TSTP Solution File: LAT072-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT072-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 06:25:25 EDT 2022
% Result : Unsatisfiable 111.49s 111.79s
% Output : Refutation 111.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT072-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 30 11:03:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 111.49/111.79 ============================== Prover9 ===============================
% 111.49/111.79 Prover9 (32) version 2009-11A, November 2009.
% 111.49/111.79 Process 6125 was started by sandbox on n019.cluster.edu,
% 111.49/111.79 Thu Jun 30 11:03:24 2022
% 111.49/111.79 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5968_n019.cluster.edu".
% 111.49/111.79 ============================== end of head ===========================
% 111.49/111.79
% 111.49/111.79 ============================== INPUT =================================
% 111.49/111.79
% 111.49/111.79 % Reading from file /tmp/Prover9_5968_n019.cluster.edu
% 111.49/111.79
% 111.49/111.79 set(prolog_style_variables).
% 111.49/111.79 set(auto2).
% 111.49/111.79 % set(auto2) -> set(auto).
% 111.49/111.79 % set(auto) -> set(auto_inference).
% 111.49/111.79 % set(auto) -> set(auto_setup).
% 111.49/111.79 % set(auto_setup) -> set(predicate_elim).
% 111.49/111.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 111.49/111.79 % set(auto) -> set(auto_limits).
% 111.49/111.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 111.49/111.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 111.49/111.79 % set(auto) -> set(auto_denials).
% 111.49/111.79 % set(auto) -> set(auto_process).
% 111.49/111.79 % set(auto2) -> assign(new_constants, 1).
% 111.49/111.79 % set(auto2) -> assign(fold_denial_max, 3).
% 111.49/111.79 % set(auto2) -> assign(max_weight, "200.000").
% 111.49/111.79 % set(auto2) -> assign(max_hours, 1).
% 111.49/111.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 111.49/111.79 % set(auto2) -> assign(max_seconds, 0).
% 111.49/111.79 % set(auto2) -> assign(max_minutes, 5).
% 111.49/111.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 111.49/111.79 % set(auto2) -> set(sort_initial_sos).
% 111.49/111.79 % set(auto2) -> assign(sos_limit, -1).
% 111.49/111.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 111.49/111.79 % set(auto2) -> assign(max_megs, 400).
% 111.49/111.79 % set(auto2) -> assign(stats, some).
% 111.49/111.79 % set(auto2) -> clear(echo_input).
% 111.49/111.79 % set(auto2) -> set(quiet).
% 111.49/111.79 % set(auto2) -> clear(print_initial_clauses).
% 111.49/111.79 % set(auto2) -> clear(print_given).
% 111.49/111.79 assign(lrs_ticks,-1).
% 111.49/111.79 assign(sos_limit,10000).
% 111.49/111.79 assign(order,kbo).
% 111.49/111.79 set(lex_order_vars).
% 111.49/111.79 clear(print_given).
% 111.49/111.79
% 111.49/111.79 % formulas(sos). % not echoed (2 formulas)
% 111.49/111.79
% 111.49/111.79 ============================== end of input ==========================
% 111.49/111.79
% 111.49/111.79 % From the command line: assign(max_seconds, 300).
% 111.49/111.79
% 111.49/111.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 111.49/111.79
% 111.49/111.79 % Formulas that are not ordinary clauses:
% 111.49/111.79
% 111.49/111.79 ============================== end of process non-clausal formulas ===
% 111.49/111.79
% 111.49/111.79 ============================== PROCESS INITIAL CLAUSES ===============
% 111.49/111.79
% 111.49/111.79 ============================== PREDICATE ELIMINATION =================
% 111.49/111.79
% 111.49/111.79 ============================== end predicate elimination =============
% 111.49/111.79
% 111.49/111.79 Auto_denials:
% 111.49/111.79 % copying label associativity to answer in negative clause
% 111.49/111.79
% 111.49/111.79 Term ordering decisions:
% 111.49/111.79 Function symbol KB weights: a=1. b=1. c=1. f=1.
% 111.49/111.79
% 111.49/111.79 ============================== end of process initial clauses ========
% 111.49/111.79
% 111.49/111.79 ============================== CLAUSES FOR SEARCH ====================
% 111.49/111.79
% 111.49/111.79 ============================== end of clauses for search =============
% 111.49/111.79
% 111.49/111.79 ============================== SEARCH ================================
% 111.49/111.79
% 111.49/111.79 % Starting search at 0.01 seconds.
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=61.000, iters=3336
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=59.000, iters=3428
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=55.000, iters=3379
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=49.000, iters=3347
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=47.000, iters=3390
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=45.000, iters=3406
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=43.000, iters=3347
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=41.000, iters=3361
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=39.000, iters=3381
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=37.000, iters=3342
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=35.000, iters=3371
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=33.000, iters=3348
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=31.000, iters=3357
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=29.000, iters=3355
% 111.49/111.79
% 111.49/111.79 Low Water (keep): wt=27.000, iters=3355
% 111.49/111.79
% 111.49/111.79 Low Water (displace): id=19299, wt=25.000
% 111.49/111.79
% 111.49/111.79 Low Water (displace): id=19314, wt=19.000
% 111.49/111.79
% 111.49/111.79 Low Water (displace): id=19433, wt=17.000
% 111.49/111.79
% 111.49/111.79 ============================== PROOF =================================
% 111.49/111.79 % SZS status Unsatisfiable
% 111.49/111.79 % SZS output start Refutation
% 111.49/111.79
% 111.49/111.79 % Proof 1 at 109.83 (+ 0.96) seconds: associativity.
% 111.49/111.79 % Length of proof is 169.
% 111.49/111.79 % Level of proof is 35.
% 111.49/111.79 % Maximum clause weight is 97.000.
% 111.49/111.79 % Given clauses 844.
% 111.49/111.79
% 111.49/111.79 1 f(f(f(f(A,B),f(B,C)),D),f(B,f(f(C,f(f(B,B),C)),C))) = B # label(oml_23A) # label(axiom). [assumption].
% 111.49/111.79 2 f(a,f(f(b,c),f(b,c))) != f(c,f(f(b,a),f(b,a))) # label(associativity) # label(negated_conjecture) # answer(associativity). [assumption].
% 111.49/111.79 3 f(c,f(f(b,a),f(b,a))) != f(a,f(f(b,c),f(b,c))) # answer(associativity). [copy(2),flip(a)].
% 111.49/111.79 7 f(A,f(f(A,B),f(f(C,f(f(f(A,B),f(A,B)),C)),C))) = f(A,B). [para(1(a,1),1(a,1,1))].
% 111.49/111.79 14 f(f(f(f(A,B),f(B,C)),D),f(B,f(f(E,f(f(B,B),E)),E))) = B. [para(1(a,1),7(a,1,2,1)),rewrite([1(14),1(14),1(20)])].
% 111.49/111.79 21 f(f(f(f(A,f(f(f(B,C),f(C,D)),E)),C),F),f(f(f(f(B,C),f(C,D)),E),f(f(V6,f(f(f(f(f(B,C),f(C,D)),E),f(f(f(B,C),f(C,D)),E)),V6)),V6))) = f(f(f(B,C),f(C,D)),E). [para(14(a,1),14(a,1,1,1,2))].
% 111.49/111.79 22 f(f(A,B),f(A,f(f(C,f(f(A,A),C)),C))) = A. [para(14(a,1),14(a,1,1,1))].
% 111.49/111.79 23 f(f(f(f(A,f(f(B,C),f(C,D))),f(f(f(B,C),f(C,D)),E)),F),f(f(f(B,C),f(C,D)),f(f(f(C,f(f(V6,f(f(C,C),V6)),V6)),C),f(C,f(f(V6,f(f(C,C),V6)),V6))))) = f(f(B,C),f(C,D)). [para(14(a,1),14(a,1,2,2,1,2))].
% 111.49/111.79 29 f(A,f(f(A,B),f(f(f(f(A,B),f(f(C,f(f(f(A,B),f(A,B)),C)),C)),f(A,B)),f(f(A,B),f(f(C,f(f(f(A,B),f(A,B)),C)),C))))) = f(A,B). [para(22(a,1),7(a,1,2,2,1,2))].
% 111.49/111.79 30 f(f(A,B),f(A,f(f(f(f(f(A,A),C),f(f(D,f(f(f(f(A,A),C),f(f(A,A),C)),D)),D)),f(f(A,A),C)),f(f(f(A,A),C),f(f(D,f(f(f(f(A,A),C),f(f(A,A),C)),D)),D))))) = A. [para(7(a,1),22(a,1,2,2,1,2))].
% 111.49/111.79 32 f(f(A,B),f(B,f(f(C,f(f(B,B),C)),C))) = B. [para(22(a,1),14(a,1,1))].
% 111.49/111.79 34 f(f(f(f(A,B),f(B,C)),D),f(B,B)) = B. [para(22(a,1),14(a,1,2,2,1,2)),rewrite([32(16)])].
% 111.49/111.79 36 f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),B)) = f(f(A,B),f(B,C)). [para(14(a,1),22(a,1,2,2,1,2)),rewrite([32(19)])].
% 111.49/111.79 38 f(f(A,B),f(A,A)) = A. [para(22(a,1),22(a,1,2,2,1,2)),rewrite([32(13)])].
% 111.49/111.79 39 f(f(A,B),f(A,f(f(A,A),C))) = A. [back_rewrite(30),rewrite([32(27)])].
% 111.49/111.79 40 f(A,f(f(A,B),f(A,B))) = f(A,B). [back_rewrite(29),rewrite([32(20)])].
% 111.49/111.79 41 f(f(f(f(A,f(f(B,C),f(C,D))),f(f(f(B,C),f(C,D)),E)),F),f(f(f(B,C),f(C,D)),C)) = f(f(B,C),f(C,D)). [back_rewrite(23),rewrite([32(25)])].
% 111.49/111.79 49 f(f(f(f(A,f(B,B)),f(f(B,B),C)),D),f(f(B,B),f(f(E,f(B,E)),E))) = f(B,B). [para(38(a,1),14(a,1,2,2,1,2,1))].
% 111.49/111.79 51 f(A,f(f(f(f(B,A),f(A,C)),D),f(f(f(B,A),f(A,C)),D))) = f(f(f(B,A),f(A,C)),D). [para(14(a,1),38(a,1,1))].
% 111.49/111.79 52 f(f(f(A,A),B),f(f(A,A),f(f(C,f(A,C)),C))) = f(A,A). [para(38(a,1),22(a,1,2,2,1,2,1))].
% 111.49/111.79 55 f(f(f(A,A),B),A) = f(A,A). [para(38(a,1),38(a,1,2))].
% 111.49/111.79 56 f(f(A,f(f(f(B,C),f(C,D)),E)),f(f(f(A,f(f(f(B,C),f(C,D)),E)),C),f(f(f(B,C),f(C,D)),E))) = f(f(A,f(f(f(B,C),f(C,D)),E)),C). [para(21(a,1),7(a,1,2,2,1,2)),rewrite([32(51)])].
% 111.49/111.79 70 f(f(f(f(A,f(f(f(B,C),f(C,D)),E)),C),F),f(f(f(f(B,C),f(C,D)),E),f(f(f(B,C),f(C,D)),E))) = f(f(f(B,C),f(C,D)),E). [para(22(a,1),21(a,1,2,2,1,2)),rewrite([32(51)])].
% 111.49/111.79 71 f(f(f(f(A,B),f(B,C)),D),f(f(f(f(E,f(f(f(A,B),f(B,C)),D)),B),F),f(f(f(E,f(f(f(A,B),f(B,C)),D)),B),F))) = f(f(f(E,f(f(f(A,B),f(B,C)),D)),B),F). [para(21(a,1),38(a,1,1))].
% 111.49/111.79 80 f(f(f(A,B),f(B,C)),f(f(A,B),f(B,C))) = f(B,f(f(A,B),f(B,C))). [para(14(a,1),55(a,1,1)),flip(a)].
% 111.49/111.79 85 f(f(f(A,f(f(f(B,C),f(C,D)),E)),C),f(f(A,f(f(f(B,C),f(C,D)),E)),C)) = f(f(f(f(B,C),f(C,D)),E),f(f(A,f(f(f(B,C),f(C,D)),E)),C)). [para(21(a,1),55(a,1,1)),flip(a)].
% 111.49/111.79 104 f(f(A,B),f(f(f(f(C,f(A,f(f(A,A),D))),f(f(A,f(f(A,A),D)),E)),F),f(f(V6,f(f(f(f(f(C,f(A,f(f(A,A),D))),f(f(A,f(f(A,A),D)),E)),F),f(f(f(C,f(A,f(f(A,A),D))),f(f(A,f(f(A,A),D)),E)),F)),V6)),V6))) = f(f(f(C,f(A,f(f(A,A),D))),f(f(A,f(f(A,A),D)),E)),F). [para(39(a,1),21(a,1,1,1))].
% 111.49/111.79 112 f(A,f(f(B,f(f(A,A),B)),B)) = f(A,A). [para(22(a,1),40(a,1,2)),flip(a)].
% 111.49/111.79 116 f(A,f(f(A,A),B)) = f(A,A). [para(39(a,1),40(a,1,2)),flip(a)].
% 111.49/111.79 117 f(f(A,B),f(f(f(f(C,f(A,A)),f(f(A,A),D)),E),f(f(f(C,f(A,A)),f(f(A,A),D)),E))) = f(f(f(C,f(A,A)),f(f(A,A),D)),E). [back_rewrite(104),rewrite([116(4),116(6),116(10),116(12),116(16),116(18),112(24),116(18),116(20)])].
% 111.49/111.79 127 f(f(A,B),f(B,B)) = B. [back_rewrite(32),rewrite([112(6)])].
% 111.49/111.79 129 f(A,f(f(B,A),f(B,A))) = f(B,A). [para(127(a,1),38(a,1,1))].
% 111.49/111.79 130 f(f(A,f(B,B)),B) = f(B,B). [para(38(a,1),127(a,1,2))].
% 111.49/111.79 131 f(f(f(f(A,f(B,B)),f(f(B,B),C)),D),B) = f(B,B). [para(38(a,1),34(a,1,2))].
% 111.49/111.79 132 f(f(A,A),f(A,B)) = A. [para(38(a,1),116(a,1,2,1)),rewrite([38(6)])].
% 111.49/111.79 134 f(f(f(A,B),f(B,C)),B) = f(B,f(f(A,B),f(B,C))). [para(34(a,1),116(a,1,2)),rewrite([80(11)])].
% 111.49/111.79 141 f(f(f(f(A,f(f(B,C),f(C,D))),f(f(f(B,C),f(C,D)),E)),F),f(C,f(f(B,C),f(C,D)))) = f(f(B,C),f(C,D)). [back_rewrite(41),rewrite([134(14)])].
% 111.49/111.79 142 f(f(f(f(A,B),f(B,C)),D),f(B,f(f(A,B),f(B,C)))) = f(f(A,B),f(B,C)). [back_rewrite(36),rewrite([134(8)])].
% 111.49/111.79 143 f(f(f(A,B),f(A,B)),A) = f(A,B). [para(38(a,1),132(a,1,2))].
% 111.49/111.79 147 f(f(f(f(A,B),f(C,B)),D),f(B,B)) = B. [para(129(a,1),34(a,1,1,1,2))].
% 111.49/111.79 148 f(f(A,f(f(B,C),f(C,D))),f(C,C)) = C. [para(129(a,1),34(a,1,1))].
% 111.49/111.79 150 f(f(A,A),f(B,A)) = A. [para(129(a,1),132(a,1,2))].
% 111.49/111.79 153 f(f(A,A),f(f(B,f(A,B)),B)) = A. [para(49(a,1),127(a,1,1)),rewrite([52(12),132(3)]),flip(a)].
% 111.49/111.79 160 f(f(f(f(A,B),f(A,C)),D),f(A,A)) = A. [para(143(a,1),34(a,1,1,1,1))].
% 111.49/111.79 161 f(f(A,A),f(f(f(B,A),f(A,C)),D)) = A. [para(34(a,1),143(a,1,1,1)),rewrite([34(6),34(12)])].
% 111.49/111.79 166 f(f(f(f(A,f(f(B,C),f(C,D))),f(f(f(B,C),f(C,D)),E)),F),f(C,C)) = C. [para(51(a,1),34(a,1,1))].
% 111.49/111.79 170 f(f(f(A,B),f(B,C)),f(f(B,f(f(A,B),f(B,C))),D)) = f(B,f(f(A,B),f(B,C))). [para(116(a,1),51(a,1,2,2)),rewrite([80(10),80(16),142(14),80(14)]),flip(a)].
% 111.49/111.79 183 f(A,f(f(f(A,B),A),f(A,B))) = f(A,A). [para(132(a,1),153(a,1,2,1,2)),rewrite([132(3)])].
% 111.49/111.79 201 f(f(f(A,B),f(C,B)),f(f(A,B),f(C,B))) = f(B,f(f(A,B),f(C,B))). [para(147(a,1),55(a,1,1)),flip(a)].
% 111.49/111.79 203 f(f(f(A,B),f(C,B)),B) = f(B,f(f(A,B),f(C,B))). [para(147(a,1),116(a,1,2)),rewrite([201(11)])].
% 111.49/111.79 207 f(f(A,f(f(B,C),f(D,C))),f(C,C)) = C. [para(129(a,1),147(a,1,1))].
% 111.49/111.79 209 f(f(A,A),f(f(f(B,A),f(C,A)),D)) = A. [para(147(a,1),143(a,1,1,1)),rewrite([147(6),147(12)])].
% 111.49/111.79 210 f(f(f(f(A,B),f(C,A)),D),f(A,A)) = A. [para(143(a,1),147(a,1,1,1,1))].
% 111.49/111.79 212 f(f(f(f(A,f(f(B,C),f(D,C))),f(f(f(B,C),f(D,C)),E)),F),f(C,C)) = C. [para(51(a,1),147(a,1,1))].
% 111.49/111.79 221 f(f(A,f(f(f(B,f(C,D)),D),E)),f(f(f(A,f(f(f(B,f(C,D)),D),E)),f(C,D)),f(f(f(B,f(C,D)),D),E))) = f(f(A,f(f(f(B,f(C,D)),D),E)),f(C,D)). [para(127(a,1),56(a,1,1,2,1,2)),rewrite([127(10),127(17),127(23)])].
% 111.49/111.79 232 f(f(A,f(f(B,f(f(C,B),D)),E)),f(f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B)),f(f(B,f(f(C,B),D)),E))) = f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B)). [para(150(a,1),56(a,1,1,2,1,1)),rewrite([150(8),150(15),150(21)])].
% 111.49/111.79 233 f(A,f(f(A,B),f(f(f(C,B),f(B,D)),A))) = f(A,B). [para(150(a,1),56(a,1,1)),rewrite([150(6),150(13)])].
% 111.49/111.79 236 f(f(f(f(f(A,B),f(B,C)),D),E),f(f(f(f(f(f(A,B),f(B,C)),D),E),B),f(f(f(A,B),f(B,C)),D))) = f(f(f(f(f(A,B),f(B,C)),D),E),B). [para(143(a,1),56(a,1,1)),rewrite([143(21),143(33)])].
% 111.49/111.79 265 f(f(A,f(f(B,C),f(B,D))),f(B,B)) = B. [para(143(a,1),148(a,1,1,2,1))].
% 111.49/111.79 282 f(f(A,A),f(f(f(A,B),f(A,C)),D)) = A. [para(160(a,1),143(a,1,1,1)),rewrite([160(6),160(12)])].
% 111.49/111.79 317 f(f(f(A,B),A),f(A,B)) = A. [para(183(a,1),127(a,1,1)),rewrite([80(10),183(6),132(3)]),flip(a)].
% 111.49/111.79 327 f(f(f(A,A),B),f(f(A,C),f(A,C))) = f(A,C). [para(116(a,1),70(a,1,1,1,1)),rewrite([132(3),132(5),132(6),132(9)])].
% 111.49/111.79 347 f(f(A,f(A,B)),A) = f(A,B). [para(38(a,1),317(a,1,1,1)),rewrite([38(5)])].
% 111.49/111.79 348 f(f(A,f(B,A)),A) = f(B,A). [para(127(a,1),317(a,1,1,1)),rewrite([127(5)])].
% 111.49/111.79 350 f(f(f(A,B),B),f(A,B)) = B. [para(129(a,1),317(a,1,1,1)),rewrite([129(6)])].
% 111.49/111.79 353 f(A,f(f(A,B),A)) = f(A,B). [para(317(a,1),51(a,2)),rewrite([317(4),317(7),40(8)])].
% 111.49/111.79 362 f(f(A,A),A) = f(A,f(A,A)). [para(150(a,1),347(a,1,1)),flip(a)].
% 111.49/111.79 367 f(f(A,B),f(A,f(A,B))) = A. [para(347(a,1),317(a,1,1))].
% 111.49/111.79 368 f(f(f(A,B),f(B,C)),f(B,B)) = f(B,f(B,B)). [para(161(a,1),348(a,1,1)),flip(a)].
% 111.49/111.79 369 f(f(A,B),f(B,f(A,B))) = B. [para(348(a,1),317(a,1,1))].
% 111.49/111.79 370 f(A,f(f(B,A),A)) = f(B,A). [para(350(a,1),317(a,1,1))].
% 111.49/111.79 379 f(f(A,B),f(f(f(A,A),C),f(f(A,A),C))) = f(f(A,A),C). [para(116(a,1),71(a,1,2,1,1,1)),rewrite([132(3),132(4),132(7),132(6),132(11),132(10)])].
% 111.49/111.79 441 f(f(A,f(f(B,C),f(C,D))),f(C,f(f(B,C),f(C,D)))) = f(f(B,C),f(C,D)). [para(80(a,1),127(a,1,2))].
% 111.49/111.79 484 f(f(A,f(f(B,C),f(D,B))),f(B,B)) = B. [para(347(a,1),207(a,1,1,2,1))].
% 111.49/111.79 497 f(f(A,A),f(B,f(f(C,A),f(D,A)))) = A. [para(129(a,1),209(a,1,2))].
% 111.49/111.79 506 f(f(A,A),f(f(f(A,B),f(C,A)),D)) = A. [para(347(a,1),209(a,1,2,1,1))].
% 111.49/111.79 515 f(f(f(A,B),f(C,A)),f(f(A,B),f(C,A))) = f(A,f(f(A,B),f(C,A))). [para(210(a,1),55(a,1,1)),flip(a)].
% 111.49/111.79 517 f(f(f(A,B),f(C,A)),A) = f(A,f(f(A,B),f(C,A))). [para(210(a,1),116(a,1,2)),rewrite([515(11)])].
% 111.49/111.79 554 f(f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B)),f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B))) = f(f(f(B,f(f(C,B),D)),E),f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B))). [para(150(a,1),85(a,1,1,1,2,1,1)),rewrite([150(10),150(18),150(22)])].
% 111.49/111.79 646 f(f(A,A),f(f(A,B),f(A,C))) = f(A,f(A,A)). [para(265(a,1),353(a,1,2)),rewrite([362(2)]),flip(a)].
% 111.49/111.79 715 f(f(A,A),f(f(A,B),f(C,A))) = f(A,f(A,A)). [para(484(a,1),353(a,1,2)),rewrite([362(2)]),flip(a)].
% 111.49/111.79 798 f(f(f(A,B),f(A,B)),f(C,f(A,f(D,f(A,B))))) = f(A,B). [para(132(a,1),497(a,1,2,2,1))].
% 111.49/111.79 804 f(f(A,A),f(B,f(f(A,C),f(D,A)))) = A. [para(347(a,1),497(a,1,2,2,1))].
% 111.49/111.79 834 f(f(f(f(A,B),f(B,A)),C),f(A,B)) = f(f(A,B),f(A,B)). [para(506(a,1),85(a,1,1,1)),rewrite([506(7),506(13)]),flip(a)].
% 111.49/111.79 992 f(f(A,B),f(f(A,B),f(A,B))) = f(A,f(A,A)). [para(327(a,1),370(a,1,2)),rewrite([362(5),646(10)])].
% 111.49/111.79 1051 f(f(A,f(A,A)),f(B,B)) = B. [para(368(a,1),207(a,1,1)),rewrite([992(5)])].
% 111.49/111.79 1069 f(f(A,A),f(B,f(B,B))) = A. [para(368(a,1),497(a,1,2)),rewrite([992(6)])].
% 111.49/111.79 1084 f(f(A,f(A,A)),B) = f(B,B). [para(38(a,1),1051(a,1,2))].
% 111.49/111.79 1088 f(f(f(A,f(A,A)),B),f(A,f(A,A))) = B. [para(1051(a,1),347(a,1,1,2)),rewrite([1051(10)])].
% 111.49/111.79 1096 f(f(A,f(A,A)),f(B,f(A,f(A,A)))) = B. [para(1051(a,1),353(a,1,2,1)),rewrite([1051(10)])].
% 111.49/111.79 1108 f(A,f(B,f(B,B))) = f(A,A). [para(38(a,1),1069(a,1,1))].
% 111.49/111.79 1233 f(c,f(f(A,f(A,A)),f(b,a))) != f(a,f(f(b,c),f(b,c))) # answer(associativity). [para(1084(a,2),3(a,1,2))].
% 111.49/111.79 1237 f(A,f(f(B,f(B,B)),f(A,C))) = f(A,C). [para(1084(a,2),40(a,1,2))].
% 111.49/111.79 1243 f(A,f(f(B,f(B,B)),f(C,A))) = f(C,A). [para(1084(a,2),129(a,1,2))].
% 111.49/111.79 1254 f(f(f(f(A,f(A,A)),f(B,C)),D),f(C,C)) = C. [para(1084(a,2),147(a,1,1,1))].
% 111.49/111.79 1268 f(A,f(A,A)) = f(B,f(B,B)). [para(1084(a,1),317(a,1,2)),rewrite([1088(6)])].
% 111.49/111.79 1269 f(f(A,f(A,A)),B) = f(B,f(A,f(A,A))). [para(1084(a,1),347(a,1,1,2)),rewrite([1051(4)]),flip(a)].
% 111.49/111.79 1297 f(f(A,f(f(B,f(B,B)),f(C,D))),f(D,D)) = D. [para(1084(a,2),207(a,1,1,2))].
% 111.49/111.79 1320 f(f(A,A),f(f(f(B,f(B,B)),f(A,C)),D)) = A. [para(1084(a,2),282(a,1,2,1))].
% 111.49/111.79 1333 f(f(f(A,f(A,A)),B),C) = f(f(B,B),C). [para(1084(a,2),117(a,2,1)),rewrite([132(4),132(4),132(6),132(6),379(7),132(7)]),flip(a)].
% 111.49/111.79 1336 f(f(A,A),f(B,f(f(C,f(C,C)),f(D,A)))) = A. [para(1084(a,2),497(a,1,2,2))].
% 111.49/111.79 1387 f(A,f(A,A)) = c_0. [new_symbol(1268)].
% 111.49/111.79 1428 f(f(A,A),f(B,f(c_0,f(C,A)))) = A. [back_rewrite(1336),rewrite([1387(3)])].
% 111.49/111.79 1431 f(f(c_0,A),B) = f(f(A,A),B). [back_rewrite(1333),rewrite([1387(2)])].
% 111.49/111.79 1443 f(f(A,A),f(f(c_0,f(A,B)),C)) = A. [back_rewrite(1320),rewrite([1387(3)])].
% 111.49/111.79 1461 f(f(A,f(c_0,f(B,C))),f(C,C)) = C. [back_rewrite(1297),rewrite([1387(2)])].
% 111.49/111.79 1477 f(c_0,A) = f(A,c_0). [back_rewrite(1269),rewrite([1387(2),1387(4)])].
% 111.49/111.79 1489 f(f(f(c_0,f(A,B)),C),f(B,B)) = B. [back_rewrite(1254),rewrite([1387(2)])].
% 111.49/111.79 1497 f(A,f(c_0,f(B,A))) = f(B,A). [back_rewrite(1243),rewrite([1387(2)])].
% 111.49/111.79 1503 f(A,f(c_0,f(A,B))) = f(A,B). [back_rewrite(1237),rewrite([1387(2)])].
% 111.49/111.79 1507 f(a,f(f(b,c),f(b,c))) != f(c,f(c_0,f(b,a))) # answer(associativity). [back_rewrite(1233),rewrite([1387(3)]),flip(a)].
% 111.49/111.79 1519 f(A,c_0) = f(A,A). [back_rewrite(1108),rewrite([1387(2)])].
% 111.49/111.79 1525 f(c_0,f(A,c_0)) = A. [back_rewrite(1096),rewrite([1387(2),1387(3)])].
% 111.49/111.79 1539 f(c_0,f(A,A)) = A. [back_rewrite(1069),rewrite([1387(3),1477(3,R)])].
% 111.49/111.79 1560 f(f(A,A),f(f(A,B),f(C,A))) = c_0. [back_rewrite(715),rewrite([1387(7)])].
% 111.49/111.79 1691 f(f(c_0,f(A,B)),f(C,f(A,f(D,f(A,B))))) = f(A,B). [back_rewrite(798),rewrite([1519(3,R),1477(3,R)])].
% 111.49/111.79 1838 f(f(A,c_0),B) = f(f(A,A),B). [back_rewrite(1431),rewrite([1477(2)])].
% 111.49/111.79 1852 f(c,f(c_0,f(b,a))) != f(a,f(c_0,f(b,c))) # answer(associativity). [back_rewrite(1507),rewrite([1519(8,R),1477(6,R)]),flip(a)].
% 111.49/111.79 1985 f(f(f(f(A,B),f(B,A)),C),f(A,B)) = f(c_0,f(A,B)). [back_rewrite(834),rewrite([1519(9,R),1477(9,R)])].
% 111.49/111.79 2110 f(f(f(A,f(f(B,A),C)),D),f(f(E,f(f(A,f(f(B,A),C)),D)),f(B,A))) = f(c_0,f(f(E,f(f(A,f(f(B,A),C)),D)),f(B,A))). [back_rewrite(554),rewrite([1519(15,R),1477(9,R)]),flip(a)].
% 111.49/111.79 2322 f(A,f(f(f(f(B,f(c_0,f(A,C))),f(f(c_0,f(A,C)),D)),A),f(A,C))) = f(f(c_0,f(A,C)),A). [para(131(a,1),134(a,1,1)),rewrite([1519(3,R),1477(3,R),1519(7,R),1477(7,R),1519(11,R),1477(11,R)]),flip(a)].
% 111.49/111.79 2323 f(f(c_0,f(A,B)),A) = f(A,B). [para(131(a,1),134(a,2,2)),rewrite([1519(3,R),1477(3,R),1519(7,R),1477(7,R),134(13),2322(13),1519(7,R),1477(7,R),1503(8)])].
% 111.49/111.79 2493 f(c_0,f(c_0,f(A,B))) = f(A,B). [para(1497(a,1),1497(a,1,2,2)),rewrite([1519(7,R),1477(5,R),1497(9)])].
% 111.49/111.79 2539 f(f(A,B),f(C,f(f(f(c_0,f(A,B)),D),f(A,B)))) = f(c_0,f(A,B)). [para(1503(a,1),804(a,1,2,2,2)),rewrite([1519(7,R),1477(5,R),2493(5)])].
% 111.49/111.79 2540 f(f(f(c_0,f(A,B)),C),f(A,B)) = f(c_0,f(A,B)). [para(55(a,1),142(a,1,1,1)),rewrite([1519(3,R),1477(3,R),1519(7,R),1477(7,R),2323(8),1519(7,R),1477(7,R),1503(8),1519(9,R),1477(9,R),2323(10),1519(9,R),1477(9,R)])].
% 111.49/111.79 2557 f(f(A,B),f(C,f(c_0,f(A,B)))) = f(c_0,f(A,B)). [back_rewrite(2539),rewrite([2540(7)])].
% 111.49/111.79 3053 f(A,f(f(B,A),f(A,B))) = f(B,f(f(B,A),f(A,B))). [para(484(a,1),170(a,1,2)),rewrite([517(4)]),flip(a)].
% 111.49/111.79 3101 f(f(c_0,f(A,B)),f(C,f(A,B))) = f(A,B). [para(2493(a,1),1428(a,1,2,2)),rewrite([1519(3,R),1477(3,R)])].
% 111.49/111.79 3116 f(f(c_0,f(A,f(B,B))),f(B,C)) = f(A,f(B,B)). [para(130(a,1),1443(a,1,2,1,2)),rewrite([1519(5,R),1477(4,R),1539(7)])].
% 111.49/111.79 3274 f(f(A,f(B,C)),f(c_0,f(B,C))) = f(B,C). [para(2493(a,1),1461(a,1,1,2)),rewrite([1519(5,R),1477(5,R)])].
% 111.49/111.79 3316 f(f(f(f(A,f(f(B,f(f(c_0,f(C,D)),E)),D)),f(f(f(B,f(f(c_0,f(C,D)),E)),D),F)),V6),f(c_0,f(f(c_0,f(C,D)),E))) = f(f(c_0,f(C,D)),E). [para(1489(a,1),166(a,1,1,1,1,2,2)),rewrite([1489(18),1519(25,R),1477(22,R)])].
% 111.49/111.79 3322 f(f(c_0,f(A,B)),f(A,f(C,f(A,B)))) = c_0. [para(38(a,1),1560(a,1,2,1)),rewrite([1519(3,R),1477(3,R)])].
% 111.49/111.79 3323 f(f(c_0,f(A,B)),f(B,f(C,f(A,B)))) = c_0. [para(127(a,1),1560(a,1,2,1)),rewrite([1519(3,R),1477(3,R)])].
% 111.49/111.79 3891 f(f(f(A,f(f(f(f(B,f(C,D)),D),E),f(F,f(f(B,f(C,D)),D)))),f(c_0,f(f(B,f(C,D)),D))),f(C,D)) = f(c_0,f(f(B,f(C,D)),D)). [para(484(a,1),221(a,1,1)),rewrite([1519(20,R),1477(18,R),1519(28,R),1477(26,R),2557(28),1519(22,R),1477(20,R)]),flip(a)].
% 111.49/111.79 4720 f(f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B)),f(f(B,f(f(C,B),D)),E)) = f(c_0,f(f(A,f(f(B,f(f(C,B),D)),E)),f(C,B))). [para(232(a,1),203(a,1,1)),rewrite([232(34),2110(24)])].
% 111.49/111.79 4734 f(f(f(f(A,f(f(B,f(f(C,f(f(D,C),E)),F)),f(D,C))),f(f(f(B,f(f(C,f(f(D,C),E)),F)),f(D,C)),V6)),V7),f(c_0,f(f(C,f(f(D,C),E)),F))) = f(f(C,f(f(D,C),E)),F). [para(232(a,1),212(a,1,1,1,1,2)),rewrite([4720(25),1503(23),1519(27,R),1477(24,R)])].
% 111.49/111.79 4770 f(A,f(f(A,B),f(B,A))) = f(A,B). [para(38(a,1),233(a,1,2,2,1))].
% 111.49/111.79 4873 f(A,f(f(B,A),f(A,B))) = f(B,A). [back_rewrite(3053),rewrite([4770(8)])].
% 111.49/111.79 4911 f(f(A,B),f(B,A)) = f(c_0,f(A,B)). [para(4873(a,1),142(a,1,2)),rewrite([1985(6)]),flip(a)].
% 111.49/111.79 4914 f(A,f(f(f(B,c_0),A),f(A,f(B,B)))) = f(f(B,B),A). [para(1838(a,2),4873(a,1,2,1))].
% 111.49/111.79 5227 f(f(c_0,f(A,B)),f(c_0,f(B,A))) = f(B,A). [para(4911(a,1),127(a,1,1)),rewrite([1519(6,R),1477(6,R)])].
% 111.49/111.79 5229 f(A,B) = f(B,A). [para(4911(a,1),150(a,1,2)),rewrite([1519(3,R),1477(3,R),5227(7)])].
% 111.49/111.79 5230 f(f(c_0,f(A,B)),f(C,f(f(D,f(A,B)),f(E,f(A,B))))) = f(A,B). [para(4911(a,1),141(a,1,1,1,1,2,1)),rewrite([5229(4),5229(5),3101(6),5229(4),1519(5,R),5229(5),5229(6),5229(7),3101(8),5229(4),5229(6),5229(7),5229(9),1519(10,R),5229(10),5229(11),5229(12),3101(13),1519(9,R),5229(9),5229(10),5229(12),1519(13,R),5229(13),5229(14),5229(15),3101(16)])].
% 111.49/111.79 5236 f(f(A,f(B,c_0)),f(A,f(B,B))) = f(c_0,f(A,f(B,c_0))). [para(1838(a,1),4911(a,1,2)),rewrite([5229(5)])].
% 111.49/111.79 5255 f(f(A,f(B,f(C,D))),f(f(B,f(C,D)),f(f(C,D),f(A,f(B,f(C,D)))))) = f(f(C,D),f(A,f(B,f(C,D)))). [para(4911(a,1),236(a,1,1,1,1,1)),rewrite([5229(4),5229(5),3101(6),5229(2),5229(3),5229(5),1519(6,R),5229(6),5229(7),5229(8),3101(9),5229(5),5229(6),5229(7),5229(8),5229(10),1519(11,R),5229(11),5229(12),5229(13),3101(14),5229(10),5229(11),5229(14),1519(15,R),5229(15),5229(16),5229(17),3101(18),5229(14),5229(15),5229(16),5229(17)])].
% 111.49/111.79 5258 f(c_0,f(f(A,f(B,f(f(C,D),f(D,E)))),f(f(B,f(f(C,D),f(D,E))),f(D,f(A,f(B,f(f(C,D),f(D,E)))))))) = f(f(B,f(f(C,D),f(D,E))),f(D,f(A,f(B,f(f(C,D),f(D,E)))))). [para(236(a,1),4911(a,1,1)),rewrite([5229(4),5229(5),5229(6),5229(10),5229(11),5229(12),5229(16),5229(17),5229(21),5229(22),5229(23),5255(24),5229(16),5229(17),5229(21),5229(22),5229(23),5229(27),5229(28)]),flip(a)].
% 111.49/111.79 5259 f(f(A,f(f(B,C),f(C,D))),f(C,f(E,f(A,f(f(B,C),f(C,D)))))) = f(c_0,f(C,f(E,f(A,f(f(B,C),f(C,D)))))). [para(236(a,1),4911(a,2,2)),rewrite([5229(4),5229(5),5229(9),5229(10),5229(11),5229(15),5229(16),5229(21),5229(22),5229(23),5229(27),5229(28),5229(32),5229(33),5229(34),1519(35,R),5229(19),5258(19),5229(16),5229(17),5229(18)])].
% 111.49/111.79 5356 f(A,f(B,c_0)) = f(A,f(B,B)). [back_rewrite(4914),rewrite([5229(3),5236(6),1503(6),5229(5)])].
% 111.49/111.79 5411 f(f(c_0,f(A,f(B,f(C,f(B,D))))),f(E,f(f(F,f(f(B,D),f(V6,f(A,f(B,f(C,f(B,D))))))),f(V7,f(f(B,D),f(V6,f(A,f(B,f(C,f(B,D)))))))))) = f(A,f(B,f(C,f(B,D)))). [back_rewrite(4734),rewrite([5229(1),5229(2),5229(4),5229(6),5229(7),5229(9),5229(10),5229(12),5229(14),5229(15),5229(16),5229(18),5229(20),5229(21),5229(23),5229(25),5229(26),5229(27),5229(29)])].
% 111.49/111.79 5642 f(f(A,B),f(B,f(C,f(A,B)))) = f(c_0,f(B,f(C,f(A,B)))). [back_rewrite(3891),rewrite([5229(3),5229(4),5229(7),5229(14),5229(16),5230(16),5229(5),5229(9)])].
% 111.49/111.79 5722 f(f(c_0,f(A,f(c_0,f(B,C)))),f(D,f(f(E,f(C,f(F,f(A,f(c_0,f(B,C)))))),f(V6,f(C,f(F,f(A,f(c_0,f(B,C))))))))) = f(A,f(c_0,f(B,C))). [back_rewrite(3316),rewrite([5229(4),5229(6),5229(11),5229(13),5229(14),5229(16),5229(21),5229(23),5229(27)])].
% 111.49/111.79 5997 f(c,f(c_0,f(a,b))) != f(a,f(c_0,f(b,c))) # answer(associativity). [back_rewrite(1852),rewrite([5229(5)])].
% 111.49/111.79 6186 f(f(A,c_0),f(B,f(c_0,f(C,A)))) = A. [para(5356(a,2),1461(a,1)),rewrite([5229(7)])].
% 111.49/111.79 6201 f(f(A,c_0),f(B,c_0)) = f(f(A,A),f(B,c_0)). [para(1519(a,1),441(a,2,1)),rewrite([5229(4),5229(11),3274(14),5229(8)])].
% 111.49/111.79 6625 f(f(A,B),f(f(A,B),f(C,f(A,f(D,f(A,B)))))) = f(C,f(A,f(D,f(A,B)))). [para(1691(a,1),369(a,1,1)),rewrite([1691(13),5229(7)])].
% 111.49/111.79 6799 f(f(A,c_0),f(B,B)) = f(f(A,A),f(B,c_0)). [para(1519(a,1),6201(a,1,2))].
% 111.49/111.79 7230 f(f(A,c_0),f(B,B)) = f(f(B,c_0),f(A,A)). [para(6799(a,2),5229(a,1))].
% 111.49/111.79 8003 f(f(A,c_0),f(B,C)) = f(f(B,C),f(A,A)). [para(3101(a,1),7230(a,1,2)),rewrite([5229(9),2493(9)])].
% 111.49/111.79 15204 f(f(A,c_0),f(B,f(f(C,A),f(B,A)))) = A. [para(3323(a,1),5259(a,1,2,2)),rewrite([5229(2),5229(7),5229(10),5229(13),3322(16),1525(11)])].
% 111.49/111.79 15255 f(f(A,B),f(c_0,f(A,f(f(C,B),f(A,B))))) = c_0. [para(15204(a,1),3322(a,1,2,2)),rewrite([5229(8)])].
% 111.49/111.79 15290 f(A,f(f(B,C),f(A,B))) = f(A,B). [para(15255(a,1),367(a,1,1)),rewrite([5229(5),6625(11),2493(8)])].
% 111.49/111.79 15336 f(A,f(f(A,B),f(B,C))) = f(A,B). [para(5229(a,1),15290(a,1,2))].
% 111.49/111.79 24911 f(A,f(c_0,f(B,f(C,f(A,B))))) = f(A,B). [para(15336(a,1),5411(a,2)),rewrite([5229(4),5642(6),5229(10),5229(13),5642(15),5229(21),5229(24),5642(26),5722(33)])].
% 111.49/111.79 24913 f(A,f(c_0,f(B,f(C,f(B,A))))) = f(B,A). [para(24911(a,1),5229(a,2)),rewrite([5229(2),5229(6),5229(7)])].
% 111.49/111.79 24928 f(A,f(c_0,f(B,f(C,f(A,A))))) = f(A,B). [para(3116(a,1),24911(a,1,2,2,2))].
% 111.49/111.79 25065 f(f(c_0,f(A,B)),f(c_0,f(B,C))) = f(C,f(c_0,f(A,B))). [para(6186(a,1),24913(a,1,2,2,2)),rewrite([5229(5)])].
% 111.49/111.79 25221 f(f(c_0,f(A,f(B,C))),f(B,B)) = f(A,f(B,c_0)). [para(24928(a,1),8003(a,1)),rewrite([5229(3),1519(9,R),5229(8),1525(8),5229(5)]),flip(a)].
% 111.49/111.79 25862 f(A,f(c_0,f(B,C))) = f(C,f(c_0,f(A,B))). [para(38(a,1),25221(a,1,1,2,2)),rewrite([1519(6,R),5229(6),25065(7),5229(7)]),flip(a)].
% 111.49/111.79 25863 $F # answer(associativity). [resolve(25862,a,5997,a(flip))].
% 111.49/111.79
% 111.49/111.79 % SZS output end Refutation
% 111.49/111.79 ============================== end of proof ==========================
% 111.49/111.79
% 111.49/111.79 ============================== STATISTICS ============================
% 111.49/111.79
% 111.49/111.79 Given=844. Generated=1793201. Kept=25861. proofs=1.
% 111.49/111.79 Usable=594. Sos=9999. Demods=10214. Limbo=0, Disabled=15269. Hints=0.
% 111.49/111.79 Megabytes=26.67.
% 111.49/111.79 User_CPU=109.83, System_CPU=0.96, Wall_clock=111.
% 111.49/111.79
% 111.49/111.79 ============================== end of statistics =====================
% 111.49/111.79
% 111.49/111.79 ============================== end of search =========================
% 111.49/111.79
% 111.49/111.79 THEOREM PROVED
% 111.49/111.79 % SZS status Unsatisfiable
% 111.49/111.79
% 111.49/111.79 Exiting with 1 proof.
% 111.49/111.79
% 111.49/111.79 Process 6125 exit (max_proofs) Thu Jun 30 11:05:15 2022
% 111.49/111.79 Prover9 interrupted
%------------------------------------------------------------------------------