25.066/25.066 NO 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 Confluence Problem: 25.066/25.066 (VAR vNonEmpty:S x:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 ) 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 Inlining of Conditions Processor [STERN17]: 25.066/25.066 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 Confluence Problem: 25.066/25.066 (VAR vNonEmpty:S x:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 ) 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 Clean CTRS Processor: 25.066/25.066 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 Confluence Problem: 25.066/25.066 (VAR x:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 ) 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 a -> c 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 a -> d 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 b -> c 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 b -> d 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 c -> e 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 c -> l 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 d -> m 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 Infeasibility Problem: 25.066/25.066 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S:S) -> x:S:S | x:S:S ->* e 25.066/25.066 g(d,x:S:S,x:S:S) -> A 25.066/25.066 h(x:S:S,x:S:S) -> g(x:S:S,x:S:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 )] 25.066/25.066 25.066/25.066 Infeasibility Conditions: 25.066/25.066 x:S:S ->* e 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 Obtaining a proof using Prover9: 25.066/25.066 25.066/25.066 -> Prover9 Output: 25.066/25.066 ============================== Prover9 =============================== 25.066/25.066 Prover9 (64) version 2009-11A, November 2009. 25.066/25.066 Process 39480 was started by ubuntu on ubuntu, 25.066/25.066 Wed Jul 14 10:12:11 2021 25.066/25.066 The command was "./prover9 -f /tmp/prover939473-0.in". 25.066/25.066 ============================== end of head =========================== 25.066/25.066 25.066/25.066 ============================== INPUT ================================= 25.066/25.066 25.066/25.066 % Reading from file /tmp/prover939473-0.in 25.066/25.066 25.066/25.066 assign(max_seconds,20). 25.066/25.066 25.066/25.066 formulas(assumptions). 25.066/25.066 ->*_s0(x,x) # label(reflexivity). 25.066/25.066 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.066/25.066 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 25.066/25.066 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 25.066/25.066 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 25.066/25.066 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 25.066/25.066 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 25.066/25.066 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 25.066/25.066 ->_s0(a,c) # label(replacement). 25.066/25.066 ->_s0(a,d) # label(replacement). 25.066/25.066 ->_s0(b,c) # label(replacement). 25.066/25.066 ->_s0(b,d) # label(replacement). 25.066/25.066 ->_s0(c,e) # label(replacement). 25.066/25.066 ->_s0(c,l) # label(replacement). 25.066/25.066 ->_s0(d,m) # label(replacement). 25.066/25.066 ->*_s0(x2,e) -> ->_s0(f(x2),x2) # label(replacement). 25.066/25.066 ->_s0(g(d,x2,x2),A) # label(replacement). 25.066/25.066 ->_s0(h(x2,x2),g(x2,x2,f(k))) # label(replacement). 25.066/25.066 ->_s0(k,l) # label(replacement). 25.066/25.066 ->_s0(k,m) # label(replacement). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 formulas(goals). 25.066/25.066 (exists x2 ->*_s0(x2,e)) # label(goal). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 ============================== end of input ========================== 25.066/25.066 25.066/25.066 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.066/25.066 25.066/25.066 % Formulas that are not ordinary clauses: 25.066/25.066 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.066/25.066 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 3 ->_s0(x1,y) -> ->_s0(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 4 ->_s0(x2,y) -> ->_s0(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 5 ->_s0(x3,y) -> ->_s0(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 6 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 7 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 8 ->*_s0(x2,e) -> ->_s0(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 25.066/25.066 9 (exists x2 ->*_s0(x2,e)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.066/25.066 25.066/25.066 ============================== end of process non-clausal formulas === 25.066/25.066 25.066/25.066 ============================== PROCESS INITIAL CLAUSES =============== 25.066/25.066 25.066/25.066 % Clauses before input processing: 25.066/25.066 25.066/25.066 formulas(usable). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 formulas(sos). 25.066/25.066 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.066/25.066 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.066/25.066 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.066/25.066 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(3)]. 25.066/25.066 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(4)]. 25.066/25.066 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(5)]. 25.066/25.066 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 25.066/25.066 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 25.066/25.066 ->_s0(a,c) # label(replacement). [assumption]. 25.066/25.066 ->_s0(a,d) # label(replacement). [assumption]. 25.066/25.066 ->_s0(b,c) # label(replacement). [assumption]. 25.066/25.066 ->_s0(b,d) # label(replacement). [assumption]. 25.066/25.066 ->_s0(c,e) # label(replacement). [assumption]. 25.066/25.066 ->_s0(c,l) # label(replacement). [assumption]. 25.066/25.066 ->_s0(d,m) # label(replacement). [assumption]. 25.066/25.066 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(8)]. 25.066/25.066 ->_s0(g(d,x,x),A) # label(replacement). [assumption]. 25.066/25.066 ->_s0(h(x,x),g(x,x,f(k))) # label(replacement). [assumption]. 25.066/25.066 ->_s0(k,l) # label(replacement). [assumption]. 25.066/25.066 ->_s0(k,m) # label(replacement). [assumption]. 25.066/25.066 -->*_s0(x,e) # label(goal). [deny(9)]. 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 formulas(demodulators). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 ============================== PREDICATE ELIMINATION ================= 25.066/25.066 25.066/25.066 No predicates eliminated. 25.066/25.066 25.066/25.066 ============================== end predicate elimination ============= 25.066/25.066 25.066/25.066 Auto_denials: 25.066/25.066 % copying label goal to answer in negative clause 25.066/25.066 25.066/25.066 Term ordering decisions: 25.066/25.066 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 25.066/25.066 Function symbol precedence: function_order([ c, d, k, e, l, m, a, b, A, h, f, g ]). 25.066/25.066 After inverse_order: (no changes). 25.066/25.066 Unfolding symbols: (none). 25.066/25.066 25.066/25.066 Auto_inference settings: 25.066/25.066 % set(neg_binary_resolution). % (HNE depth_diff=-7) 25.066/25.066 % clear(ordered_res). % (HNE depth_diff=-7) 25.066/25.066 % set(ur_resolution). % (HNE depth_diff=-7) 25.066/25.066 % set(ur_resolution) -> set(pos_ur_resolution). 25.066/25.066 % set(ur_resolution) -> set(neg_ur_resolution). 25.066/25.066 25.066/25.066 Auto_process settings: (no changes). 25.066/25.066 25.066/25.066 kept: 10 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.066/25.066 kept: 11 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.066/25.066 kept: 12 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.066/25.066 kept: 13 -->_s0(x,y) | ->_s0(g(x,z,u),g(y,z,u)) # label(congruence). [clausify(3)]. 25.066/25.066 kept: 14 -->_s0(x,y) | ->_s0(g(z,x,u),g(z,y,u)) # label(congruence). [clausify(4)]. 25.066/25.066 kept: 15 -->_s0(x,y) | ->_s0(g(z,u,x),g(z,u,y)) # label(congruence). [clausify(5)]. 25.066/25.066 kept: 16 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 25.066/25.066 kept: 17 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 25.066/25.066 kept: 18 ->_s0(a,c) # label(replacement). [assumption]. 25.066/25.066 kept: 19 ->_s0(a,d) # label(replacement). [assumption]. 25.066/25.066 kept: 20 ->_s0(b,c) # label(replacement). [assumption]. 25.066/25.066 kept: 21 ->_s0(b,d) # label(replacement). [assumption]. 25.066/25.066 kept: 22 ->_s0(c,e) # label(replacement). [assumption]. 25.066/25.066 kept: 23 ->_s0(c,l) # label(replacement). [assumption]. 25.066/25.066 kept: 24 ->_s0(d,m) # label(replacement). [assumption]. 25.066/25.066 kept: 25 -->*_s0(x,e) | ->_s0(f(x),x) # label(replacement). [clausify(8)]. 25.066/25.066 kept: 26 ->_s0(g(d,x,x),A) # label(replacement). [assumption]. 25.066/25.066 kept: 27 ->_s0(h(x,x),g(x,x,f(k))) # label(replacement). [assumption]. 25.066/25.066 kept: 28 ->_s0(k,l) # label(replacement). [assumption]. 25.066/25.066 kept: 29 ->_s0(k,m) # label(replacement). [assumption]. 25.066/25.066 kept: 30 -->*_s0(x,e) # label(goal) # answer(goal). [deny(9)]. 25.066/25.066 25.066/25.066 ============================== PROOF ================================= 25.066/25.066 25.066/25.066 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.066/25.066 % Length of proof is 4. 25.066/25.066 % Level of proof is 2. 25.066/25.066 % Maximum clause weight is 3.000. 25.066/25.066 % Given clauses 0. 25.066/25.066 25.066/25.066 9 (exists x2 ->*_s0(x2,e)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.066/25.066 10 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.066/25.066 30 -->*_s0(x,e) # label(goal) # answer(goal). [deny(9)]. 25.066/25.066 31 $F # answer(goal). [resolve(30,a,10,a)]. 25.066/25.066 25.066/25.066 ============================== end of proof ========================== 25.066/25.066 25.066/25.066 ============================== STATISTICS ============================ 25.066/25.066 25.066/25.066 Given=0. Generated=21. Kept=21. proofs=1. 25.066/25.066 Usable=0. Sos=0. Demods=0. Limbo=20, Disabled=21. Hints=0. 25.066/25.066 Kept_by_rule=0, Deleted_by_rule=0. 25.066/25.066 Forward_subsumed=0. Back_subsumed=0. 25.066/25.066 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.066/25.066 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.066/25.066 Demod_attempts=0. Demod_rewrites=0. 25.066/25.066 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.066/25.066 Nonunit_fsub_feature_tests=4. Nonunit_bsub_feature_tests=0. 25.066/25.066 Megabytes=0.07. 25.066/25.066 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.066/25.066 25.066/25.066 ============================== end of statistics ===================== 25.066/25.066 25.066/25.066 ============================== end of search ========================= 25.066/25.066 25.066/25.066 THEOREM PROVED 25.066/25.066 25.066/25.066 Exiting with 1 proof. 25.066/25.066 25.066/25.066 Process 39480 exit (max_proofs) Wed Jul 14 10:12:11 2021 25.066/25.066 25.066/25.066 25.066/25.066 The problem is feasible. 25.066/25.066 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 k -> l 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 CRule InfChecker Info: 25.066/25.066 k -> m 25.066/25.066 Rule remains 25.066/25.066 Proof: 25.066/25.066 NO_CONDS 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 Confluence Problem: 25.066/25.066 (VAR x:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 ) 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 25.066/25.066 Critical Pairs Processor: 25.066/25.066 -> Rules: 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 -> Vars: 25.066/25.066 "x", "x", "x" 25.066/25.066 -> FVars: 25.066/25.066 "x2", "x3", "x4" 25.066/25.066 -> PVars: 25.066/25.066 "x": ["x2", "x3", "x4"] 25.066/25.066 25.066/25.066 -> Rlps: 25.066/25.066 crule: a -> c, id: 1, possubterms: a-> [] 25.066/25.066 crule: a -> d, id: 2, possubterms: a-> [] 25.066/25.066 crule: b -> c, id: 3, possubterms: b-> [] 25.066/25.066 crule: b -> d, id: 4, possubterms: b-> [] 25.066/25.066 crule: c -> e, id: 5, possubterms: c-> [] 25.066/25.066 crule: c -> l, id: 6, possubterms: c-> [] 25.066/25.066 crule: d -> m, id: 7, possubterms: d-> [] 25.066/25.066 crule: f(x2:S) -> x2:S | x2:S ->* e, id: 8, possubterms: f(x2:S)-> [] 25.066/25.066 crule: g(d,x3:S,x3:S) -> A, id: 9, possubterms: g(d,x3:S,x3:S)-> [], d-> [1] 25.066/25.066 crule: h(x4:S,x4:S) -> g(x4:S,x4:S,f(k)), id: 10, possubterms: h(x4:S,x4:S)-> [] 25.066/25.066 crule: k -> l, id: 11, possubterms: k-> [] 25.066/25.066 crule: k -> m, id: 12, possubterms: k-> [] 25.066/25.066 25.066/25.066 -> Unifications: 25.066/25.066 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 25.066/25.066 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 25.066/25.066 R6 unifies with R5 at p: [], l: c, lp: c, conds: {}, sig: {}, l': c, r: l, r': e 25.066/25.066 R9 unifies with R7 at p: [1], l: g(d,x3:S,x3:S), lp: d, conds: {}, sig: {}, l': d, r: A, r': m 25.066/25.066 R12 unifies with R11 at p: [], l: k, lp: k, conds: {}, sig: {}, l': k, r: m, r': l 25.066/25.066 25.066/25.066 -> Critical pairs info: 25.066/25.066 => Not trivial, Overlay, N1 25.066/25.066 => Not trivial, Overlay, N2 25.066/25.066 => Not trivial, Overlay, N3 25.066/25.066 => Not trivial, Not overlay, N4 25.066/25.066 25.066/25.066 -> Problem conclusions: 25.066/25.066 Not left linear, Not right linear, Not linear 25.066/25.066 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 25.066/25.066 CTRS Type: 1 25.066/25.066 Deterministic, Strongly deterministic 25.066/25.066 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.066/25.066 Maybe right-stable CTRS, Not overlay CTRS 25.066/25.066 Maybe normal CTRS, Maybe almost normal CTRS 25.066/25.066 Maybe terminating CTRS, Maybe joinable CCPs 25.066/25.066 Maybe level confluent 25.066/25.066 Maybe confluent 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 Confluence Problem: 25.066/25.066 (VAR x:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 ) 25.066/25.066 Critical Pairs: 25.066/25.066 => Not trivial, Overlay, N1 25.066/25.066 => Not trivial, Overlay, N2 25.066/25.066 => Not trivial, Overlay, N3 25.066/25.066 => Not trivial, Not overlay, N4 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 25.066/25.066 Conditional Critical Pairs Distributor Processor 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 Confluence Problem: 25.066/25.066 (VAR x:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 ) 25.066/25.066 Critical Pairs: 25.066/25.066 => Not trivial, Overlay, N1 25.066/25.066 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.066/25.066 25.066/25.066 Infeasible Convergence No Conditions CCP Processor: 25.066/25.066 Infeasible convergence? 25.066/25.066 YES 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 Infeasibility Problem: 25.066/25.066 [(VAR vNonEmpty:S x:S z:S) 25.066/25.066 (STRATEGY CONTEXTSENSITIVE 25.066/25.066 (a) 25.066/25.066 (b) 25.066/25.066 (c) 25.066/25.066 (d) 25.066/25.066 (f 1) 25.066/25.066 (g 1 2 3) 25.066/25.066 (h 1 2) 25.066/25.066 (k) 25.066/25.066 (A) 25.066/25.066 (e) 25.066/25.066 (fSNonEmpty) 25.066/25.066 (l) 25.066/25.066 (m) 25.066/25.066 ) 25.066/25.066 (RULES 25.066/25.066 a -> c 25.066/25.066 a -> d 25.066/25.066 b -> c 25.066/25.066 b -> d 25.066/25.066 c -> e 25.066/25.066 c -> l 25.066/25.066 d -> m 25.066/25.066 f(x:S) -> x:S | x:S ->* e 25.066/25.066 g(d,x:S,x:S) -> A 25.066/25.066 h(x:S,x:S) -> g(x:S,x:S,f(k)) 25.066/25.066 k -> l 25.066/25.066 k -> m 25.066/25.066 )] 25.066/25.066 25.066/25.066 Infeasibility Conditions: 25.066/25.066 l ->* z:S, m ->* z:S 25.066/25.066 25.066/25.066 Problem 1: 25.066/25.066 25.066/25.066 Obtaining a model using Mace4: 25.066/25.066 25.066/25.066 -> Usable Rules: 25.066/25.066 Empty 25.066/25.066 25.066/25.066 -> Mace4 Output: 25.066/25.066 ============================== Mace4 ================================= 25.066/25.066 Mace4 (64) version 2009-11A, November 2009. 25.066/25.066 Process 39527 was started by ubuntu on ubuntu, 25.066/25.066 Wed Jul 14 10:12:11 2021 25.066/25.066 The command was "./mace4 -c -f /tmp/mace439499-2.in". 25.066/25.066 ============================== end of head =========================== 25.066/25.066 25.066/25.066 ============================== INPUT ================================= 25.066/25.066 25.066/25.066 % Reading from file /tmp/mace439499-2.in 25.066/25.066 25.066/25.066 assign(max_seconds,20). 25.066/25.066 25.066/25.066 formulas(assumptions). 25.066/25.066 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 25.066/25.066 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence). 25.066/25.066 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence). 25.066/25.066 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence). 25.066/25.066 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 25.066/25.066 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 25.066/25.066 ->*(x,x) # label(reflexivity). 25.066/25.066 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 formulas(goals). 25.066/25.066 (exists x2 (->*(l,x2) & ->*(m,x2))) # label(goal). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 ============================== end of input ========================== 25.066/25.066 25.066/25.066 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.066/25.066 25.066/25.066 % Formulas that are not ordinary clauses: 25.066/25.066 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 2 ->(x1,y) -> ->(g(x1,x2,x3),g(y,x2,x3)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 3 ->(x2,y) -> ->(g(x1,x2,x3),g(x1,y,x3)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 4 ->(x3,y) -> ->(g(x1,x2,x3),g(x1,x2,y)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.066/25.066 7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.066/25.066 8 (exists x2 (->*(l,x2) & ->*(m,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 25.066/25.066 25.066/25.066 ============================== end of process non-clausal formulas === 25.066/25.066 25.066/25.066 ============================== CLAUSES FOR SEARCH ==================== 25.066/25.066 25.066/25.066 formulas(mace4_clauses). 25.066/25.066 -->(x,y) | ->(f(x),f(y)) # label(congruence). 25.066/25.066 -->(x,y) | ->(g(x,z,u),g(y,z,u)) # label(congruence). 25.066/25.066 -->(x,y) | ->(g(z,x,u),g(z,y,u)) # label(congruence). 25.066/25.066 -->(x,y) | ->(g(z,u,x),g(z,u,y)) # label(congruence). 25.066/25.066 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 25.066/25.066 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 25.066/25.066 ->*(x,x) # label(reflexivity). 25.066/25.066 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.066/25.066 -->*(l,x) | -->*(m,x) # label(goal). 25.066/25.066 end_of_list. 25.066/25.066 25.066/25.066 ============================== end of clauses for search ============= 25.066/25.066 25.066/25.066 % There are no natural numbers in the input. 25.066/25.066 25.066/25.066 ============================== DOMAIN SIZE 2 ========================= 25.066/25.066 25.066/25.066 ============================== MODEL ================================= 25.066/25.066 25.066/25.066 interpretation( 2, [number=1, seconds=0], [ 25.066/25.066 25.066/25.066 function(l, [ 0 ]), 25.066/25.066 25.066/25.066 function(m, [ 1 ]), 25.066/25.066 25.066/25.066 function(f(_), [ 0, 0 ]), 25.066/25.066 25.066/25.066 function(h(_,_), [ 25.066/25.066 0, 0, 25.066/25.066 0, 0 ]), 25.066/25.066 25.066/25.066 function(g(_,_,_), [ 25.066/25.066 0, 0, 25.066/25.066 0, 0, 25.066/25.066 0, 0, 25.066/25.066 0, 0 ]), 25.066/25.066 25.066/25.066 relation(->*(_,_), [ 25.066/25.066 1, 0, 25.066/25.066 0, 1 ]), 25.066/25.066 25.066/25.066 relation(->(_,_), [ 25.066/25.066 0, 0, 25.066/25.066 0, 0 ]) 25.066/25.066 ]). 25.066/25.066 25.066/25.066 ============================== end of model ========================== 25.066/25.066 25.066/25.066 ============================== STATISTICS ============================ 25.066/25.066 25.066/25.066 For domain size 2. 25.066/25.066 25.066/25.066 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.066/25.066 Ground clauses: seen=80, kept=76. 25.066/25.066 Selections=16, assignments=16, propagations=8, current_models=1. 25.066/25.066 Rewrite_terms=140, rewrite_bools=89, indexes=8. 25.066/25.066 Rules_from_neg_clauses=1, cross_offs=1. 25.066/25.066 25.066/25.066 ============================== end of statistics ===================== 25.066/25.066 25.066/25.066 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.066/25.066 25.066/25.066 Exiting with 1 model. 25.066/25.066 25.066/25.066 Process 39527 exit (max_models) Wed Jul 14 10:12:11 2021 25.066/25.066 The process finished Wed Jul 14 10:12:11 2021 25.066/25.066 25.066/25.066 25.066/25.066 Mace4 cooked interpretation: 25.066/25.066 25.066/25.066 25.066/25.066 25.066/25.066 The problem is infeasible. 25.066/25.066 25.066/25.066 25.066/25.066 The problem is not joinable. 25.066/25.066 30.66user 1.45system 0:25.66elapsed 125%CPU (0avgtext+0avgdata 223136maxresident)k 25.066/25.066 0inputs+0outputs (0major+119584minor)pagefaults 0swaps