20.045/20.045 NO 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 Confluence Problem: 20.045/20.045 (VAR vNonEmpty x) 20.045/20.045 (REPLACEMENT-MAP 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1, 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1, 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 ) 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Inlining of Conditions Processor [STERN17]: 20.045/20.045 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 Confluence Problem: 20.045/20.045 (VAR vNonEmpty x) 20.045/20.045 (REPLACEMENT-MAP 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1, 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1, 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 ) 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Clean CTRS Processor: 20.045/20.045 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 Confluence Problem: 20.045/20.045 (VAR x) 20.045/20.045 (REPLACEMENT-MAP 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1, 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1, 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 ) 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 a -> c 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO_CONDS 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 b -> c 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO_CONDS 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Infeasibility Problem: 20.045/20.045 [(VAR vNonEmpty x vNonEmpty x) 20.045/20.045 (STRATEGY CONTEXTSENSITIVE 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 )] 20.045/20.045 20.045/20.045 Infeasibility Conditions: 20.045/20.045 s(x) ->* t 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Obtaining a proof using Prover9: 20.045/20.045 20.045/20.045 -> Prover9 Output: 20.045/20.045 ============================== Prover9 =============================== 20.045/20.045 Prover9 (64) version 2009-11A, November 2009. 20.045/20.045 Process 61969 was started by ubuntu on ubuntu, 20.045/20.045 Wed Mar 9 09:50:00 2022 20.045/20.045 The command was "./prover9 -f /tmp/prover961960-0.in". 20.045/20.045 ============================== end of head =========================== 20.045/20.045 20.045/20.045 ============================== INPUT ================================= 20.045/20.045 20.045/20.045 % Reading from file /tmp/prover961960-0.in 20.045/20.045 20.045/20.045 assign(max_seconds,20). 20.045/20.045 20.045/20.045 formulas(assumptions). 20.045/20.045 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 20.045/20.045 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 20.045/20.045 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 20.045/20.045 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 20.045/20.045 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 20.045/20.045 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 20.045/20.045 ->_s0(a,c) # label(replacement). 20.045/20.045 ->_s0(b,c) # label(replacement). 20.045/20.045 ->*_s0(s(x1),t) -> ->_s0(f(x1),A) # label(replacement). 20.045/20.045 ->*_s0(s(x1),t) -> ->_s0(f(x1),B) # label(replacement). 20.045/20.045 ->_s0(g(x1,x1),h(x1,x1)) # label(replacement). 20.045/20.045 ->_s0(s(a),t) # label(replacement). 20.045/20.045 ->_s0(s(b),t) # label(replacement). 20.045/20.045 ->*_s0(x,x) # label(reflexivity). 20.045/20.045 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(goals). 20.045/20.045 (exists x3 ->*_s0(s(x3),t)) # label(goal). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== end of input ========================== 20.045/20.045 20.045/20.045 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.045/20.045 20.045/20.045 % Formulas that are not ordinary clauses: 20.045/20.045 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 2 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 3 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 4 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 7 ->*_s0(s(x1),t) -> ->_s0(f(x1),A) # label(replacement) # label(non_clause). [assumption]. 20.045/20.045 8 ->*_s0(s(x1),t) -> ->_s0(f(x1),B) # label(replacement) # label(non_clause). [assumption]. 20.045/20.045 9 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.045/20.045 10 (exists x3 ->*_s0(s(x3),t)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.045/20.045 20.045/20.045 ============================== end of process non-clausal formulas === 20.045/20.045 20.045/20.045 ============================== PROCESS INITIAL CLAUSES =============== 20.045/20.045 20.045/20.045 % Clauses before input processing: 20.045/20.045 20.045/20.045 formulas(usable). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(sos). 20.045/20.045 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 -->*_s0(s(x),t) | ->_s0(f(x),A) # label(replacement). [clausify(7)]. 20.045/20.045 -->*_s0(s(x),t) | ->_s0(f(x),B) # label(replacement). [clausify(8)]. 20.045/20.045 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 -->*_s0(s(x),t) # label(goal). [deny(10)]. 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(demodulators). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== PREDICATE ELIMINATION ================= 20.045/20.045 20.045/20.045 No predicates eliminated. 20.045/20.045 20.045/20.045 ============================== end predicate elimination ============= 20.045/20.045 20.045/20.045 Auto_denials: 20.045/20.045 % copying label goal to answer in negative clause 20.045/20.045 20.045/20.045 Term ordering decisions: 20.045/20.045 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.045/20.045 Function symbol precedence: function_order([ t, a, b, c, A, B, h, g, s, f ]). 20.045/20.045 After inverse_order: (no changes). 20.045/20.045 Unfolding symbols: (none). 20.045/20.045 20.045/20.045 Auto_inference settings: 20.045/20.045 % set(neg_binary_resolution). % (HNE depth_diff=-6) 20.045/20.045 % clear(ordered_res). % (HNE depth_diff=-6) 20.045/20.045 % set(ur_resolution). % (HNE depth_diff=-6) 20.045/20.045 % set(ur_resolution) -> set(pos_ur_resolution). 20.045/20.045 % set(ur_resolution) -> set(neg_ur_resolution). 20.045/20.045 20.045/20.045 Auto_process settings: (no changes). 20.045/20.045 20.045/20.045 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 kept: 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 kept: 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 kept: 14 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 kept: 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 kept: 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 kept: 17 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 kept: 18 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 kept: 19 -->*_s0(s(x),t) | ->_s0(f(x),A) # label(replacement). [clausify(7)]. 20.045/20.045 kept: 20 -->*_s0(s(x),t) | ->_s0(f(x),B) # label(replacement). [clausify(8)]. 20.045/20.045 kept: 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 kept: 22 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 kept: 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 kept: 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 kept: 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 kept: 26 -->*_s0(s(x),t) # label(goal) # answer(goal). [deny(10)]. 20.045/20.045 20.045/20.045 ============================== end of process initial clauses ======== 20.045/20.045 20.045/20.045 ============================== CLAUSES FOR SEARCH ==================== 20.045/20.045 20.045/20.045 % Clauses after input processing: 20.045/20.045 20.045/20.045 formulas(usable). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(sos). 20.045/20.045 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 14 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 17 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 18 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 22 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 26 -->*_s0(s(x),t) # label(goal) # answer(goal). [deny(10)]. 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(demodulators). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== end of clauses for search ============= 20.045/20.045 20.045/20.045 ============================== SEARCH ================================ 20.045/20.045 20.045/20.045 % Starting search at 0.00 seconds. 20.045/20.045 20.045/20.045 given #1 (I,wt=8): 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 20.045/20.045 given #2 (I,wt=10): 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 20.045/20.045 given #3 (I,wt=10): 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 20.045/20.045 given #4 (I,wt=8): 14 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 20.045/20.045 given #5 (I,wt=10): 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 20.045/20.045 given #6 (I,wt=10): 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 20.045/20.045 given #7 (I,wt=3): 17 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #8 (I,wt=3): 18 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #9 (I,wt=7): 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #10 (I,wt=4): 22 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #11 (I,wt=4): 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #12 (I,wt=3): 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 20.045/20.045 given #13 (I,wt=9): 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 20.045/20.045 ============================== PROOF ================================= 20.045/20.045 20.045/20.045 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.045/20.045 % Length of proof is 8. 20.045/20.045 % Level of proof is 3. 20.045/20.045 % Maximum clause weight is 9.000. 20.045/20.045 % Given clauses 13. 20.045/20.045 20.045/20.045 9 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.045/20.045 10 (exists x3 ->*_s0(s(x3),t)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.045/20.045 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 26 -->*_s0(s(x),t) # label(goal) # answer(goal). [deny(10)]. 20.045/20.045 57 ->*_s0(s(b),t). [ur(25,a,23,a,b,24,a)]. 20.045/20.045 58 $F # answer(goal). [resolve(57,a,26,a)]. 20.045/20.045 20.045/20.045 ============================== end of proof ========================== 20.045/20.045 20.045/20.045 ============================== STATISTICS ============================ 20.045/20.045 20.045/20.045 Given=13. Generated=47. Kept=47. proofs=1. 20.045/20.045 Usable=13. Sos=31. Demods=0. Limbo=0, Disabled=18. Hints=0. 20.045/20.045 Kept_by_rule=0, Deleted_by_rule=0. 20.045/20.045 Forward_subsumed=0. Back_subsumed=2. 20.045/20.045 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.045/20.045 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.045/20.045 Demod_attempts=0. Demod_rewrites=0. 20.045/20.045 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.045/20.045 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=16. 20.045/20.045 Megabytes=0.12. 20.045/20.045 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.045/20.045 20.045/20.045 ============================== end of statistics ===================== 20.045/20.045 20.045/20.045 ============================== end of search ========================= 20.045/20.045 20.045/20.045 THEOREM PROVED 20.045/20.045 20.045/20.045 Exiting with 1 proof. 20.045/20.045 20.045/20.045 Process 61969 exit (max_proofs) Wed Mar 9 09:50:00 2022 20.045/20.045 20.045/20.045 20.045/20.045 The problem is feasible. 20.045/20.045 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Infeasibility Problem: 20.045/20.045 [(VAR vNonEmpty x vNonEmpty x) 20.045/20.045 (STRATEGY CONTEXTSENSITIVE 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 )] 20.045/20.045 20.045/20.045 Infeasibility Conditions: 20.045/20.045 s(x) ->* t 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Obtaining a proof using Prover9: 20.045/20.045 20.045/20.045 -> Prover9 Output: 20.045/20.045 ============================== Prover9 =============================== 20.045/20.045 Prover9 (64) version 2009-11A, November 2009. 20.045/20.045 Process 61993 was started by ubuntu on ubuntu, 20.045/20.045 Wed Mar 9 09:50:00 2022 20.045/20.045 The command was "./prover9 -f /tmp/prover961984-0.in". 20.045/20.045 ============================== end of head =========================== 20.045/20.045 20.045/20.045 ============================== INPUT ================================= 20.045/20.045 20.045/20.045 % Reading from file /tmp/prover961984-0.in 20.045/20.045 20.045/20.045 assign(max_seconds,20). 20.045/20.045 20.045/20.045 formulas(assumptions). 20.045/20.045 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 20.045/20.045 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 20.045/20.045 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 20.045/20.045 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 20.045/20.045 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 20.045/20.045 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 20.045/20.045 ->_s0(a,c) # label(replacement). 20.045/20.045 ->_s0(b,c) # label(replacement). 20.045/20.045 ->*_s0(s(x1),t) -> ->_s0(f(x1),A) # label(replacement). 20.045/20.045 ->*_s0(s(x1),t) -> ->_s0(f(x1),B) # label(replacement). 20.045/20.045 ->_s0(g(x1,x1),h(x1,x1)) # label(replacement). 20.045/20.045 ->_s0(s(a),t) # label(replacement). 20.045/20.045 ->_s0(s(b),t) # label(replacement). 20.045/20.045 ->*_s0(x,x) # label(reflexivity). 20.045/20.045 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(goals). 20.045/20.045 (exists x3 ->*_s0(s(x3),t)) # label(goal). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== end of input ========================== 20.045/20.045 20.045/20.045 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.045/20.045 20.045/20.045 % Formulas that are not ordinary clauses: 20.045/20.045 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 2 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 3 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 4 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 7 ->*_s0(s(x1),t) -> ->_s0(f(x1),A) # label(replacement) # label(non_clause). [assumption]. 20.045/20.045 8 ->*_s0(s(x1),t) -> ->_s0(f(x1),B) # label(replacement) # label(non_clause). [assumption]. 20.045/20.045 9 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.045/20.045 10 (exists x3 ->*_s0(s(x3),t)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.045/20.045 20.045/20.045 ============================== end of process non-clausal formulas === 20.045/20.045 20.045/20.045 ============================== PROCESS INITIAL CLAUSES =============== 20.045/20.045 20.045/20.045 % Clauses before input processing: 20.045/20.045 20.045/20.045 formulas(usable). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(sos). 20.045/20.045 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 -->*_s0(s(x),t) | ->_s0(f(x),A) # label(replacement). [clausify(7)]. 20.045/20.045 -->*_s0(s(x),t) | ->_s0(f(x),B) # label(replacement). [clausify(8)]. 20.045/20.045 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 -->*_s0(s(x),t) # label(goal). [deny(10)]. 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(demodulators). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== PREDICATE ELIMINATION ================= 20.045/20.045 20.045/20.045 No predicates eliminated. 20.045/20.045 20.045/20.045 ============================== end predicate elimination ============= 20.045/20.045 20.045/20.045 Auto_denials: 20.045/20.045 % copying label goal to answer in negative clause 20.045/20.045 20.045/20.045 Term ordering decisions: 20.045/20.045 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.045/20.045 Function symbol precedence: function_order([ t, a, b, c, A, B, h, g, s, f ]). 20.045/20.045 After inverse_order: (no changes). 20.045/20.045 Unfolding symbols: (none). 20.045/20.045 20.045/20.045 Auto_inference settings: 20.045/20.045 % set(neg_binary_resolution). % (HNE depth_diff=-6) 20.045/20.045 % clear(ordered_res). % (HNE depth_diff=-6) 20.045/20.045 % set(ur_resolution). % (HNE depth_diff=-6) 20.045/20.045 % set(ur_resolution) -> set(pos_ur_resolution). 20.045/20.045 % set(ur_resolution) -> set(neg_ur_resolution). 20.045/20.045 20.045/20.045 Auto_process settings: (no changes). 20.045/20.045 20.045/20.045 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 kept: 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 kept: 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 kept: 14 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 kept: 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 kept: 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 kept: 17 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 kept: 18 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 kept: 19 -->*_s0(s(x),t) | ->_s0(f(x),A) # label(replacement). [clausify(7)]. 20.045/20.045 kept: 20 -->*_s0(s(x),t) | ->_s0(f(x),B) # label(replacement). [clausify(8)]. 20.045/20.045 kept: 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 kept: 22 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 kept: 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 kept: 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 kept: 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 kept: 26 -->*_s0(s(x),t) # label(goal) # answer(goal). [deny(10)]. 20.045/20.045 20.045/20.045 ============================== end of process initial clauses ======== 20.045/20.045 20.045/20.045 ============================== CLAUSES FOR SEARCH ==================== 20.045/20.045 20.045/20.045 % Clauses after input processing: 20.045/20.045 20.045/20.045 formulas(usable). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(sos). 20.045/20.045 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 14 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 17 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 18 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 22 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 26 -->*_s0(s(x),t) # label(goal) # answer(goal). [deny(10)]. 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(demodulators). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== end of clauses for search ============= 20.045/20.045 20.045/20.045 ============================== SEARCH ================================ 20.045/20.045 20.045/20.045 % Starting search at 0.00 seconds. 20.045/20.045 20.045/20.045 given #1 (I,wt=8): 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 20.045/20.045 20.045/20.045 given #2 (I,wt=10): 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 20.045/20.045 20.045/20.045 given #3 (I,wt=10): 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 20.045/20.045 20.045/20.045 given #4 (I,wt=8): 14 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(4)]. 20.045/20.045 20.045/20.045 given #5 (I,wt=10): 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 20.045/20.045 20.045/20.045 given #6 (I,wt=10): 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 20.045/20.045 20.045/20.045 given #7 (I,wt=3): 17 ->_s0(a,c) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #8 (I,wt=3): 18 ->_s0(b,c) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #9 (I,wt=7): 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #10 (I,wt=4): 22 ->_s0(s(a),t) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #11 (I,wt=4): 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 20.045/20.045 given #12 (I,wt=3): 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 20.045/20.045 given #13 (I,wt=9): 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 20.045/20.045 ============================== PROOF ================================= 20.045/20.045 20.045/20.045 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.045/20.045 % Length of proof is 8. 20.045/20.045 % Level of proof is 3. 20.045/20.045 % Maximum clause weight is 9.000. 20.045/20.045 % Given clauses 13. 20.045/20.045 20.045/20.045 9 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.045/20.045 10 (exists x3 ->*_s0(s(x3),t)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.045/20.045 23 ->_s0(s(b),t) # label(replacement). [assumption]. 20.045/20.045 24 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.045/20.045 25 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 20.045/20.045 26 -->*_s0(s(x),t) # label(goal) # answer(goal). [deny(10)]. 20.045/20.045 57 ->*_s0(s(b),t). [ur(25,a,23,a,b,24,a)]. 20.045/20.045 58 $F # answer(goal). [resolve(57,a,26,a)]. 20.045/20.045 20.045/20.045 ============================== end of proof ========================== 20.045/20.045 20.045/20.045 ============================== STATISTICS ============================ 20.045/20.045 20.045/20.045 Given=13. Generated=47. Kept=47. proofs=1. 20.045/20.045 Usable=13. Sos=31. Demods=0. Limbo=0, Disabled=18. Hints=0. 20.045/20.045 Kept_by_rule=0, Deleted_by_rule=0. 20.045/20.045 Forward_subsumed=0. Back_subsumed=2. 20.045/20.045 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.045/20.045 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.045/20.045 Demod_attempts=0. Demod_rewrites=0. 20.045/20.045 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.045/20.045 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=16. 20.045/20.045 Megabytes=0.12. 20.045/20.045 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.045/20.045 20.045/20.045 ============================== end of statistics ===================== 20.045/20.045 20.045/20.045 ============================== end of search ========================= 20.045/20.045 20.045/20.045 THEOREM PROVED 20.045/20.045 20.045/20.045 Exiting with 1 proof. 20.045/20.045 20.045/20.045 Process 61993 exit (max_proofs) Wed Mar 9 09:50:00 2022 20.045/20.045 20.045/20.045 20.045/20.045 The problem is feasible. 20.045/20.045 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO_CONDS 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 s(a) -> t 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO_CONDS 20.045/20.045 20.045/20.045 CRule InfChecker Info: 20.045/20.045 s(b) -> t 20.045/20.045 Rule remains 20.045/20.045 Proof: 20.045/20.045 NO_CONDS 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 Confluence Problem: 20.045/20.045 (VAR x) 20.045/20.045 (REPLACEMENT-MAP 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1, 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1, 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 ) 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 20.045/20.045 Critical Pairs Processor: 20.045/20.045 -> Rules: 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 -> Vars: 20.045/20.045 "x" 20.045/20.045 20.045/20.045 -> Rlps: 20.045/20.045 crule: a -> c, id: 1, possubterms: a-> [] 20.045/20.045 crule: b -> c, id: 2, possubterms: b-> [] 20.045/20.045 crule: f(x) -> A | s(x) ->* t, id: 3, possubterms: f(x)-> [] 20.045/20.045 crule: f(x) -> B | s(x) ->* t, id: 4, possubterms: f(x)-> [] 20.045/20.045 crule: g(x,x) -> h(x,x), id: 5, possubterms: g(x,x)-> [] 20.045/20.045 crule: s(a) -> t, id: 6, possubterms: s(a)-> [], a-> [1] 20.045/20.045 crule: s(b) -> t, id: 7, possubterms: s(b)-> [], b-> [1] 20.045/20.045 20.045/20.045 -> Unifications: 20.045/20.045 R4 unifies with R3 at p: [], l: f(x), lp: f(x), conds: {s(x) ->* t, s(x') ->* t}, sig: {x -> x'}, l': f(x'), r: B, r': A 20.045/20.045 R6 unifies with R1 at p: [1], l: s(a), lp: a, conds: {}, sig: {}, l': a, r: t, r': c 20.045/20.045 R7 unifies with R2 at p: [1], l: s(b), lp: b, conds: {}, sig: {}, l': b, r: t, r': c 20.045/20.045 20.045/20.045 -> Critical pairs info: 20.045/20.045 | s(x') ->* t => Not trivial, Overlay, NW2, N1 20.045/20.045 => Not trivial, Not overlay, NW2, N2 20.045/20.045 20.045/20.045 -> Problem conclusions: 20.045/20.045 Not left linear, Not right linear, Not linear 20.045/20.045 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.045/20.045 CTRS Type: 1 20.045/20.045 Deterministic, Strongly deterministic 20.045/20.045 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.045/20.045 Maybe right-stable CTRS, Not overlay CTRS 20.045/20.045 Maybe normal CTRS, Maybe almost normal CTRS 20.045/20.045 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.045/20.045 Maybe level confluent 20.045/20.045 Maybe confluent 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 Confluence Problem: 20.045/20.045 (VAR x x') 20.045/20.045 (REPLACEMENT-MAP 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1, 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1, 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 ) 20.045/20.045 Critical Pairs: 20.045/20.045 | s(x') ->* t => Not trivial, Overlay, NW2, N1 20.045/20.045 => Not trivial, Not overlay, NW2, N2 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 20.045/20.045 Conditional Critical Pairs Distributor Processor 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 Confluence Problem: 20.045/20.045 (VAR x x') 20.045/20.045 (REPLACEMENT-MAP 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1, 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1, 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 ) 20.045/20.045 Critical Pairs: 20.045/20.045 => Not trivial, Not overlay, NW2, N2 20.045/20.045 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.045/20.045 20.045/20.045 Infeasible Convergence No Conditions CCP Processor: 20.045/20.045 Infeasible convergence? 20.045/20.045 YES 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Infeasibility Problem: 20.045/20.045 [(VAR vNonEmpty x x1 vNonEmpty z) 20.045/20.045 (STRATEGY CONTEXTSENSITIVE 20.045/20.045 (a) 20.045/20.045 (b) 20.045/20.045 (f 1) 20.045/20.045 (g 1 2) 20.045/20.045 (s 1) 20.045/20.045 (A) 20.045/20.045 (B) 20.045/20.045 (c) 20.045/20.045 (fSNonEmpty) 20.045/20.045 (h 1 2) 20.045/20.045 (t) 20.045/20.045 ) 20.045/20.045 (RULES 20.045/20.045 a -> c 20.045/20.045 b -> c 20.045/20.045 f(x) -> A | s(x) ->* t 20.045/20.045 f(x) -> B | s(x) ->* t 20.045/20.045 g(x,x) -> h(x,x) 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 )] 20.045/20.045 20.045/20.045 Infeasibility Conditions: 20.045/20.045 s(c) ->* z, t ->* z 20.045/20.045 20.045/20.045 Problem 1: 20.045/20.045 20.045/20.045 Obtaining a model using Mace4: 20.045/20.045 20.045/20.045 -> Usable Rules: 20.045/20.045 s(a) -> t 20.045/20.045 s(b) -> t 20.045/20.045 20.045/20.045 -> Mace4 Output: 20.045/20.045 ============================== Mace4 ================================= 20.045/20.045 Mace4 (64) version 2009-11A, November 2009. 20.045/20.045 Process 62056 was started by ubuntu on ubuntu, 20.045/20.045 Wed Mar 9 09:50:00 2022 20.045/20.045 The command was "./mace4 -c -f /tmp/mace462010-2.in". 20.045/20.045 ============================== end of head =========================== 20.045/20.045 20.045/20.045 ============================== INPUT ================================= 20.045/20.045 20.045/20.045 % Reading from file /tmp/mace462010-2.in 20.045/20.045 20.045/20.045 assign(max_seconds,20). 20.045/20.045 20.045/20.045 formulas(assumptions). 20.045/20.045 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 20.045/20.045 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 20.045/20.045 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 20.045/20.045 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 20.045/20.045 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 20.045/20.045 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 20.045/20.045 ->(s(a),t) # label(replacement). 20.045/20.045 ->(s(b),t) # label(replacement). 20.045/20.045 ->*(x,x) # label(reflexivity). 20.045/20.045 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 formulas(goals). 20.045/20.045 (exists x4 (->*(s(c),x4) & ->*(t,x4))) # label(goal). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== end of input ========================== 20.045/20.045 20.045/20.045 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.045/20.045 20.045/20.045 % Formulas that are not ordinary clauses: 20.045/20.045 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 4 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.045/20.045 7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.045/20.045 8 (exists x4 (->*(s(c),x4) & ->*(t,x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.045/20.045 20.045/20.045 ============================== end of process non-clausal formulas === 20.045/20.045 20.045/20.045 ============================== CLAUSES FOR SEARCH ==================== 20.045/20.045 20.045/20.045 formulas(mace4_clauses). 20.045/20.045 -->(x,y) | ->(f(x),f(y)) # label(congruence). 20.045/20.045 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 20.045/20.045 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 20.045/20.045 -->(x,y) | ->(s(x),s(y)) # label(congruence). 20.045/20.045 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 20.045/20.045 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 20.045/20.045 ->(s(a),t) # label(replacement). 20.045/20.045 ->(s(b),t) # label(replacement). 20.045/20.045 ->*(x,x) # label(reflexivity). 20.045/20.045 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.045/20.045 -->*(s(c),x) | -->*(t,x) # label(goal). 20.045/20.045 end_of_list. 20.045/20.045 20.045/20.045 ============================== end of clauses for search ============= 20.045/20.045 20.045/20.045 % There are no natural numbers in the input. 20.045/20.045 20.045/20.045 ============================== DOMAIN SIZE 2 ========================= 20.045/20.045 20.045/20.045 ============================== MODEL ================================= 20.045/20.045 20.045/20.045 interpretation( 2, [number=1, seconds=0], [ 20.045/20.045 20.045/20.045 function(t, [ 0 ]), 20.045/20.045 20.045/20.045 function(a, [ 0 ]), 20.045/20.045 20.045/20.045 function(b, [ 0 ]), 20.045/20.045 20.045/20.045 function(c, [ 1 ]), 20.045/20.045 20.045/20.045 function(f(_), [ 0, 0 ]), 20.045/20.045 20.045/20.045 function(s(_), [ 0, 1 ]), 20.045/20.045 20.045/20.045 function(h(_,_), [ 20.045/20.045 0, 0, 20.045/20.045 0, 0 ]), 20.045/20.045 20.045/20.045 function(g(_,_), [ 20.045/20.045 0, 0, 20.045/20.045 0, 0 ]), 20.045/20.045 20.045/20.045 relation(->*(_,_), [ 20.045/20.045 1, 0, 20.045/20.045 0, 1 ]), 20.045/20.045 20.045/20.045 relation(->(_,_), [ 20.045/20.045 1, 0, 20.045/20.045 0, 0 ]) 20.045/20.045 ]). 20.045/20.045 20.045/20.045 ============================== end of model ========================== 20.045/20.045 20.045/20.045 ============================== STATISTICS ============================ 20.045/20.045 20.045/20.045 For domain size 2. 20.045/20.045 20.045/20.045 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.045/20.045 Ground clauses: seen=54, kept=50. 20.045/20.045 Selections=15, assignments=16, propagations=13, current_models=1. 20.045/20.045 Rewrite_terms=102, rewrite_bools=70, indexes=13. 20.045/20.045 Rules_from_neg_clauses=3, cross_offs=3. 20.045/20.045 20.045/20.045 ============================== end of statistics ===================== 20.045/20.045 20.045/20.045 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.045/20.045 20.045/20.045 Exiting with 1 model. 20.045/20.045 20.045/20.045 Process 62056 exit (max_models) Wed Mar 9 09:50:00 2022 20.045/20.045 The process finished Wed Mar 9 09:50:00 2022 20.045/20.045 20.045/20.045 20.045/20.045 Mace4 cooked interpretation: 20.045/20.045 20.045/20.045 20.045/20.045 20.045/20.045 The problem is infeasible. 20.045/20.045 20.045/20.045 20.045/20.045 The problem is not joinable. 20.045/20.045 16.67user 0.63system 0:20.45elapsed 84%CPU (0avgtext+0avgdata 62396maxresident)k 20.045/20.045 8inputs+0outputs (0major+38553minor)pagefaults 0swaps