k(x))). [ur(11,a,21,a)]. 43.002/43.002 43.002/43.002 given #89 (A,wt=9): 47 ->_s0(U91(x,c),U91(x,k(g(b)))). [ur(10,a,18,a)]. 43.002/43.002 43.002/43.002 given #90 (F,wt=10): 307 -->_s0(k(U91(h(f(b)),b)),k(g(b))) # answer(goal). [ur(23,b,22,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #91 (F,wt=8): 345 -->_s0(U91(h(f(b)),b),g(b)) # answer(goal). [resolve(307,a,14,b)]. 43.002/43.002 43.002/43.002 given #92 (F,wt=13): 74 -->*_s0(k(g(b)),x) | -->_s0(k(f(a)),y) | -->*_s0(y,x) # answer(goal). [resolve(24,a,23,c)]. 43.002/43.002 43.002/43.002 given #93 (F,wt=10): 353 -->*_s0(k(g(b)),b) | -->_s0(k(f(a)),a) # answer(goal). [resolve(74,c,72,a)]. 43.002/43.002 43.002/43.002 given #94 (T,wt=7): 91 ->_s0(k(k(a)),k(k(b))). [ur(14,a,31,a)]. 43.002/43.002 43.002/43.002 given #95 (T,wt=7): 92 ->_s0(g(k(a)),g(k(b))). [ur(13,a,31,a)]. 43.002/43.002 43.002/43.002 given #96 (T,wt=7): 93 ->_s0(h(k(a)),h(k(b))). [ur(12,a,31,a)]. 43.002/43.002 43.002/43.002 given #97 (T,wt=7): 94 ->_s0(f(k(a)),f(k(b))). [ur(11,a,31,a)]. 43.002/43.002 43.002/43.002 given #98 (A,wt=9): 48 ->_s0(U91(c,x),U91(k(g(b)),x)). [ur(9,a,18,a)]. 43.002/43.002 43.002/43.002 given #99 (F,wt=10): 357 -->*_s0(k(g(b)),x) | -->_s0(k(f(a)),x) # answer(goal). [resolve(74,c,22,a)]. 43.002/43.002 43.002/43.002 given #100 (F,wt=10): 396 -->*_s0(k(g(b)),k(x)) | -->_s0(f(a),x) # answer(goal). [resolve(357,b,14,b)]. 43.002/43.002 43.002/43.002 given #101 (F,wt=7): 398 -->*_s0(k(g(b)),k(f(b))) # answer(goal). [resolve(396,b,34,a)]. 43.002/43.002 43.002/43.002 given #102 (F,wt=7): 402 -->_s0(k(g(b)),h(f(b))) # answer(goal). [ur(23,b,67,a,c,398,a)]. 43.002/43.002 43.002/43.002 given #103 (T,wt=7): 98 ->_s0(k(g(a)),k(g(b))). [ur(14,a,32,a)]. 43.002/43.002 43.002/43.002 given #104 (T,wt=7): 99 ->_s0(g(g(a)),g(g(b))). [ur(13,a,32,a)]. 43.002/43.002 43.002/43.002 given #105 (T,wt=7): 100 ->_s0(h(g(a)),h(g(b))). [ur(12,a,32,a)]. 43.002/43.002 43.002/43.002 given #106 (T,wt=7): 101 ->_s0(f(g(a)),f(g(b))). [ur(11,a,32,a)]. 43.002/43.002 43.002/43.002 given #107 (A,wt=10): 49 ->_s0(k(f(x)),k(U91(h(f(x)),x))). [ur(14,a,19,a)]. 43.002/43.002 43.002/43.002 given #108 (F,wt=7): 403 -->_s0(k(g(b)),k(f(b))) # answer(goal). [ur(23,b,22,a,c,398,a)]. 43.002/43.002 43.002/43.002 given #109 (F,wt=5): 441 -->_s0(g(b),f(b)) # answer(goal). [resolve(403,a,14,b)]. 43.002/43.002 43.002/43.002 given #110 (F,wt=10): 399 -->*_s0(k(g(b)),k(U91(h(f(a)),a))) # answer(goal). [resolve(396,b,19,a)]. 43.002/43.002 43.002/43.002 given #111 (F,wt=10): 400 -->*_s0(k(g(b)),k(f(x))) | -->_s0(a,x) # answer(goal). [resolve(396,b,11,b)]. 43.002/43.002 43.002/43.002 given #112 (T,wt=7): 105 ->_s0(k(h(a)),k(h(b))). [ur(14,a,33,a)]. 43.002/43.002 43.002/43.002 given #113 (T,wt=7): 106 ->_s0(g(h(a)),g(h(b))). [ur(13,a,33,a)]. 43.002/43.002 43.002/43.002 given #114 (T,wt=7): 107 ->_s0(h(h(a)),h(h(b))). [ur(12,a,33,a)]. 43.002/43.002 43.002/43.002 given #115 (T,wt=7): 108 ->_s0(f(h(a)),f(h(b))). [ur(11,a,33,a)]. 43.002/43.002 43.002/43.002 given #116 (A,wt=10): 50 ->_s0(g(f(x)),g(U91(h(f(x)),x))). [ur(13,a,19,a)]. 43.002/43.002 43.002/43.002 given #117 (F,wt=10): 401 -->_s0(k(g(b)),x) | -->*_s0(x,k(f(b))) # answer(goal). [resolve(398,a,23,c)]. 43.002/43.002 43.002/43.002 given #118 (F,wt=10): 443 -->_s0(k(g(b)),h(U91(h(f(a)),a))) # answer(goal). [ur(23,b,67,a,c,399,a)]. 43.002/43.002 43.002/43.002 given #119 (F,wt=10): 444 -->_s0(k(g(b)),k(U91(h(f(a)),a))) # answer(goal). [ur(23,b,22,a,c,399,a)]. 43.002/43.002 43.002/43.002 given #120 (F,wt=8): 484 -->_s0(g(b),U91(h(f(a)),a)) # answer(goal). [resolve(444,a,14,b)]. 43.002/43.002 43.002/43.002 given #121 (T,wt=7): 124 ->_s0(k(f(a)),k(f(b))). [ur(14,a,34,a)]. 43.002/43.002 43.002/43.002 given #122 (T,wt=7): 125 ->_s0(g(f(a)),g(f(b))). [ur(13,a,34,a)]. 43.002/43.002 43.002/43.002 given #123 (T,wt=7): 126 ->_s0(h(f(a)),h(f(b))). [ur(12,a,34,a)]. 43.002/43.002 43.002/43.002 given #124 (T,wt=7): 127 ->_s0(f(f(a)),f(f(b))). [ur(11,a,34,a)]. 43.002/43.002 43.002/43.002 given #125 (A,wt=10): 51 ->_s0(h(f(x)),h(U91(h(f(x)),x))). [ur(12,a,19,a)]. 43.002/43.002 43.002/43.002 given #126 (F,wt=10): 482 -->*_s0(k(x),k(f(b))) | -->_s0(g(b),x) # answer(goal). [resolve(401,a,14,b)]. 43.002/43.002 43.002/43.002 given #127 (F,wt=10): 485 -->*_s0(k(g(b)),x) | -->*_s0(k(f(b)),x) # answer(goal). [resolve(124,a,74,b)]. 43.002/43.002 43.002/43.002 given #128 (F,wt=10): 524 -->*_s0(k(g(x)),k(f(b))) | -->_s0(b,x) # answer(goal). [resolve(482,b,13,b)]. 43.002/43.002 43.002/43.002 given #129 (F,wt=12): 348 -->*_s0(k(g(b)),k(b)) | -->_s0(k(f(a)),h(a)) # answer(goal). [resolve(74,c,132,a)]. 43.002/43.002 43.002/43.002 given #130 (T,wt=7): 134 ->*_s0(h(f(a)),k(g(b))). [ur(23,a,20,a,b,70,a)]. 43.002/43.002 43.002/43.002 given #131 (T,wt=7): 162 ->*_s0(U91(x,a),U91(x,b)). [ur(23,a,35,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #132 (T,wt=7): 169 ->*_s0(U91(a,x),U91(b,x)). [ur(23,a,36,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #133 (T,wt=7): 185 ->*_s0(k(c),k(k(f(a)))). [ur(23,a,37,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #134 (A,wt=10): 52 ->_s0(f(f(x)),f(U91(h(f(x)),x))). [ur(11,a,19,a)]. 43.002/43.002 43.002/43.002 given #135 (F,wt=7): 529 -->_s0(k(f(b)),h(f(a))) # answer(goal). [resolve(134,a,158,b)]. 43.002/43.002 43.002/43.002 given #136 (F,wt=7): 530 -->_s0(k(f(a)),h(f(a))) # answer(goal). [resolve(134,a,87,b)]. 43.002/43.002 43.002/43.002 given #137 (F,wt=10): 531 -->_s0(k(U91(h(f(b)),b)),h(f(a))) # answer(goal). [ur(23,b,134,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #138 (F,wt=10): 532 -->_s0(k(U91(h(f(a)),a)),h(f(a))) # answer(goal). [ur(23,b,134,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #139 (T,wt=7): 192 ->*_s0(g(c),g(k(f(a)))). [ur(23,a,38,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #140 (T,wt=7): 199 ->*_s0(h(c),k(k(f(a)))). [ur(23,a,39,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #141 (T,wt=7): 200 ->*_s0(h(c),h(k(f(a)))). [ur(23,a,39,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #142 (T,wt=7): 207 ->*_s0(f(c),f(k(f(a)))). [ur(23,a,40,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #143 (A,wt=12): 53 ->_s0(U91(x,f(y)),U91(x,U91(h(f(y)),y))). [ur(10,a,19,a)]. 43.002/43.002 43.002/43.002 given #144 (F,wt=12): 349 -->*_s0(k(g(b)),f(b)) | -->_s0(k(f(a)),f(a)) # answer(goal). [resolve(74,c,123,a)]. 43.002/43.002 43.002/43.002 given #145 (F,wt=12): 350 -->*_s0(k(g(b)),h(b)) | -->_s0(k(f(a)),h(a)) # answer(goal). [resolve(74,c,104,a)]. 43.002/43.002 43.002/43.002 given #146 (F,wt=12): 351 -->*_s0(k(g(b)),g(b)) | -->_s0(k(f(a)),g(a)) # answer(goal). [resolve(74,c,97,a)]. 43.002/43.002 43.002/43.002 given #147 (F,wt=12): 352 -->*_s0(k(g(b)),k(b)) | -->_s0(k(f(a)),k(a)) # answer(goal). [resolve(74,c,90,a)]. 43.002/43.002 43.002/43.002 given #148 (T,wt=7): 228 ->*_s0(k(c),k(k(g(b)))). [ur(23,a,43,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #149 (T,wt=7): 235 ->*_s0(g(c),g(k(g(b)))). [ur(23,a,44,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #150 (T,wt=7): 242 ->*_s0(h(c),k(k(g(b)))). [ur(23,a,45,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #151 (T,wt=7): 243 ->*_s0(h(c),h(k(g(b)))). [ur(23,a,45,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #152 (A,wt=12): 54 ->_s0(U91(f(x),y),U91(U91(h(f(x)),x),y)). [ur(9,a,19,a)]. 43.002/43.002 43.002/43.002 given #153 (F,wt=10): 568 -->*_s0(k(g(b)),k(b)) | -->_s0(f(a),a) # answer(goal). [resolve(352,b,14,b)]. 43.002/43.002 43.002/43.002 given #154 (F,wt=12): 355 -->*_s0(k(g(b)),k(x)) | -->_s0(k(f(a)),h(x)) # answer(goal). [resolve(74,c,67,a)]. 43.002/43.002 43.002/43.002 given #155 (F,wt=13): 76 -->*_s0(k(f(a)),x) | -->_s0(k(g(b)),y) | -->*_s0(y,x) # answer(goal). [resolve(24,b,23,c)]. 43.002/43.002 43.002/43.002 given #156 (F,wt=10): 605 -->*_s0(k(f(a)),b) | -->_s0(k(g(b)),a) # answer(goal). [resolve(76,c,72,a)]. 43.002/43.002 43.002/43.002 given #157 (T,wt=7): 250 ->*_s0(f(c),f(k(g(b)))). [ur(23,a,46,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #158 (T,wt=7): 268 ->*_s0(k(h(f(a))),k(c)). [ur(23,a,55,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #159 (T,wt=7): 275 ->*_s0(g(h(f(a))),g(c)). [ur(23,a,56,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #160 (T,wt=7): 282 ->*_s0(h(h(f(a))),k(c)). [ur(23,a,57,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #161 (A,wt=9): 59 ->_s0(U91(x,h(f(a))),U91(x,c)). [ur(10,a,20,a)]. 43.002/43.002 43.002/43.002 given #162 (F,wt=10): 608 -->*_s0(k(f(a)),x) | -->_s0(k(g(b)),x) # answer(goal). [resolve(76,c,22,a)]. 43.002/43.002 43.002/43.002 given #163 (F,wt=10): 629 -->*_s0(k(f(a)),k(x)) | -->_s0(g(b),x) # answer(goal). [resolve(608,b,14,b)]. 43.002/43.002 43.002/43.002 given #164 (F,wt=10): 631 -->*_s0(k(f(a)),k(g(x))) | -->_s0(b,x) # answer(goal). [resolve(629,b,13,b)]. 43.002/43.002 43.002/43.002 given #165 (F,wt=12): 600 -->*_s0(k(f(a)),k(b)) | -->_s0(k(g(b)),h(a)) # answer(goal). [resolve(76,c,132,a)]. 43.002/43.002 43.002/43.002 given #166 (T,wt=7): 283 ->*_s0(h(h(f(a))),h(c)). [ur(23,a,57,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #167 (T,wt=7): 290 ->*_s0(f(h(f(a))),f(c)). [ur(23,a,58,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #168 (T,wt=7): 309 ->*_s0(k(h(x)),k(k(x))). [ur(23,a,61,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #169 (T,wt=7): 316 ->*_s0(g(h(x)),g(k(x))). [ur(23,a,62,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #170 (A,wt=9): 60 ->_s0(U91(h(f(a)),x),U91(c,x)). [ur(9,a,20,a)]. 43.002/43.002 43.002/43.002 given #171 (F,wt=12): 601 -->*_s0(k(f(a)),f(b)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(76,c,123,a)]. 43.002/43.002 43.002/43.002 given #172 (F,wt=12): 602 -->*_s0(k(f(a)),h(b)) | -->_s0(k(g(b)),h(a)) # answer(goal). [resolve(76,c,104,a)]. 43.002/43.002 43.002/43.002 given #173 (F,wt=12): 603 -->*_s0(k(f(a)),g(b)) | -->_s0(k(g(b)),g(a)) # answer(goal). [resolve(76,c,97,a)]. 43.002/43.002 43.002/43.002 given #174 (F,wt=12): 604 -->*_s0(k(f(a)),k(b)) | -->_s0(k(g(b)),k(a)) # answer(goal). [resolve(76,c,90,a)]. 43.002/43.002 43.002/43.002 given #175 (T,wt=7): 323 ->*_s0(h(h(x)),k(k(x))). [ur(23,a,63,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #176 (T,wt=7): 324 ->*_s0(h(h(x)),h(k(x))). [ur(23,a,63,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #177 (T,wt=7): 331 ->*_s0(f(h(x)),f(k(x))). [ur(23,a,64,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #178 (T,wt=7): 359 ->*_s0(k(k(a)),k(k(b))). [ur(23,a,91,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #179 (A,wt=9): 65 ->_s0(U91(x,h(y)),U91(x,k(y))). [ur(10,a,21,a)]. 43.002/43.002 43.002/43.002 given #180 (F,wt=10): 657 -->*_s0(k(f(a)),k(b)) | -->_s0(g(b),a) # answer(goal). [resolve(604,b,14,b)]. 43.002/43.002 43.002/43.002 given #181 (F,wt=12): 606 -->*_s0(k(f(a)),k(x)) | -->_s0(k(g(b)),h(x)) # answer(goal). [resolve(76,c,67,a)]. 43.002/43.002 43.002/43.002 given #182 (F,wt=13): 120 -->_s0(k(g(b)),x) | -->_s0(x,y) | -->*_s0(y,k(f(a))) # answer(goal). [resolve(85,b,23,c)]. 43.002/43.002 43.002/43.002 given #183 (F,wt=8): 743 -->_s0(k(g(b)),x) | -->_s0(x,c) # answer(goal). [resolve(120,c,71,a)]. 43.002/43.002 43.002/43.002 given #184 (T,wt=7): 366 ->*_s0(g(k(a)),g(k(b))). [ur(23,a,92,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #185 (T,wt=7): 373 ->*_s0(h(k(a)),k(k(b))). [ur(23,a,93,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #186 (T,wt=7): 374 ->*_s0(h(k(a)),h(k(b))). [ur(23,a,93,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #187 (T,wt=7): 381 ->*_s0(f(k(a)),f(k(b))). [ur(23,a,94,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #188 (A,wt=9): 66 ->_s0(U91(h(x),y),U91(k(x),y)). [ur(9,a,21,a)]. 43.002/43.002 43.002/43.002 given #189 (F,wt=8): 747 -->_s0(k(x),c) | -->_s0(g(b),x) # answer(goal). [resolve(743,a,14,b)]. 43.002/43.002 43.002/43.002 given #190 (F,wt=8): 766 -->_s0(k(g(x)),c) | -->_s0(b,x) # answer(goal). [resolve(747,b,13,b)]. 43.002/43.002 43.002/43.002 given #191 (F,wt=10): 735 -->_s0(k(g(b)),a) | -->*_s0(b,k(f(a))) # answer(goal). [resolve(120,b,16,a)]. 43.002/43.002 43.002/43.002 given #192 (F,wt=10): 744 -->_s0(k(g(b)),x) | -->_s0(x,h(f(a))) # answer(goal). [resolve(120,c,67,a)]. 43.002/43.002 43.002/43.002 given #193 (T,wt=7): 404 ->*_s0(k(g(a)),k(g(b))). [ur(23,a,98,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #194 (T,wt=7): 411 ->*_s0(g(g(a)),g(g(b))). [ur(23,a,99,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #195 (T,wt=7): 418 ->*_s0(h(g(a)),k(g(b))). [ur(23,a,100,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #196 (T,wt=7): 419 ->*_s0(h(g(a)),h(g(b))). [ur(23,a,100,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #197 (A,wt=8): 69 ->*_s0(f(x),U91(h(f(x)),x)). [ur(23,a,19,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #198 (F,wt=5): 770 -->_s0(f(b),g(a)) # answer(goal). [resolve(404,a,226,a)]. 43.002/43.002 43.002/43.002 given #199 (F,wt=5): 772 -->_s0(f(a),g(a)) # answer(goal). [resolve(404,a,121,a)]. 43.002/43.002 43.002/43.002 given #200 (F,wt=7): 771 -->_s0(k(f(b)),k(g(a))) # answer(goal). [resolve(404,a,158,b)]. 43.002/43.002 43.002/43.002 given #201 (F,wt=7): 773 -->_s0(k(f(a)),k(g(a))) # answer(goal). [resolve(404,a,87,b)]. 43.002/43.002 43.002/43.002 given #202 (T,wt=7): 426 ->*_s0(f(g(a)),f(g(b))). [ur(23,a,101,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #203 (T,wt=7): 446 ->*_s0(k(h(a)),k(h(b))). [ur(23,a,105,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #204 (T,wt=7): 453 ->*_s0(g(h(a)),g(h(b))). [ur(23,a,106,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #205 (T,wt=7): 460 ->*_s0(h(h(a)),k(h(b))). [ur(23,a,107,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #206 (A,wt=8): 73 ->*_s0(U91(k(g(b)),x),g(x)). [ur(23,a,15,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #207 (F,wt=7): 781 -->_s0(k(f(b)),h(g(a))) # answer(goal). [resolve(418,a,158,b)]. 43.002/43.002 43.002/43.002 given #208 (F,wt=7): 782 -->_s0(k(f(a)),h(g(a))) # answer(goal). [resolve(418,a,87,b)]. 43.002/43.002 43.002/43.002 given #209 (F,wt=10): 746 -->_s0(k(g(b)),x) | -->_s0(x,k(f(a))) # answer(goal). [resolve(120,c,22,a)]. 43.002/43.002 43.002/43.002 given #210 (F,wt=10): 768 -->_s0(k(x),h(f(a))) | -->_s0(g(b),x) # answer(goal). [resolve(744,a,14,b)]. 43.002/43.002 43.002/43.002 given #211 (T,wt=6): 815 ->*_s0(U91(c,x),g(x)). [ur(23,a,48,a,b,73,a)]. 43.002/43.002 43.002/43.002 given #212 (T,wt=6): 828 ->*_s0(U91(c,a),g(b)). [ur(23,a,35,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #213 (T,wt=7): 461 ->*_s0(h(h(a)),h(h(b))). [ur(23,a,107,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #214 (T,wt=7): 468 ->*_s0(f(h(a)),f(h(b))). [ur(23,a,108,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #215 (A,wt=10): 78 ->*_s0(k(U91(k(g(b)),x)),k(g(x))). [ur(23,a,25,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #216 (F,wt=8): 837 -->_s0(f(b),U91(k(g(b)),b)) # answer(goal). [resolve(78,a,226,a)]. 43.002/43.002 43.002/43.002 given #217 (F,wt=8): 839 -->_s0(f(a),U91(k(g(b)),b)) # answer(goal). [resolve(78,a,121,a)]. 43.002/43.002 43.002/43.002 given #218 (F,wt=10): 769 -->_s0(k(g(b)),h(x)) | -->_s0(x,f(a)) # answer(goal). [resolve(744,b,12,b)]. 43.002/43.002 43.002/43.002 given #219 (F,wt=10): 775 -->_s0(k(U91(h(f(b)),b)),k(g(a))) # answer(goal). [ur(23,b,404,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #220 (T,wt=7): 486 ->*_s0(k(f(a)),k(f(b))). [ur(23,a,124,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #221 (T,wt=5): 847 ->*_s0(c,k(f(b))). [ur(23,a,17,a,b,486,a)]. 43.002/43.002 43.002/43.002 given #222 (T,wt=7): 493 ->*_s0(g(f(a)),g(f(b))). [ur(23,a,125,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #223 (T,wt=7): 500 ->*_s0(h(f(a)),k(f(b))). [ur(23,a,126,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #224 (A,wt=12): 79 ->_s0(k(k(U91(k(g(b)),x))),k(k(g(x)))). [ur(14,a,25,a)]. 43.002/43.002 43.002/43.002 given #225 (F,wt=8): 846 -->_s0(U91(h(f(b)),b),g(a)) # answer(goal). [resolve(775,a,14,b)]. 43.002/43.002 43.002/43.002 given #226 (F,wt=10): 776 -->_s0(k(U91(h(f(a)),a)),k(g(a))) # answer(goal). [ur(23,b,404,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #227 (F,wt=8): 859 -->_s0(U91(h(f(a)),a),g(a)) # answer(goal). [resolve(776,a,14,b)]. 43.002/43.002 43.002/43.002 given #228 (F,wt=10): 784 -->_s0(k(U91(h(f(b)),b)),h(g(a))) # answer(goal). [ur(23,b,418,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #229 (T,wt=7): 501 ->*_s0(h(f(a)),h(f(b))). [ur(23,a,126,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #230 (T,wt=7): 508 ->*_s0(f(f(a)),f(f(b))). [ur(23,a,127,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #231 (T,wt=7): 536 ->*_s0(U91(a,a),U91(b,b)). [ur(23,a,36,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #232 (T,wt=7): 640 ->*_s0(k(h(a)),k(k(b))). [ur(23,a,105,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #233 (A,wt=12): 80 ->_s0(g(k(U91(k(g(b)),x))),g(k(g(x)))). [ur(13,a,25,a)]. 43.002/43.002 43.002/43.002 given #234 (F,wt=10): 785 -->_s0(k(U91(h(f(a)),a)),h(g(a))) # answer(goal). [ur(23,b,418,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #235 (F,wt=10): 817 -->_s0(k(x),k(f(a))) | -->_s0(g(b),x) # answer(goal). [resolve(746,a,14,b)]. 43.002/43.002 43.002/43.002 given #236 (F,wt=8): 874 -->_s0(g(b),x) | -->_s0(x,f(a)) # answer(goal). [resolve(817,a,14,b)]. 43.002/43.002 43.002/43.002 given #237 (F,wt=8): 876 -->_s0(g(x),f(a)) | -->_s0(b,x) # answer(goal). [resolve(874,a,13,b)]. 43.002/43.002 43.002/43.002 given #238 (T,wt=7): 643 ->*_s0(g(h(a)),g(k(b))). [ur(23,a,106,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #239 (T,wt=7): 660 ->*_s0(h(h(a)),k(k(b))). [ur(23,a,107,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #240 (T,wt=7): 663 ->*_s0(h(h(a)),h(k(b))). [ur(23,a,107,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #241 (T,wt=7): 666 ->*_s0(f(h(a)),f(k(b))). [ur(23,a,108,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #242 (A,wt=12): 81 ->_s0(h(k(U91(k(g(b)),x))),h(k(g(x)))). [ur(12,a,25,a)]. 43.002/43.002 43.002/43.002 given #243 (F,wt=8): 877 -->_s0(g(b),f(x)) | -->_s0(x,a) # answer(goal). [resolve(874,b,11,b)]. 43.002/43.002 43.002/43.002 given #244 (F,wt=10): 818 -->_s0(k(g(b)),k(x)) | -->_s0(x,f(a)) # answer(goal). [resolve(746,b,14,b)]. 43.002/43.002 43.002/43.002 given #245 (F,wt=10): 819 -->_s0(k(g(x)),h(f(a))) | -->_s0(b,x) # answer(goal). [resolve(768,b,13,b)]. 43.002/43.002 43.002/43.002 given #246 (F,wt=10): 838 -->_s0(k(f(b)),k(U91(k(g(b)),b))) # answer(goal). [resolve(78,a,158,b)]. 43.002/43.002 43.002/43.002 given #247 (T,wt=8): 146 ->*_s0(U91(k(g(b)),a),g(b)). [ur(23,a,15,a,b,97,a)]. 43.002/43.002 43.002/43.002 given #248 (T,wt=8): 538 ->*_s0(f(a),U91(h(f(a)),b)). [ur(23,a,19,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #249 (T,wt=8): 799 ->*_s0(f(a),U91(h(f(b)),b)). [ur(23,a,34,a,b,69,a)]. 43.002/43.002 43.002/43.002 given #250 (T,wt=8): 813 ->*_s0(U91(h(g(b)),x),g(x)). [ur(23,a,66,a,b,73,a)]. 43.002/43.002 43.002/43.002 given #251 (A,wt=12): 82 ->_s0(f(k(U91(k(g(b)),x))),f(k(g(x)))). [ur(11,a,25,a)]. 43.002/43.002 43.002/43.002 given #252 (F,wt=10): 840 -->_s0(k(f(a)),k(U91(k(g(b)),b))) # answer(goal). [resolve(78,a,87,b)]. 43.002/43.002 43.002/43.002 given #253 (F,wt=10): 845 -->_s0(k(g(b)),h(f(x))) | -->_s0(x,a) # answer(goal). [resolve(769,b,11,b)]. 43.002/43.002 43.002/43.002 given #254 (F,wt=10): 875 -->_s0(k(g(x)),k(f(a))) | -->_s0(b,x) # answer(goal). [resolve(817,b,13,b)]. 43.002/43.002 43.002/43.002 given #255 (F,wt=10): 896 -->_s0(k(g(b)),k(f(x))) | -->_s0(x,a) # answer(goal). [resolve(818,b,11,b)]. 43.002/43.002 43.002/43.002 given #256 (T,wt=8): 822 ->*_s0(U91(c,h(x)),g(k(x))). [ur(23,a,65,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #257 (T,wt=8): 823 ->*_s0(U91(h(f(a)),x),g(x)). [ur(23,a,60,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #258 (T,wt=5): 931 ->*_s0(f(a),g(a)). [ur(23,a,19,a,b,823,a)]. 43.002/43.002 43.002/43.002 given #259 (T,wt=8): 824 ->*_s0(U91(c,h(f(a))),g(c)). [ur(23,a,59,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #260 (A,wt=14): 83 ->_s0(U91(x,k(U91(k(g(b)),y))),U91(x,k(g(y)))). [ur(10,a,25,a)]. 43.002/43.002 43.002/43.002 given #261 (F,wt=12): 723 -->_s0(k(g(b)),f(a)) | -->*_s0(f(b),k(f(a))) # answer(goal). [resolve(120,b,34,a)]. 43.002/43.002 43.002/43.002 given #262 (F,wt=12): 724 -->_s0(k(g(b)),h(a)) | -->*_s0(h(b),k(f(a))) # answer(goal). [resolve(120,b,33,a)]. 43.002/43.002 43.002/43.002 given #263 (F,wt=12): 725 -->_s0(k(g(b)),g(a)) | -->*_s0(g(b),k(f(a))) # answer(goal). [resolve(120,b,32,a)]. 43.002/43.002 43.002/43.002 given #264 (F,wt=12): 726 -->_s0(k(g(b)),k(a)) | -->*_s0(k(b),k(f(a))) # answer(goal). [resolve(120,b,31,a)]. 43.002/43.002 43.002/43.002 given #265 (T,wt=8): 826 ->*_s0(U91(c,c),g(k(g(b)))). [ur(23,a,47,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #266 (T,wt=8): 827 ->*_s0(U91(c,c),g(k(f(a)))). [ur(23,a,41,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #267 (T,wt=8): 832 ->*_s0(U91(h(f(a)),a),g(b)). [ur(23,a,60,a,b,828,a)]. 43.002/43.002 43.002/43.002 given #268 (T,wt=5): 961 ->*_s0(f(a),g(b)). [ur(23,a,19,a,b,832,a)]. 43.002/43.002 43.002/43.002 given #269 (A,wt=14): 84 ->_s0(U91(k(U91(k(g(b)),x)),y),U91(k(g(x)),y)). [ur(9,a,25,a)]. 43.002/43.002 43.002/43.002 given #270 (F,wt=10): 952 -->*_s0(k(b),k(f(a))) | -->_s0(g(b),a) # answer(goal). [resolve(726,a,14,b)]. 43.002/43.002 43.002/43.002 given #271 (F,wt=12): 733 -->_s0(k(g(b)),h(x)) | -->*_s0(k(x),k(f(a))) # answer(goal). [resolve(120,b,21,a)]. 43.002/43.002 43.002/43.002 given #272 (F,wt=12): 932 -->*_s0(k(f(a)),g(a)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(931,a,76,c)]. 43.002/43.002 43.002/43.002 given #273 (F,wt=12): 933 -->*_s0(k(g(b)),g(a)) | -->_s0(k(f(a)),f(a)) # answer(goal). [resolve(931,a,74,c)]. 43.002/43.002 43.002/43.002 given #274 (T,wt=8): 899 ->*_s0(U91(h(g(b)),a),g(b)). [ur(23,a,66,a,b,146,a)]. 43.002/43.002 43.002/43.002 given #275 (T,wt=9): 95 ->_s0(U91(x,k(a)),U91(x,k(b))). [ur(10,a,31,a)]. 43.002/43.002 43.002/43.002 given #276 (T,wt=8): 983 ->*_s0(U91(c,k(a)),g(k(b))). [ur(23,a,95,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #277 (T,wt=8): 995 ->*_s0(U91(c,h(a)),g(k(b))). [ur(23,a,65,a,b,983,a)]. 43.002/43.002 43.002/43.002 given #278 (A,wt=9): 96 ->_s0(U91(k(a),x),U91(k(b),x)). [ur(9,a,31,a)]. 43.002/43.002 43.002/43.002 given #279 (F,wt=12): 962 -->*_s0(k(f(a)),g(b)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(961,a,76,c)]. 43.002/43.002 43.002/43.002 given #280 (F,wt=12): 963 -->*_s0(k(g(b)),g(b)) | -->_s0(k(f(a)),f(a)) # answer(goal). [resolve(961,a,74,c)]. 43.002/43.002 43.002/43.002 given #281 (F,wt=13): 122 -->_s0(k(f(a)),x) | -->_s0(x,y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(87,b,23,c)]. 43.002/43.002 43.002/43.002 given #282 (F,wt=8): 1086 -->_s0(k(f(a)),x) | -->_s0(x,c) # answer(goal). [resolve(122,c,70,a)]. 43.002/43.002 43.002/43.002 given #283 (T,wt=9): 102 ->_s0(U91(x,g(a)),U91(x,g(b))). [ur(10,a,32,a)]. 43.002/43.002 43.002/43.002 given #284 (T,wt=8): 1097 ->*_s0(U91(c,g(a)),g(g(b))). [ur(23,a,102,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #285 (T,wt=9): 103 ->_s0(U91(g(a),x),U91(g(b),x)). [ur(9,a,32,a)]. 43.002/43.002 43.002/43.002 given #286 (T,wt=9): 109 ->_s0(U91(x,h(a)),U91(x,h(b))). [ur(10,a,33,a)]. 43.002/43.002 43.002/43.002 given #287 (A,wt=9): 110 ->_s0(U91(h(a),x),U91(h(b),x)). [ur(9,a,33,a)]. 43.002/43.002 43.002/43.002 given #288 (F,wt=8): 1093 -->_s0(k(x),c) | -->_s0(f(a),x) # answer(goal). [resolve(1086,a,14,b)]. 43.002/43.002 43.002/43.002 given #289 (F,wt=8): 1143 -->_s0(k(f(x)),c) | -->_s0(a,x) # answer(goal). [resolve(1093,b,11,b)]. 43.002/43.002 43.002/43.002 given #290 (F,wt=10): 1074 -->_s0(k(f(a)),a) | -->*_s0(b,k(g(b))) # answer(goal). [resolve(122,b,16,a)]. 43.002/43.002 43.002/43.002 given #291 (F,wt=10): 1082 -->_s0(k(f(a)),x) | -->_s0(x,h(g(a))) # answer(goal). [resolve(122,c,418,a)]. 43.002/43.002 43.002/43.002 given #292 (T,wt=8): 1123 ->*_s0(U91(c,h(a)),g(h(b))). [ur(23,a,109,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #293 (T,wt=9): 128 ->_s0(U91(x,f(a)),U91(x,f(b))). [ur(10,a,34,a)]. 43.002/43.002 43.002/43.002 given #294 (T,wt=8): 1152 ->*_s0(U91(c,f(a)),g(f(b))). [ur(23,a,128,a,b,815,a)]. 43.002/43.002 43.002/43.002 given #295 (T,wt=9): 129 ->_s0(U91(f(a),x),U91(f(b),x)). [ur(9,a,34,a)]. 43.002/43.002 43.002/43.002 given #296 (A,wt=10): 111 ->*_s0(g(U91(k(g(b)),x)),g(g(x))). [ur(23,a,26,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #297 (F,wt=10): 1083 -->_s0(k(f(a)),x) | -->_s0(x,k(g(a))) # answer(goal). [resolve(122,c,404,a)]. 43.002/43.002 43.002/43.002 given #298 (F,wt=10): 1084 -->_s0(k(f(a)),x) | -->_s0(x,h(f(a))) # answer(goal). [resolve(122,c,134,a)]. 43.002/43.002 43.002/43.002 given #299 (F,wt=10): 1087 -->_s0(k(f(a)),x) | -->_s0(x,h(g(b))) # answer(goal). [resolve(122,c,67,a)]. 43.002/43.002 43.002/43.002 given #300 (F,wt=10): 1089 -->_s0(k(f(a)),x) | -->_s0(x,k(g(b))) # answer(goal). [resolve(122,c,22,a)]. 43.002/43.002 43.002/43.002 given #301 (T,wt=9): 163 ->_s0(k(U91(x,a)),k(U91(x,b))). [ur(14,a,35,a)]. 43.002/43.002 43.002/43.002 given #302 (T,wt=9): 164 ->_s0(g(U91(x,a)),g(U91(x,b))). [ur(13,a,35,a)]. 43.002/43.002 43.002/43.002 given #303 (T,wt=9): 165 ->_s0(h(U91(x,a)),h(U91(x,b))). [ur(12,a,35,a)]. 43.002/43.002 43.002/43.002 given #304 (T,wt=9): 166 ->_s0(f(U91(x,a)),f(U91(x,b))). [ur(11,a,35,a)]. 43.002/43.002 43.002/43.002 given #305 (A,wt=12): 112 ->_s0(k(g(U91(k(g(b)),x))),k(g(g(x)))). [ur(14,a,26,a)]. 43.002/43.002 43.002/43.002 given #306 (F,wt=10): 1090 -->_s0(k(f(a)),h(U91(k(g(b)),a))) # answer(goal). [ur(122,b,27,a,c,418,a)]. 43.002/43.002 43.002/43.002 given #307 (F,wt=10): 1091 -->_s0(k(f(a)),h(U91(k(g(b)),b))) # answer(goal). [ur(122,b,27,a,c,67,a)]. 43.002/43.002 43.002/43.002 given #308 (F,wt=10): 1092 -->_s0(k(f(a)),k(U91(k(g(b)),a))) # answer(goal). [ur(122,b,25,a,c,404,a)]. 43.002/43.002 43.002/43.002 given #309 (F,wt=8): 1232 -->_s0(f(a),U91(k(g(b)),a)) # answer(goal). [resolve(1092,a,14,b)]. 43.002/43.002 43.002/43.002 given #310 (T,wt=9): 170 ->_s0(k(U91(a,x)),k(U91(b,x))). [ur(14,a,36,a)]. 43.002/43.002 43.002/43.002 given #311 (T,wt=9): 171 ->_s0(g(U91(a,x)),g(U91(b,x))). [ur(13,a,36,a)]. 43.002/43.002 43.002/43.002 given #312 (T,wt=9): 172 ->_s0(h(U91(a,x)),h(U91(b,x))). [ur(12,a,36,a)]. 43.002/43.002 43.002/43.002 given #313 (T,wt=9): 173 ->_s0(f(U91(a,x)),f(U91(b,x))). [ur(11,a,36,a)]. 43.002/43.002 43.002/43.002 given #314 (A,wt=12): 113 ->_s0(g(g(U91(k(g(b)),x))),g(g(g(x)))). [ur(13,a,26,a)]. 43.002/43.002 43.002/43.002 given #315 (F,wt=10): 1145 -->_s0(k(x),h(g(a))) | -->_s0(f(a),x) # answer(goal). [resolve(1082,a,14,b)]. 43.002/43.002 43.002/43.002 given #316 (F,wt=10): 1146 -->_s0(k(f(a)),h(x)) | -->_s0(x,g(a)) # answer(goal). [resolve(1082,b,12,b)]. 43.002/43.002 43.002/43.002 given #317 (F,wt=10): 1176 -->_s0(k(x),k(g(a))) | -->_s0(f(a),x) # answer(goal). [resolve(1083,a,14,b)]. 43.002/43.002 43.002/43.002 given #318 (F,wt=8): 1282 -->_s0(f(a),x) | -->_s0(x,g(a)) # answer(goal). [resolve(1176,a,14,b)]. 43.002/43.002 43.002/43.002 given #319 (T,wt=9): 186 ->_s0(k(k(c)),k(k(k(f(a))))). [ur(14,a,37,a)]. 43.002/43.002 43.002/43.002 given #320 (T,wt=9): 187 ->_s0(g(k(c)),g(k(k(f(a))))). [ur(13,a,37,a)]. 43.002/43.002 43.002/43.002 given #321 (T,wt=9): 188 ->_s0(h(k(c)),h(k(k(f(a))))). [ur(12,a,37,a)]. 43.002/43.002 43.002/43.002 given #322 (T,wt=9): 189 ->_s0(f(k(c)),f(k(k(f(a))))). [ur(11,a,37,a)]. 43.002/43.002 43.002/43.002 given #323 (A,wt=12): 114 ->_s0(h(g(U91(k(g(b)),x))),h(g(g(x)))). [ur(12,a,26,a)]. 43.002/43.002 43.002/43.002 given #324 (F,wt=8): 1284 -->_s0(f(x),g(a)) | -->_s0(a,x) # answer(goal). [resolve(1282,a,11,b)]. 43.002/43.002 43.002/43.002 given #325 (F,wt=8): 1285 -->_s0(f(a),g(x)) | -->_s0(x,a) # answer(goal). [resolve(1282,b,13,b)]. 43.002/43.002 43.002/43.002 given #326 (F,wt=10): 1177 -->_s0(k(f(a)),k(x)) | -->_s0(x,g(a)) # answer(goal). [resolve(1083,b,14,b)]. 43.002/43.002 43.002/43.002 given #327 (F,wt=10): 1178 -->_s0(k(x),h(f(a))) | -->_s0(f(a),x) # answer(goal). [resolve(1084,a,14,b)]. 43.002/43.002 43.002/43.002 given #328 (T,wt=9): 193 ->_s0(k(g(c)),k(g(k(f(a))))). [ur(14,a,38,a)]. 43.002/43.002 43.002/43.002 given #329 (T,wt=9): 194 ->_s0(g(g(c)),g(g(k(f(a))))). [ur(13,a,38,a)]. 43.002/43.002 43.002/43.002 given #330 (T,wt=9): 195 ->_s0(h(g(c)),h(g(k(f(a))))). [ur(12,a,38,a)]. 43.002/43.002 43.002/43.002 given #331 (T,wt=9): 196 ->_s0(f(g(c)),f(g(k(f(a))))). [ur(11,a,38,a)]. 43.002/43.002 43.002/43.002 given #332 (A,wt=12): 115 ->_s0(f(g(U91(k(g(b)),x))),f(g(g(x)))). [ur(11,a,26,a)]. 43.002/43.002 43.002/43.002 given #333 (F,wt=10): 1179 -->_s0(k(f(a)),h(x)) | -->_s0(x,f(a)) # answer(goal). [resolve(1084,b,12,b)]. 43.002/43.002 43.002/43.002 given #334 (F,wt=10): 1180 -->_s0(k(x),h(g(b))) | -->_s0(f(a),x) # answer(goal). [resolve(1087,a,14,b)]. 43.002/43.002 43.002/43.002 given #335 (F,wt=10): 1181 -->_s0(k(f(a)),h(x)) | -->_s0(x,g(b)) # answer(goal). [resolve(1087,b,12,b)]. 43.002/43.002 43.002/43.002 given #336 (F,wt=10): 1182 -->_s0(k(x),k(g(b))) | -->_s0(f(a),x) # answer(goal). [resolve(1089,a,14,b)]. 43.002/43.002 43.002/43.002 given #337 (T,wt=9): 201 ->_s0(k(h(c)),k(h(k(f(a))))). [ur(14,a,39,a)]. 43.002/43.002 43.002/43.002 given #338 (T,wt=9): 202 ->_s0(g(h(c)),g(h(k(f(a))))). [ur(13,a,39,a)]. 43.002/43.002 43.002/43.002 given #339 (T,wt=9): 203 ->_s0(h(h(c)),h(h(k(f(a))))). [ur(12,a,39,a)]. 43.002/43.002 43.002/43.002 given #340 (T,wt=9): 204 ->_s0(f(h(c)),f(h(k(f(a))))). [ur(11,a,39,a)]. 43.002/43.002 43.002/43.002 given #341 (A,wt=14): 116 ->_s0(U91(x,g(U91(k(g(b)),y))),U91(x,g(g(y)))). [ur(10,a,26,a)]. 43.002/43.002 43.002/43.002 given #342 (F,wt=8): 1387 -->_s0(f(a),x) | -->_s0(x,g(b)) # answer(goal). [resolve(1182,a,14,b)]. 43.002/43.002 43.002/43.002 given #343 (F,wt=8): 1446 -->_s0(f(x),g(b)) | -->_s0(a,x) # answer(goal). [resolve(1387,a,11,b)]. 43.002/43.002 43.002/43.002 given #344 (F,wt=8): 1447 -->_s0(f(a),g(x)) | -->_s0(x,b) # answer(goal). [resolve(1387,b,13,b)]. 43.002/43.002 43.002/43.002 given #345 (F,wt=10): 1183 -->_s0(k(f(a)),k(x)) | -->_s0(x,g(b)) # answer(goal). [resolve(1089,b,14,b)]. 43.002/43.002 43.002/43.002 given #346 (T,wt=9): 208 ->_s0(k(f(c)),k(f(k(f(a))))). [ur(14,a,40,a)]. 43.002/43.002 43.002/43.002 given #347 (T,wt=9): 209 ->_s0(g(f(c)),g(f(k(f(a))))). [ur(13,a,40,a)]. 43.002/43.002 43.002/43.002 given #348 (T,wt=9): 210 ->_s0(h(f(c)),h(f(k(f(a))))). [ur(12,a,40,a)]. 43.002/43.002 43.002/43.002 given #349 (T,wt=9): 211 ->_s0(f(f(c)),f(f(k(f(a))))). [ur(11,a,40,a)]. 43.002/43.002 43.002/43.002 given #350 (A,wt=14): 117 ->_s0(U91(g(U91(k(g(b)),x)),y),U91(g(g(x)),y)). [ur(9,a,26,a)]. 43.002/43.002 43.002/43.002 given #351 (F,wt=10): 1193 -->*_s0(k(U91(h(f(a)),b)),k(g(b))) # answer(goal). [ur(122,a,49,a,b,163,a)]. 43.002/43.002 43.002/43.002 given #352 (F,wt=8): 1502 -->_s0(k(U91(h(f(a)),b)),c) # answer(goal). [ur(23,b,70,a,c,1193,a)]. 43.002/43.002 43.002/43.002 given #353 (F,wt=10): 1280 -->_s0(k(f(x)),h(g(a))) | -->_s0(a,x) # answer(goal). [resolve(1145,b,11,b)]. 43.002/43.002 43.002/43.002 given #354 (F,wt=10): 1281 -->_s0(k(f(a)),h(g(x))) | -->_s0(x,a) # answer(goal). [resolve(1146,b,13,b)]. 43.002/43.002 43.002/43.002 given #355 (T,wt=9): 229 ->_s0(k(k(c)),k(k(k(g(b))))). [ur(14,a,43,a)]. 43.002/43.002 43.002/43.002 given #356 (T,wt=9): 230 ->_s0(g(k(c)),g(k(k(g(b))))). [ur(13,a,43,a)]. 43.002/43.002 43.002/43.002 given #357 (T,wt=9): 231 ->_s0(h(k(c)),h(k(k(g(b))))). [ur(12,a,43,a)]. 43.002/43.002 43.002/43.002 given #358 (T,wt=9): 232 ->_s0(f(k(c)),f(k(k(g(b))))). [ur(11,a,43,a)]. 43.002/43.002 43.002/43.002 given #359 (A,wt=10): 135 ->*_s0(h(U91(k(g(b)),x)),k(g(x))). [ur(23,a,27,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #360 (F,wt=10): 1283 -->_s0(k(f(x)),k(g(a))) | -->_s0(a,x) # answer(goal). [resolve(1176,b,11,b)]. 43.002/43.002 43.002/43.002 given #361 (F,wt=10): 1334 -->_s0(k(f(a)),k(g(x))) | -->_s0(x,a) # answer(goal). [resolve(1177,b,13,b)]. 43.002/43.002 43.002/43.002 given #362 (F,wt=10): 1335 -->_s0(k(f(x)),h(f(a))) | -->_s0(a,x) # answer(goal). [resolve(1178,b,11,b)]. 43.002/43.002 43.002/43.002 given #363 (F,wt=10): 1384 -->_s0(k(f(a)),h(f(x))) | -->_s0(x,a) # answer(goal). [resolve(1179,b,11,b)]. 43.002/43.002 43.002/43.002 given #364 (T,wt=9): 236 ->_s0(k(g(c)),k(g(k(g(b))))). [ur(14,a,44,a)]. 43.002/43.002 43.002/43.002 given #365 (T,wt=9): 237 ->_s0(g(g(c)),g(g(k(g(b))))). [ur(13,a,44,a)]. 43.002/43.002 43.002/43.002 given #366 (T,wt=9): 238 ->_s0(h(g(c)),h(g(k(g(b))))). [ur(12,a,44,a)]. 43.002/43.002 43.002/43.002 given #367 (T,wt=9): 239 ->_s0(f(g(c)),f(g(k(g(b))))). [ur(11,a,44,a)]. 43.002/43.002 43.002/43.002 given #368 (A,wt=10): 136 ->*_s0(h(U91(k(g(b)),x)),h(g(x))). [ur(23,a,27,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #369 (F,wt=10): 1385 -->_s0(k(f(x)),h(g(b))) | -->_s0(a,x) # answer(goal). [resolve(1180,b,11,b)]. 43.002/43.002 43.002/43.002 given #370 (F,wt=10): 1386 -->_s0(k(f(a)),h(g(x))) | -->_s0(x,b) # answer(goal). [resolve(1181,b,13,b)]. 43.002/43.002 43.002/43.002 given #371 (F,wt=10): 1388 -->_s0(k(f(x)),k(g(b))) | -->_s0(a,x) # answer(goal). [resolve(1182,b,11,b)]. 43.002/43.002 43.002/43.002 given #372 (F,wt=10): 1448 -->_s0(k(f(a)),k(g(x))) | -->_s0(x,b) # answer(goal). [resolve(1183,b,13,b)]. 43.002/43.002 43.002/43.002 given #373 (T,wt=9): 244 ->_s0(k(h(c)),k(h(k(g(b))))). [ur(14,a,45,a)]. 43.002/43.002 43.002/43.002 given #374 (T,wt=9): 245 ->_s0(g(h(c)),g(h(k(g(b))))). [ur(13,a,45,a)]. 43.002/43.002 43.002/43.002 given #375 (T,wt=9): 246 ->_s0(h(h(c)),h(h(k(g(b))))). [ur(12,a,45,a)]. 43.002/43.002 43.002/43.002 given #376 (T,wt=9): 247 ->_s0(f(h(c)),f(h(k(g(b))))). [ur(11,a,45,a)]. 43.002/43.002 43.002/43.002 given #377 (A,wt=12): 137 ->_s0(k(h(U91(k(g(b)),x))),k(h(g(x)))). [ur(14,a,27,a)]. 43.002/43.002 43.002/43.002 given #378 (F,wt=10): 1498 -->_s0(k(U91(h(f(a)),b)),h(g(a))) # answer(goal). [ur(23,b,418,a,c,1193,a)]. 43.002/43.002 43.002/43.002 given #379 (F,wt=10): 1499 -->_s0(k(U91(h(f(a)),b)),k(g(a))) # answer(goal). [ur(23,b,404,a,c,1193,a)]. 43.002/43.002 43.002/43.002 given #380 (F,wt=8): 1643 -->_s0(U91(h(f(a)),b),g(a)) # answer(goal). [resolve(1499,a,14,b)]. 43.002/43.002 43.002/43.002 given #381 (F,wt=10): 1500 -->_s0(k(U91(h(f(a)),b)),h(f(a))) # answer(goal). [ur(23,b,134,a,c,1193,a)]. 43.002/43.002 43.002/43.002 given #382 (T,wt=9): 251 ->_s0(k(f(c)),k(f(k(g(b))))). [ur(14,a,46,a)]. 43.002/43.002 43.002/43.002 given #383 (T,wt=9): 252 ->_s0(g(f(c)),g(f(k(g(b))))). [ur(13,a,46,a)]. 43.002/43.002 43.002/43.002 given #384 (T,wt=9): 253 ->_s0(h(f(c)),h(f(k(g(b))))). [ur(12,a,46,a)]. 43.002/43.002 43.002/43.002 given #385 (T,wt=9): 254 ->_s0(f(f(c)),f(f(k(g(b))))). [ur(11,a,46,a)]. 43.002/43.002 43.002/43.002 given #386 (A,wt=12): 138 ->_s0(g(h(U91(k(g(b)),x))),g(h(g(x)))). [ur(13,a,27,a)]. 43.002/43.002 43.002/43.002 given #387 (F,wt=10): 1503 -->_s0(k(U91(h(f(a)),b)),h(g(b))) # answer(goal). [ur(23,b,67,a,c,1193,a)]. 43.002/43.002 43.002/43.002 given #388 (F,wt=10): 1504 -->_s0(k(U91(h(f(a)),b)),k(g(b))) # answer(goal). [ur(23,b,22,a,c,1193,a)]. 43.002/43.002 43.002/43.002 given #389 (F,wt=8): 1692 -->_s0(U91(h(f(a)),b),g(b)) # answer(goal). [resolve(1504,a,14,b)]. 43.002/43.002 43.002/43.002 given #390 (F,wt=10): 1543 -->_s0(k(f(b)),h(U91(k(g(b)),b))) # answer(goal). [resolve(135,a,158,b)]. 43.002/43.002 43.002/43.002 given #391 (T,wt=9): 257 ->*_s0(U91(x,c),U91(x,k(f(a)))). [ur(23,a,41,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #392 (T,wt=9): 269 ->_s0(k(k(h(f(a)))),k(k(c))). [ur(14,a,55,a)]. 43.002/43.002 43.002/43.002 given #393 (T,wt=9): 270 ->_s0(g(k(h(f(a)))),g(k(c))). [ur(13,a,55,a)]. 43.002/43.002 43.002/43.002 given #394 (T,wt=9): 271 ->_s0(h(k(h(f(a)))),h(k(c))). [ur(12,a,55,a)]. 43.002/43.002 43.002/43.002 given #395 (A,wt=12): 139 ->_s0(h(h(U91(k(g(b)),x))),h(h(g(x)))). [ur(12,a,27,a)]. 43.002/43.002 43.002/43.002 given #396 (F,wt=12): 1062 -->_s0(k(f(a)),f(a)) | -->*_s0(f(b),k(g(b))) # answer(goal). [resolve(122,b,34,a)]. 43.002/43.002 43.002/43.002 given #397 (F,wt=12): 1063 -->_s0(k(f(a)),h(a)) | -->*_s0(h(b),k(g(b))) # answer(goal). [resolve(122,b,33,a)]. 43.002/43.002 43.002/43.002 given #398 (F,wt=12): 1064 -->_s0(k(f(a)),g(a)) | -->*_s0(g(b),k(g(b))) # answer(goal). [resolve(122,b,32,a)]. 43.002/43.002 43.002/43.002 given #399 (F,wt=12): 1065 -->_s0(k(f(a)),k(a)) | -->*_s0(k(b),k(g(b))) # answer(goal). [resolve(122,b,31,a)]. 43.002/43.002 43.002/43.002 given #400 (T,wt=9): 272 ->_s0(f(k(h(f(a)))),f(k(c))). [ur(11,a,55,a)]. 43.002/43.002 43.002/43.002 given #401 (T,wt=9): 276 ->_s0(k(g(h(f(a)))),k(g(c))). [ur(14,a,56,a)]. 43.002/43.002 43.002/43.002 given #402 (T,wt=9): 277 ->_s0(g(g(h(f(a)))),g(g(c))). [ur(13,a,56,a)]. 43.002/43.002 43.002/43.002 given #403 (T,wt=9): 278 ->_s0(h(g(h(f(a)))),h(g(c))). [ur(12,a,56,a)]. 43.002/43.002 43.002/43.002 given #404 (A,wt=12): 140 ->_s0(f(h(U91(k(g(b)),x))),f(h(g(x)))). [ur(11,a,27,a)]. 43.002/43.002 43.002/43.002 given #405 (F,wt=10): 1751 -->*_s0(k(b),k(g(b))) | -->_s0(f(a),a) # answer(goal). [resolve(1065,a,14,b)]. 43.002/43.002 43.002/43.002 given #406 (F,wt=12): 1072 -->_s0(k(f(a)),h(x)) | -->*_s0(k(x),k(g(b))) # answer(goal). [resolve(122,b,21,a)]. 43.002/43.002 43.002/43.002 given #407 (F,wt=13): 143 -->_s0(g(b),x) | -->_s0(k(x),y) | -->*_s0(y,k(f(a))) # answer(goal). [resolve(119,a,23,c)]. 43.002/43.002 43.002/43.002 given #408 (F,wt=12): 1818 -->_s0(g(b),h(a)) | -->*_s0(k(h(b)),k(f(a))) # answer(goal). [resolve(143,b,105,a)]. 43.002/43.002 43.002/43.002 given #409 (T,wt=9): 279 ->_s0(f(g(h(f(a)))),f(g(c))). [ur(11,a,56,a)]. 43.002/43.002 43.002/43.002 given #410 (T,wt=9): 284 ->_s0(k(h(h(f(a)))),k(h(c))). [ur(14,a,57,a)]. 43.002/43.002 43.002/43.002 given #411 (T,wt=9): 285 ->_s0(g(h(h(f(a)))),g(h(c))). [ur(13,a,57,a)]. 43.002/43.002 43.002/43.002 given #412 (T,wt=9): 286 ->_s0(h(h(h(f(a)))),h(h(c))). [ur(12,a,57,a)]. 43.002/43.002 43.002/43.002 given #413 (A,wt=14): 141 ->_s0(U91(x,h(U91(k(g(b)),y))),U91(x,h(g(y)))). [ur(10,a,27,a)]. 43.002/43.002 43.002/43.002 given #414 (F,wt=12): 1819 -->_s0(g(b),k(a)) | -->*_s0(k(k(b)),k(f(a))) # answer(goal). [resolve(143,b,91,a)]. 43.002/43.002 43.002/43.002 given #415 (F,wt=12): 1821 -->_s0(g(b),h(x)) | -->*_s0(k(k(x)),k(f(a))) # answer(goal). [resolve(143,b,61,a)]. 43.002/43.002 43.002/43.002 given #416 (F,wt=12): 1822 -->_s0(g(b),h(f(a))) | -->*_s0(k(c),k(f(a))) # answer(goal). [resolve(143,b,55,a)]. 43.002/43.002 43.002/43.002 given #417 (F,wt=12): 1824 -->_s0(g(b),c) | -->*_s0(k(k(g(b))),k(f(a))) # answer(goal). [resolve(143,b,43,a)]. 43.002/43.002 43.002/43.002 given #418 (T,wt=9): 287 ->_s0(f(h(h(f(a)))),f(h(c))). [ur(11,a,57,a)]. 43.002/43.002 43.002/43.002 given #419 (T,wt=9): 291 ->_s0(k(f(h(f(a)))),k(f(c))). [ur(14,a,58,a)]. 43.002/43.002 43.002/43.002 given #420 (T,wt=9): 292 ->_s0(g(f(h(f(a)))),g(f(c))). [ur(13,a,58,a)]. 43.002/43.002 43.002/43.002 given #421 (T,wt=9): 293 ->_s0(h(f(h(f(a)))),h(f(c))). [ur(12,a,58,a)]. 43.002/43.002 43.002/43.002 given #422 (A,wt=14): 142 ->_s0(U91(h(U91(k(g(b)),x)),y),U91(h(g(x)),y)). [ur(9,a,27,a)]. 43.002/43.002 43.002/43.002 given #423 (F,wt=12): 1825 -->_s0(g(b),c) | -->*_s0(k(k(f(a))),k(f(a))) # answer(goal). [resolve(143,b,37,a)]. 43.002/43.002 43.002/43.002 given #424 (F,wt=13): 154 -->_s0(f(a),x) | -->_s0(k(x),y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(121,a,23,c)]. 43.002/43.002 43.002/43.002 given #425 (F,wt=12): 1962 -->_s0(f(a),h(a)) | -->*_s0(k(h(b)),k(g(b))) # answer(goal). [resolve(154,b,105,a)]. 43.002/43.002 43.002/43.002 given #426 (F,wt=12): 1963 -->_s0(f(a),k(a)) | -->*_s0(k(k(b)),k(g(b))) # answer(goal). [resolve(154,b,91,a)]. 43.002/43.002 43.002/43.002 given #427 (T,wt=9): 294 ->_s0(f(f(h(f(a)))),f(f(c))). [ur(11,a,58,a)]. 43.002/43.002 43.002/43.002 given #428 (T,wt=9): 297 ->*_s0(U91(c,x),U91(k(f(a)),x)). [ur(23,a,42,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #429 (T,wt=9): 310 ->_s0(k(k(h(x))),k(k(k(x)))). [ur(14,a,61,a)]. 43.002/43.002 43.002/43.002 given #430 (T,wt=9): 311 ->_s0(g(k(h(x))),g(k(k(x)))). [ur(13,a,61,a)]. 43.002/43.002 43.002/43.002 given #431 (A,wt=10): 147 ->*_s0(f(U91(k(g(b)),x)),f(g(x))). [ur(23,a,28,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #432 (F,wt=12): 1965 -->_s0(f(a),h(x)) | -->*_s0(k(k(x)),k(g(b))) # answer(goal). [resolve(154,b,61,a)]. 43.002/43.002 43.002/43.002 given #433 (F,wt=12): 1966 -->_s0(f(a),h(f(a))) | -->*_s0(k(c),k(g(b))) # answer(goal). [resolve(154,b,55,a)]. 43.002/43.002 43.002/43.002 given #434 (F,wt=12): 1968 -->_s0(f(a),c) | -->*_s0(k(k(g(b))),k(g(b))) # answer(goal). [resolve(154,b,43,a)]. 43.002/43.002 43.002/43.002 given #435 (F,wt=12): 1969 -->_s0(f(a),c) | -->*_s0(k(k(f(a))),k(g(b))) # answer(goal). [resolve(154,b,37,a)]. 43.002/43.002 43.002/43.002 given #436 (T,wt=9): 312 ->_s0(h(k(h(x))),h(k(k(x)))). [ur(12,a,61,a)]. 43.002/43.002 43.002/43.002 given #437 (T,wt=9): 313 ->_s0(f(k(h(x))),f(k(k(x)))). [ur(11,a,61,a)]. 43.002/43.002 43.002/43.002 given #438 (T,wt=9): 317 ->_s0(k(g(h(x))),k(g(k(x)))). [ur(14,a,62,a)]. 43.002/43.002 43.002/43.002 given #439 (T,wt=9): 318 ->_s0(g(g(h(x))),g(g(k(x)))). [ur(13,a,62,a)]. 43.002/43.002 43.002/43.002 given #440 (A,wt=12): 148 ->_s0(k(f(U91(k(g(b)),x))),k(f(g(x)))). [ur(14,a,28,a)]. 43.002/43.002 43.002/43.002 given #441 (F,wt=13): 184 -->_s0(b,x) | -->_s0(k(g(x)),y) | -->*_s0(y,k(f(a))) # answer(goal). [resolve(144,a,23,c)]. 43.002/43.002 43.002/43.002 given #442 (F,wt=12): 2078 -->_s0(b,h(x)) | -->*_s0(k(g(k(x))),k(f(a))) # answer(goal). [resolve(184,b,317,a)]. 43.002/43.002 43.002/43.002 given #443 (F,wt=12): 2079 -->_s0(b,h(f(a))) | -->*_s0(k(g(c)),k(f(a))) # answer(goal). [resolve(184,b,276,a)]. 43.002/43.002 43.002/43.002 given #444 (F,wt=12): 2080 -->_s0(b,c) | -->*_s0(k(g(k(g(b)))),k(f(a))) # answer(goal). [resolve(184,b,236,a)]. 43.002/43.002 43.002/43.002 given #445 (T,wt=9): 319 ->_s0(h(g(h(x))),h(g(k(x)))). [ur(12,a,62,a)]. 43.002/43.002 43.002/43.002 given #446 (T,wt=9): 320 ->_s0(f(g(h(x))),f(g(k(x)))). [ur(11,a,62,a)]. 43.002/43.002 43.002/43.002 given #447 (T,wt=9): 325 ->_s0(k(h(h(x))),k(h(k(x)))). [ur(14,a,63,a)]. 43.002/43.002 43.002/43.002 given #448 (T,wt=9): 326 ->_s0(g(h(h(x))),g(h(k(x)))). [ur(13,a,63,a)]. 43.002/43.002 43.002/43.002 given #449 (A,wt=12): 149 ->_s0(g(f(U91(k(g(b)),x))),g(f(g(x)))). [ur(13,a,28,a)]. 43.002/43.002 43.002/43.002 given #450 (F,wt=12): 2081 -->_s0(b,c) | -->*_s0(k(g(k(f(a)))),k(f(a))) # answer(goal). [resolve(184,b,193,a)]. 43.002/43.002 43.002/43.002 given #451 (F,wt=13): 221 -->_s0(k(U91(h(f(a)),a)),x) | -->*_s0(x,k(g(b))) # answer(goal). [resolve(156,a,23,c)]. 43.002/43.002 43.002/43.002 given #452 (F,wt=13): 225 -->_s0(a,x) | -->_s0(k(f(x)),y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(157,a,23,c)]. 43.002/43.002 43.002/43.002 given #453 (F,wt=12): 2142 -->_s0(a,h(f(a))) | -->*_s0(k(f(c)),k(g(b))) # answer(goal). [resolve(225,b,291,a)]. 43.002/43.002 43.002/43.002 given #454 (T,wt=9): 327 ->_s0(h(h(h(x))),h(h(k(x)))). [ur(12,a,63,a)]. 43.002/43.002 43.002/43.002 given #455 (T,wt=9): 328 ->_s0(f(h(h(x))),f(h(k(x)))). [ur(11,a,63,a)]. 43.002/43.002 43.002/43.002 given #456 (T,wt=9): 332 ->_s0(k(f(h(x))),k(f(k(x)))). [ur(14,a,64,a)]. 43.002/43.002 43.002/43.002 given #457 (T,wt=9): 333 ->_s0(g(f(h(x))),g(f(k(x)))). [ur(13,a,64,a)]. 43.002/43.002 43.002/43.002 given #458 (A,wt=12): 150 ->_s0(h(f(U91(k(g(b)),x))),h(f(g(x)))). [ur(12,a,28,a)]. 43.002/43.002 43.002/43.002 given #459 (F,wt=12): 2143 -->_s0(a,c) | -->*_s0(k(f(k(g(b)))),k(g(b))) # answer(goal). [resolve(225,b,251,a)]. 43.002/43.002 43.002/43.002 given #460 (F,wt=12): 2144 -->_s0(a,c) | -->*_s0(k(f(k(f(a)))),k(g(b))) # answer(goal). [resolve(225,b,208,a)]. 43.002/43.002 43.002/43.002 given #461 (F,wt=12): 2175 -->_s0(a,h(x)) | -->*_s0(k(f(k(x))),k(g(b))) # answer(goal). [resolve(332,a,225,b)]. 43.002/43.002 43.002/43.002 given #462 (F,wt=13): 227 -->_s0(k(f(b)),x) | -->_s0(x,y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(158,b,23,c)]. 43.002/43.002 43.002/43.002 given #463 (T,wt=9): 334 ->_s0(h(f(h(x))),h(f(k(x)))). [ur(12,a,64,a)]. 43.002/43.002 43.002/43.002 given #464 (T,wt=9): 335 ->_s0(f(f(h(x))),f(f(k(x)))). [ur(11,a,64,a)]. 43.002/43.002 43.002/43.002 given #465 (T,wt=9): 338 ->*_s0(U91(x,c),U91(x,k(g(b)))). [ur(23,a,47,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #466 (T,wt=9): 360 ->_s0(k(k(k(a))),k(k(k(b)))). [ur(14,a,91,a)]. 43.002/43.002 43.002/43.002 given #467 (A,wt=12): 151 ->_s0(f(f(U91(k(g(b)),x))),f(f(g(x)))). [ur(11,a,28,a)]. 43.002/43.002 43.002/43.002 given #468 (F,wt=8): 2377 -->_s0(k(f(b)),x) | -->_s0(x,c) # answer(goal). [resolve(227,c,70,a)]. 43.002/43.002 43.002/43.002 given #469 (F,wt=8): 2444 -->_s0(k(x),c) | -->_s0(f(b),x) # answer(goal). [resolve(2377,a,14,b)]. 43.002/43.002 43.002/43.002 given #470 (F,wt=8): 2445 -->_s0(k(f(x)),c) | -->_s0(b,x) # answer(goal). [resolve(2444,b,11,b)]. 43.002/43.002 43.002/43.002 given #471 (F,wt=10): 2364 -->_s0(k(f(b)),a) | -->*_s0(b,k(g(b))) # answer(goal). [resolve(227,b,16,a)]. 43.002/43.002 43.002/43.002 given #472 (T,wt=9): 361 ->_s0(g(k(k(a))),g(k(k(b)))). [ur(13,a,91,a)]. 43.002/43.002 43.002/43.002 given #473 (T,wt=9): 362 ->_s0(h(k(k(a))),h(k(k(b)))). [ur(12,a,91,a)]. 43.002/43.002 43.002/43.002 given #474 (T,wt=9): 363 ->_s0(f(k(k(a))),f(k(k(b)))). [ur(11,a,91,a)]. 43.002/43.002 43.002/43.002 given #475 (T,wt=9): 367 ->_s0(k(g(k(a))),k(g(k(b)))). [ur(14,a,92,a)]. 43.002/43.002 43.002/43.002 given #476 (A,wt=14): 152 ->_s0(U91(x,f(U91(k(g(b)),y))),U91(x,f(g(y)))). [ur(10,a,28,a)]. 43.002/43.002 43.002/43.002 given #477 (F,wt=10): 2372 -->_s0(k(f(b)),x) | -->_s0(x,h(g(a))) # answer(goal). [resolve(227,c,418,a)]. 43.002/43.002 43.002/43.002 given #478 (F,wt=10): 2373 -->_s0(k(f(b)),x) | -->_s0(x,k(g(a))) # answer(goal). [resolve(227,c,404,a)]. 43.002/43.002 43.002/43.002 given #479 (F,wt=10): 2375 -->_s0(k(f(b)),x) | -->_s0(x,h(f(a))) # answer(goal). [resolve(227,c,134,a)]. 43.002/43.002 43.002/43.002 given #480 (F,wt=10): 2378 -->_s0(k(f(b)),x) | -->_s0(x,h(g(b))) # answer(goal). [resolve(227,c,67,a)]. 43.002/43.002 43.002/43.002 given #481 (T,wt=9): 368 ->_s0(g(g(k(a))),g(g(k(b)))). [ur(13,a,92,a)]. 43.002/43.002 43.002/43.002 given #482 (T,wt=9): 369 ->_s0(h(g(k(a))),h(g(k(b)))). [ur(12,a,92,a)]. 43.002/43.002 43.002/43.002 given #483 (T,wt=9): 370 ->_s0(f(g(k(a))),f(g(k(b)))). [ur(11,a,92,a)]. 43.002/43.002 43.002/43.002 given #484 (T,wt=9): 375 ->_s0(k(h(k(a))),k(h(k(b)))). [ur(14,a,93,a)]. 43.002/43.002 43.002/43.002 given #485 (A,wt=14): 153 ->_s0(U91(f(U91(k(g(b)),x)),y),U91(f(g(x)),y)). [ur(9,a,28,a)]. 43.002/43.002 43.002/43.002 given #486 (F,wt=10): 2380 -->_s0(k(f(b)),x) | -->_s0(x,k(g(b))) # answer(goal). [resolve(227,c,22,a)]. 43.002/43.002 43.002/43.002 given #487 (F,wt=10): 2381 -->_s0(k(f(b)),h(U91(k(g(b)),a))) # answer(goal). [ur(227,b,165,a,c,135,a)]. 43.002/43.002 43.002/43.002 given #488 (F,wt=10): 2382 -->_s0(k(f(b)),k(U91(k(g(b)),a))) # answer(goal). [ur(227,b,163,a,c,78,a)]. 43.002/43.002 43.002/43.002 given #489 (F,wt=8): 2576 -->_s0(f(b),U91(k(g(b)),a)) # answer(goal). [resolve(2382,a,14,b)]. 43.002/43.002 43.002/43.002 given #490 (T,wt=9): 376 ->_s0(g(h(k(a))),g(h(k(b)))). [ur(13,a,93,a)]. 43.002/43.002 43.002/43.002 given #491 (T,wt=9): 377 ->_s0(h(h(k(a))),h(h(k(b)))). [ur(12,a,93,a)]. 43.002/43.002 43.002/43.002 given #492 (T,wt=9): 378 ->_s0(f(h(k(a))),f(h(k(b)))). [ur(11,a,93,a)]. 43.002/43.002 43.002/43.002 given #493 (T,wt=9): 382 ->_s0(k(f(k(a))),k(f(k(b)))). [ur(14,a,94,a)]. 43.002/43.002 43.002/43.002 given #494 (A,wt=11): 167 ->_s0(U91(x,U91(y,a)),U91(x,U91(y,b))). [ur(10,a,35,a)]. 43.002/43.002 43.002/43.002 given #495 (F,wt=10): 2508 -->_s0(k(x),h(g(a))) | -->_s0(f(b),x) # answer(goal). [resolve(2372,a,14,b)]. 43.002/43.002 43.002/43.002 given #496 (F,wt=10): 2509 -->_s0(k(f(b)),h(x)) | -->_s0(x,g(a)) # answer(goal). [resolve(2372,b,12,b)]. 43.002/43.002 43.002/43.002 given #497 (F,wt=10): 2510 -->_s0(k(x),k(g(a))) | -->_s0(f(b),x) # answer(goal). [resolve(2373,a,14,b)]. 43.002/43.002 43.002/43.002 given #498 (F,wt=8): 2644 -->_s0(f(b),x) | -->_s0(x,g(a)) # answer(goal). [resolve(2510,a,14,b)]. 43.002/43.002 43.002/43.002 given #499 (T,wt=9): 383 ->_s0(g(f(k(a))),g(f(k(b)))). [ur(13,a,94,a)]. 43.002/43.002 43.002/43.002 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2649 (0.00 of 0.06 sec). 43.002/43.002 43.002/43.002 given #500 (T,wt=9): 384 ->_s0(h(f(k(a))),h(f(k(b)))). [ur(12,a,94,a)]. 43.002/43.002 43.002/43.002 given #501 (T,wt=9): 385 ->_s0(f(f(k(a))),f(f(k(b)))). [ur(11,a,94,a)]. 43.002/43.002 43.002/43.002 given #502 (T,wt=9): 388 ->*_s0(U91(c,x),U91(k(g(b)),x)). [ur(23,a,48,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #503 (A,wt=11): 168 ->_s0(U91(U91(x,a),y),U91(U91(x,b),y)). [ur(9,a,35,a)]. 43.002/43.002 43.002/43.002 given #504 (F,wt=8): 2646 -->_s0(f(x),g(a)) | -->_s0(b,x) # answer(goal). [resolve(2644,a,11,b)]. 43.002/43.002 43.002/43.002 given #505 (F,wt=8): 2647 -->_s0(f(b),g(x)) | -->_s0(x,a) # answer(goal). [resolve(2644,b,13,b)]. 43.002/43.002 43.002/43.002 given #506 (F,wt=10): 2511 -->_s0(k(f(b)),k(x)) | -->_s0(x,g(a)) # answer(goal). [resolve(2373,b,14,b)]. 43.002/43.002 43.002/43.002 given #507 (F,wt=10): 2512 -->_s0(k(x),h(f(a))) | -->_s0(f(b),x) # answer(goal). [resolve(2375,a,14,b)]. 43.002/43.002 43.002/43.002 given #508 (T,wt=9): 405 ->_s0(k(k(g(a))),k(k(g(b)))). [ur(14,a,98,a)]. 43.002/43.002 43.002/43.002 given #509 (T,wt=9): 406 ->_s0(g(k(g(a))),g(k(g(b)))). [ur(13,a,98,a)]. 43.002/43.002 43.002/43.002 given #510 (T,wt=9): 407 ->_s0(h(k(g(a))),h(k(g(b)))). [ur(12,a,98,a)]. 43.002/43.002 43.002/43.002 given #511 (T,wt=9): 408 ->_s0(f(k(g(a))),f(k(g(b)))). [ur(11,a,98,a)]. 43.002/43.002 43.002/43.002 given #512 (A,wt=11): 174 ->_s0(U91(x,U91(a,y)),U91(x,U91(b,y))). [ur(10,a,36,a)]. 43.002/43.002 43.002/43.002 given #513 (F,wt=10): 2513 -->_s0(k(f(b)),h(x)) | -->_s0(x,f(a)) # answer(goal). [resolve(2375,b,12,b)]. 43.002/43.002 43.002/43.002 given #514 (F,wt=10): 2514 -->_s0(k(x),h(g(b))) | -->_s0(f(b),x) # answer(goal). [resolve(2378,a,14,b)]. 43.002/43.002 43.002/43.002 given #515 (F,wt=10): 2515 -->_s0(k(f(b)),h(x)) | -->_s0(x,g(b)) # answer(goal). [resolve(2378,b,12,b)]. 43.002/43.002 43.002/43.002 given #516 (F,wt=10): 2574 -->_s0(k(x),k(g(b))) | -->_s0(f(b),x) # answer(goal). [resolve(2380,a,14,b)]. 43.002/43.002 43.002/43.002 given #517 (T,wt=9): 412 ->_s0(k(g(g(a))),k(g(g(b)))). [ur(14,a,99,a)]. 43.002/43.002 43.002/43.002 given #518 (T,wt=9): 413 ->_s0(g(g(g(a))),g(g(g(b)))). [ur(13,a,99,a)]. 43.002/43.002 43.002/43.002 given #519 (T,wt=9): 414 ->_s0(h(g(g(a))),h(g(g(b)))). [ur(12,a,99,a)]. 43.002/43.002 43.002/43.002 given #520 (T,wt=9): 415 ->_s0(f(g(g(a))),f(g(g(b)))). [ur(11,a,99,a)]. 43.002/43.002 43.002/43.002 given #521 (A,wt=11): 175 ->_s0(U91(U91(a,x),y),U91(U91(b,x),y)). [ur(9,a,36,a)]. 43.002/43.002 43.002/43.002 given #522 (F,wt=8): 2775 -->_s0(f(b),x) | -->_s0(x,g(b)) # answer(goal). [resolve(2574,a,14,b)]. 43.002/43.002 43.002/43.002 given #523 (F,wt=8): 2835 -->_s0(f(x),g(b)) | -->_s0(b,x) # answer(goal). [resolve(2775,a,11,b)]. 43.002/43.002 43.002/43.002 given #524 (F,wt=8): 2836 -->_s0(f(b),g(x)) | -->_s0(x,b) # answer(goal). [resolve(2775,b,13,b)]. 43.002/43.002 43.002/43.002 given #525 (F,wt=10): 2575 -->_s0(k(f(b)),k(x)) | -->_s0(x,g(b)) # answer(goal). [resolve(2380,b,14,b)]. 43.002/43.002 43.002/43.002 given #526 (T,wt=9): 420 ->_s0(k(h(g(a))),k(h(g(b)))). [ur(14,a,100,a)]. 43.002/43.002 43.002/43.002 given #527 (T,wt=9): 421 ->_s0(g(h(g(a))),g(h(g(b)))). [ur(13,a,100,a)]. 43.002/43.002 43.002/43.002 given #528 (T,wt=9): 422 ->_s0(h(h(g(a))),h(h(g(b)))). [ur(12,a,100,a)]. 43.002/43.002 43.002/43.002 given #529 (T,wt=9): 423 ->_s0(f(h(g(a))),f(h(g(b)))). [ur(11,a,100,a)]. 43.002/43.002 43.002/43.002 given #530 (A,wt=12): 176 ->*_s0(U91(x,U91(k(g(b)),y)),U91(x,g(y))). [ur(23,a,29,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #531 (F,wt=10): 2642 -->_s0(k(f(x)),h(g(a))) | -->_s0(b,x) # answer(goal). [resolve(2508,b,11,b)]. 43.002/43.002 43.002/43.002 given #532 (F,wt=10): 2643 -->_s0(k(f(b)),h(g(x))) | -->_s0(x,a) # answer(goal). [resolve(2509,b,13,b)]. 43.002/43.002 43.002/43.002 given #533 (F,wt=10): 2645 -->_s0(k(f(x)),k(g(a))) | -->_s0(b,x) # answer(goal). [resolve(2510,b,11,b)]. 43.002/43.002 43.002/43.002 given #534 (F,wt=10): 2709 -->_s0(k(f(b)),k(g(x))) | -->_s0(x,a) # answer(goal). [resolve(2511,b,13,b)]. 43.002/43.002 43.002/43.002 given #535 (T,wt=9): 427 ->_s0(k(f(g(a))),k(f(g(b)))). [ur(14,a,101,a)]. 43.002/43.002 43.002/43.002 given #536 (T,wt=9): 428 ->_s0(g(f(g(a))),g(f(g(b)))). [ur(13,a,101,a)]. 43.002/43.002 43.002/43.002 given #537 (T,wt=9): 429 ->_s0(h(f(g(a))),h(f(g(b)))). [ur(12,a,101,a)]. 43.002/43.002 43.002/43.002 given #538 (T,wt=9): 430 ->_s0(f(f(g(a))),f(f(g(b)))). [ur(11,a,101,a)]. 43.002/43.002 43.002/43.002 given #539 (A,wt=14): 177 ->_s0(k(U91(x,U91(k(g(b)),y))),k(U91(x,g(y)))). [ur(14,a,29,a)]. 43.002/43.002 43.002/43.002 given #540 (F,wt=10): 2710 -->_s0(k(f(x)),h(f(a))) | -->_s0(b,x) # answer(goal). [resolve(2512,b,11,b)]. 43.002/43.002 43.002/43.002 given #541 (F,wt=10): 2772 -->_s0(k(f(b)),h(f(x))) | -->_s0(x,a) # answer(goal). [resolve(2513,b,11,b)]. 43.002/43.002 43.002/43.002 given #542 (F,wt=10): 2773 -->_s0(k(f(x)),h(g(b))) | -->_s0(b,x) # answer(goal). [resolve(2514,b,11,b)]. 43.002/43.002 43.002/43.002 given #543 (F,wt=10): 2774 -->_s0(k(f(b)),h(g(x))) | -->_s0(x,b) # answer(goal). [resolve(2515,b,13,b)]. 43.002/43.002 43.002/43.002 given #544 (T,wt=9): 447 ->_s0(k(k(h(a))),k(k(h(b)))). [ur(14,a,105,a)]. 43.002/43.002 43.002/43.002 given #545 (T,wt=9): 448 ->_s0(g(k(h(a))),g(k(h(b)))). [ur(13,a,105,a)]. 43.002/43.002 43.002/43.002 given #546 (T,wt=9): 449 ->_s0(h(k(h(a))),h(k(h(b)))). [ur(12,a,105,a)]. 43.002/43.002 43.002/43.002 given #547 (T,wt=9): 450 ->_s0(f(k(h(a))),f(k(h(b)))). [ur(11,a,105,a)]. 43.002/43.002 43.002/43.002 given #548 (A,wt=14): 178 ->_s0(g(U91(x,U91(k(g(b)),y))),g(U91(x,g(y)))). [ur(13,a,29,a)]. 43.002/43.002 43.002/43.002 given #549 (F,wt=10): 2776 -->_s0(k(f(x)),k(g(b))) | -->_s0(b,x) # answer(goal). [resolve(2574,b,11,b)]. 43.002/43.002 43.002/43.002 given #550 (F,wt=10): 2837 -->_s0(k(f(b)),k(g(x))) | -->_s0(x,b) # answer(goal). [resolve(2575,b,13,b)]. 43.002/43.002 43.002/43.002 given #551 (F,wt=12): 2352 -->_s0(k(f(b)),f(a)) | -->*_s0(f(b),k(g(b))) # answer(goal). [resolve(227,b,34,a)]. 43.002/43.002 43.002/43.002 given #552 (F,wt=12): 2353 -->_s0(k(f(b)),h(a)) | -->*_s0(h(b),k(g(b))) # answer(goal). [resolve(227,b,33,a)]. 43.002/43.002 43.002/43.002 given #553 (T,wt=9): 454 ->_s0(k(g(h(a))),k(g(h(b)))). [ur(14,a,106,a)]. 43.002/43.002 43.002/43.002 given #554 (T,wt=9): 455 ->_s0(g(g(h(a))),g(g(h(b)))). [ur(13,a,106,a)]. 43.002/43.002 43.002/43.002 given #555 (T,wt=9): 456 ->_s0(h(g(h(a))),h(g(h(b)))). [ur(12,a,106,a)]. 43.002/43.002 43.002/43.002 given #556 (T,wt=9): 457 ->_s0(f(g(h(a))),f(g(h(b)))). [ur(11,a,106,a)]. 43.002/43.002 43.002/43.002 given #557 (A,wt=14): 179 ->_s0(h(U91(x,U91(k(g(b)),y))),h(U91(x,g(y)))). [ur(12,a,29,a)]. 43.002/43.002 43.002/43.002 given #558 (F,wt=12): 2354 -->_s0(k(f(b)),g(a)) | -->*_s0(g(b),k(g(b))) # answer(goal). [resolve(227,b,32,a)]. 43.002/43.002 43.002/43.002 given #559 (F,wt=12): 2355 -->_s0(k(f(b)),k(a)) | -->*_s0(k(b),k(g(b))) # answer(goal). [resolve(227,b,31,a)]. 43.002/43.002 43.002/43.002 given #560 (F,wt=10): 3079 -->*_s0(k(b),k(g(b))) | -->_s0(f(b),a) # answer(goal). [resolve(2355,a,14,b)]. 43.002/43.002 43.002/43.002 given #561 (F,wt=12): 2362 -->_s0(k(f(b)),h(x)) | -->*_s0(k(x),k(g(b))) # answer(goal). [resolve(227,b,21,a)]. 43.002/43.002 43.002/43.002 given #562 (T,wt=9): 462 ->_s0(k(h(h(a))),k(h(h(b)))). [ur(14,a,107,a)]. 43.002/43.002 43.002/43.002 given #563 (T,wt=9): 463 ->_s0(g(h(h(a))),g(h(h(b)))). [ur(13,a,107,a)]. 43.002/43.002 43.002/43.002 given #564 (T,wt=9): 464 ->_s0(h(h(h(a))),h(h(h(b)))). [ur(12,a,107,a)]. 43.002/43.002 43.002/43.002 given #565 (T,wt=9): 465 ->_s0(f(h(h(a))),f(h(h(b)))). [ur(11,a,107,a)]. 43.002/43.002 43.002/43.002 given #566 (A,wt=14): 180 ->_s0(f(U91(x,U91(k(g(b)),y))),f(U91(x,g(y)))). [ur(11,a,29,a)]. 43.002/43.002 43.002/43.002 given #567 (F,wt=12): 2480 -->_s0(b,k(a)) | -->*_s0(k(g(k(b))),k(f(a))) # answer(goal). [resolve(367,a,184,b)]. 43.002/43.002 43.002/43.002 given #568 (F,wt=12): 2614 -->_s0(a,k(a)) | -->*_s0(k(f(k(b))),k(g(b))) # answer(goal). [resolve(382,a,225,b)]. 43.002/43.002 43.002/43.002 given #569 (F,wt=12): 2778 -->_s0(b,g(a)) | -->*_s0(k(g(g(b))),k(f(a))) # answer(goal). [resolve(412,a,184,b)]. 43.002/43.002 43.002/43.002 given #570 (F,wt=12): 2906 -->_s0(a,g(a)) | -->*_s0(k(f(g(b))),k(g(b))) # answer(goal). [resolve(427,a,225,b)]. 43.002/43.002 43.002/43.002 given #571 (T,wt=9): 469 ->_s0(k(f(h(a))),k(f(h(b)))). [ur(14,a,108,a)]. 43.002/43.002 43.002/43.002 given #572 (T,wt=9): 470 ->_s0(g(f(h(a))),g(f(h(b)))). [ur(13,a,108,a)]. 43.002/43.002 43.002/43.002 given #573 (T,wt=9): 471 ->_s0(h(f(h(a))),h(f(h(b)))). [ur(12,a,108,a)]. 43.002/43.002 43.002/43.002 given #574 (T,wt=9): 472 ->_s0(f(f(h(a))),f(f(h(b)))). [ur(11,a,108,a)]. 43.002/43.002 43.002/43.002 given #575 (A,wt=16): 181 ->_s0(U91(x,U91(y,U91(k(g(b)),z))),U91(x,U91(y,g(z)))). [ur(10,a,29,a)]. 43.002/43.002 43.002/43.002 given #576 (F,wt=12): 3021 -->_s0(b,h(a)) | -->*_s0(k(g(h(b))),k(f(a))) # answer(goal). [resolve(454,a,184,b)]. 43.002/43.002 43.002/43.002 given #577 (F,wt=12): 3149 -->_s0(a,h(a)) | -->*_s0(k(f(h(b))),k(g(b))) # answer(goal). [resolve(469,a,225,b)]. 43.002/43.002 43.002/43.002 given #578 (F,wt=13): 265 -->_s0(f(b),x) | -->_s0(k(x),y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(226,a,23,c)]. 43.002/43.002 43.002/43.002 given #579 (F,wt=12): 3247 -->_s0(f(b),h(a)) | -->*_s0(k(h(b)),k(g(b))) # answer(goal). [resolve(265,b,105,a)]. 43.002/43.002 43.002/43.002 given #580 (T,wt=9): 487 ->_s0(k(k(f(a))),k(k(f(b)))). [ur(14,a,124,a)]. 43.002/43.002 43.002/43.002 given #581 (T,wt=9): 488 ->_s0(g(k(f(a))),g(k(f(b)))). [ur(13,a,124,a)]. 43.002/43.002 43.002/43.002 given #582 (T,wt=9): 489 ->_s0(h(k(f(a))),h(k(f(b)))). [ur(12,a,124,a)]. 43.002/43.002 43.002/43.002 given #583 (T,wt=9): 490 ->_s0(f(k(f(a))),f(k(f(b)))). [ur(11,a,124,a)]. 43.002/43.002 43.002/43.002 given #584 (A,wt=16): 182 ->_s0(U91(U91(x,U91(k(g(b)),y)),z),U91(U91(x,g(y)),z)). [ur(9,a,29,a)]. 43.002/43.002 43.002/43.002 given #585 (F,wt=12): 3248 -->_s0(f(b),k(a)) | -->*_s0(k(k(b)),k(g(b))) # answer(goal). [resolve(265,b,91,a)]. 43.002/43.002 43.002/43.002 given #586 (F,wt=12): 3250 -->_s0(f(b),h(x)) | -->*_s0(k(k(x)),k(g(b))) # answer(goal). [resolve(265,b,61,a)]. 43.002/43.002 43.002/43.002 given #587 (F,wt=12): 3251 -->_s0(f(b),h(f(a))) | -->*_s0(k(c),k(g(b))) # answer(goal). [resolve(265,b,55,a)]. 43.002/43.002 43.002/43.002 given #588 (F,wt=12): 3253 -->_s0(f(b),c) | -->*_s0(k(k(g(b))),k(g(b))) # answer(goal). [resolve(265,b,43,a)]. 43.002/43.002 43.002/43.002 given #589 (T,wt=9): 494 ->_s0(k(g(f(a))),k(g(f(b)))). [ur(14,a,125,a)]. 43.002/43.002 43.002/43.002 given #590 (T,wt=9): 495 ->_s0(g(g(f(a))),g(g(f(b)))). [ur(13,a,125,a)]. 43.002/43.002 43.002/43.002 given #591 (T,wt=9): 496 ->_s0(h(g(f(a))),h(g(f(b)))). [ur(12,a,125,a)]. 43.002/43.002 43.002/43.002 given #592 (T,wt=9): 497 ->_s0(f(g(f(a))),f(g(f(b)))). [ur(11,a,125,a)]. 43.002/43.002 43.002/43.002 given #593 (A,wt=11): 190 ->_s0(U91(x,k(c)),U91(x,k(k(f(a))))). [ur(10,a,37,a)]. 43.002/43.002 43.002/43.002 given #594 (F,wt=12): 3254 -->_s0(f(b),c) | -->*_s0(k(k(f(a))),k(g(b))) # answer(goal). [resolve(265,b,37,a)]. 43.002/43.002 43.002/43.002 given #595 (F,wt=12): 3326 -->_s0(b,f(a)) | -->*_s0(k(g(f(b))),k(f(a))) # answer(goal). [resolve(494,a,184,b)]. 43.002/43.002 43.002/43.002 given #596 (F,wt=13): 304 -->_s0(k(U91(h(f(b)),b)),x) | -->*_s0(x,k(g(b))) # answer(goal). [resolve(266,a,23,c)]. 43.002/43.002 43.002/43.002 given #597 (F,wt=13): 308 -->_s0(b,x) | -->_s0(k(f(x)),y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(267,a,23,c)]. 43.002/43.002 43.002/43.002 given #598 (T,wt=9): 502 ->_s0(k(h(f(a))),k(h(f(b)))). [ur(14,a,126,a)]. 43.002/43.002 43.002/43.002 given #599 (T,wt=9): 503 ->_s0(g(h(f(a))),g(h(f(b)))). [ur(13,a,126,a)]. 43.002/43.002 43.002/43.002 given #600 (T,wt=9): 504 ->_s0(h(h(f(a))),h(h(f(b)))). [ur(12,a,126,a)]. 43.002/43.002 43.002/43.002 given #601 (T,wt=9): 505 ->_s0(f(h(f(a))),f(h(f(b)))). [ur(11,a,126,a)]. 43.002/43.002 43.002/43.002 given #602 (A,wt=11): 191 ->_s0(U91(k(c),x),U91(k(k(f(a))),x)). [ur(9,a,37,a)]. 43.002/43.002 43.002/43.002 given #603 (F,wt=12): 3391 -->_s0(b,h(a)) | -->*_s0(k(f(h(b))),k(g(b))) # answer(goal). [resolve(308,b,469,a)]. 43.002/43.002 43.002/43.002 given #604 (F,wt=12): 3392 -->_s0(b,g(a)) | -->*_s0(k(f(g(b))),k(g(b))) # answer(goal). [resolve(308,b,427,a)]. 43.002/43.002 43.002/43.002 given #605 (F,wt=12): 3393 -->_s0(b,k(a)) | -->*_s0(k(f(k(b))),k(g(b))) # answer(goal). [resolve(308,b,382,a)]. 43.002/43.002 43.002/43.002 given #606 (F,wt=12): 3394 -->_s0(b,h(x)) | -->*_s0(k(f(k(x))),k(g(b))) # answer(goal). [resolve(308,b,332,a)]. 43.002/43.002 43.002/43.002 given #607 (T,wt=9): 509 ->_s0(k(f(f(a))),k(f(f(b)))). [ur(14,a,127,a)]. 43.002/43.002 43.002/43.002 given #608 (T,wt=9): 510 ->_s0(g(f(f(a))),g(f(f(b)))). [ur(13,a,127,a)]. 43.002/43.002 43.002/43.002 given #609 (T,wt=9): 511 ->_s0(h(f(f(a))),h(f(f(b)))). [ur(12,a,127,a)]. 43.002/43.002 43.002/43.002 given #610 (T,wt=9): 512 ->_s0(f(f(f(a))),f(f(f(b)))). [ur(11,a,127,a)]. 43.002/43.002 43.002/43.002 given #611 (A,wt=11): 197 ->_s0(U91(x,g(c)),U91(x,g(k(f(a))))). [ur(10,a,38,a)]. 43.002/43.002 43.002/43.002 given #612 (F,wt=12): 3395 -->_s0(b,h(f(a))) | -->*_s0(k(f(c)),k(g(b))) # answer(goal). [resolve(308,b,291,a)]. 43.002/43.002 43.002/43.002 given #613 (F,wt=12): 3396 -->_s0(b,c) | -->*_s0(k(f(k(g(b)))),k(g(b))) # answer(goal). [resolve(308,b,251,a)]. 43.002/43.002 43.002/43.002 given #614 (F,wt=12): 3397 -->_s0(b,c) | -->*_s0(k(f(k(f(a)))),k(g(b))) # answer(goal). [resolve(308,b,208,a)]. 43.002/43.002 43.002/43.002 given #615 (F,wt=12): 3472 -->_s0(b,f(a)) | -->*_s0(k(f(f(b))),k(g(b))) # answer(goal). [resolve(509,a,308,b)]. 43.002/43.002 43.002/43.002 given #616 (T,wt=9): 534 ->*_s0(U91(c,a),U91(k(g(b)),b)). [ur(23,a,48,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #617 (T,wt=9): 535 ->*_s0(U91(c,a),U91(k(f(a)),b)). [ur(23,a,42,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #618 (T,wt=9): 540 ->*_s0(U91(a,c),U91(b,k(g(b)))). [ur(23,a,47,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #619 (T,wt=9): 541 ->*_s0(U91(a,c),U91(b,k(f(a)))). [ur(23,a,41,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #620 (A,wt=11): 198 ->_s0(U91(g(c),x),U91(g(k(f(a))),x)). [ur(9,a,38,a)]. 43.002/43.002 43.002/43.002 given #621 (F,wt=12): 3475 -->_s0(a,f(a)) | -->*_s0(k(f(f(b))),k(g(b))) # answer(goal). [resolve(509,a,225,b)]. 43.002/43.002 43.002/43.002 given #622 (F,wt=13): 347 -->*_s0(k(g(b)),x) | -->*_s0(k(y),x) | -->_s0(f(a),y) # answer(goal). [resolve(74,b,14,b)]. 43.002/43.002 43.002/43.002 given #623 (F,wt=12): 3566 -->*_s0(k(g(b)),k(k(b))) | -->_s0(f(a),h(a)) # answer(goal). [resolve(347,b,640,a)]. 43.002/43.002 43.002/43.002 given #624 (F,wt=12): 3567 -->*_s0(k(g(b)),k(h(b))) | -->_s0(f(a),h(a)) # answer(goal). [resolve(347,b,446,a)]. 43.002/43.002 43.002/43.002 given #625 (T,wt=9): 570 ->*_s0(k(h(f(a))),k(k(g(b)))). [ur(23,a,55,a,b,228,a)]. 43.002/43.002 43.002/43.002 given #626 (T,wt=9): 572 ->*_s0(g(h(f(a))),g(k(g(b)))). [ur(23,a,56,a,b,235,a)]. 43.002/43.002 43.002/43.002 given #627 (T,wt=9): 575 ->*_s0(h(h(f(a))),k(k(g(b)))). [ur(23,a,57,a,b,242,a)]. 43.002/43.002 43.002/43.002 given #628 (T,wt=9): 577 ->*_s0(h(h(f(a))),h(k(g(b)))). [ur(23,a,57,a,b,243,a)]. 43.002/43.002 43.002/43.002 given #629 (A,wt=11): 205 ->_s0(U91(x,h(c)),U91(x,h(k(f(a))))). [ur(10,a,39,a)]. 43.002/43.002 43.002/43.002 given #630 (F,wt=12): 3568 -->*_s0(k(g(b)),k(k(b))) | -->_s0(f(a),k(a)) # answer(goal). [resolve(347,b,359,a)]. 43.002/43.002 43.002/43.002 given #631 (F,wt=12): 3569 -->*_s0(k(g(b)),k(k(x))) | -->_s0(f(a),h(x)) # answer(goal). [resolve(347,b,309,a)]. 43.002/43.002 43.002/43.002 given #632 (F,wt=12): 3570 -->*_s0(k(g(b)),k(c)) | -->_s0(f(a),h(f(a))) # answer(goal). [resolve(347,b,268,a)]. 43.002/43.002 43.002/43.002 given #633 (F,wt=12): 3571 -->*_s0(k(g(b)),k(k(g(b)))) | -->_s0(f(a),c) # answer(goal). [resolve(347,b,228,a)]. 43.002/43.002 43.002/43.002 given #634 (T,wt=9): 612 ->*_s0(f(h(f(a))),f(k(g(b)))). [ur(23,a,58,a,b,250,a)]. 43.002/43.002 43.002/43.002 given #635 (T,wt=9): 620 ->*_s0(U91(a,h(f(a))),U91(b,c)). [ur(23,a,59,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #636 (T,wt=9): 621 ->*_s0(U91(x,h(f(a))),U91(x,c)). [ur(23,a,59,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #637 (T,wt=9): 645 ->*_s0(U91(h(f(a)),a),U91(c,b)). [ur(23,a,60,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #638 (A,wt=11): 206 ->_s0(U91(h(c),x),U91(h(k(f(a))),x)). [ur(9,a,39,a)]. 43.002/43.002 43.002/43.002 given #639 (F,wt=12): 3572 -->*_s0(k(g(b)),k(k(f(a)))) | -->_s0(f(a),c) # answer(goal). [resolve(347,b,185,a)]. 43.002/43.002 43.002/43.002 given #640 (F,wt=13): 358 -->_s0(k(f(a)),a) | -->_s0(k(g(b)),x) | -->*_s0(x,b) # answer(goal). [resolve(353,a,23,c)]. 43.002/43.002 43.002/43.002 given #641 (F,wt=10): 3654 -->_s0(k(f(a)),a) | -->_s0(k(g(b)),a) # answer(goal). [resolve(358,c,72,a)]. 43.002/43.002 43.002/43.002 given #642 (F,wt=10): 3656 -->_s0(k(f(a)),a) | -->_s0(k(g(b)),b) # answer(goal). [resolve(358,c,22,a)]. 43.002/43.002 43.002/43.002 given #643 (T,wt=6): 3636 ->*_s0(f(a),U91(c,b)). [ur(23,a,19,a,b,645,a)]. 43.002/43.002 43.002/43.002 given #644 (T,wt=9): 646 ->*_s0(U91(h(f(a)),x),U91(c,x)). [ur(23,a,60,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #645 (T,wt=6): 3677 ->*_s0(f(a),U91(c,a)). [ur(23,a,19,a,b,646,a)]. 43.002/43.002 43.002/43.002 given #646 (T,wt=9): 669 ->*_s0(U91(a,h(x)),U91(b,k(x))). [ur(23,a,65,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #647 (A,wt=11): 212 ->_s0(U91(x,f(c)),U91(x,f(k(f(a))))). [ur(10,a,40,a)]. 43.002/43.002 43.002/43.002 given #648 (F,wt=13): 395 -->_s0(k(f(a)),x) | -->_s0(k(g(b)),y) | -->*_s0(y,x) # answer(goal). [resolve(357,a,23,c)]. 43.002/43.002 43.002/43.002 given #649 (F,wt=10): 3798 -->_s0(k(f(a)),b) | -->_s0(k(g(b)),a) # answer(goal). [resolve(395,c,72,a)]. 43.002/43.002 43.002/43.002 given #650 (F,wt=10): 3802 -->_s0(k(f(a)),x) | -->_s0(k(g(b)),x) # answer(goal). [resolve(395,c,22,a)]. 43.002/43.002 43.002/43.002 given #651 (F,wt=10): 3803 -->_s0(k(g(b)),k(x)) | -->_s0(f(a),x) # answer(goal). [resolve(3802,a,14,b)]. 43.002/43.002 43.002/43.002 given #652 (T,wt=9): 670 ->*_s0(U91(x,h(y)),U91(x,k(y))). [ur(23,a,65,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #653 (T,wt=9): 758 ->*_s0(U91(h(x),a),U91(k(x),b)). [ur(23,a,66,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #654 (T,wt=8): 3837 ->*_s0(f(a),U91(k(f(a)),b)). [ur(23,a,19,a,b,758,a)]. 43.002/43.002 43.002/43.002 given #655 (T,wt=9): 759 ->*_s0(U91(h(x),y),U91(k(x),y)). [ur(23,a,66,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #656 (A,wt=11): 213 ->_s0(U91(f(c),x),U91(f(k(f(a))),x)). [ur(9,a,40,a)]. 43.002/43.002 43.002/43.002 given #657 (F,wt=8): 3805 -->_s0(f(a),x) | -->_s0(g(b),x) # answer(goal). [resolve(3803,a,14,b)]. 43.002/43.002 43.002/43.002 given #658 (F,wt=8): 3880 -->_s0(g(b),f(x)) | -->_s0(a,x) # answer(goal). [resolve(3805,a,11,b)]. 43.002/43.002 43.002/43.002 given #659 (F,wt=8): 3881 -->_s0(f(a),g(x)) | -->_s0(b,x) # answer(goal). [resolve(3805,b,13,b)]. 43.002/43.002 43.002/43.002 given #660 (F,wt=10): 3804 -->_s0(k(f(a)),k(x)) | -->_s0(g(b),x) # answer(goal). [resolve(3802,b,14,b)]. 43.002/43.002 43.002/43.002 given #661 (T,wt=8): 3863 ->*_s0(f(x),U91(k(f(x)),x)). [ur(23,a,19,a,b,759,a)]. 43.002/43.002 43.002/43.002 given #662 (T,wt=8): 3934 ->*_s0(f(a),U91(k(f(b)),b)). [ur(23,a,34,a,b,3863,a)]. 43.002/43.002 43.002/43.002 given #663 (T,wt=9): 985 ->*_s0(U91(a,k(a)),U91(b,k(b))). [ur(23,a,95,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #664 (T,wt=9): 986 ->*_s0(U91(x,k(a)),U91(x,k(b))). [ur(23,a,95,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #665 (A,wt=12): 214 ->*_s0(U91(U91(k(g(b)),x),y),U91(g(x),y)). [ur(23,a,30,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #666 (F,wt=10): 3806 -->_s0(k(g(b)),k(f(x))) | -->_s0(a,x) # answer(goal). [resolve(3803,b,11,b)]. 43.002/43.002 43.002/43.002 given #667 (F,wt=10): 3882 -->_s0(k(f(a)),k(g(x))) | -->_s0(b,x) # answer(goal). [resolve(3804,b,13,b)]. 43.002/43.002 43.002/43.002 given #668 (F,wt=12): 3711 -->_s0(k(f(a)),g(b)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(395,c,961,a)]. 43.002/43.002 43.002/43.002 given #669 (F,wt=12): 3712 -->_s0(k(f(a)),g(a)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(395,c,931,a)]. 43.002/43.002 43.002/43.002 given #670 (T,wt=9): 1000 ->*_s0(U91(k(a),a),U91(k(b),b)). [ur(23,a,96,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #671 (T,wt=9): 1001 ->*_s0(U91(k(a),x),U91(k(b),x)). [ur(23,a,96,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #672 (T,wt=9): 1099 ->*_s0(U91(a,g(a)),U91(b,g(b))). [ur(23,a,102,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #673 (T,wt=9): 1100 ->*_s0(U91(x,g(a)),U91(x,g(b))). [ur(23,a,102,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #674 (A,wt=14): 215 ->_s0(k(U91(U91(k(g(b)),x),y)),k(U91(g(x),y))). [ur(14,a,30,a)]. 43.002/43.002 43.002/43.002 given #675 (F,wt=12): 3790 -->_s0(k(f(a)),k(b)) | -->_s0(k(g(b)),h(a)) # answer(goal). [resolve(395,c,132,a)]. 43.002/43.002 43.002/43.002 given #676 (F,wt=10): 4040 -->_s0(k(g(b)),h(a)) | -->_s0(f(a),b) # answer(goal). [resolve(3790,a,14,b)]. 43.002/43.002 43.002/43.002 given #677 (F,wt=12): 3791 -->_s0(k(f(a)),f(b)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(395,c,123,a)]. 43.002/43.002 43.002/43.002 given #678 (F,wt=12): 3793 -->_s0(k(f(a)),h(b)) | -->_s0(k(g(b)),h(a)) # answer(goal). [resolve(395,c,104,a)]. 43.002/43.002 43.002/43.002 given #679 (T,wt=9): 1112 ->*_s0(U91(g(a),a),U91(g(b),b)). [ur(23,a,103,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #680 (T,wt=9): 1113 ->*_s0(U91(g(a),x),U91(g(b),x)). [ur(23,a,103,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #681 (T,wt=9): 1125 ->*_s0(U91(a,h(a)),U91(b,h(b))). [ur(23,a,109,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #682 (T,wt=9): 1126 ->*_s0(U91(x,h(a)),U91(x,h(b))). [ur(23,a,109,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #683 (A,wt=14): 216 ->_s0(g(U91(U91(k(g(b)),x),y)),g(U91(g(x),y))). [ur(13,a,30,a)]. 43.002/43.002 43.002/43.002 given #684 (F,wt=12): 3794 -->_s0(k(f(a)),g(b)) | -->_s0(k(g(b)),g(a)) # answer(goal). [resolve(395,c,97,a)]. 43.002/43.002 43.002/43.002 given #685 (F,wt=12): 3795 -->_s0(k(f(a)),k(b)) | -->_s0(k(g(b)),k(a)) # answer(goal). [resolve(395,c,90,a)]. 43.002/43.002 43.002/43.002 given #686 (F,wt=10): 4093 -->_s0(k(g(b)),k(a)) | -->_s0(f(a),b) # answer(goal). [resolve(3795,a,14,b)]. 43.002/43.002 43.002/43.002 given #687 (F,wt=8): 4095 -->_s0(f(a),b) | -->_s0(g(b),a) # answer(goal). [resolve(4093,a,14,b)]. 43.002/43.002 43.002/43.002 given #688 (T,wt=9): 1135 ->*_s0(U91(h(a),a),U91(h(b),b)). [ur(23,a,110,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #689 (T,wt=9): 1136 ->*_s0(U91(h(a),x),U91(h(b),x)). [ur(23,a,110,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #690 (T,wt=9): 1154 ->*_s0(U91(a,f(a)),U91(b,f(b))). [ur(23,a,128,a,b,169,a)]. 43.002/43.002 43.002/43.002 given #691 (T,wt=9): 1155 ->*_s0(U91(x,f(a)),U91(x,f(b))). [ur(23,a,128,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #692 (A,wt=14): 217 ->_s0(h(U91(U91(k(g(b)),x),y)),h(U91(g(x),y))). [ur(12,a,30,a)]. 43.002/43.002 43.002/43.002 given #693 (F,wt=10): 4094 -->_s0(k(f(a)),k(b)) | -->_s0(g(b),a) # answer(goal). [resolve(3795,b,14,b)]. 43.002/43.002 43.002/43.002 given #694 (F,wt=12): 3800 -->_s0(k(f(a)),k(x)) | -->_s0(k(g(b)),h(x)) # answer(goal). [resolve(395,c,67,a)]. 43.002/43.002 43.002/43.002 given #695 (F,wt=10): 4146 -->_s0(k(g(b)),h(x)) | -->_s0(f(a),x) # answer(goal). [resolve(3800,a,14,b)]. 43.002/43.002 43.002/43.002 given #696 (F,wt=10): 4147 -->_s0(k(g(b)),h(f(x))) | -->_s0(a,x) # answer(goal). [resolve(4146,b,11,b)]. 43.002/43.002 43.002/43.002 given #697 (T,wt=9): 1166 ->*_s0(U91(f(a),a),U91(f(b),b)). [ur(23,a,129,a,b,162,a)]. 43.002/43.002 43.002/43.002 given #698 (T,wt=9): 1167 ->*_s0(U91(f(a),x),U91(f(b),x)). [ur(23,a,129,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #699 (T,wt=9): 1186 ->*_s0(k(U91(x,a)),k(U91(x,b))). [ur(23,a,163,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #700 (T,wt=9): 1196 ->*_s0(g(U91(x,a)),g(U91(x,b))). [ur(23,a,164,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #701 (A,wt=14): 218 ->_s0(f(U91(U91(k(g(b)),x),y)),f(U91(g(x),y))). [ur(11,a,30,a)]. 43.002/43.002 43.002/43.002 given #702 (F,wt=10): 4173 -->*_s0(k(g(b)),k(U91(h(f(a)),b))) # answer(goal). [ur(347,b,1186,a,c,19,a)]. 43.002/43.002 43.002/43.002 given #703 (F,wt=10): 4193 -->_s0(k(g(b)),h(U91(h(f(a)),b))) # answer(goal). [ur(23,b,67,a,c,4173,a)]. 43.002/43.002 43.002/43.002 given #704 (F,wt=10): 4194 -->_s0(k(g(b)),k(U91(h(f(a)),b))) # answer(goal). [ur(23,b,22,a,c,4173,a)]. 43.002/43.002 43.002/43.002 given #705 (F,wt=8): 4195 -->_s0(g(b),U91(h(f(a)),b)) # answer(goal). [resolve(4194,a,14,b)]. 43.002/43.002 43.002/43.002 given #706 (T,wt=9): 1205 ->*_s0(h(U91(x,a)),k(U91(x,b))). [ur(23,a,165,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #707 (T,wt=9): 1206 ->*_s0(h(U91(x,a)),h(U91(x,b))). [ur(23,a,165,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #708 (T,wt=9): 1216 ->*_s0(f(U91(x,a)),f(U91(x,b))). [ur(23,a,166,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #709 (T,wt=9): 1235 ->*_s0(k(U91(a,x)),k(U91(b,x))). [ur(23,a,170,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #710 (A,wt=16): 219 ->_s0(U91(x,U91(U91(k(g(b)),y),z)),U91(x,U91(g(y),z))). [ur(10,a,30,a)]. 43.002/43.002 43.002/43.002 given #711 (F,wt=13): 397 -->_s0(f(a),x) | -->_s0(k(g(b)),y) | -->*_s0(y,k(x)) # answer(goal). [resolve(396,a,23,c)]. 43.002/43.002 43.002/43.002 given #712 (F,wt=12): 4247 -->_s0(f(a),k(b)) | -->_s0(k(g(b)),h(h(a))) # answer(goal). [resolve(397,c,660,a)]. 43.002/43.002 43.002/43.002 given #713 (F,wt=12): 4248 -->_s0(f(a),k(b)) | -->_s0(k(g(b)),k(h(a))) # answer(goal). [resolve(397,c,640,a)]. 43.002/43.002 43.002/43.002 given #714 (F,wt=10): 4266 -->_s0(f(a),k(b)) | -->_s0(g(b),h(a)) # answer(goal). [resolve(4248,b,14,b)]. 43.002/43.002 43.002/43.002 given #715 (T,wt=9): 1244 ->*_s0(g(U91(a,x)),g(U91(b,x))). [ur(23,a,171,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #716 (T,wt=9): 1253 ->*_s0(h(U91(a,x)),k(U91(b,x))). [ur(23,a,172,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #717 (T,wt=9): 1254 ->*_s0(h(U91(a,x)),h(U91(b,x))). [ur(23,a,172,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #718 (T,wt=9): 1264 ->*_s0(f(U91(a,x)),f(U91(b,x))). [ur(23,a,173,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #719 (A,wt=16): 220 ->_s0(U91(U91(U91(k(g(b)),x),y),z),U91(U91(g(x),y),z)). [ur(9,a,30,a)]. 43.002/43.002 43.002/43.002 given #720 (F,wt=12): 4251 -->_s0(f(a),h(b)) | -->_s0(k(g(b)),h(h(a))) # answer(goal). [resolve(397,c,460,a)]. 43.002/43.002 43.002/43.002 given #721 (F,wt=12): 4252 -->_s0(f(a),h(b)) | -->_s0(k(g(b)),k(h(a))) # answer(goal). [resolve(397,c,446,a)]. 43.002/43.002 43.002/43.002 given #722 (F,wt=10): 4304 -->_s0(f(a),h(b)) | -->_s0(g(b),h(a)) # answer(goal). [resolve(4252,b,14,b)]. 43.002/43.002 43.002/43.002 given #723 (F,wt=12): 4253 -->_s0(f(a),k(b)) | -->_s0(k(g(b)),h(k(a))) # answer(goal). [resolve(397,c,373,a)]. 43.002/43.002 43.002/43.002 given #724 (T,wt=9): 1288 ->*_s0(k(k(c)),k(k(k(f(a))))). [ur(23,a,186,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #725 (T,wt=9): 1297 ->*_s0(g(k(c)),g(k(k(f(a))))). [ur(23,a,187,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #726 (T,wt=9): 1306 ->*_s0(h(k(c)),k(k(k(f(a))))). [ur(23,a,188,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #727 (T,wt=9): 1307 ->*_s0(h(k(c)),h(k(k(f(a))))). [ur(23,a,188,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #728 (A,wt=11): 233 ->_s0(U91(x,k(c)),U91(x,k(k(g(b))))). [ur(10,a,43,a)]. 43.002/43.002 43.002/43.002 given #729 (F,wt=12): 4254 -->_s0(f(a),k(b)) | -->_s0(k(g(b)),k(k(a))) # answer(goal). [resolve(397,c,359,a)]. 43.002/43.002 43.002/43.002 given #730 (F,wt=10): 4344 -->_s0(f(a),k(b)) | -->_s0(g(b),k(a)) # answer(goal). [resolve(4254,b,14,b)]. 43.002/43.002 43.002/43.002 given #731 (F,wt=12): 4255 -->_s0(f(a),k(x)) | -->_s0(k(g(b)),h(h(x))) # answer(goal). [resolve(397,c,323,a)]. 43.002/43.002 43.002/43.002 given #732 (F,wt=12): 4256 -->_s0(f(a),k(x)) | -->_s0(k(g(b)),k(h(x))) # answer(goal). [resolve(397,c,309,a)]. 43.002/43.002 43.002/43.002 given #733 (T,wt=9): 1317 ->*_s0(f(k(c)),f(k(k(f(a))))). [ur(23,a,189,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #734 (T,wt=9): 1338 ->*_s0(k(g(c)),k(g(k(f(a))))). [ur(23,a,193,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #735 (T,wt=9): 1347 ->*_s0(g(g(c)),g(g(k(f(a))))). [ur(23,a,194,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #736 (T,wt=9): 1356 ->*_s0(h(g(c)),k(g(k(f(a))))). [ur(23,a,195,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #737 (A,wt=11): 234 ->_s0(U91(k(c),x),U91(k(k(g(b))),x)). [ur(9,a,43,a)]. 43.002/43.002 43.002/43.002 given #738 (F,wt=10): 4345 -->_s0(f(a),k(x)) | -->_s0(g(b),h(x)) # answer(goal). [resolve(4256,b,14,b)]. 43.002/43.002 43.002/43.002 given #739 (F,wt=12): 4257 -->_s0(f(a),c) | -->_s0(k(g(b)),h(h(f(a)))) # answer(goal). [resolve(397,c,282,a)]. 43.002/43.002 43.002/43.002 given #740 (F,wt=12): 4258 -->_s0(f(a),c) | -->_s0(k(g(b)),k(h(f(a)))) # answer(goal). [resolve(397,c,268,a)]. 43.002/43.002 43.002/43.002 given #741 (F,wt=10): 4384 -->_s0(f(a),c) | -->_s0(g(b),h(f(a))) # answer(goal). [resolve(4258,b,14,b)]. 43.002/43.002 43.002/43.002 given #742 (T,wt=9): 1357 ->*_s0(h(g(c)),h(g(k(f(a))))). [ur(23,a,195,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #743 (T,wt=9): 1367 ->*_s0(f(g(c)),f(g(k(f(a))))). [ur(23,a,196,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #744 (T,wt=9): 1391 ->*_s0(k(h(c)),k(k(k(f(a))))). [ur(23,a,201,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #745 (T,wt=9): 1392 ->*_s0(k(h(c)),k(h(k(f(a))))). [ur(23,a,201,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #746 (A,wt=11): 240 ->_s0(U91(x,g(c)),U91(x,g(k(g(b))))). [ur(10,a,44,a)]. 43.002/43.002 43.002/43.002 given #747 (F,wt=12): 4259 -->_s0(f(a),k(g(b))) | -->_s0(k(g(b)),h(c)) # answer(goal). [resolve(397,c,242,a)]. 43.002/43.002 43.002/43.002 given #748 (F,wt=12): 4260 -->_s0(f(a),k(g(b))) | -->_s0(k(g(b)),k(c)) # answer(goal). [resolve(397,c,228,a)]. 43.002/43.002 43.002/43.002 given #749 (F,wt=10): 4427 -->_s0(f(a),k(g(b))) | -->_s0(g(b),c) # answer(goal). [resolve(4260,b,14,b)]. 43.002/43.002 43.002/43.002 given #750 (F,wt=12): 4261 -->_s0(f(a),k(f(a))) | -->_s0(k(g(b)),h(c)) # answer(goal). [resolve(397,c,199,a)]. 43.002/43.002 43.002/43.002 given #751 (T,wt=9): 1401 ->*_s0(g(h(c)),g(k(k(f(a))))). [ur(23,a,202,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #752 (T,wt=9): 1402 ->*_s0(g(h(c)),g(h(k(f(a))))). [ur(23,a,202,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #753 (T,wt=9): 1411 ->*_s0(h(h(c)),h(k(k(f(a))))). [ur(23,a,203,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #754 (T,wt=9): 1412 ->*_s0(h(h(c)),k(k(k(f(a))))). [ur(23,a,203,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #755 (A,wt=11): 241 ->_s0(U91(g(c),x),U91(g(k(g(b))),x)). [ur(9,a,44,a)]. 43.002/43.002 43.002/43.002 given #756 (F,wt=12): 4262 -->_s0(f(a),k(f(a))) | -->_s0(k(g(b)),k(c)) # answer(goal). [resolve(397,c,185,a)]. 43.002/43.002 43.002/43.002 given #757 (F,wt=10): 4462 -->_s0(f(a),k(f(a))) | -->_s0(g(b),c) # answer(goal). [resolve(4262,b,14,b)]. 43.002/43.002 43.002/43.002 given #758 (F,wt=13): 433 -->*_s0(k(g(b)),x) | -->*_s0(k(U91(h(f(a)),a)),x) # answer(goal). [resolve(49,a,74,b)]. 43.002/43.002 43.002/43.002 given #759 (F,wt=13): 442 -->_s0(k(g(b)),x) | -->*_s0(x,k(U91(h(f(a)),a))) # answer(goal). [resolve(399,a,23,c)]. 43.002/43.002 43.002/43.002 given #760 (T,wt=9): 1413 ->*_s0(h(h(c)),k(h(k(f(a))))). [ur(23,a,203,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #761 (T,wt=9): 1414 ->*_s0(h(h(c)),h(h(k(f(a))))). [ur(23,a,203,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #762 (T,wt=9): 1423 ->*_s0(f(h(c)),f(k(k(f(a))))). [ur(23,a,204,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #763 (T,wt=9): 1425 ->*_s0(f(h(c)),f(h(k(f(a))))). [ur(23,a,204,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #764 (A,wt=11): 248 ->_s0(U91(x,h(c)),U91(x,h(k(g(b))))). [ur(10,a,45,a)]. 43.002/43.002 43.002/43.002 given #765 (F,wt=13): 445 -->_s0(a,x) | -->_s0(k(g(b)),y) | -->*_s0(y,k(f(x))) # answer(goal). [resolve(400,a,23,c)]. 43.002/43.002 43.002/43.002 given #766 (F,wt=13): 483 -->_s0(k(g(b)),x) | -->_s0(x,y) | -->*_s0(y,k(f(b))) # answer(goal). [resolve(401,b,23,c)]. 43.002/43.002 43.002/43.002 given #767 (F,wt=10): 4763 -->_s0(k(g(b)),a) | -->*_s0(b,k(f(b))) # answer(goal). [resolve(483,b,16,a)]. 43.002/43.002 43.002/43.002 given #768 (F,wt=10): 4771 -->_s0(k(g(b)),x) | -->_s0(x,h(f(b))) # answer(goal). [resolve(483,c,67,a)]. 43.002/43.002 43.002/43.002 given #769 (T,wt=9): 1451 ->*_s0(k(f(c)),k(f(k(f(a))))). [ur(23,a,208,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #770 (T,wt=9): 1460 ->*_s0(g(f(c)),g(f(k(f(a))))). [ur(23,a,209,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #771 (T,wt=9): 1469 ->*_s0(h(f(c)),k(f(k(f(a))))). [ur(23,a,210,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #772 (T,wt=9): 1470 ->*_s0(h(f(c)),h(f(k(f(a))))). [ur(23,a,210,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #773 (A,wt=11): 249 ->_s0(U91(h(c),x),U91(h(k(g(b))),x)). [ur(9,a,45,a)]. 43.002/43.002 43.002/43.002 given #774 (F,wt=10): 4773 -->_s0(k(g(b)),x) | -->_s0(x,k(f(b))) # answer(goal). [resolve(483,c,22,a)]. 43.002/43.002 43.002/43.002 given #775 (F,wt=10): 4775 -->_s0(k(x),h(f(b))) | -->_s0(g(b),x) # answer(goal). [resolve(4771,a,14,b)]. 43.002/43.002 43.002/43.002 given #776 (F,wt=10): 4776 -->_s0(k(g(b)),h(x)) | -->_s0(x,f(b)) # answer(goal). [resolve(4771,b,12,b)]. 43.002/43.002 43.002/43.002 given #777 (F,wt=10): 4817 -->_s0(k(x),k(f(b))) | -->_s0(g(b),x) # answer(goal). [resolve(4773,a,14,b)]. 43.002/43.002 43.002/43.002 given #778 (T,wt=9): 1480 ->*_s0(f(f(c)),f(f(k(f(a))))). [ur(23,a,211,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #779 (T,wt=9): 1507 ->*_s0(k(k(c)),k(k(k(g(b))))). [ur(23,a,229,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #780 (T,wt=9): 1516 ->*_s0(g(k(c)),g(k(k(g(b))))). [ur(23,a,230,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #781 (T,wt=9): 1525 ->*_s0(h(k(c)),k(k(k(g(b))))). [ur(23,a,231,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #782 (A,wt=11): 255 ->_s0(U91(x,f(c)),U91(x,f(k(g(b))))). [ur(10,a,46,a)]. 43.002/43.002 43.002/43.002 given #783 (F,wt=8): 4821 -->_s0(g(b),x) | -->_s0(x,f(b)) # answer(goal). [resolve(4817,a,14,b)]. 43.002/43.002 43.002/43.002 given #784 (F,wt=8): 4866 -->_s0(g(x),f(b)) | -->_s0(b,x) # answer(goal). [resolve(4821,a,13,b)]. 43.002/43.002 43.002/43.002 given #785 (F,wt=8): 4867 -->_s0(g(b),f(x)) | -->_s0(x,b) # answer(goal). [resolve(4821,b,11,b)]. 43.002/43.002 43.002/43.002 given #786 (F,wt=10): 4818 -->_s0(k(g(b)),k(x)) | -->_s0(x,f(b)) # answer(goal). [resolve(4773,b,14,b)]. 43.002/43.002 43.002/43.002 given #787 (T,wt=9): 1526 ->*_s0(h(k(c)),h(k(k(g(b))))). [ur(23,a,231,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #788 (T,wt=9): 1536 ->*_s0(f(k(c)),f(k(k(g(b))))). [ur(23,a,232,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #789 (T,wt=9): 1552 ->*_s0(k(g(c)),k(g(k(g(b))))). [ur(23,a,236,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #790 (T,wt=9): 1561 ->*_s0(g(g(c)),g(g(k(g(b))))). [ur(23,a,237,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #791 (A,wt=11): 256 ->_s0(U91(f(c),x),U91(f(k(g(b))),x)). [ur(9,a,46,a)]. 43.002/43.002 43.002/43.002 given #792 (F,wt=10): 4819 -->_s0(k(g(x)),h(f(b))) | -->_s0(b,x) # answer(goal). [resolve(4775,b,13,b)]. 43.002/43.002 43.002/43.002 given #793 (F,wt=10): 4820 -->_s0(k(g(b)),h(f(x))) | -->_s0(x,b) # answer(goal). [resolve(4776,b,11,b)]. 43.002/43.002 43.002/43.002 given #794 (F,wt=10): 4822 -->_s0(k(g(x)),k(f(b))) | -->_s0(b,x) # answer(goal). [resolve(4817,b,13,b)]. 43.002/43.002 43.002/43.002 given #795 (F,wt=10): 4868 -->_s0(k(g(b)),k(f(x))) | -->_s0(x,b) # answer(goal). [resolve(4818,b,11,b)]. 43.002/43.002 43.002/43.002 given #796 (T,wt=9): 1570 ->*_s0(h(g(c)),k(g(k(g(b))))). [ur(23,a,238,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #797 (T,wt=9): 1571 ->*_s0(h(g(c)),h(g(k(g(b))))). [ur(23,a,238,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #798 (T,wt=9): 1581 ->*_s0(f(g(c)),f(g(k(g(b))))). [ur(23,a,239,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #799 (T,wt=9): 1592 ->*_s0(k(h(c)),k(k(k(g(b))))). [ur(23,a,244,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #800 (A,wt=11): 258 ->_s0(k(U91(x,c)),k(U91(x,k(f(a))))). [ur(14,a,41,a)]. 43.002/43.002 43.002/43.002 given #801 (F,wt=12): 4751 -->_s0(k(g(b)),f(a)) | -->*_s0(f(b),k(f(b))) # answer(goal). [resolve(483,b,34,a)]. 43.002/43.002 43.002/43.002 given #802 (F,wt=12): 4752 -->_s0(k(g(b)),h(a)) | -->*_s0(h(b),k(f(b))) # answer(goal). [resolve(483,b,33,a)]. 43.002/43.002 43.002/43.002 given #803 (F,wt=12): 4753 -->_s0(k(g(b)),g(a)) | -->*_s0(g(b),k(f(b))) # answer(goal). [resolve(483,b,32,a)]. 43.002/43.002 43.002/43.002 given #804 (F,wt=12): 4754 -->_s0(k(g(b)),k(a)) | -->*_s0(k(b),k(f(b))) # answer(goal). [resolve(483,b,31,a)]. 43.002/43.002 43.002/43.002 given #805 (T,wt=9): 1593 ->*_s0(k(h(c)),k(h(k(g(b))))). [ur(23,a,244,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #806 (T,wt=9): 1602 ->*_s0(g(h(c)),g(k(k(g(b))))). [ur(23,a,245,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #807 (T,wt=9): 1603 ->*_s0(g(h(c)),g(h(k(g(b))))). [ur(23,a,245,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #808 (T,wt=9): 1612 ->*_s0(h(h(c)),h(k(k(g(b))))). [ur(23,a,246,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #809 (A,wt=11): 259 ->_s0(g(U91(x,c)),g(U91(x,k(f(a))))). [ur(13,a,41,a)]. 43.002/43.002 43.002/43.002 given #810 (F,wt=10): 4950 -->*_s0(k(b),k(f(b))) | -->_s0(g(b),a) # answer(goal). [resolve(4754,a,14,b)]. 43.002/43.002 43.002/43.002 given #811 (F,wt=12): 4761 -->_s0(k(g(b)),h(x)) | -->*_s0(k(x),k(f(b))) # answer(goal). [resolve(483,b,21,a)]. 43.002/43.002 43.002/43.002 given #812 (F,wt=12): 4777 -->_s0(a,k(f(a))) | -->_s0(k(g(b)),k(f(c))) # answer(goal). [resolve(1451,a,445,c)]. 43.002/43.002 43.002/43.002 given #813 (F,wt=10): 4985 -->_s0(a,k(f(a))) | -->_s0(g(b),f(c)) # answer(goal). [resolve(4777,b,14,b)]. 43.002/43.002 43.002/43.002 given #814 (T,wt=9): 1613 ->*_s0(h(h(c)),k(k(k(g(b))))). [ur(23,a,246,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #815 (T,wt=9): 1614 ->*_s0(h(h(c)),k(h(k(g(b))))). [ur(23,a,246,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #816 (T,wt=9): 1615 ->*_s0(h(h(c)),h(h(k(g(b))))). [ur(23,a,246,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #817 (T,wt=9): 1624 ->*_s0(f(h(c)),f(k(k(g(b))))). [ur(23,a,247,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #818 (A,wt=11): 260 ->_s0(h(U91(x,c)),h(U91(x,k(f(a))))). [ur(12,a,41,a)]. 43.002/43.002 43.002/43.002 given #819 (F,wt=12): 4786 -->_s0(a,k(f(a))) | -->_s0(k(g(b)),h(f(c))) # answer(goal). [resolve(1469,a,445,c)]. 43.002/43.002 43.002/43.002 given #820 (F,wt=13): 523 -->_s0(g(b),x) | -->_s0(k(x),y) | -->*_s0(y,k(f(b))) # answer(goal). [resolve(482,a,23,c)]. 43.002/43.002 43.002/43.002 given #821 (F,wt=12): 5058 -->_s0(g(b),h(a)) | -->*_s0(k(h(b)),k(f(b))) # answer(goal). [resolve(523,b,105,a)]. 43.002/43.002 43.002/43.002 given #822 (F,wt=12): 5059 -->_s0(g(b),k(a)) | -->*_s0(k(k(b)),k(f(b))) # answer(goal). [resolve(523,b,91,a)]. 43.002/43.002 43.002/43.002 given #823 (T,wt=9): 1626 ->*_s0(f(h(c)),f(h(k(g(b))))). [ur(23,a,247,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #824 (T,wt=9): 1646 ->*_s0(k(f(c)),k(f(k(g(b))))). [ur(23,a,251,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #825 (T,wt=9): 1655 ->*_s0(g(f(c)),g(f(k(g(b))))). [ur(23,a,252,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #826 (T,wt=9): 1664 ->*_s0(h(f(c)),k(f(k(g(b))))). [ur(23,a,253,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #827 (A,wt=11): 261 ->_s0(f(U91(x,c)),f(U91(x,k(f(a))))). [ur(11,a,41,a)]. 43.002/43.002 43.002/43.002 given #828 (F,wt=12): 5061 -->_s0(g(b),h(x)) | -->*_s0(k(k(x)),k(f(b))) # answer(goal). [resolve(523,b,61,a)]. 43.002/43.002 43.002/43.002 given #829 (F,wt=12): 5062 -->_s0(g(b),h(f(a))) | -->*_s0(k(c),k(f(b))) # answer(goal). [resolve(523,b,55,a)]. 43.002/43.002 43.002/43.002 given #830 (F,wt=12): 5064 -->_s0(g(b),c) | -->*_s0(k(k(g(b))),k(f(b))) # answer(goal). [resolve(523,b,43,a)]. 43.002/43.002 43.002/43.002 given #831 (F,wt=12): 5065 -->_s0(g(b),c) | -->*_s0(k(k(f(a))),k(f(b))) # answer(goal). [resolve(523,b,37,a)]. 43.002/43.002 43.002/43.002 given #832 (T,wt=9): 1665 ->*_s0(h(f(c)),h(f(k(g(b))))). [ur(23,a,253,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #833 (T,wt=9): 1675 ->*_s0(f(f(c)),f(f(k(g(b))))). [ur(23,a,254,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #834 (T,wt=9): 1710 ->*_s0(k(k(h(f(a)))),k(k(c))). [ur(23,a,269,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #835 (T,wt=9): 1719 ->*_s0(g(k(h(f(a)))),g(k(c))). [ur(23,a,270,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #836 (A,wt=13): 262 ->_s0(U91(x,U91(y,c)),U91(x,U91(y,k(f(a))))). [ur(10,a,41,a)]. 43.002/43.002 43.002/43.002 given #837 (F,wt=12): 5075 -->_s0(a,k(g(b))) | -->_s0(k(g(b)),k(f(c))) # answer(goal). [resolve(1646,a,445,c)]. 43.002/43.002 43.002/43.002 given #838 (F,wt=10): 5153 -->_s0(a,k(g(b))) | -->_s0(g(b),f(c)) # answer(goal). [resolve(5075,b,14,b)]. 43.002/43.002 43.002/43.002 given #839 (F,wt=12): 5086 -->_s0(a,k(g(b))) | -->_s0(k(g(b)),h(f(c))) # answer(goal). [resolve(1664,a,445,c)]. 43.002/43.002 43.002/43.002 given #840 (F,wt=13): 525 -->*_s0(k(f(b)),x) | -->_s0(k(g(b)),y) | -->*_s0(y,x) # answer(goal). [resolve(485,a,23,c)]. 43.002/43.002 43.002/43.002 given #841 (T,wt=9): 1728 ->*_s0(h(k(h(f(a)))),k(k(c))). [ur(23,a,271,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #842 (T,wt=9): 1729 ->*_s0(h(k(h(f(a)))),h(k(c))). [ur(23,a,271,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #843 (T,wt=9): 1756 ->*_s0(f(k(h(f(a)))),f(k(c))). [ur(23,a,272,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #844 (T,wt=9): 1765 ->*_s0(k(g(h(f(a)))),k(g(c))). [ur(23,a,276,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #845 (A,wt=13): 263 ->_s0(U91(U91(x,c),y),U91(U91(x,k(f(a))),y)). [ur(9,a,41,a)]. 43.002/43.002 43.002/43.002 given #846 (F,wt=10): 5336 -->*_s0(k(f(b)),b) | -->_s0(k(g(b)),a) # answer(goal). [resolve(525,c,72,a)]. 43.002/43.002 43.002/43.002 given #847 (F,wt=10): 5340 -->*_s0(k(f(b)),x) | -->_s0(k(g(b)),x) # answer(goal). [resolve(525,c,22,a)]. 43.002/43.002 43.002/43.002 given #848 (F,wt=10): 5385 -->*_s0(k(f(b)),k(x)) | -->_s0(g(b),x) # answer(goal). [resolve(5340,b,14,b)]. 43.002/43.002 43.002/43.002 given #849 (F,wt=10): 5387 -->*_s0(k(f(b)),k(g(x))) | -->_s0(b,x) # answer(goal). [resolve(5385,b,13,b)]. 43.002/43.002 43.002/43.002 given #850 (T,wt=9): 1774 ->*_s0(g(g(h(f(a)))),g(g(c))). [ur(23,a,277,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #851 (T,wt=9): 1783 ->*_s0(h(g(h(f(a)))),k(g(c))). [ur(23,a,278,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #852 (T,wt=9): 1784 ->*_s0(h(g(h(f(a)))),h(g(c))). [ur(23,a,278,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #853 (T,wt=9): 1833 ->*_s0(f(g(h(f(a)))),f(g(c))). [ur(23,a,279,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #854 (A,wt=11): 273 ->_s0(U91(x,k(h(f(a)))),U91(x,k(c))). [ur(10,a,55,a)]. 43.002/43.002 43.002/43.002 given #855 (F,wt=12): 5244 -->*_s0(k(f(b)),g(b)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(525,c,961,a)]. 43.002/43.002 43.002/43.002 given #856 (F,wt=12): 5245 -->*_s0(k(f(b)),g(a)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(525,c,931,a)]. 43.002/43.002 43.002/43.002 given #857 (F,wt=12): 5328 -->*_s0(k(f(b)),k(b)) | -->_s0(k(g(b)),h(a)) # answer(goal). [resolve(525,c,132,a)]. 43.002/43.002 43.002/43.002 given #858 (F,wt=12): 5329 -->*_s0(k(f(b)),f(b)) | -->_s0(k(g(b)),f(a)) # answer(goal). [resolve(525,c,123,a)]. 43.002/43.002 43.002/43.002 given #859 (T,wt=9): 1843 ->*_s0(k(h(h(f(a)))),k(k(c))). [ur(23,a,284,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #860 (T,wt=9): 1844 ->*_s0(k(h(h(f(a)))),k(h(c))). [ur(23,a,284,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #861 (T,wt=9): 1853 ->*_s0(g(h(h(f(a)))),g(k(c))). [ur(23,a,285,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #862 (T,wt=9): 1854 ->*_s0(g(h(h(f(a)))),g(h(c))). [ur(23,a,285,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #863 (A,wt=11): 274 ->_s0(U91(k(h(f(a))),x),U91(k(c),x)). [ur(9,a,55,a)]. 43.002/43.002 43.002/43.002 given #864 (F,wt=12): 5331 -->*_s0(k(f(b)),h(b)) | -->_s0(k(g(b)),h(a)) # answer(goal). [resolve(525,c,104,a)]. 43.002/43.002 43.002/43.002 given #865 (F,wt=12): 5332 -->*_s0(k(f(b)),g(b)) | -->_s0(k(g(b)),g(a)) # answer(goal). [resolve(525,c,97,a)]. 43.002/43.002 43.002/43.002 given #866 (F,wt=12): 5333 -->*_s0(k(f(b)),k(b)) | -->_s0(k(g(b)),k(a)) # answer(goal). [resolve(525,c,90,a)]. 43.002/43.002 43.002/43.002 given #867 (F,wt=10): 5485 -->*_s0(k(f(b)),k(b)) | -->_s0(g(b),a) # answer(goal). [resolve(5333,b,14,b)]. 43.002/43.002 43.002/43.002 given #868 (T,wt=9): 1863 ->*_s0(h(h(h(f(a)))),h(k(c))). [ur(23,a,286,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #869 (T,wt=9): 1864 ->*_s0(h(h(h(f(a)))),k(k(c))). [ur(23,a,286,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #870 (T,wt=9): 1865 ->*_s0(h(h(h(f(a)))),k(h(c))). [ur(23,a,286,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #871 (T,wt=9): 1866 ->*_s0(h(h(h(f(a)))),h(h(c))). [ur(23,a,286,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #872 (A,wt=11): 280 ->_s0(U91(x,g(h(f(a)))),U91(x,g(c))). [ur(10,a,56,a)]. 43.002/43.002 43.002/43.002 given #873 (F,wt=12): 5338 -->*_s0(k(f(b)),k(x)) | -->_s0(k(g(b)),h(x)) # answer(goal). [resolve(525,c,67,a)]. 43.002/43.002 43.002/43.002 given #874 (F,wt=13): 526 -->*_s0(k(g(b)),x) | -->_s0(k(f(b)),y) | -->*_s0(y,x) # answer(goal). [resolve(485,b,23,c)]. 43.002/43.002 43.002/43.002 given #875 (F,wt=10): 5727 -->*_s0(k(g(b)),b) | -->_s0(k(f(b)),a) # answer(goal). [resolve(526,c,72,a)]. 43.002/43.002 43.002/43.002 given #876 (F,wt=10): 5731 -->*_s0(k(g(b)),x) | -->_s0(k(f(b)),x) # answer(goal). [resolve(526,c,22,a)]. 43.002/43.002 43.002/43.002 given #877 (T,wt=9): 1894 ->*_s0(f(h(h(f(a)))),f(k(c))). [ur(23,a,287,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #878 (T,wt=9): 1896 ->*_s0(f(h(h(f(a)))),f(h(c))). [ur(23,a,287,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #879 (T,wt=9): 1906 ->*_s0(k(f(h(f(a)))),k(f(c))). [ur(23,a,291,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #880 (T,wt=9): 1915 ->*_s0(g(f(h(f(a)))),g(f(c))). [ur(23,a,292,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #881 (A,wt=11): 281 ->_s0(U91(g(h(f(a))),x),U91(g(c),x)). [ur(9,a,56,a)]. 43.002/43.002 43.002/43.002 given #882 (F,wt=10): 5732 -->*_s0(k(g(b)),k(U91(h(f(b)),b))) # answer(goal). [ur(526,b,49,a,c,22,a)]. 43.002/43.002 43.002/43.002 given #883 (F,wt=10): 5735 -->*_s0(k(g(b)),k(x)) | -->_s0(f(b),x) # answer(goal). [resolve(5731,b,14,b)]. 43.002/43.002 43.002/43.002 given #884 (F,wt=10): 5782 -->_s0(k(g(b)),h(U91(h(f(b)),a))) # answer(goal). [ur(23,b,1205,a,c,5732,a)]. 43.002/43.002 43.002/43.002 given #885 (F,wt=10): 5783 -->_s0(k(g(b)),k(U91(h(f(b)),a))) # answer(goal). [ur(23,b,1186,a,c,5732,a)]. 43.002/43.002 43.002/43.002 given #886 (T,wt=9): 1924 ->*_s0(h(f(h(f(a)))),k(f(c))). [ur(23,a,293,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #887 (T,wt=9): 1925 ->*_s0(h(f(h(f(a)))),h(f(c))). [ur(23,a,293,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #888 (T,wt=9): 1980 ->*_s0(f(f(h(f(a)))),f(f(c))). [ur(23,a,294,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #889 (T,wt=9): 2005 ->*_s0(k(k(h(x))),k(k(k(x)))). [ur(23,a,310,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #890 (A,wt=11): 288 ->_s0(U91(x,h(h(f(a)))),U91(x,h(c))). [ur(10,a,57,a)]. 43.002/43.002 43.002/43.002 given #891 (F,wt=8): 5788 -->_s0(g(b),U91(h(f(b)),a)) # answer(goal). [resolve(5783,a,14,b)]. 43.002/43.002 43.002/43.002 given #892 (F,wt=10): 5784 -->_s0(k(g(b)),h(U91(h(f(b)),b))) # answer(goal). [ur(23,b,67,a,c,5732,a)]. 43.002/43.002 43.002/43.002 given #893 (F,wt=10): 5785 -->_s0(k(g(b)),k(U91(h(f(b)),b))) # answer(goal). [ur(23,b,22,a,c,5732,a)]. 43.002/43.002 43.002/43.002 given #894 (F,wt=8): 5841 -->_s0(g(b),U91(h(f(b)),b)) # answer(goal). [resolve(5785,a,14,b)]. 43.002/43.002 43.002/43.002 given #895 (T,wt=9): 2014 ->*_s0(g(k(h(x))),g(k(k(x)))). [ur(23,a,311,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #896 (T,wt=9): 2029 ->*_s0(h(k(h(x))),k(k(k(x)))). [ur(23,a,312,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #897 (T,wt=9): 2030 ->*_s0(h(k(h(x))),h(k(k(x)))). [ur(23,a,312,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #898 (T,wt=9): 2040 ->*_s0(f(k(h(x))),f(k(k(x)))). [ur(23,a,313,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #899 (A,wt=11): 289 ->_s0(U91(h(h(f(a))),x),U91(h(c),x)). [ur(9,a,57,a)]. 43.002/43.002 43.002/43.002 given #900 (F,wt=10): 5787 -->*_s0(k(g(b)),k(f(x))) | -->_s0(b,x) # answer(goal). [resolve(5735,b,11,b)]. 43.002/43.002 43.002/43.002 given #901 (F,wt=12): 5636 -->*_s0(k(g(b)),g(b)) | -->_s0(k(f(b)),f(a)) # answer(goal). [resolve(526,c,961,a)]. 43.002/43.002 43.002/43.002 given #902 (F,wt=12): 5637 -->*_s0(k(g(b)),g(a)) | -->_s0(k(f(b)),f(a)) # answer(goal). [resolve(526,c,931,a)]. 43.002/43.002 43.002/43.002 given #903 (F,wt=12): 5719 -->*_s0(k(g(b)),k(b)) | -->_s0(k(f(b)),h(a)) # answer(goal). [resolve(526,c,132,a)]. 43.002/43.002 43.002/43.002 given #904 (T,wt=9): 2051 ->*_s0(k(g(h(x))),k(g(k(x)))). [ur(23,a,317,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #905 (T,wt=9): 2060 ->*_s0(g(g(h(x))),g(g(k(x)))). [ur(23,a,318,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #906 (T,wt=9): 2090 ->*_s0(h(g(h(x))),k(g(k(x)))). [ur(23,a,319,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #907 (T,wt=9): 2091 ->*_s0(h(g(h(x))),h(g(k(x)))). [ur(23,a,319,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #908 (A,wt=11): 295 ->_s0(U91(x,f(h(f(a)))),U91(x,f(c))). [ur(10,a,58,a)]. 43.002/43.002 43.002/43.002 given #909 (F,wt=12): 5720 -->*_s0(k(g(b)),f(b)) | -->_s0(k(f(b)),f(a)) # answer(goal). [resolve(526,c,123,a)]. 43.002/43.002 43.002/43.002 given #910 (F,wt=12): 5722 -->*_s0(k(g(b)),h(b)) | -->_s0(k(f(b)),h(a)) # answer(goal). [resolve(526,c,104,a)]. 43.002/43.002 43.002/43.002 given #911 (F,wt=12): 5723 -->*_s0(k(g(b)),g(b)) | -->_s0(k(f(b)),g(a)) # answer(goal). [resolve(526,c,97,a)]. 43.002/43.002 43.002/43.002 given #912 (F,wt=12): 5724 -->*_s0(k(g(b)),k(b)) | -->_s0(k(f(b)),k(a)) # answer(goal). [resolve(526,c,90,a)]. 43.002/43.002 43.002/43.002 given #913 (T,wt=9): 2101 ->*_s0(f(g(h(x))),f(g(k(x)))). [ur(23,a,320,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #914 (T,wt=9): 2112 ->*_s0(k(h(h(x))),k(k(k(x)))). [ur(23,a,325,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #915 (T,wt=9): 2113 ->*_s0(k(h(h(x))),k(h(k(x)))). [ur(23,a,325,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #916 (T,wt=9): 2122 ->*_s0(g(h(h(x))),g(k(k(x)))). [ur(23,a,326,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #917 (A,wt=11): 296 ->_s0(U91(f(h(f(a))),x),U91(f(c),x)). [ur(9,a,58,a)]. 43.002/43.002 43.002/43.002 given #918 (F,wt=10): 5955 -->*_s0(k(g(b)),k(b)) | -->_s0(f(b),a) # answer(goal). [resolve(5724,b,14,b)]. 43.002/43.002 43.002/43.002 given #919 (F,wt=12): 5729 -->*_s0(k(g(b)),k(x)) | -->_s0(k(f(b)),h(x)) # answer(goal). [resolve(526,c,67,a)]. 43.002/43.002 43.002/43.002 given #920 (F,wt=12): 5748 -->_s0(a,c) | -->_s0(k(g(b)),k(f(h(f(a))))) # answer(goal). [resolve(1906,a,445,c)]. 43.002/43.002 43.002/43.002 given #921 (F,wt=10): 6009 -->_s0(a,c) | -->_s0(g(b),f(h(f(a)))) # answer(goal). [resolve(5748,b,14,b)]. 43.002/43.002 43.002/43.002 given #922 (T,wt=9): 2123 ->*_s0(g(h(h(x))),g(h(k(x)))). [ur(23,a,326,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #923 (T,wt=9): 2154 ->*_s0(h(h(h(x))),h(k(k(x)))). [ur(23,a,327,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #924 (T,wt=9): 2155 ->*_s0(h(h(h(x))),k(k(k(x)))). [ur(23,a,327,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #925 (T,wt=9): 2156 ->*_s0(h(h(h(x))),k(h(k(x)))). [ur(23,a,327,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #926 (A,wt=11): 298 ->_s0(k(U91(c,x)),k(U91(k(f(a)),x))). [ur(14,a,42,a)]. 43.002/43.002 43.002/43.002 given #927 (F,wt=12): 5791 -->_s0(a,c) | -->_s0(k(g(b)),h(f(h(f(a))))) # answer(goal). [resolve(1924,a,445,c)]. 43.002/43.002 43.002/43.002 given #928 (F,wt=13): 527 -->_s0(b,x) | -->_s0(k(g(x)),y) | -->*_s0(y,k(f(b))) # answer(goal). [resolve(524,a,23,c)]. 43.002/43.002 43.002/43.002 given #929 (F,wt=12): 6053 -->_s0(b,f(a)) | -->*_s0(k(g(f(b))),k(f(b))) # answer(goal). [resolve(527,b,494,a)]. 43.002/43.002 43.002/43.002 given #930 (F,wt=12): 6054 -->_s0(b,h(a)) | -->*_s0(k(g(h(b))),k(f(b))) # answer(goal). [resolve(527,b,454,a)]. 43.002/43.002 43.002/43.002 given #931 (T,wt=9): 2157 ->*_s0(h(h(h(x))),h(h(k(x)))). [ur(23,a,327,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #932 (T,wt=9): 2166 ->*_s0(f(h(h(x))),f(k(k(x)))). [ur(23,a,328,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #933 (T,wt=9): 2168 ->*_s0(f(h(h(x))),f(h(k(x)))). [ur(23,a,328,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #934 (T,wt=9): 2180 ->*_s0(k(f(h(x))),k(f(k(x)))). [ur(23,a,332,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #935 (A,wt=11): 299 ->_s0(g(U91(c,x)),g(U91(k(f(a)),x))). [ur(13,a,42,a)]. 43.002/43.002 43.002/43.002 given #936 (F,wt=12): 6055 -->_s0(b,g(a)) | -->*_s0(k(g(g(b))),k(f(b))) # answer(goal). [resolve(527,b,412,a)]. 43.002/43.002 43.002/43.002 given #937 (F,wt=12): 6056 -->_s0(b,k(a)) | -->*_s0(k(g(k(b))),k(f(b))) # answer(goal). [resolve(527,b,367,a)]. 43.002/43.002 43.002/43.002 given #938 (F,wt=12): 6057 -->_s0(b,h(x)) | -->*_s0(k(g(k(x))),k(f(b))) # answer(goal). [resolve(527,b,317,a)]. 43.002/43.002 43.002/43.002 given #939 (F,wt=12): 6058 -->_s0(b,h(f(a))) | -->*_s0(k(g(c)),k(f(b))) # answer(goal). [resolve(527,b,276,a)]. 43.002/43.002 43.002/43.002 given #940 (T,wt=9): 2189 ->*_s0(g(f(h(x))),g(f(k(x)))). [ur(23,a,333,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #941 (T,wt=9): 2386 ->*_s0(h(f(h(x))),k(f(k(x)))). [ur(23,a,334,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #942 (T,wt=9): 2387 ->*_s0(h(f(h(x))),h(f(k(x)))). [ur(23,a,334,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #943 (T,wt=9): 2398 ->*_s0(f(f(h(x))),f(f(k(x)))). [ur(23,a,335,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #944 (A,wt=11): 300 ->_s0(h(U91(c,x)),h(U91(k(f(a)),x))). [ur(12,a,42,a)]. 43.002/43.002 43.002/43.002 given #945 (F,wt=12): 6059 -->_s0(b,c) | -->*_s0(k(g(k(g(b)))),k(f(b))) # answer(goal). [resolve(527,b,236,a)]. 43.002/43.002 43.002/43.002 given #946 (F,wt=12): 6060 -->_s0(b,c) | -->*_s0(k(g(k(f(a)))),k(f(b))) # answer(goal). [resolve(527,b,193,a)]. 43.002/43.002 43.002/43.002 given #947 (F,wt=12): 6086 -->_s0(a,k(x)) | -->_s0(k(g(b)),k(f(h(x)))) # answer(goal). [resolve(2180,a,445,c)]. 43.002/43.002 43.002/43.002 given #948 (F,wt=10): 6152 -->_s0(a,k(x)) | -->_s0(g(b),f(h(x))) # answer(goal). [resolve(6086,b,14,b)]. 43.002/43.002 43.002/43.002 given #949 (T,wt=9): 2426 ->*_s0(k(k(k(a))),k(k(k(b)))). [ur(23,a,360,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #950 (T,wt=9): 2450 ->*_s0(g(k(k(a))),g(k(k(b)))). [ur(23,a,361,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #951 (T,wt=9): 2460 ->*_s0(h(k(k(a))),k(k(k(b)))). [ur(23,a,362,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #952 (T,wt=9): 2461 ->*_s0(h(k(k(a))),h(k(k(b)))). [ur(23,a,362,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #953 (A,wt=11): 301 ->_s0(f(U91(c,x)),f(U91(k(f(a)),x))). [ur(11,a,42,a)]. 43.002/43.002 43.002/43.002 given #954 (F,wt=12): 6118 -->_s0(a,k(x)) | -->_s0(k(g(b)),h(f(h(x)))) # answer(goal). [resolve(2386,a,445,c)]. 43.002/43.002 43.002/43.002 given #955 (F,wt=13): 586 -->_s0(f(a),a) | -->_s0(k(g(b)),x) | -->*_s0(x,k(b)) # answer(goal). [resolve(568,a,23,c)]. 43.002/43.002 43.002/43.002 given #956 (F,wt=10): 6192 -->_s0(f(a),a) | -->_s0(k(g(b)),h(b)) # answer(goal). [resolve(586,c,67,a)]. 43.002/43.002 43.002/43.002 given #957 (F,wt=10): 6194 -->_s0(f(a),a) | -->_s0(k(g(b)),k(b)) # answer(goal). [resolve(586,c,22,a)]. 43.002/43.002 43.002/43.002 given #958 (T,wt=9): 2472 ->*_s0(f(k(k(a))),f(k(k(b)))). [ur(23,a,363,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #959 (T,wt=9): 2485 ->*_s0(k(g(k(a))),k(g(k(b)))). [ur(23,a,367,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #960 (T,wt=9): 2519 ->*_s0(g(g(k(a))),g(g(k(b)))). [ur(23,a,368,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #961 (T,wt=9): 2529 ->*_s0(h(g(k(a))),k(g(k(b)))). [ur(23,a,369,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #962 (A,wt=13): 302 ->_s0(U91(x,U91(c,y)),U91(x,U91(k(f(a)),y))). [ur(10,a,42,a)]. 43.002/43.002 43.002/43.002 given #963 (F,wt=8): 6195 -->_s0(f(a),a) | -->_s0(g(b),b) # answer(goal). [resolve(6194,b,14,b)]. 43.002/43.002 43.002/43.002 given #964 (F,wt=13): 588 -->*_s0(k(f(a)),x) | -->*_s0(k(y),x) | -->_s0(g(b),y) # answer(goal). [resolve(76,b,14,b)]. 43.002/43.002 43.002/43.002 given #965 (F,wt=12): 6273 -->*_s0(k(f(a)),k(k(b))) | -->_s0(g(b),h(a)) # answer(goal). [resolve(588,b,640,a)]. 43.002/43.002 43.002/43.002 given #966 (F,wt=12): 6275 -->*_s0(k(f(a)),k(h(b))) | -->_s0(g(b),h(a)) # answer(goal). [resolve(588,b,446,a)]. 43.002/43.002 43.002/43.002 given #967 (T,wt=9): 2530 ->*_s0(h(g(k(a))),h(g(k(b)))). [ur(23,a,369,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #968 (T,wt=9): 2541 ->*_s0(f(g(k(a))),f(g(k(b)))). [ur(23,a,370,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #969 (T,wt=9): 2553 ->*_s0(k(h(k(a))),k(k(k(b)))). [ur(23,a,375,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #970 (T,wt=9): 2554 ->*_s0(k(h(k(a))),k(h(k(b)))). [ur(23,a,375,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #971 (A,wt=13): 303 ->_s0(U91(U91(c,x),y),U91(U91(k(f(a)),x),y)). [ur(9,a,42,a)]. 43.002/43.002 43.002/43.002 given #972 (F,wt=12): 6276 -->*_s0(k(f(a)),k(k(b))) | -->_s0(g(b),k(a)) # answer(goal). [resolve(588,b,359,a)]. 43.002/43.002 43.002/43.002 given #973 (F,wt=12): 6277 -->*_s0(k(f(a)),k(k(x))) | -->_s0(g(b),h(x)) # answer(goal). [resolve(588,b,309,a)]. 43.002/43.002 43.002/43.002 given #974 (F,wt=12): 6278 -->*_s0(k(f(a)),k(c)) | -->_s0(g(b),h(f(a))) # answer(goal). [resolve(588,b,268,a)]. 43.002/43.002 43.002/43.002 given #975 (F,wt=12): 6279 -->*_s0(k(f(a)),k(k(g(b)))) | -->_s0(g(b),c) # answer(goal). [resolve(588,b,228,a)]. 43.002/43.002 43.002/43.002 given #976 (T,wt=9): 2580 ->*_s0(g(h(k(a))),g(k(k(b)))). [ur(23,a,376,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #977 (T,wt=9): 2581 ->*_s0(g(h(k(a))),g(h(k(b)))). [ur(23,a,376,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #978 (T,wt=9): 2591 ->*_s0(h(h(k(a))),h(k(k(b)))). [ur(23,a,377,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #979 (T,wt=9): 2592 ->*_s0(h(h(k(a))),k(k(k(b)))). [ur(23,a,377,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #980 (A,wt=11): 314 ->_s0(U91(x,k(h(y))),U91(x,k(k(y)))). [ur(10,a,61,a)]. 43.002/43.002 43.002/43.002 given #981 (F,wt=12): 6280 -->*_s0(k(f(a)),k(k(f(a)))) | -->_s0(g(b),c) # answer(goal). [resolve(588,b,185,a)]. 43.002/43.002 43.002/43.002 given #982 (F,wt=13): 609 -->_s0(k(g(b)),a) | -->_s0(k(f(a)),x) | -->*_s0(x,b) # answer(goal). [resolve(605,a,23,c)]. 43.002/43.002 43.002/43.002 given #983 (F,wt=13): 628 -->_s0(k(g(b)),x) | -->_s0(k(f(a)),y) | -->*_s0(y,x) # answer(goal). [resolve(608,a,23,c)]. 43.002/43.002 43.002/43.002 given #984 (F,wt=12): 6544 -->_s0(k(g(b)),g(b)) | -->_s0(k(f(a)),f(a)) # answer(goal). [resolve(628,c,961,a)]. 43.002/43.002 43.002/43.002 given #985 (T,wt=9): 2593 ->*_s0(h(h(k(a))),k(h(k(b)))). [ur(23,a,377,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #986 (T,wt=9): 2594 ->*_s0(h(h(k(a))),h(h(k(b)))). [ur(23,a,377,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #987 (T,wt=9): 2604 ->*_s0(f(h(k(a))),f(k(k(b)))). [ur(23,a,378,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #988 (T,wt=9): 2606 ->*_s0(f(h(k(a))),f(h(k(b)))). [ur(23,a,378,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #989 (A,wt=11): 315 ->_s0(U91(k(h(x)),y),U91(k(k(x)),y)). [ur(9,a,61,a)]. 43.002/43.002 43.002/43.002 given #990 (F,wt=12): 6545 -->_s0(k(g(b)),g(a)) | -->_s0(k(f(a)),f(a)) # answer(goal). [resolve(628,c,931,a)]. 43.002/43.002 43.002/43.002 given #991 (F,wt=12): 6627 -->_s0(k(g(b)),k(b)) | -->_s0(k(f(a)),h(a)) # answer(goal). [resolve(628,c,132,a)]. 43.002/43.002 43.002/43.002 given #992 (F,wt=10): 6684 -->_s0(k(f(a)),h(a)) | -->_s0(g(b),b) # answer(goal). [resolve(6627,a,14,b)]. 43.002/43.002 43.002/43.002 given #993 (F,wt=12): 6628 -->_s0(k(g(b)),f(b)) | -->_s0(k(f(a)),f(a)) # answer(goal). [resolve(628,c,123,a)]. 43.002/43.002 43.002/43.002 given #994 (T,wt=9): 2619 ->*_s0(k(f(k(a))),k(f(k(b)))). [ur(23,a,382,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #995 (T,wt=9): 2651 ->*_s0(g(f(k(a))),g(f(k(b)))). [ur(23,a,383,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #996 (T,wt=9): 2661 ->*_s0(h(f(k(a))),k(f(k(b)))). [ur(23,a,384,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #997 (T,wt=9): 2662 ->*_s0(h(f(k(a))),h(f(k(b)))). [ur(23,a,384,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #998 (A,wt=11): 321 ->_s0(U91(x,g(h(y))),U91(x,g(k(y)))). [ur(10,a,62,a)]. 43.002/43.002 43.002/43.002 given #999 (F,wt=12): 6630 -->_s0(k(g(b)),h(b)) | -->_s0(k(f(a)),h(a)) # answer(goal). [resolve(628,c,104,a)]. 43.002/43.002 43.002/43.002 given #1000 (F,wt=12): 6631 -->_s0(k(g(b)),g(b)) | -->_s0(k(f(a)),g(a)) # answer(goal). [resolve(628,c,97,a)]. 43.002/43.002 43.002/43.002 given #1001 (F,wt=12): 6632 -->_s0(k(g(b)),k(b)) | -->_s0(k(f(a)),k(a)) # answer(goal). [resolve(628,c,90,a)]. 43.002/43.002 43.002/43.002 given #1002 (F,wt=10): 6740 -->_s0(k(f(a)),k(a)) | -->_s0(g(b),b) # answer(goal). [resolve(6632,a,14,b)]. 43.002/43.002 43.002/43.002 given #1003 (T,wt=9): 2673 ->*_s0(f(f(k(a))),f(f(k(b)))). [ur(23,a,385,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1004 (T,wt=9): 2716 ->*_s0(k(k(g(a))),k(k(g(b)))). [ur(23,a,405,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1005 (T,wt=9): 2726 ->*_s0(g(k(g(a))),g(k(g(b)))). [ur(23,a,406,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1006 (T,wt=9): 2736 ->*_s0(h(k(g(a))),k(k(g(b)))). [ur(23,a,407,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1007 (A,wt=11): 322 ->_s0(U91(g(h(x)),y),U91(g(k(x)),y)). [ur(9,a,62,a)]. 43.002/43.002 43.002/43.002 given #1008 (F,wt=12): 6636 -->_s0(k(g(b)),k(x)) | -->_s0(k(f(a)),h(x)) # answer(goal). [resolve(628,c,67,a)]. 43.002/43.002 43.002/43.002 given #1009 (F,wt=10): 6794 -->_s0(k(f(a)),h(x)) | -->_s0(g(b),x) # answer(goal). [resolve(6636,a,14,b)]. 43.002/43.002 43.002/43.002 given #1010 (F,wt=10): 6795 -->_s0(k(f(a)),h(g(x))) | -->_s0(b,x) # answer(goal). [resolve(6794,b,13,b)]. 43.002/43.002 43.002/43.002 given #1011 (F,wt=12): 6689 -->_s0(a,k(b)) | -->_s0(k(g(b)),k(f(k(a)))) # answer(goal). [resolve(2619,a,445,c)]. 43.002/43.002 43.002/43.002 given #1012 (T,wt=9): 2737 ->*_s0(h(k(g(a))),h(k(g(b)))). [ur(23,a,407,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1013 (T,wt=9): 2748 ->*_s0(f(k(g(a))),f(k(g(b)))). [ur(23,a,408,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1014 (T,wt=9): 2783 ->*_s0(k(g(g(a))),k(g(g(b)))). [ur(23,a,412,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1015 (T,wt=9): 2793 ->*_s0(g(g(g(a))),g(g(g(b)))). [ur(23,a,413,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1016 (A,wt=11): 329 ->_s0(U91(x,h(h(y))),U91(x,h(k(y)))). [ur(10,a,63,a)]. 43.002/43.002 43.002/43.002 given #1017 (F,wt=10): 6796 -->_s0(a,k(b)) | -->_s0(g(b),f(k(a))) # answer(goal). [resolve(6689,b,14,b)]. 43.002/43.002 43.002/43.002 given #1018 (F,wt=12): 6705 -->_s0(a,k(b)) | -->_s0(k(g(b)),h(f(k(a)))) # answer(goal). [resolve(2661,a,445,c)]. 43.002/43.002 43.002/43.002 given #1019 (F,wt=13): 630 -->_s0(g(b),x) | -->_s0(k(f(a)),y) | -->*_s0(y,k(x)) # answer(goal). [resolve(629,a,23,c)]. 43.002/43.002 43.002/43.002 given #1020 (F,wt=12): 6917 -->_s0(g(b),k(b)) | -->_s0(k(f(a)),h(h(a))) # answer(goal). [resolve(630,c,660,a)]. 43.002/43.002 43.002/43.002 given #1021 (T,wt=9): 2803 ->*_s0(h(g(g(a))),k(g(g(b)))). [ur(23,a,414,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1022 (T,wt=9): 2804 ->*_s0(h(g(g(a))),h(g(g(b)))). [ur(23,a,414,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1023 (T,wt=9): 2815 ->*_s0(f(g(g(a))),f(g(g(b)))). [ur(23,a,415,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1024 (T,wt=9): 2843 ->*_s0(k(h(g(a))),k(k(g(b)))). [ur(23,a,420,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #1025 (A,wt=11): 330 ->_s0(U91(h(h(x)),y),U91(h(k(x)),y)). [ur(9,a,63,a)]. 43.002/43.002 43.002/43.002 given #1026 (F,wt=12): 6918 -->_s0(g(b),k(b)) | -->_s0(k(f(a)),k(h(a))) # answer(goal). [resolve(630,c,640,a)]. 43.002/43.002 43.002/43.002 given #1027 (F,wt=10): 6996 -->_s0(g(b),k(b)) | -->_s0(f(a),h(a)) # answer(goal). [resolve(6918,b,14,b)]. 43.002/43.002 43.002/43.002 given #1028 (F,wt=12): 6921 -->_s0(g(b),h(b)) | -->_s0(k(f(a)),h(h(a))) # answer(goal). [resolve(630,c,460,a)]. 43.002/43.002 43.002/43.002 given #1029 (F,wt=12): 6922 -->_s0(g(b),h(b)) | -->_s0(k(f(a)),k(h(a))) # answer(goal). [resolve(630,c,446,a)]. 43.002/43.002 43.002/43.002 given #1030 (T,wt=9): 2844 ->*_s0(k(h(g(a))),k(h(g(b)))). [ur(23,a,420,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1031 (T,wt=9): 2854 ->*_s0(g(h(g(a))),g(k(g(b)))). [ur(23,a,421,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #1032 (T,wt=9): 2855 ->*_s0(g(h(g(a))),g(h(g(b)))). [ur(23,a,421,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1033 (T,wt=9): 2865 ->*_s0(h(h(g(a))),h(k(g(b)))). [ur(23,a,422,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #1034 (A,wt=11): 336 ->_s0(U91(x,f(h(y))),U91(x,f(k(y)))). [ur(10,a,64,a)]. 43.002/43.002 43.002/43.002 given #1035 (F,wt=10): 6997 -->_s0(g(b),h(b)) | -->_s0(f(a),h(a)) # answer(goal). [resolve(6922,b,14,b)]. 43.002/43.002 43.002/43.002 given #1036 (F,wt=12): 6923 -->_s0(g(b),k(b)) | -->_s0(k(f(a)),h(k(a))) # answer(goal). [resolve(630,c,373,a)]. 43.002/43.002 43.002/43.002 given #1037 (F,wt=12): 6924 -->_s0(g(b),k(b)) | -->_s0(k(f(a)),k(k(a))) # answer(goal). [resolve(630,c,359,a)]. 43.002/43.002 43.002/43.002 given #1038 (F,wt=10): 7056 -->_s0(g(b),k(b)) | -->_s0(f(a),k(a)) # answer(goal). [resolve(6924,b,14,b)]. 43.002/43.002 43.002/43.002 given #1039 (T,wt=9): 2866 ->*_s0(h(h(g(a))),k(k(g(b)))). [ur(23,a,422,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #1040 (T,wt=9): 2867 ->*_s0(h(h(g(a))),k(h(g(b)))). [ur(23,a,422,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1041 (T,wt=9): 2868 ->*_s0(h(h(g(a))),h(h(g(b)))). [ur(23,a,422,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1042 (T,wt=9): 2878 ->*_s0(f(h(g(a))),f(k(g(b)))). [ur(23,a,423,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #1043 (A,wt=11): 337 ->_s0(U91(f(h(x)),y),U91(f(k(x)),y)). [ur(9,a,64,a)]. 43.002/43.002 43.002/43.002 given #1044 (F,wt=12): 6925 -->_s0(g(b),k(x)) | -->_s0(k(f(a)),h(h(x))) # answer(goal). [resolve(630,c,323,a)]. 43.002/43.002 43.002/43.002 given #1045 (F,wt=12): 6926 -->_s0(g(b),k(x)) | -->_s0(k(f(a)),k(h(x))) # answer(goal). [resolve(630,c,309,a)]. 43.002/43.002 43.002/43.002 given #1046 (F,wt=10): 7110 -->_s0(g(b),k(x)) | -->_s0(f(a),h(x)) # answer(goal). [resolve(6926,b,14,b)]. 43.002/43.002 43.002/43.002 given #1047 (F,wt=12): 6927 -->_s0(g(b),c) | -->_s0(k(f(a)),h(h(f(a)))) # answer(goal). [resolve(630,c,282,a)]. 43.002/43.002 43.002/43.002 given #1048 (T,wt=9): 2880 ->*_s0(f(h(g(a))),f(h(g(b)))). [ur(23,a,423,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1049 (T,wt=9): 2911 ->*_s0(k(f(g(a))),k(f(g(b)))). [ur(23,a,427,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1050 (T,wt=9): 2921 ->*_s0(g(f(g(a))),g(f(g(b)))). [ur(23,a,428,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1051 (T,wt=9): 2931 ->*_s0(h(f(g(a))),k(f(g(b)))). [ur(23,a,429,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1052 (A,wt=11): 339 ->_s0(k(U91(x,c)),k(U91(x,k(g(b))))). [ur(14,a,47,a)]. 43.002/43.002 43.002/43.002 given #1053 (F,wt=12): 6928 -->_s0(g(b),c) | -->_s0(k(f(a)),k(h(f(a)))) # answer(goal). [resolve(630,c,268,a)]. 43.002/43.002 43.002/43.002 given #1054 (F,wt=10): 7164 -->_s0(g(b),c) | -->_s0(f(a),h(f(a))) # answer(goal). [resolve(6928,b,14,b)]. 43.002/43.002 43.002/43.002 given #1055 (F,wt=12): 6929 -->_s0(g(b),k(g(b))) | -->_s0(k(f(a)),h(c)) # answer(goal). [resolve(630,c,242,a)]. 43.002/43.002 43.002/43.002 given #1056 (F,wt=12): 6930 -->_s0(g(b),k(g(b))) | -->_s0(k(f(a)),k(c)) # answer(goal). [resolve(630,c,228,a)]. 43.002/43.002 43.002/43.002 given #1057 (T,wt=9): 2932 ->*_s0(h(f(g(a))),h(f(g(b)))). [ur(23,a,429,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1058 (T,wt=9): 2943 ->*_s0(f(f(g(a))),f(f(g(b)))). [ur(23,a,430,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1059 (T,wt=9): 2968 ->*_s0(k(k(h(a))),k(k(h(b)))). [ur(23,a,447,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1060 (T,wt=9): 2978 ->*_s0(g(k(h(a))),g(k(h(b)))). [ur(23,a,448,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1061 (A,wt=11): 340 ->_s0(g(U91(x,c)),g(U91(x,k(g(b))))). [ur(13,a,47,a)]. 43.002/43.002 43.002/43.002 given #1062 (F,wt=10): 7165 -->_s0(g(b),k(g(b))) | -->_s0(f(a),c) # answer(goal). [resolve(6930,b,14,b)]. 43.002/43.002 43.002/43.002 given #1063 (F,wt=12): 6931 -->_s0(g(b),k(f(a))) | -->_s0(k(f(a)),h(c)) # answer(goal). [resolve(630,c,199,a)]. 43.002/43.002 43.002/43.002 given #1064 (F,wt=12): 6932 -->_s0(g(b),k(f(a))) | -->_s0(k(f(a)),k(c)) # answer(goal). [resolve(630,c,185,a)]. 43.002/43.002 43.002/43.002 given #1065 (F,wt=10): 7209 -->_s0(g(b),k(f(a))) | -->_s0(f(a),c) # answer(goal). [resolve(6932,b,14,b)]. 43.002/43.002 43.002/43.002 given #1066 (T,wt=9): 2988 ->*_s0(h(k(h(a))),k(k(h(b)))). [ur(23,a,449,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1067 (T,wt=9): 2989 ->*_s0(h(k(h(a))),h(k(h(b)))). [ur(23,a,449,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1068 (T,wt=9): 3000 ->*_s0(f(k(h(a))),f(k(h(b)))). [ur(23,a,450,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1069 (T,wt=9): 3026 ->*_s0(k(g(h(a))),k(g(h(b)))). [ur(23,a,454,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1070 (A,wt=11): 341 ->_s0(h(U91(x,c)),h(U91(x,k(g(b))))). [ur(12,a,47,a)]. 43.002/43.002 43.002/43.002 given #1071 (F,wt=12): 7123 -->_s0(a,g(b)) | -->_s0(k(g(b)),k(f(g(a)))) # answer(goal). [resolve(2911,a,445,c)]. 43.002/43.002 43.002/43.002 given #1072 (F,wt=10): 7255 -->_s0(a,g(b)) | -->_s0(g(b),f(g(a))) # answer(goal). [resolve(7123,b,14,b)]. 43.002/43.002 43.002/43.002 given #1073 (F,wt=12): 7142 -->_s0(a,g(b)) | -->_s0(k(g(b)),h(f(g(a)))) # answer(goal). [resolve(2931,a,445,c)]. 43.002/43.002 43.002/43.002 given #1074 (F,wt=13): 632 -->_s0(b,x) | -->_s0(k(f(a)),y) | -->*_s0(y,k(g(x))) # answer(goal). [resolve(631,a,23,c)]. 43.002/43.002 43.002/43.002 given #1075 (T,wt=9): 3036 ->*_s0(g(g(h(a))),g(g(h(b)))). [ur(23,a,455,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1076 (T,wt=9): 3046 ->*_s0(h(g(h(a))),k(g(h(b)))). [ur(23,a,456,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1077 (T,wt=9): 3047 ->*_s0(h(g(h(a))),h(g(h(b)))). [ur(23,a,456,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1078 (T,wt=9): 3058 ->*_s0(f(g(h(a))),f(g(h(b)))). [ur(23,a,457,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1079 (A,wt=11): 342 ->_s0(f(U91(x,c)),f(U91(x,k(g(b))))). [ur(11,a,47,a)]. 43.002/43.002 43.002/43.002 given #1080 (F,wt=12): 7258 -->_s0(b,h(b)) | -->_s0(k(f(a)),k(g(h(a)))) # answer(goal). [resolve(632,c,3026,a)]. 43.002/43.002 43.002/43.002 given #1081 (F,wt=10): 7320 -->_s0(b,h(b)) | -->_s0(f(a),g(h(a))) # answer(goal). [resolve(7258,b,14,b)]. 43.002/43.002 43.002/43.002 given #1082 (F,wt=12): 7259 -->_s0(b,g(b)) | -->_s0(k(f(a)),h(g(g(a)))) # answer(goal). [resolve(632,c,2803,a)]. 43.002/43.002 43.002/43.002 given #1083 (F,wt=12): 7260 -->_s0(b,g(b)) | -->_s0(k(f(a)),k(g(g(a)))) # answer(goal). [resolve(632,c,2783,a)]. 43.002/43.002 43.002/43.002 given #1084 (T,wt=9): 3088 ->*_s0(k(h(h(a))),k(k(h(b)))). [ur(23,a,462,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #1085 (T,wt=9): 3089 ->*_s0(k(h(h(a))),k(h(h(b)))). [ur(23,a,462,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1086 (T,wt=9): 3099 ->*_s0(g(h(h(a))),g(k(h(b)))). [ur(23,a,463,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #1087 (T,wt=9): 3100 ->*_s0(g(h(h(a))),g(h(h(b)))). [ur(23,a,463,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1088 (A,wt=13): 343 ->_s0(U91(x,U91(y,c)),U91(x,U91(y,k(g(b))))). [ur(10,a,47,a)]. 43.002/43.002 43.002/43.002 given #1089 (F,wt=10): 7321 -->_s0(b,g(b)) | -->_s0(f(a),g(g(a))) # answer(goal). [resolve(7260,b,14,b)]. 43.002/43.002 43.002/43.002 given #1090 (F,wt=12): 7261 -->_s0(b,k(b)) | -->_s0(k(f(a)),h(g(k(a)))) # answer(goal). [resolve(632,c,2529,a)]. 43.002/43.002 43.002/43.002 given #1091 (F,wt=12): 7262 -->_s0(b,k(b)) | -->_s0(k(f(a)),k(g(k(a)))) # answer(goal). [resolve(632,c,2485,a)]. 43.002/43.002 43.002/43.002 given #1092 (F,wt=10): 7382 -->_s0(b,k(b)) | -->_s0(f(a),g(k(a))) # answer(goal). [resolve(7262,b,14,b)]. 43.002/43.002 43.002/43.002 given #1093 (T,wt=9): 3110 ->*_s0(h(h(h(a))),h(k(h(b)))). [ur(23,a,464,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #1094 (T,wt=9): 3111 ->*_s0(h(h(h(a))),k(k(h(b)))). [ur(23,a,464,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #1095 (T,wt=9): 3112 ->*_s0(h(h(h(a))),k(h(h(b)))). [ur(23,a,464,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1096 (T,wt=9): 3113 ->*_s0(h(h(h(a))),h(h(h(b)))). [ur(23,a,464,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1097 (A,wt=13): 344 ->_s0(U91(U91(x,c),y),U91(U91(x,k(g(b))),y)). [ur(9,a,47,a)]. 43.002/43.002 43.002/43.002 given #1098 (F,wt=12): 7263 -->_s0(b,k(x)) | -->_s0(k(f(a)),h(g(h(x)))) # answer(goal). [resolve(632,c,2090,a)]. 43.002/43.002 43.002/43.002 given #1099 (F,wt=12): 7264 -->_s0(b,k(x)) | -->_s0(k(f(a)),k(g(h(x)))) # answer(goal). [resolve(632,c,2051,a)]. 43.002/43.002 43.002/43.002 given #1100 (F,wt=10): 7433 -->_s0(b,k(x)) | -->_s0(f(a),g(h(x))) # answer(goal). [resolve(7264,b,14,b)]. 43.002/43.002 43.002/43.002 given #1101 (F,wt=12): 7265 -->_s0(b,c) | -->_s0(k(f(a)),h(g(h(f(a))))) # answer(goal). [resolve(632,c,1783,a)]. 43.002/43.002 43.002/43.002 given #1102 (T,wt=9): 3123 ->*_s0(f(h(h(a))),f(k(h(b)))). [ur(23,a,465,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #1103 (T,wt=9): 3125 ->*_s0(f(h(h(a))),f(h(h(b)))). [ur(23,a,465,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1104 (T,wt=9): 3154 ->*_s0(k(f(h(a))),k(f(h(b)))). [ur(23,a,469,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1105 (T,wt=9): 3164 ->*_s0(g(f(h(a))),g(f(h(b)))). [ur(23,a,470,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1106 (A,wt=16): 346 -->_s0(k(f(a)),x) | -->*_s0(x,y) | -->_s0(k(g(b)),z) | -->*_s0(z,y) # answer(goal). [resolve(74,a,23,c)]. 43.002/43.002 43.002/43.002 given #1107 (F,wt=12): 7266 -->_s0(b,c) | -->_s0(k(f(a)),k(g(h(f(a))))) # answer(goal). [resolve(632,c,1765,a)]. 43.002/43.002 43.002/43.002 given #1108 (F,wt=10): 8053 -->_s0(b,c) | -->_s0(f(a),g(h(f(a)))) # answer(goal). [resolve(7266,b,14,b)]. 43.002/43.002 43.002/43.002 given #1109 (F,wt=12): 7267 -->_s0(b,k(g(b))) | -->_s0(k(f(a)),h(g(c))) # answer(goal). [resolve(632,c,1570,a)]. 43.002/43.002 43.002/43.002 given #1110 (F,wt=12): 7268 -->_s0(b,k(g(b))) | -->_s0(k(f(a)),k(g(c))) # answer(goal). [resolve(632,c,1552,a)]. 43.002/43.002 43.002/43.002 given #1111 (T,wt=9): 3174 ->*_s0(h(f(h(a))),k(f(h(b)))). [ur(23,a,471,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1112 (T,wt=9): 3175 ->*_s0(h(f(h(a))),h(f(h(b)))). [ur(23,a,471,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1113 (T,wt=9): 3186 ->*_s0(f(f(h(a))),f(f(h(b)))). [ur(23,a,472,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1114 (T,wt=9): 3267 ->*_s0(k(k(f(a))),k(k(f(b)))). [ur(23,a,487,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1115 (A,wt=16): 356 -->*_s0(k(g(b)),x) | -->_s0(k(f(a)),y) | -->_s0(y,z) | -->*_s0(z,x) # answer(goal). [resolve(74,c,23,c)]. 43.002/43.002 43.002/43.002 given #1116 (F,wt=10): 8054 -->_s0(b,k(g(b))) | -->_s0(f(a),g(c)) # answer(goal). [resolve(7268,b,14,b)]. 43.002/43.002 43.002/43.002 given #1117 (F,wt=12): 7269 -->_s0(b,k(f(a))) | -->_s0(k(f(a)),h(g(c))) # answer(goal). [resolve(632,c,1356,a)]. 43.002/43.002 43.002/43.002 given #1118 (F,wt=12): 7270 -->_s0(b,k(f(a))) | -->_s0(k(f(a)),k(g(c))) # answer(goal). [resolve(632,c,1338,a)]. 43.002/43.002 43.002/43.002 given #1119 (F,wt=10): 8701 -->_s0(b,k(f(a))) | -->_s0(f(a),g(c)) # answer(goal). [resolve(7270,b,14,b)]. 43.002/43.002 43.002/43.002 given #1120 (T,wt=7): 8094 ->*_s0(k(c),k(k(f(b)))). [ur(23,a,37,a,b,3267,a)]. 43.002/43.002 43.002/43.002 given #1121 (T,wt=7): 8715 ->*_s0(h(c),k(k(f(b)))). [ur(23,a,21,a,b,8094,a)]. 43.002/43.002 43.002/43.002 given #1122 (T,wt=9): 3277 ->*_s0(g(k(f(a))),g(k(f(b)))). [ur(23,a,488,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1123 (T,wt=7): 8736 ->*_s0(g(c),g(k(f(b)))). [ur(23,a,38,a,b,3277,a)]. 43.002/43.002 43.002/43.002 given #1124 (A,wt=11): 364 ->_s0(U91(x,k(k(a))),U91(x,k(k(b)))). [ur(10,a,91,a)]. 43.002/43.002 43.002/43.002 given #1125 (F,wt=12): 7282 -->_s0(b,h(b)) | -->_s0(k(f(a)),h(g(h(a)))) # answer(goal). [resolve(3046,a,632,c)]. 43.002/43.002 43.002/43.002 given #1126 (F,wt=12): 7451 -->_s0(a,h(b)) | -->_s0(k(g(b)),k(f(h(a)))) # answer(goal). [resolve(3154,a,445,c)]. 43.002/43.002 43.002/43.002 given #1127 (F,wt=10): 8773 -->_s0(a,h(b)) | -->_s0(g(b),f(h(a))) # answer(goal). [resolve(7451,b,14,b)]. 43.002/43.002 43.002/43.002 given #1128 (F,wt=12): 8059 -->_s0(a,h(b)) | -->_s0(k(g(b)),h(f(h(a)))) # answer(goal). [resolve(3174,a,445,c)]. 43.002/43.002 43.002/43.002 given #1129 (T,wt=9): 3287 ->*_s0(h(k(f(a))),k(k(f(b)))). [ur(23,a,489,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1130 (T,wt=9): 3288 ->*_s0(h(k(f(a))),h(k(f(b)))). [ur(23,a,489,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1131 (T,wt=7): 8794 ->*_s0(h(c),h(k(f(b)))). [ur(23,a,39,a,b,3288,a)]. 43.002/43.002 43.002/43.002 given #1132 (T,wt=9): 3299 ->*_s0(f(k(f(a))),f(k(f(b)))). [ur(23,a,490,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1133 (A,wt=11): 365 ->_s0(U91(k(k(a)),x),U91(k(k(b)),x)). [ur(9,a,91,a)]. 43.002/43.002 43.002/43.002 given #1134 (F,wt=12): 8702 -->_s0(g(b),k(f(b))) | -->_s0(k(f(a)),k(c)) # answer(goal). [resolve(8094,a,630,c)]. 43.002/43.002 43.002/43.002 given #1135 (F,wt=10): 8836 -->_s0(g(b),k(f(b))) | -->_s0(f(a),c) # answer(goal). [resolve(8702,b,14,b)]. 43.002/43.002 43.002/43.002 given #1136 (F,wt=12): 8704 -->*_s0(k(f(a)),k(k(f(b)))) | -->_s0(g(b),c) # answer(goal). [resolve(8094,a,588,b)]. 43.002/43.002 43.002/43.002 given #1137 (F,wt=12): 8707 -->_s0(f(a),k(f(b))) | -->_s0(k(g(b)),k(c)) # answer(goal). [resolve(8094,a,397,c)]. 43.002/43.002 43.002/43.002 given #1138 (T,wt=7): 8813 ->*_s0(f(c),f(k(f(b)))). [ur(23,a,40,a,b,3299,a)]. 43.002/43.002 43.002/43.002 given #1139 (T,wt=9): 3331 ->*_s0(k(g(f(a))),k(g(f(b)))). [ur(23,a,494,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1140 (T,wt=9): 3341 ->*_s0(g(g(f(a))),g(g(f(b)))). [ur(23,a,495,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1141 (T,wt=9): 3351 ->*_s0(h(g(f(a))),k(g(f(b)))). [ur(23,a,496,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1142 (A,wt=11): 371 ->_s0(U91(x,g(k(a))),U91(x,g(k(b)))). [ur(10,a,92,a)]. 43.002/43.002 43.002/43.002 given #1143 (F,wt=10): 8838 -->_s0(f(a),k(f(b))) | -->_s0(g(b),c) # answer(goal). [resolve(8707,b,14,b)]. 43.002/43.002 43.002/43.002 given #1144 (F,wt=12): 8710 -->*_s0(k(g(b)),k(k(f(b)))) | -->_s0(f(a),c) # answer(goal). [resolve(8094,a,347,b)]. 43.002/43.002 43.002/43.002 given #1145 (F,wt=12): 8716 -->_s0(g(b),k(f(b))) | -->_s0(k(f(a)),h(c)) # answer(goal). [resolve(8715,a,630,c)]. 43.002/43.002 43.002/43.002 given #1146 (F,wt=12): 8720 -->_s0(f(a),k(f(b))) | -->_s0(k(g(b)),h(c)) # answer(goal). [resolve(8715,a,397,c)]. 43.002/43.002 43.002/43.002 given #1147 (T,wt=9): 3352 ->*_s0(h(g(f(a))),h(g(f(b)))). [ur(23,a,496,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1148 (T,wt=9): 3363 ->*_s0(f(g(f(a))),f(g(f(b)))). [ur(23,a,497,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1149 (T,wt=9): 3410 ->*_s0(k(h(f(a))),k(k(f(b)))). [ur(23,a,502,a,b,309,a)]. 43.002/43.002 43.002/43.002 given #1150 (T,wt=9): 3411 ->*_s0(k(h(f(a))),k(h(f(b)))). [ur(23,a,502,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1151 (A,wt=11): 372 ->_s0(U91(g(k(a)),x),U91(g(k(b)),x)). [ur(9,a,92,a)]. 43.002/43.002 43.002/43.002 given #1152 (F,wt=12): 8848 -->_s0(b,f(b)) | -->_s0(k(f(a)),k(g(f(a)))) # answer(goal). [resolve(3331,a,632,c)]. 43.002/43.002 43.002/43.002 given #1153 (F,wt=10): 8981 -->_s0(b,f(b)) | -->_s0(f(a),g(f(a))) # answer(goal). [resolve(8848,b,14,b)]. 43.002/43.002 43.002/43.002 given #1154 (F,wt=12): 8874 -->_s0(b,f(b)) | -->_s0(k(f(a)),h(g(f(a)))) # answer(goal). [resolve(3351,a,632,c)]. 43.002/43.002 43.002/43.002 given #1155 (F,wt=13): 677 -->_s0(g(b),a) | -->_s0(k(f(a)),x) | -->*_s0(x,k(b)) # answer(goal). [resolve(657,a,23,c)]. 43.002/43.002 43.002/43.002 given #1156 (T,wt=9): 3421 ->*_s0(g(h(f(a))),g(k(f(b)))). [ur(23,a,503,a,b,316,a)]. 43.002/43.002 43.002/43.002 given #1157 (T,wt=9): 3422 ->*_s0(g(h(f(a))),g(h(f(b)))). [ur(23,a,503,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1158 (T,wt=9): 3432 ->*_s0(h(h(f(a))),h(k(f(b)))). [ur(23,a,504,a,b,324,a)]. 43.002/43.002 43.002/43.002 given #1159 (T,wt=9): 3433 ->*_s0(h(h(f(a))),k(k(f(b)))). [ur(23,a,504,a,b,323,a)]. 43.002/43.002 43.002/43.002 given #1160 (A,wt=11): 379 ->_s0(U91(x,h(k(a))),U91(x,h(k(b)))). [ur(10,a,93,a)]. 43.002/43.002 43.002/43.002 given #1161 (F,wt=10): 8984 -->_s0(g(b),a) | -->_s0(k(f(a)),h(b)) # answer(goal). [resolve(677,c,67,a)]. 43.002/43.002 43.002/43.002 given #1162 (F,wt=13): 767 -->_s0(k(g(b)),a) | -->_s0(b,x) | -->*_s0(x,k(f(a))) # answer(goal). [resolve(735,b,23,c)]. 43.002/43.002 43.002/43.002 given #1163 (F,wt=8): 9054 -->_s0(k(g(b)),a) | -->_s0(b,c) # answer(goal). [resolve(767,c,71,a)]. 43.002/43.002 43.002/43.002 given #1164 (F,wt=10): 9055 -->_s0(k(g(b)),a) | -->_s0(b,h(f(a))) # answer(goal). [resolve(767,c,67,a)]. 43.002/43.002 43.002/43.002 given #1165 (T,wt=9): 3434 ->*_s0(h(h(f(a))),k(h(f(b)))). [ur(23,a,504,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1166 (T,wt=9): 3435 ->*_s0(h(h(f(a))),h(h(f(b)))). [ur(23,a,504,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1167 (T,wt=9): 3445 ->*_s0(f(h(f(a))),f(k(f(b)))). [ur(23,a,505,a,b,331,a)]. 43.002/43.002 43.002/43.002 given #1168 (T,wt=9): 3447 ->*_s0(f(h(f(a))),f(h(f(b)))). [ur(23,a,505,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1169 (A,wt=11): 380 ->_s0(U91(h(k(a)),x),U91(h(k(b)),x)). [ur(9,a,93,a)]. 43.002/43.002 43.002/43.002 given #1170 (F,wt=10): 9057 -->_s0(k(g(b)),a) | -->_s0(b,k(f(a))) # answer(goal). [resolve(767,c,22,a)]. 43.002/43.002 43.002/43.002 given #1171 (F,wt=13): 820 -->*_s0(k(f(a)),g(x)) | -->_s0(k(g(b)),U91(c,x)) # answer(goal). [resolve(815,a,76,c)]. 43.002/43.002 43.002/43.002 given #1172 (F,wt=13): 821 -->*_s0(k(g(b)),g(x)) | -->_s0(k(f(a)),U91(c,x)) # answer(goal). [resolve(815,a,74,c)]. 43.002/43.002 43.002/43.002 given #1173 (F,wt=13): 830 -->*_s0(k(f(a)),g(b)) | -->_s0(k(g(b)),U91(c,a)) # answer(goal). [resolve(828,a,76,c)]. 43.002/43.002 43.002/43.002 given #1174 (T,wt=9): 3480 ->*_s0(k(f(f(a))),k(f(f(b)))). [ur(23,a,509,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1175 (T,wt=9): 3490 ->*_s0(g(f(f(a))),g(f(f(b)))). [ur(23,a,510,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1176 (T,wt=9): 3500 ->*_s0(h(f(f(a))),k(f(f(b)))). [ur(23,a,511,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #1177 (T,wt=9): 3501 ->*_s0(h(f(f(a))),h(f(f(b)))). [ur(23,a,511,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1178 (A,wt=11): 386 ->_s0(U91(x,f(k(a))),U91(x,f(k(b)))). [ur(10,a,94,a)]. 43.002/43.002 43.002/43.002 given #1179 (F,wt=12): 9125 -->_s0(a,f(b)) | -->_s0(k(g(b)),k(f(f(a)))) # answer(goal). [resolve(3480,a,445,c)]. 43.002/43.002 43.002/43.002 given #1180 (F,wt=10): 9190 -->_s0(a,f(b)) | -->_s0(g(b),f(f(a))) # answer(goal). [resolve(9125,b,14,b)]. 43.002/43.002 43.002/43.002 given #1181 (F,wt=12): 9148 -->_s0(a,f(b)) | -->_s0(k(g(b)),h(f(f(a)))) # answer(goal). [resolve(3500,a,445,c)]. 43.002/43.002 43.002/43.002 given #1182 (F,wt=13): 831 -->*_s0(k(g(b)),g(b)) | -->_s0(k(f(a)),U91(c,a)) # answer(goal). [resolve(828,a,74,c)]. 43.002/43.002 43.002/43.002 given #1183 (T,wt=9): 3512 ->*_s0(f(f(f(a))),f(f(f(b)))). [ur(23,a,512,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #1184 (T,wt=9): 3684 ->*_s0(U91(a,h(a)),U91(b,k(b))). [ur(23,a,109,a,b,669,a)]. 43.002/43.002 43.002/43.002 given #1185 (T,wt=9): 3823 ->*_s0(U91(x,h(a)),U91(x,k(b))). [ur(23,a,109,a,b,670,a)]. 43.002/43.002 43.002/43.002 given #1186 (T,wt=9): 3836 ->*_s0(U91(h(a),a),U91(k(b),b)). [ur(23,a,110,a,b,758,a)]. 43.002/43.002 43.002/43.002 given #1187 (A,wt=11): 387 ->_s0(U91(f(k(a)),x),U91(f(k(b)),x)). [ur(9,a,94,a)]. 43.002/43.002 43.002/43.002 given #1188 (F,wt=13): 843 -->_s0(k(U91(h(f(b)),b)),k(U91(k(g(b)),b))) # answer(goal). [ur(23,b,78,a,c,266,a)]. 43.002/43.002 43.002/43.002 given #1189 (F,wt=11): 9291 -->_s0(U91(h(f(b)),b),U91(k(g(b)),b)) # answer(goal). [resolve(843,a,14,b)]. 43.002/43.002 43.002/43.002 given #1190 (F,wt=7): 9292 -->_s0(h(f(b)),k(g(b))) # answer(goal). [resolve(9291,a,9,b)]. 43.002/43.002 43.002/43.002 given #1191 (F,wt=13): 844 -->_s0(k(U91(h(f(a)),a)),k(U91(k(g(b)),b))) # answer(goal). [ur(23,b,78,a,c,156,a)]. 43.002/43.002 43.002/43.002 given #1192 (T,wt=9): 3857 ->*_s0(U91(h(a),x),U91(k(b),x)). [ur(23,a,110,a,b,759,a)]. 43.002/43.002 43.002/43.002 given #1193 (T,wt=9): 4171 ->*_s0(k(U91(a,a)),k(U91(b,b))). [ur(23,a,170,a,b,1186,a)]. 43.002/43.002 43.002/43.002 given #1194 (T,wt=9): 4178 ->*_s0(g(U91(a,a)),g(U91(b,b))). [ur(23,a,171,a,b,1196,a)]. 43.002/43.002 43.002/43.002 given #1195 (T,wt=9): 4200 ->*_s0(h(U91(a,a)),k(U91(b,b))). [ur(23,a,172,a,b,1205,a)]. 43.002/43.002 43.002/43.002 given #1196 (A,wt=11): 389 ->_s0(k(U91(c,x)),k(U91(k(g(b)),x))). [ur(14,a,48,a)]. 43.002/43.002 43.002/43.002 given #1197 (F,wt=6): 9397 -->_s0(f(b),U91(c,b)) # answer(goal). [ur(265,b,389,a,c,78,a)]. 43.002/43.002 43.002/43.002 given #1198 (F,wt=6): 9399 -->_s0(f(a),U91(c,b)) # answer(goal). [ur(154,b,389,a,c,78,a)]. 43.002/43.002 43.002/43.002 given #1199 (F,wt=8): 9396 -->_s0(k(f(a)),k(U91(c,b))) # answer(goal). [ur(356,a,22,a,c,389,a,d,78,a)]. 43.002/43.002 43.002/43.002 given #1200 (F,wt=8): 9398 -->_s0(k(f(b)),k(U91(c,b))) # answer(goal). [ur(227,b,389,a,c,78,a)]. 43.002/43.002 43.002/43.002 given #1201 (T,wt=8): 9388 ->*_s0(k(U91(c,x)),k(g(x))). [ur(23,a,389,a,b,78,a)]. 43.002/43.002 43.002/43.002 ============================== PROOF ================================= 43.002/43.002 43.002/43.002 % Proof 1 at 0.24 (+ 0.00) seconds: goal. 43.002/43.002 % Length of proof is 31. 43.002/43.002 % Level of proof is 6. 43.002/43.002 % Maximum clause weight is 13.000. 43.002/43.002 % Given clauses 1201. 43.002/43.002 43.002/43.002 1 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(k(f(a)),x2) & ->*_s0(k(g(b)),x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(k(f(a)),x) | -->*_s0(k(g(b)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 25 ->_s0(k(U91(k(g(b)),x)),k(g(x))). [ur(14,a,15,a)]. 43.002/43.002 35 ->_s0(U91(x,a),U91(x,b)). [ur(10,a,16,a)]. 43.002/43.002 48 ->_s0(U91(c,x),U91(k(g(b)),x)). [ur(9,a,18,a)]. 43.002/43.002 49 ->_s0(k(f(x)),k(U91(h(f(x)),x))). [ur(14,a,19,a)]. 43.002/43.002 60 ->_s0(U91(h(f(a)),x),U91(c,x)). [ur(9,a,20,a)]. 43.002/43.002 77 -->*_s0(k(f(a)),k(g(b))) # answer(goal). [resolve(24,b,22,a)]. 43.002/43.002 78 ->*_s0(k(U91(k(g(b)),x)),k(g(x))). [ur(23,a,25,a,b,22,a)]. 43.002/43.002 87 -->_s0(k(f(a)),x) | -->*_s0(x,k(g(b))) # answer(goal). [resolve(77,a,23,c)]. 43.002/43.002 122 -->_s0(k(f(a)),x) | -->_s0(x,y) | -->*_s0(y,k(g(b))) # answer(goal). [resolve(87,b,23,c)]. 43.002/43.002 163 ->_s0(k(U91(x,a)),k(U91(x,b))). [ur(14,a,35,a)]. 43.002/43.002 389 ->_s0(k(U91(c,x)),k(U91(k(g(b)),x))). [ur(14,a,48,a)]. 43.002/43.002 647 ->_s0(k(U91(h(f(a)),x)),k(U91(c,x))). [ur(14,a,60,a)]. 43.002/43.002 1193 -->*_s0(k(U91(h(f(a)),b)),k(g(b))) # answer(goal). [ur(122,a,49,a,b,163,a)]. 43.002/43.002 9388 ->*_s0(k(U91(c,x)),k(g(x))). [ur(23,a,389,a,b,78,a)]. 43.002/43.002 9433 $F # answer(goal). [ur(23,b,9388,a,c,1193,a),unit_del(a,647)]. 43.002/43.002 43.002/43.002 ============================== end of proof ========================== 43.002/43.002 43.002/43.002 ============================== STATISTICS ============================ 43.002/43.002 43.002/43.002 Given=1201. Generated=10840. Kept=9424. proofs=1. 43.002/43.002 Usable=1201. Sos=8189. Demods=0. Limbo=33, Disabled=17. Hints=0. 43.002/43.002 Kept_by_rule=0, Deleted_by_rule=0. 43.002/43.002 Forward_subsumed=1415. Back_subsumed=1. 43.002/43.002 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 43.002/43.002 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 43.002/43.002 Demod_attempts=0. Demod_rewrites=0. 43.002/43.002 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 43.002/43.002 Nonunit_fsub_feature_tests=468342. Nonunit_bsub_feature_tests=9573. 43.002/43.002 Megabytes=13.62. 43.002/43.002 User_CPU=0.24, System_CPU=0.00, Wall_clock=1. 43.002/43.002 43.002/43.002 ============================== end of statistics ===================== 43.002/43.002 43.002/43.002 ============================== end of search ========================= 43.002/43.002 43.002/43.002 THEOREM PROVED 43.002/43.002 43.002/43.002 Exiting with 1 proof. 43.002/43.002 43.002/43.002 Process 120701 exit (max_proofs) Fri Jul 16 15:39:00 2021 43.002/43.002 43.002/43.002 43.002/43.002 The problem is feasible. 43.002/43.002 43.002/43.002 43.002/43.002 The problem is joinable. 43.002/43.002 43.002/43.002 Problem 1.2: 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 Critical Pairs: 43.002/43.002 => Not trivial, Not overlay, N2 43.002/43.002 Terminating:"YES" 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 Huet InfChecker Processor: 43.002/43.002 Infeasible convergence? 43.002/43.002 NO 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Infeasibility Problem: 43.002/43.002 [(VAR vNonEmpty:S x:S z:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (U91 1 2) 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 U91(k(g(b)),x:S) -> g(x:S) 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U91(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 )] 43.002/43.002 Infeasibility Conditions: 43.002/43.002 h(U91(h(f(a)),a)) ->* z:S, c ->* z:S 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Obtaining a proof using Prover9: 43.002/43.002 43.002/43.002 -> Prover9 Output: 43.002/43.002 ============================== Prover9 =============================== 43.002/43.002 Prover9 (64) version 2009-11A, November 2009. 43.002/43.002 Process 120778 was started by ubuntu on ubuntu, 43.002/43.002 Fri Jul 16 15:39:06 2021 43.002/43.002 The command was "./prover9 -f /tmp/prover9120769-0.in". 43.002/43.002 ============================== end of head =========================== 43.002/43.002 43.002/43.002 ============================== INPUT ================================= 43.002/43.002 43.002/43.002 % Reading from file /tmp/prover9120769-0.in 43.002/43.002 43.002/43.002 assign(max_seconds,20). 43.002/43.002 43.002/43.002 formulas(assumptions). 43.002/43.002 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence). 43.002/43.002 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 43.002/43.002 ->_s0(U91(k(g(b)),x1),g(x1)) # label(replacement). 43.002/43.002 ->_s0(a,b) # label(replacement). 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). 43.002/43.002 ->_s0(f(x1),U91(h(f(x1)),x1)) # label(replacement). 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). 43.002/43.002 ->_s0(h(x1),k(x1)) # label(replacement). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). 43.002/43.002 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(goals). 43.002/43.002 (exists x2 (->*_s0(h(U91(h(f(a)),a)),x2) & ->*_s0(c,x2))) # label(goal). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of input ========================== 43.002/43.002 43.002/43.002 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 43.002/43.002 43.002/43.002 % Formulas that are not ordinary clauses: 43.002/43.002 1 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 4 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 5 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(h(U91(h(f(a)),a)),x2) & ->*_s0(c,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 43.002/43.002 ============================== end of process non-clausal formulas === 43.002/43.002 43.002/43.002 ============================== PROCESS INITIAL CLAUSES =============== 43.002/43.002 43.002/43.002 % Clauses before input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 -->*_s0(h(U91(h(f(a)),a)),x) | -->*_s0(c,x) # label(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== PREDICATE ELIMINATION ================= 43.002/43.002 43.002/43.002 No predicates eliminated. 43.002/43.002 43.002/43.002 ============================== end predicate elimination ============= 43.002/43.002 43.002/43.002 Auto_denials: 43.002/43.002 % copying label goal to answer in negative clause 43.002/43.002 43.002/43.002 Term ordering decisions: 43.002/43.002 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 43.002/43.002 Function symbol precedence: function_order([ a, c, b, U91, k, f, h, g ]). 43.002/43.002 After inverse_order: (no changes). 43.002/43.002 Unfolding symbols: (none). 43.002/43.002 43.002/43.002 Auto_inference settings: 43.002/43.002 % set(neg_binary_resolution). % (HNE depth_diff=-6) 43.002/43.002 % clear(ordered_res). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution) -> set(pos_ur_resolution). 43.002/43.002 % set(ur_resolution) -> set(neg_ur_resolution). 43.002/43.002 43.002/43.002 Auto_process settings: 43.002/43.002 % set(unit_deletion). % (Horn set with negative nonunits) 43.002/43.002 43.002/43.002 kept: 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 kept: 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 kept: 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 kept: 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 kept: 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 kept: 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 kept: 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 kept: 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 kept: 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 kept: 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 kept: 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 kept: 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 kept: 24 -->*_s0(h(U91(h(f(a)),a)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 ============================== end of process initial clauses ======== 43.002/43.002 43.002/43.002 ============================== CLAUSES FOR SEARCH ==================== 43.002/43.002 43.002/43.002 % Clauses after input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(h(U91(h(f(a)),a)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of clauses for search ============= 43.002/43.002 43.002/43.002 ============================== SEARCH ================================ 43.002/43.002 43.002/43.002 % Starting search at 0.00 seconds. 43.002/43.002 43.002/43.002 given #1 (I,wt=10): 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 43.002/43.002 given #2 (I,wt=10): 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 43.002/43.002 given #3 (I,wt=8): 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 43.002/43.002 given #4 (I,wt=8): 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 43.002/43.002 given #5 (I,wt=8): 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 43.002/43.002 given #6 (I,wt=8): 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 43.002/43.002 given #7 (I,wt=8): 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #8 (I,wt=3): 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #9 (I,wt=5): 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #10 (I,wt=5): 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #11 (I,wt=8): 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #12 (I,wt=5): 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #13 (I,wt=5): 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #14 (I,wt=3): 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 43.002/43.002 given #15 (I,wt=9): 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 43.002/43.002 given #16 (I,wt=11): 24 -->*_s0(h(U91(h(f(a)),a)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 given #17 (A,wt=10): 25 ->_s0(k(U91(k(g(b)),x)),k(g(x))). [ur(14,a,15,a)]. 43.002/43.002 43.002/43.002 given #18 (F,wt=8): 75 -->*_s0(c,h(U91(h(f(a)),a))) # answer(goal). [resolve(24,a,22,a)]. 43.002/43.002 43.002/43.002 given #19 (F,wt=8): 77 -->*_s0(h(U91(h(f(a)),a)),c) # answer(goal). [resolve(24,b,22,a)]. 43.002/43.002 43.002/43.002 given #20 (F,wt=8): 86 -->_s0(c,h(U91(h(f(a)),a))) # answer(goal). [ur(23,b,22,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #21 (F,wt=8): 90 -->_s0(h(U91(h(f(a)),a)),c) # answer(goal). [ur(23,b,22,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #22 (T,wt=3): 72 ->*_s0(a,b). [ur(23,a,16,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #23 (T,wt=5): 31 ->_s0(k(a),k(b)). [ur(14,a,16,a)]. 43.002/43.002 43.002/43.002 given #24 (T,wt=5): 32 ->_s0(g(a),g(b)). [ur(13,a,16,a)]. 43.002/43.002 43.002/43.002 given #25 (T,wt=5): 33 ->_s0(h(a),h(b)). [ur(12,a,16,a)]. 43.002/43.002 43.002/43.002 given #26 (A,wt=10): 26 ->_s0(g(U91(k(g(b)),x)),g(g(x))). [ur(13,a,15,a)]. 43.002/43.002 43.002/43.002 given #27 (F,wt=8): 91 -->*_s0(k(U91(h(f(a)),a)),c) # answer(goal). [ur(23,a,21,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #28 (F,wt=8): 121 -->_s0(k(U91(h(f(a)),a)),c) # answer(goal). [ur(23,b,22,a,c,91,a)]. 43.002/43.002 43.002/43.002 given #29 (F,wt=10): 87 -->*_s0(k(g(b)),h(U91(h(f(a)),a))) # answer(goal). [ur(23,a,18,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #30 (F,wt=10): 88 -->*_s0(k(f(a)),h(U91(h(f(a)),a))) # answer(goal). [ur(23,a,17,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #31 (T,wt=5): 34 ->_s0(f(a),f(b)). [ur(11,a,16,a)]. 43.002/43.002 43.002/43.002 given #32 (T,wt=5): 67 ->*_s0(h(x),k(x)). [ur(23,a,21,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #33 (T,wt=5): 68 ->*_s0(h(f(a)),c). [ur(23,a,20,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #34 (T,wt=5): 70 ->*_s0(c,k(g(b))). [ur(23,a,18,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #35 (A,wt=10): 27 ->_s0(h(U91(k(g(b)),x)),h(g(x))). [ur(12,a,15,a)]. 43.002/43.002 43.002/43.002 given #36 (F,wt=8): 133 -->*_s0(c,k(U91(h(f(a)),a))) # answer(goal). [resolve(67,a,24,a)]. 43.002/43.002 43.002/43.002 given #37 (F,wt=8): 148 -->_s0(c,k(U91(h(f(a)),a))) # answer(goal). [ur(23,b,22,a,c,133,a)]. 43.002/43.002 43.002/43.002 given #38 (F,wt=10): 123 -->_s0(k(g(b)),h(U91(h(f(a)),a))) # answer(goal). [ur(23,b,22,a,c,87,a)]. 43.002/43.002 43.002/43.002 given #39 (F,wt=10): 125 -->_s0(k(f(a)),h(U91(h(f(a)),a))) # answer(goal). [ur(23,b,22,a,c,88,a)]. 43.002/43.002 43.002/43.002 given #40 (T,wt=5): 71 ->*_s0(c,k(f(a))). [ur(23,a,17,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #41 (T,wt=5): 92 ->*_s0(k(a),k(b)). [ur(23,a,31,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #42 (T,wt=5): 99 ->*_s0(g(a),g(b)). [ur(23,a,32,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #43 (T,wt=5): 106 ->*_s0(h(a),h(b)). [ur(23,a,33,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #44 (A,wt=10): 28 ->_s0(f(U91(k(g(b)),x)),f(g(x))). [ur(11,a,15,a)]. 43.002/43.002 43.002/43.002 given #45 (F,wt=10): 135 -->_s0(k(U91(h(f(a)),a)),h(f(a))) # answer(goal). [ur(23,b,68,a,c,91,a)]. 43.002/43.002 43.002/43.002 given #46 (F,wt=10): 136 -->_s0(h(U91(h(f(a)),a)),h(f(a))) # answer(goal). [ur(23,b,68,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #47 (F,wt=8): 160 -->_s0(U91(h(f(a)),a),f(a)) # answer(goal). [resolve(136,a,12,b)]. 43.002/43.002 43.002/43.002 given #48 (F,wt=10): 137 -->*_s0(h(U91(h(f(a)),a)),k(g(b))) # answer(goal). [resolve(70,a,24,b)]. 43.002/43.002 43.002/43.002 given #49 (T,wt=5): 126 ->*_s0(f(a),f(b)). [ur(23,a,34,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #50 (T,wt=5): 134 ->*_s0(h(a),k(b)). [ur(23,a,33,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #51 (T,wt=7): 35 ->_s0(U91(x,a),U91(x,b)). [ur(10,a,16,a)]. 43.002/43.002 43.002/43.002 given #52 (T,wt=7): 36 ->_s0(U91(a,x),U91(b,x)). [ur(9,a,16,a)]. 43.002/43.002 43.002/43.002 given #53 (A,wt=12): 29 ->_s0(U91(x,U91(k(g(b)),y)),U91(x,g(y))). [ur(10,a,15,a)]. 43.002/43.002 43.002/43.002 given #54 (F,wt=10): 149 -->*_s0(k(g(b)),k(U91(h(f(a)),a))) # answer(goal). [ur(23,a,18,a,c,133,a)]. 43.002/43.002 43.002/43.002 given #55 (F,wt=10): 150 -->*_s0(k(f(a)),k(U91(h(f(a)),a))) # answer(goal). [ur(23,a,17,a,c,133,a)]. 43.002/43.002 43.002/43.002 ============================== PROOF ================================= 43.002/43.002 43.002/43.002 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 43.002/43.002 % Length of proof is 15. 43.002/43.002 % Level of proof is 5. 43.002/43.002 % Maximum clause weight is 11.000. 43.002/43.002 % Given clauses 55. 43.002/43.002 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(h(U91(h(f(a)),a)),x2) & ->*_s0(c,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(h(U91(h(f(a)),a)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 49 ->_s0(k(f(x)),k(U91(h(f(x)),x))). [ur(14,a,19,a)]. 43.002/43.002 67 ->*_s0(h(x),k(x)). [ur(23,a,21,a,b,22,a)]. 43.002/43.002 133 -->*_s0(c,k(U91(h(f(a)),a))) # answer(goal). [resolve(67,a,24,a)]. 43.002/43.002 150 -->*_s0(k(f(a)),k(U91(h(f(a)),a))) # answer(goal). [ur(23,a,17,a,c,133,a)]. 43.002/43.002 189 $F # answer(goal). [ur(23,b,22,a,c,150,a),unit_del(a,49)]. 43.002/43.002 43.002/43.002 ============================== end of proof ========================== 43.002/43.002 43.002/43.002 ============================== STATISTICS ============================ 43.002/43.002 43.002/43.002 Given=55. Generated=193. Kept=180. proofs=1. 43.002/43.002 Usable=55. Sos=124. Demods=0. Limbo=1, Disabled=16. Hints=0. 43.002/43.002 Kept_by_rule=0, Deleted_by_rule=0. 43.002/43.002 Forward_subsumed=12. Back_subsumed=0. 43.002/43.002 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 43.002/43.002 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 43.002/43.002 Demod_attempts=0. Demod_rewrites=0. 43.002/43.002 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 43.002/43.002 Nonunit_fsub_feature_tests=7. Nonunit_bsub_feature_tests=56. 43.002/43.002 Megabytes=0.37. 43.002/43.002 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 43.002/43.002 43.002/43.002 ============================== end of statistics ===================== 43.002/43.002 43.002/43.002 ============================== end of search ========================= 43.002/43.002 43.002/43.002 THEOREM PROVED 43.002/43.002 43.002/43.002 Exiting with 1 proof. 43.002/43.002 43.002/43.002 Process 120778 exit (max_proofs) Fri Jul 16 15:39:06 2021 43.002/43.002 43.002/43.002 43.002/43.002 The problem is feasible. 43.002/43.002 43.002/43.002 43.002/43.002 The problem is joinable. 43.002/43.002 43.002/43.002 Problem 1.3: 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 Critical Pairs: 43.002/43.002 => Not trivial, Not overlay, N3 43.002/43.002 Terminating:"YES" 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 Huet InfChecker Processor: 43.002/43.002 Infeasible convergence? 43.002/43.002 NO 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Infeasibility Problem: 43.002/43.002 [(VAR vNonEmpty:S x:S z:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (U91 1 2) 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 U91(k(g(b)),x:S) -> g(x:S) 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U91(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 )] 43.002/43.002 Infeasibility Conditions: 43.002/43.002 h(f(b)) ->* z:S, c ->* z:S 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Obtaining a proof using Prover9: 43.002/43.002 43.002/43.002 -> Prover9 Output: 43.002/43.002 ============================== Prover9 =============================== 43.002/43.002 Prover9 (64) version 2009-11A, November 2009. 43.002/43.002 Process 120800 was started by ubuntu on ubuntu, 43.002/43.002 Fri Jul 16 15:39:06 2021 43.002/43.002 The command was "./prover9 -f /tmp/prover9120791-0.in". 43.002/43.002 ============================== end of head =========================== 43.002/43.002 43.002/43.002 ============================== INPUT ================================= 43.002/43.002 43.002/43.002 % Reading from file /tmp/prover9120791-0.in 43.002/43.002 43.002/43.002 assign(max_seconds,20). 43.002/43.002 43.002/43.002 formulas(assumptions). 43.002/43.002 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence). 43.002/43.002 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 43.002/43.002 ->_s0(U91(k(g(b)),x1),g(x1)) # label(replacement). 43.002/43.002 ->_s0(a,b) # label(replacement). 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). 43.002/43.002 ->_s0(f(x1),U91(h(f(x1)),x1)) # label(replacement). 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). 43.002/43.002 ->_s0(h(x1),k(x1)) # label(replacement). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). 43.002/43.002 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(goals). 43.002/43.002 (exists x2 (->*_s0(h(f(b)),x2) & ->*_s0(c,x2))) # label(goal). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of input ========================== 43.002/43.002 43.002/43.002 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 43.002/43.002 43.002/43.002 % Formulas that are not ordinary clauses: 43.002/43.002 1 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 4 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 5 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(h(f(b)),x2) & ->*_s0(c,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 43.002/43.002 ============================== end of process non-clausal formulas === 43.002/43.002 43.002/43.002 ============================== PROCESS INITIAL CLAUSES =============== 43.002/43.002 43.002/43.002 % Clauses before input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 -->*_s0(h(f(b)),x) | -->*_s0(c,x) # label(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== PREDICATE ELIMINATION ================= 43.002/43.002 43.002/43.002 No predicates eliminated. 43.002/43.002 43.002/43.002 ============================== end predicate elimination ============= 43.002/43.002 43.002/43.002 Auto_denials: 43.002/43.002 % copying label goal to answer in negative clause 43.002/43.002 43.002/43.002 Term ordering decisions: 43.002/43.002 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 43.002/43.002 Function symbol precedence: function_order([ a, c, b, U91, k, f, h, g ]). 43.002/43.002 After inverse_order: (no changes). 43.002/43.002 Unfolding symbols: (none). 43.002/43.002 43.002/43.002 Auto_inference settings: 43.002/43.002 % set(neg_binary_resolution). % (HNE depth_diff=-6) 43.002/43.002 % clear(ordered_res). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution) -> set(pos_ur_resolution). 43.002/43.002 % set(ur_resolution) -> set(neg_ur_resolution). 43.002/43.002 43.002/43.002 Auto_process settings: 43.002/43.002 % set(unit_deletion). % (Horn set with negative nonunits) 43.002/43.002 43.002/43.002 kept: 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 kept: 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 kept: 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 kept: 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 kept: 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 kept: 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 kept: 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 kept: 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 kept: 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 kept: 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 kept: 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 kept: 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 kept: 24 -->*_s0(h(f(b)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 ============================== end of process initial clauses ======== 43.002/43.002 43.002/43.002 ============================== CLAUSES FOR SEARCH ==================== 43.002/43.002 43.002/43.002 % Clauses after input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(h(f(b)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of clauses for search ============= 43.002/43.002 43.002/43.002 ============================== SEARCH ================================ 43.002/43.002 43.002/43.002 % Starting search at 0.00 seconds. 43.002/43.002 43.002/43.002 given #1 (I,wt=10): 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 43.002/43.002 given #2 (I,wt=10): 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 43.002/43.002 given #3 (I,wt=8): 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 43.002/43.002 given #4 (I,wt=8): 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 43.002/43.002 given #5 (I,wt=8): 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 43.002/43.002 given #6 (I,wt=8): 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 43.002/43.002 given #7 (I,wt=8): 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #8 (I,wt=3): 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #9 (I,wt=5): 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #10 (I,wt=5): 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #11 (I,wt=8): 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #12 (I,wt=5): 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #13 (I,wt=5): 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #14 (I,wt=3): 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 43.002/43.002 given #15 (I,wt=9): 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 43.002/43.002 given #16 (I,wt=8): 24 -->*_s0(h(f(b)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 given #17 (A,wt=10): 25 ->_s0(k(U91(k(g(b)),x)),k(g(x))). [ur(14,a,15,a)]. 43.002/43.002 43.002/43.002 given #18 (F,wt=5): 75 -->*_s0(c,h(f(b))) # answer(goal). [resolve(24,a,22,a)]. 43.002/43.002 43.002/43.002 given #19 (F,wt=5): 77 -->*_s0(h(f(b)),c) # answer(goal). [resolve(24,b,22,a)]. 43.002/43.002 43.002/43.002 given #20 (F,wt=5): 86 -->_s0(c,h(f(b))) # answer(goal). [ur(23,b,22,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #21 (F,wt=5): 90 -->_s0(h(f(b)),c) # answer(goal). [ur(23,b,22,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #22 (T,wt=3): 72 ->*_s0(a,b). [ur(23,a,16,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #23 (T,wt=5): 31 ->_s0(k(a),k(b)). [ur(14,a,16,a)]. 43.002/43.002 43.002/43.002 given #24 (T,wt=5): 32 ->_s0(g(a),g(b)). [ur(13,a,16,a)]. 43.002/43.002 43.002/43.002 given #25 (T,wt=5): 33 ->_s0(h(a),h(b)). [ur(12,a,16,a)]. 43.002/43.002 43.002/43.002 given #26 (A,wt=10): 26 ->_s0(g(U91(k(g(b)),x)),g(g(x))). [ur(13,a,15,a)]. 43.002/43.002 43.002/43.002 given #27 (F,wt=5): 91 -->*_s0(k(f(b)),c) # answer(goal). [ur(23,a,21,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #28 (F,wt=5): 121 -->_s0(k(f(b)),c) # answer(goal). [ur(23,b,22,a,c,91,a)]. 43.002/43.002 43.002/43.002 given #29 (F,wt=7): 87 -->*_s0(k(g(b)),h(f(b))) # answer(goal). [ur(23,a,18,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #30 (F,wt=7): 88 -->*_s0(k(f(a)),h(f(b))) # answer(goal). [ur(23,a,17,a,c,75,a)]. 43.002/43.002 43.002/43.002 given #31 (T,wt=5): 34 ->_s0(f(a),f(b)). [ur(11,a,16,a)]. 43.002/43.002 43.002/43.002 given #32 (T,wt=5): 67 ->*_s0(h(x),k(x)). [ur(23,a,21,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #33 (T,wt=5): 68 ->*_s0(h(f(a)),c). [ur(23,a,20,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #34 (T,wt=5): 70 ->*_s0(c,k(g(b))). [ur(23,a,18,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #35 (A,wt=10): 27 ->_s0(h(U91(k(g(b)),x)),h(g(x))). [ur(12,a,15,a)]. 43.002/43.002 43.002/43.002 given #36 (F,wt=5): 133 -->*_s0(c,k(f(b))) # answer(goal). [resolve(67,a,24,a)]. 43.002/43.002 43.002/43.002 given #37 (F,wt=5): 148 -->_s0(c,k(f(b))) # answer(goal). [ur(23,b,22,a,c,133,a)]. 43.002/43.002 43.002/43.002 given #38 (F,wt=7): 123 -->_s0(k(g(b)),h(f(b))) # answer(goal). [ur(23,b,22,a,c,87,a)]. 43.002/43.002 43.002/43.002 given #39 (F,wt=7): 125 -->_s0(k(f(a)),h(f(b))) # answer(goal). [ur(23,b,22,a,c,88,a)]. 43.002/43.002 43.002/43.002 given #40 (T,wt=5): 71 ->*_s0(c,k(f(a))). [ur(23,a,17,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #41 (T,wt=5): 92 ->*_s0(k(a),k(b)). [ur(23,a,31,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #42 (T,wt=5): 99 ->*_s0(g(a),g(b)). [ur(23,a,32,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #43 (T,wt=5): 106 ->*_s0(h(a),h(b)). [ur(23,a,33,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #44 (A,wt=10): 28 ->_s0(f(U91(k(g(b)),x)),f(g(x))). [ur(11,a,15,a)]. 43.002/43.002 43.002/43.002 given #45 (F,wt=7): 135 -->_s0(k(f(b)),h(f(a))) # answer(goal). [ur(23,b,68,a,c,91,a)]. 43.002/43.002 43.002/43.002 given #46 (F,wt=7): 136 -->_s0(h(f(b)),h(f(a))) # answer(goal). [ur(23,b,68,a,c,77,a)]. 43.002/43.002 43.002/43.002 given #47 (F,wt=5): 160 -->_s0(f(b),f(a)) # answer(goal). [resolve(136,a,12,b)]. 43.002/43.002 43.002/43.002 given #48 (F,wt=3): 161 -->_s0(b,a) # answer(goal). [resolve(160,a,11,b)]. 43.002/43.002 43.002/43.002 given #49 (T,wt=5): 126 ->*_s0(f(a),f(b)). [ur(23,a,34,a,b,22,a)]. 43.002/43.002 43.002/43.002 given #50 (T,wt=5): 134 ->*_s0(h(a),k(b)). [ur(23,a,33,a,b,67,a)]. 43.002/43.002 43.002/43.002 given #51 (T,wt=7): 35 ->_s0(U91(x,a),U91(x,b)). [ur(10,a,16,a)]. 43.002/43.002 43.002/43.002 given #52 (T,wt=7): 36 ->_s0(U91(a,x),U91(b,x)). [ur(9,a,16,a)]. 43.002/43.002 43.002/43.002 given #53 (A,wt=12): 29 ->_s0(U91(x,U91(k(g(b)),y)),U91(x,g(y))). [ur(10,a,15,a)]. 43.002/43.002 43.002/43.002 given #54 (F,wt=7): 137 -->*_s0(h(f(b)),k(g(b))) # answer(goal). [resolve(70,a,24,b)]. 43.002/43.002 43.002/43.002 given #55 (F,wt=7): 149 -->*_s0(k(g(b)),k(f(b))) # answer(goal). [ur(23,a,18,a,c,133,a)]. 43.002/43.002 43.002/43.002 given #56 (F,wt=7): 150 -->*_s0(k(f(a)),k(f(b))) # answer(goal). [ur(23,a,17,a,c,133,a)]. 43.002/43.002 43.002/43.002 ============================== PROOF ================================= 43.002/43.002 43.002/43.002 % Proof 1 at 0.01 (+ 0.00) seconds: goal. 43.002/43.002 % Length of proof is 18. 43.002/43.002 % Level of proof is 5. 43.002/43.002 % Maximum clause weight is 9.000. 43.002/43.002 % Given clauses 56. 43.002/43.002 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(h(f(b)),x2) & ->*_s0(c,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(h(f(b)),x) | -->*_s0(c,x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 34 ->_s0(f(a),f(b)). [ur(11,a,16,a)]. 43.002/43.002 67 ->*_s0(h(x),k(x)). [ur(23,a,21,a,b,22,a)]. 43.002/43.002 127 ->_s0(k(f(a)),k(f(b))). [ur(14,a,34,a)]. 43.002/43.002 133 -->*_s0(c,k(f(b))) # answer(goal). [resolve(67,a,24,a)]. 43.002/43.002 150 -->*_s0(k(f(a)),k(f(b))) # answer(goal). [ur(23,a,17,a,c,133,a)]. 43.002/43.002 190 $F # answer(goal). [ur(23,b,22,a,c,150,a),unit_del(a,127)]. 43.002/43.002 43.002/43.002 ============================== end of proof ========================== 43.002/43.002 43.002/43.002 ============================== STATISTICS ============================ 43.002/43.002 43.002/43.002 Given=56. Generated=195. Kept=181. proofs=1. 43.002/43.002 Usable=56. Sos=124. Demods=0. Limbo=1, Disabled=16. Hints=0. 43.002/43.002 Kept_by_rule=0, Deleted_by_rule=0. 43.002/43.002 Forward_subsumed=13. Back_subsumed=0. 43.002/43.002 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 43.002/43.002 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 43.002/43.002 Demod_attempts=0. Demod_rewrites=0. 43.002/43.002 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 43.002/43.002 Nonunit_fsub_feature_tests=7. Nonunit_bsub_feature_tests=57. 43.002/43.002 Megabytes=0.35. 43.002/43.002 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. 43.002/43.002 43.002/43.002 ============================== end of statistics ===================== 43.002/43.002 43.002/43.002 ============================== end of search ========================= 43.002/43.002 43.002/43.002 THEOREM PROVED 43.002/43.002 43.002/43.002 Exiting with 1 proof. 43.002/43.002 43.002/43.002 Process 120800 exit (max_proofs) Fri Jul 16 15:39:06 2021 43.002/43.002 43.002/43.002 43.002/43.002 The problem is feasible. 43.002/43.002 43.002/43.002 43.002/43.002 The problem is joinable. 43.002/43.002 43.002/43.002 Problem 1.4: 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 Confluence Problem: 43.002/43.002 (VAR x:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 (U9_1 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U9_1(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 U9_1(k(g(b)),x:S) -> g(x:S) 43.002/43.002 ) 43.002/43.002 Critical Pairs: 43.002/43.002 => Not trivial, Overlay, N4 43.002/43.002 Terminating:"YES" 43.002/43.002 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 43.002/43.002 43.002/43.002 Huet InfChecker Processor: 43.002/43.002 Infeasible convergence? 43.002/43.002 NO 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Infeasibility Problem: 43.002/43.002 [(VAR vNonEmpty:S x:S z:S) 43.002/43.002 (STRATEGY CONTEXTSENSITIVE 43.002/43.002 (U91 1 2) 43.002/43.002 (a) 43.002/43.002 (c) 43.002/43.002 (f 1) 43.002/43.002 (h 1) 43.002/43.002 (b) 43.002/43.002 (fSNonEmpty) 43.002/43.002 (g 1) 43.002/43.002 (k 1) 43.002/43.002 ) 43.002/43.002 (RULES 43.002/43.002 U91(k(g(b)),x:S) -> g(x:S) 43.002/43.002 a -> b 43.002/43.002 c -> k(f(a)) 43.002/43.002 c -> k(g(b)) 43.002/43.002 f(x:S) -> U91(h(f(x:S)),x:S) 43.002/43.002 h(f(a)) -> c 43.002/43.002 h(x:S) -> k(x:S) 43.002/43.002 )] 43.002/43.002 Infeasibility Conditions: 43.002/43.002 c ->* z:S, k(f(a)) ->* z:S 43.002/43.002 43.002/43.002 Problem 1: 43.002/43.002 43.002/43.002 Obtaining a proof using Prover9: 43.002/43.002 43.002/43.002 -> Prover9 Output: 43.002/43.002 ============================== Prover9 =============================== 43.002/43.002 Prover9 (64) version 2009-11A, November 2009. 43.002/43.002 Process 120822 was started by ubuntu on ubuntu, 43.002/43.002 Fri Jul 16 15:39:06 2021 43.002/43.002 The command was "./prover9 -f /tmp/prover9120813-0.in". 43.002/43.002 ============================== end of head =========================== 43.002/43.002 43.002/43.002 ============================== INPUT ================================= 43.002/43.002 43.002/43.002 % Reading from file /tmp/prover9120813-0.in 43.002/43.002 43.002/43.002 assign(max_seconds,20). 43.002/43.002 43.002/43.002 formulas(assumptions). 43.002/43.002 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence). 43.002/43.002 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence). 43.002/43.002 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 43.002/43.002 ->_s0(U91(k(g(b)),x1),g(x1)) # label(replacement). 43.002/43.002 ->_s0(a,b) # label(replacement). 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). 43.002/43.002 ->_s0(f(x1),U91(h(f(x1)),x1)) # label(replacement). 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). 43.002/43.002 ->_s0(h(x1),k(x1)) # label(replacement). 43.002/43.002 ->*_s0(x,x) # label(reflexivity). 43.002/43.002 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(goals). 43.002/43.002 (exists x2 (->*_s0(c,x2) & ->*_s0(k(f(a)),x2))) # label(goal). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of input ========================== 43.002/43.002 43.002/43.002 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 43.002/43.002 43.002/43.002 % Formulas that are not ordinary clauses: 43.002/43.002 1 ->_s0(x1,y) -> ->_s0(U91(x1,x2),U91(y,x2)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 2 ->_s0(x2,y) -> ->_s0(U91(x1,x2),U91(x1,y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 3 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 4 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 5 ->_s0(x1,y) -> ->_s0(g(x1),g(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 6 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(c,x2) & ->*_s0(k(f(a)),x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 43.002/43.002 ============================== end of process non-clausal formulas === 43.002/43.002 43.002/43.002 ============================== PROCESS INITIAL CLAUSES =============== 43.002/43.002 43.002/43.002 % Clauses before input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 -->*_s0(c,x) | -->*_s0(k(f(a)),x) # label(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== PREDICATE ELIMINATION ================= 43.002/43.002 43.002/43.002 No predicates eliminated. 43.002/43.002 43.002/43.002 ============================== end predicate elimination ============= 43.002/43.002 43.002/43.002 Auto_denials: 43.002/43.002 % copying label goal to answer in negative clause 43.002/43.002 43.002/43.002 Term ordering decisions: 43.002/43.002 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 43.002/43.002 Function symbol precedence: function_order([ a, c, b, U91, k, f, h, g ]). 43.002/43.002 After inverse_order: (no changes). 43.002/43.002 Unfolding symbols: (none). 43.002/43.002 43.002/43.002 Auto_inference settings: 43.002/43.002 % set(neg_binary_resolution). % (HNE depth_diff=-6) 43.002/43.002 % clear(ordered_res). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution). % (HNE depth_diff=-6) 43.002/43.002 % set(ur_resolution) -> set(pos_ur_resolution). 43.002/43.002 % set(ur_resolution) -> set(neg_ur_resolution). 43.002/43.002 43.002/43.002 Auto_process settings: 43.002/43.002 % set(unit_deletion). % (Horn set with negative nonunits) 43.002/43.002 43.002/43.002 kept: 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 kept: 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 kept: 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 kept: 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 kept: 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 kept: 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 kept: 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 kept: 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 kept: 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 kept: 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 kept: 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 kept: 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 kept: 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 kept: 24 -->*_s0(c,x) | -->*_s0(k(f(a)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 ============================== end of process initial clauses ======== 43.002/43.002 43.002/43.002 ============================== CLAUSES FOR SEARCH ==================== 43.002/43.002 43.002/43.002 % Clauses after input processing: 43.002/43.002 43.002/43.002 formulas(usable). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(sos). 43.002/43.002 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(c,x) | -->*_s0(k(f(a)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 formulas(demodulators). 43.002/43.002 end_of_list. 43.002/43.002 43.002/43.002 ============================== end of clauses for search ============= 43.002/43.002 43.002/43.002 ============================== SEARCH ================================ 43.002/43.002 43.002/43.002 % Starting search at 0.00 seconds. 43.002/43.002 43.002/43.002 given #1 (I,wt=10): 9 -->_s0(x,y) | ->_s0(U91(x,z),U91(y,z)) # label(congruence). [clausify(1)]. 43.002/43.002 43.002/43.002 given #2 (I,wt=10): 10 -->_s0(x,y) | ->_s0(U91(z,x),U91(z,y)) # label(congruence). [clausify(2)]. 43.002/43.002 43.002/43.002 given #3 (I,wt=8): 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(3)]. 43.002/43.002 43.002/43.002 given #4 (I,wt=8): 12 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(4)]. 43.002/43.002 43.002/43.002 given #5 (I,wt=8): 13 -->_s0(x,y) | ->_s0(g(x),g(y)) # label(congruence). [clausify(5)]. 43.002/43.002 43.002/43.002 given #6 (I,wt=8): 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(6)]. 43.002/43.002 43.002/43.002 given #7 (I,wt=8): 15 ->_s0(U91(k(g(b)),x),g(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #8 (I,wt=3): 16 ->_s0(a,b) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #9 (I,wt=5): 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #10 (I,wt=5): 18 ->_s0(c,k(g(b))) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #11 (I,wt=8): 19 ->_s0(f(x),U91(h(f(x)),x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #12 (I,wt=5): 20 ->_s0(h(f(a)),c) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #13 (I,wt=5): 21 ->_s0(h(x),k(x)) # label(replacement). [assumption]. 43.002/43.002 43.002/43.002 given #14 (I,wt=3): 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 43.002/43.002 given #15 (I,wt=9): 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 43.002/43.002 given #16 (I,wt=8): 24 -->*_s0(c,x) | -->*_s0(k(f(a)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 43.002/43.002 ============================== PROOF ================================= 43.002/43.002 43.002/43.002 % Proof 1 at 0.01 (+ 0.00) seconds: goal. 43.002/43.002 % Length of proof is 8. 43.002/43.002 % Level of proof is 3. 43.002/43.002 % Maximum clause weight is 9.000. 43.002/43.002 % Given clauses 16. 43.002/43.002 43.002/43.002 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 43.002/43.002 8 (exists x2 (->*_s0(c,x2) & ->*_s0(k(f(a)),x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 43.002/43.002 17 ->_s0(c,k(f(a))) # label(replacement). [assumption]. 43.002/43.002 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 43.002/43.002 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 43.002/43.002 24 -->*_s0(c,x) | -->*_s0(k(f(a)),x) # label(goal) # answer(goal). [deny(8)]. 43.002/43.002 71 ->*_s0(c,k(f(a))). [ur(23,a,17,a,b,22,a)]. 43.002/43.002 77 $F # answer(goal). [resolve(24,b,22,a),unit_del(a,71)]. 43.002/43.002 43.002/43.002 ============================== end of proof ========================== 43.002/43.002 43.002/43.002 ============================== STATISTICS ============================ 43.002/43.002 43.002/43.002 Given=16. Generated=69. Kept=68. proofs=1. 43.002/43.002 Usable=16. Sos=49. Demods=0. Limbo=3, Disabled=16. Hints=0. 43.002/43.002 Kept_by_rule=0, Deleted_by_rule=0. 43.002/43.002 Forward_subsumed=0. Back_subsumed=0. 43.002/43.002 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 43.002/43.002 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 43.002/43.002 Demod_attempts=0. Demod_rewrites=0. 43.002/43.002 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 43.002/43.002 Nonunit_fsub_feature_tests=4. Nonunit_bsub_feature_tests=11. 43.002/43.002 Megabytes=0.16. 43.002/43.002 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. 43.002/43.002 43.002/43.002 ============================== end of statistics ===================== 43.002/43.002 43.002/43.002 ============================== end of search ========================= 43.002/43.002 43.002/43.002 THEOREM PROVED 43.002/43.002 43.002/43.002 Exiting with 1 proof. 43.002/43.002 43.002/43.002 Process 120822 exit (max_proofs) Fri Jul 16 15:39:06 2021 43.002/43.002 43.002/43.002 43.002/43.002 The problem is feasible. 43.002/43.002 43.002/43.002 43.002/43.002 The problem is joinable. 43.002/43.002 26.92user 1.05system 0:43.02elapsed 65%CPU (0avgtext+0avgdata 95432maxresident)k 43.002/43.002 0inputs+0outputs (0major+75509minor)pagefaults 0swaps