TSTP Solution File: LAT076-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT076-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 06:25:26 EDT 2022
% Result : Unsatisfiable 83.03s 83.39s
% Output : Refutation 83.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LAT076-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.30 % Computer : n015.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 600
% 0.11/0.30 % DateTime : Wed Jun 29 10:27:10 EDT 2022
% 0.11/0.30 % CPUTime :
% 45.02/45.35 ============================== Prover9 ===============================
% 45.02/45.35 Prover9 (32) version 2009-11A, November 2009.
% 45.02/45.35 Process 3118 was started by sandbox2 on n015.cluster.edu,
% 45.02/45.35 Wed Jun 29 10:27:11 2022
% 45.02/45.35 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2965_n015.cluster.edu".
% 45.02/45.35 ============================== end of head ===========================
% 45.02/45.35
% 45.02/45.35 ============================== INPUT =================================
% 45.02/45.35
% 45.02/45.35 % Reading from file /tmp/Prover9_2965_n015.cluster.edu
% 45.02/45.35
% 45.02/45.35 set(prolog_style_variables).
% 45.02/45.35 set(auto2).
% 45.02/45.35 % set(auto2) -> set(auto).
% 45.02/45.35 % set(auto) -> set(auto_inference).
% 45.02/45.35 % set(auto) -> set(auto_setup).
% 45.02/45.35 % set(auto_setup) -> set(predicate_elim).
% 45.02/45.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 45.02/45.35 % set(auto) -> set(auto_limits).
% 45.02/45.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 45.02/45.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 45.02/45.35 % set(auto) -> set(auto_denials).
% 45.02/45.35 % set(auto) -> set(auto_process).
% 45.02/45.35 % set(auto2) -> assign(new_constants, 1).
% 45.02/45.35 % set(auto2) -> assign(fold_denial_max, 3).
% 45.02/45.35 % set(auto2) -> assign(max_weight, "200.000").
% 45.02/45.35 % set(auto2) -> assign(max_hours, 1).
% 45.02/45.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 45.02/45.35 % set(auto2) -> assign(max_seconds, 0).
% 45.02/45.35 % set(auto2) -> assign(max_minutes, 5).
% 45.02/45.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 45.02/45.35 % set(auto2) -> set(sort_initial_sos).
% 45.02/45.35 % set(auto2) -> assign(sos_limit, -1).
% 45.02/45.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 45.02/45.35 % set(auto2) -> assign(max_megs, 400).
% 45.02/45.35 % set(auto2) -> assign(stats, some).
% 45.02/45.35 % set(auto2) -> clear(echo_input).
% 45.02/45.35 % set(auto2) -> set(quiet).
% 45.02/45.35 % set(auto2) -> clear(print_initial_clauses).
% 45.02/45.35 % set(auto2) -> clear(print_given).
% 45.02/45.35 assign(lrs_ticks,-1).
% 45.02/45.35 assign(sos_limit,10000).
% 45.02/45.35 assign(order,kbo).
% 45.02/45.35 set(lex_order_vars).
% 45.02/45.35 clear(print_given).
% 45.02/45.35
% 45.02/45.35 % formulas(sos). % not echoed (2 formulas)
% 45.02/45.35
% 45.02/45.35 ============================== end of input ==========================
% 45.02/45.35
% 45.02/45.35 % From the command line: assign(max_seconds, 300).
% 45.02/45.35
% 45.02/45.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 45.02/45.35
% 45.02/45.35 % Formulas that are not ordinary clauses:
% 45.02/45.35
% 45.02/45.35 ============================== end of process non-clausal formulas ===
% 45.02/45.35
% 45.02/45.35 ============================== PROCESS INITIAL CLAUSES ===============
% 45.02/45.35
% 45.02/45.35 ============================== PREDICATE ELIMINATION =================
% 45.02/45.35
% 45.02/45.35 ============================== end predicate elimination =============
% 45.02/45.35
% 45.02/45.35 Auto_denials:
% 45.02/45.35 % copying label associativity to answer in negative clause
% 45.02/45.35
% 45.02/45.35 Term ordering decisions:
% 45.02/45.35 Function symbol KB weights: a=1. b=1. c=1. f=1.
% 45.02/45.35
% 45.02/45.35 ============================== end of process initial clauses ========
% 45.02/45.35
% 45.02/45.35 ============================== CLAUSES FOR SEARCH ====================
% 45.02/45.35
% 45.02/45.35 ============================== end of clauses for search =============
% 45.02/45.35
% 45.02/45.35 ============================== SEARCH ================================
% 45.02/45.35
% 45.02/45.35 % Starting search at 0.01 seconds.
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=195.000, iters=3345
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=193.000, iters=3478
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=191.000, iters=3504
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=169.000, iters=3451
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=163.000, iters=3414
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=161.000, iters=3428
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=157.000, iters=3336
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=147.000, iters=3379
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=145.000, iters=3405
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=131.000, iters=3460
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=127.000, iters=3426
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=125.000, iters=3423
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=121.000, iters=3400
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=117.000, iters=3361
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=113.000, iters=3388
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=111.000, iters=3378
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=109.000, iters=3430
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=105.000, iters=3366
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=101.000, iters=3360
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=93.000, iters=3355
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=91.000, iters=3338
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=87.000, iters=3345
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=85.000, iters=3395
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=79.000, iters=3393
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=75.000, iters=3343
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=67.000, iters=3443
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=63.000, iters=3356
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=57.000, iters=3428
% 45.02/45.35
% 45.02/45.35 Low Water (keep): wt=55.000, iters=3353
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=51.000, iters=3391
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=49.000, iters=3443
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=47.000, iters=3383
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=45.000, iters=3367
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=43.000, iters=3349
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=41.000, iters=3336
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=39.000, iters=3334
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=37.000, iters=3390
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=35.000, iters=3424
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=33.000, iters=3356
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=31.000, iters=3336
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=9618, wt=199.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=9806, wt=197.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=9800, wt=195.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=9899, wt=193.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=6634, wt=191.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=6470, wt=189.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=5806, wt=185.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=18315, wt=23.000
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=29.000, iters=3364
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=18957, wt=21.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=18966, wt=19.000
% 83.03/83.39
% 83.03/83.39 Low Water (displace): id=20010, wt=17.000
% 83.03/83.39
% 83.03/83.39 Low Water (keep): wt=27.000, iters=3336
% 83.03/83.39
% 83.03/83.39 ============================== PROOF =================================
% 83.03/83.39 % SZS status Unsatisfiable
% 83.03/83.39 % SZS output start Refutation
% 83.03/83.39
% 83.03/83.39 % Proof 1 at 81.96 (+ 0.47) seconds: associativity.
% 83.03/83.39 % Length of proof is 143.
% 83.03/83.39 % Level of proof is 32.
% 83.03/83.39 % Maximum clause weight is 187.000.
% 83.03/83.39 % Given clauses 568.
% 83.03/83.39
% 83.03/83.39 1 f(f(f(f(A,B),f(C,B)),D),f(B,f(f(f(f(f(f(A,A),B),C),C),B),A))) = B # label(mol_27B1) # label(axiom). [assumption].
% 83.03/83.39 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].
% 83.03/83.39 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)].
% 83.03/83.39 4 f(f(f(A,f(B,f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)))),E),f(f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)),f(f(f(f(f(f(f(f(f(C,A),f(D,A)),F),f(f(f(C,A),f(D,A)),F)),f(A,f(f(f(f(f(f(C,C),A),D),D),A),C))),B),B),f(A,f(f(f(f(f(f(C,C),A),D),D),A),C))),f(f(f(C,A),f(D,A)),F)))) = f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)). [para(1(a,1),1(a,1,1,1,1))].
% 83.03/83.39 5 f(f(f(f(A,f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),B),E),f(f(B,f(f(f(f(f(f(C,C),B),D),D),B),C)),f(f(f(f(f(f(A,A),f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),f(f(f(C,B),f(D,B)),F)),f(f(f(C,B),f(D,B)),F)),f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),A))) = f(B,f(f(f(f(f(f(C,C),B),D),D),B),C)). [para(1(a,1),1(a,1,1,1,2))].
% 83.03/83.39 6 f(f(A,B),f(f(f(f(f(f(f(C,C),A),D),D),A),C),f(f(f(f(f(f(f(f(C,A),f(D,A)),f(f(C,A),f(D,A))),f(f(f(f(f(f(C,C),A),D),D),A),C)),A),A),f(f(f(f(f(f(C,C),A),D),D),A),C)),f(f(C,A),f(D,A))))) = f(f(f(f(f(f(C,C),A),D),D),A),C). [para(1(a,1),1(a,1,1,1))].
% 83.03/83.39 7 f(A,f(f(B,A),f(f(f(f(f(f(f(C,A),f(C,A)),f(B,A)),D),D),f(B,A)),f(C,A)))) = f(B,A). [para(1(a,1),1(a,1,1))].
% 83.03/83.39 17 f(f(A,f(f(B,C),f(D,C))),f(C,f(f(f(f(f(f(B,B),C),D),D),C),B))) = C. [para(7(a,1),1(a,1,1))].
% 83.03/83.39 26 f(A,f(f(B,A),f(f(f(f(f(f(C,C),f(B,A)),f(D,A)),f(D,A)),f(B,A)),C))) = f(B,A). [para(17(a,1),1(a,1,1))].
% 83.03/83.39 64 f(f(A,B),f(f(f(C,B),f(A,B)),B)) = f(f(C,B),f(A,B)). [para(17(a,1),26(a,1,2,2))].
% 83.03/83.39 67 f(f(f(f(A,B),f(C,B)),D),f(B,f(f(f(f(f(f(C,C),B),f(f(A,B),f(C,B))),f(f(A,B),f(C,B))),B),C))) = B. [para(64(a,1),1(a,1,1,1))].
% 83.03/83.39 70 f(f(f(f(A,f(B,A)),f(A,f(B,A))),C),f(f(f(f(f(A,A),f(B,A)),A),A),f(B,A))) = f(B,A). [para(64(a,1),1(a,1,2))].
% 83.03/83.39 73 f(f(A,f(f(f(f(f(f(B,B),A),C),C),A),B)),f(A,f(f(f(f(f(f(B,B),A),C),C),A),B))) = A. [para(1(a,1),64(a,1,2,1)),rewrite([1(33)])].
% 83.03/83.39 85 f(f(f(f(A,B),f(C,B)),B),f(f(f(A,B),f(C,B)),f(f(f(f(f(f(D,D),f(f(A,B),f(C,B))),f(E,f(f(f(A,B),f(C,B)),B))),f(E,f(f(f(A,B),f(C,B)),B))),f(f(A,B),f(C,B))),D))) = f(f(A,B),f(C,B)). [para(64(a,1),26(a,1,2,1)),rewrite([64(14),64(30),64(37)])].
% 83.03/83.39 90 f(f(f(f(A,B),f(C,B)),B),f(f(f(A,B),f(C,B)),B)) = f(f(A,B),f(C,B)). [para(64(a,1),64(a,1,2,1)),rewrite([64(15)])].
% 83.03/83.39 100 f(A,f(f(f(f(B,A),f(C,A)),f(f(f(f(f(f(D,D),f(f(B,A),f(C,A))),E),E),f(f(B,A),f(C,A))),D)),f(f(f(f(f(f(F,F),f(f(f(B,A),f(C,A)),f(f(f(f(f(f(D,D),f(f(B,A),f(C,A))),E),E),f(f(B,A),f(C,A))),D))),f(f(f(D,f(f(B,A),f(C,A))),f(E,f(f(B,A),f(C,A)))),V6)),f(f(f(D,f(f(B,A),f(C,A))),f(E,f(f(B,A),f(C,A)))),V6)),f(f(f(B,A),f(C,A)),f(f(f(f(f(f(D,D),f(f(B,A),f(C,A))),E),E),f(f(B,A),f(C,A))),D))),F))) = f(f(f(B,A),f(C,A)),f(f(f(f(f(f(D,D),f(f(B,A),f(C,A))),E),E),f(f(B,A),f(C,A))),D)). [para(17(a,1),5(a,1,1))].
% 83.03/83.39 105 f(f(f(f(A,f(B,f(f(f(f(f(f(C,C),B),f(f(D,B),f(C,B))),f(f(D,B),f(C,B))),B),C))),B),E),f(f(B,f(f(f(f(f(f(C,C),B),f(f(D,B),f(C,B))),f(f(D,B),f(C,B))),B),C)),f(f(f(f(f(f(A,A),f(B,f(f(f(f(f(f(C,C),B),f(f(D,B),f(C,B))),f(f(D,B),f(C,B))),B),C))),f(f(f(D,B),f(C,B)),F)),f(f(f(D,B),f(C,B)),F)),f(B,f(f(f(f(f(f(C,C),B),f(f(D,B),f(C,B))),f(f(D,B),f(C,B))),B),C))),A))) = f(B,f(f(f(f(f(f(C,C),B),f(f(D,B),f(C,B))),f(f(D,B),f(C,B))),B),C)). [para(64(a,1),5(a,1,2,2,1,1,1,2,1)),rewrite([64(55)])].
% 83.03/83.39 111 f(f(f(A,f(B,f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)))),f(A,f(f(f(f(f(f(C,C),A),D),D),A),C))),f(f(A,f(B,f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)))),f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)))) = f(A,f(B,f(A,f(f(f(f(f(f(C,C),A),D),D),A),C)))). [para(1(a,1),90(a,1,1,1,1)),rewrite([1(29),1(47)])].
% 83.03/83.39 112 f(f(f(f(A,f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),B),f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),f(f(f(A,f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),B),f(B,f(f(f(f(f(f(C,C),B),D),D),B),C)))) = f(f(A,f(B,f(f(f(f(f(f(C,C),B),D),D),B),C))),B). [para(1(a,1),90(a,1,1,1,2)),rewrite([1(37),1(55)])].
% 83.03/83.39 152 f(f(f(A,B),f(A,B)),f(f(A,B),f(A,B))) = f(A,B). [para(70(a,1),90(a,1,1,1)),rewrite([70(18),70(22)])].
% 83.03/83.39 164 f(f(A,A),f(A,A)) = A. [para(1(a,1),152(a,1,1,1)),rewrite([1(12),1(13),1(13),1(15)])].
% 83.03/83.39 170 f(A,f(f(f(f(f(f(B,B),A),C),C),A),B)) = f(A,A). [para(4(a,1),152(a,1,1,1)),rewrite([4(58),73(15),4(51),4(58),73(15),4(52)]),flip(a)].
% 83.03/83.39 181 f(A,f(f(B,A),f(B,A))) = f(B,A). [para(7(a,1),152(a,2)),rewrite([170(13),170(17),170(22),170(26),164(19)])].
% 83.03/83.39 185 f(f(A,B),f(B,B)) = B. [para(152(a,1),17(a,1,1)),rewrite([170(8)])].
% 83.03/83.39 192 f(f(A,f(f(B,C),f(D,C))),f(C,C)) = C. [para(17(a,1),152(a,2)),rewrite([170(11),170(17),170(24),170(30),164(27)])].
% 83.03/83.39 199 f(f(A,B),f(A,A)) = A. [para(152(a,1),5(a,1,1,1,1,2,2,1,1,1)),rewrite([164(5),185(5),164(3),185(3),164(5),164(5),164(6),185(6),164(4),164(6),164(6),164(7),185(7),164(5),164(8),164(15),164(21),164(21),164(22),185(22),164(20),170(20),164(7),164(7),164(8),185(8),164(6)])].
% 83.03/83.39 205 f(f(f(A,B),f(C,B)),f(f(A,B),f(C,B))) = f(f(f(A,B),f(C,B)),B). [para(90(a,1),152(a,1,1)),rewrite([90(12)])].
% 83.03/83.39 227 f(f(A,f(B,B)),B) = f(B,B). [back_rewrite(112),rewrite([170(7),170(10),185(5),170(7),170(10),185(5),170(8)]),flip(a)].
% 83.03/83.39 228 f(A,f(B,f(A,A))) = f(A,A). [back_rewrite(111),rewrite([170(7),170(10),199(5),170(7),170(10),199(5),170(8)]),flip(a)].
% 83.03/83.39 231 f(f(f(A,A),B),A) = f(A,A). [back_rewrite(105),rewrite([170(13),227(3),170(15),170(17),170(29),170(20),164(5),170(16)])].
% 83.03/83.39 235 f(f(f(A,B),f(C,B)),B) = f(B,f(f(A,B),f(C,B))). [back_rewrite(100),rewrite([170(16),205(7),170(21),205(12),170(48),205(39),170(39),90(9),170(20),205(11)]),flip(a)].
% 83.03/83.39 241 f(f(A,f(f(B,A),f(C,A))),f(A,f(f(B,A),f(C,A)))) = f(f(B,A),f(C,A)). [back_rewrite(85),rewrite([235(4),235(16),235(22),170(30),205(11),235(8)])].
% 83.03/83.39 246 f(f(f(f(A,B),f(C,B)),D),f(B,B)) = B. [back_rewrite(67),rewrite([170(17)])].
% 83.03/83.39 276 f(f(A,B),f(f(f(f(f(f(f(C,C),A),D),D),A),C),f(f(f(f(f(f(A,f(f(C,A),f(D,A))),f(f(f(f(f(f(C,C),A),D),D),A),C)),A),A),f(f(f(f(f(f(C,C),A),D),D),A),C)),f(f(C,A),f(D,A))))) = f(f(f(f(f(f(C,C),A),D),D),A),C). [back_rewrite(6),rewrite([205(14),235(11)])].
% 83.03/83.39 312 f(f(f(A,B),f(C,B)),f(f(A,B),f(C,B))) = f(B,f(f(A,B),f(C,B))). [back_rewrite(205),rewrite([235(11)])].
% 83.03/83.39 328 f(f(A,B),f(B,f(f(C,B),f(A,B)))) = f(f(C,B),f(A,B)). [back_rewrite(64),rewrite([235(5)])].
% 83.03/83.39 343 f(f(A,A),f(B,A)) = A. [para(185(a,1),228(a,1,2,2)),rewrite([199(6)])].
% 83.03/83.39 349 f(A,f(f(A,A),B)) = f(A,A). [para(185(a,1),170(a,1,2,1,1,1)),rewrite([227(3)])].
% 83.03/83.39 350 f(f(A,A),f(A,B)) = A. [para(185(a,1),170(a,1,2,1)),rewrite([343(6)])].
% 83.03/83.39 351 f(A,f(f(f(f(B,B),B),A),B)) = f(A,A). [para(199(a,1),170(a,1,2,1,1,1)),rewrite([350(4)])].
% 83.03/83.39 352 f(A,f(f(f(f(B,B),A),A),B)) = f(A,A). [para(199(a,1),170(a,1,2,1,1))].
% 83.03/83.39 373 f(f(f(A,B),f(A,B)),A) = f(A,B). [para(199(a,1),350(a,1,2))].
% 83.03/83.39 374 f(f(A,B),f(f(f(f(A,C),C),f(A,B)),A)) = f(f(A,B),f(A,B)). [para(350(a,1),170(a,1,2,1,1,1,1))].
% 83.03/83.39 391 f(f(A,f(B,f(C,f(B,D)))),f(f(B,D),f(B,D))) = f(B,D). [para(350(a,1),192(a,1,1,2,1))].
% 83.03/83.39 399 f(f(A,f(f(B,C),f(D,B))),f(B,B)) = B. [para(373(a,1),192(a,1,1,2,1))].
% 83.03/83.39 400 f(f(A,f(f(B,C),f(C,D))),f(C,C)) = C. [para(373(a,1),192(a,1,1,2,2))].
% 83.03/83.39 415 f(f(A,A),f(f(f(B,A),f(C,A)),D)) = A. [para(246(a,1),373(a,1,1,1)),rewrite([246(6),246(12)])].
% 83.03/83.39 416 f(f(f(f(A,B),f(C,A)),D),f(A,A)) = A. [para(373(a,1),246(a,1,1,1,1))].
% 83.03/83.39 477 f(f(A,A),f(B,f(f(A,C),f(D,A)))) = A. [para(399(a,1),373(a,1,1,1)),rewrite([399(6),399(12)])].
% 83.03/83.39 493 f(f(f(A,B),f(B,C)),f(f(A,B),f(B,C))) = f(f(f(A,B),f(B,C)),B). [para(400(a,1),170(a,1,2)),flip(a)].
% 83.03/83.39 497 f(f(f(A,B),f(B,C)),B) = f(B,f(f(A,B),f(B,C))). [para(400(a,1),231(a,1,1)),rewrite([493(11)]),flip(a)].
% 83.03/83.39 499 f(f(A,A),f(B,f(f(C,A),f(A,D)))) = A. [para(400(a,1),373(a,1,1,1)),rewrite([400(6),400(12)])].
% 83.03/83.39 507 f(f(f(A,B),f(B,C)),f(f(A,B),f(B,C))) = f(B,f(f(A,B),f(B,C))). [back_rewrite(493),rewrite([497(11)])].
% 83.03/83.39 533 f(A,f(f(f(f(f(B,A),C),C),A),f(B,A))) = f(A,A). [para(235(a,1),170(a,1,2,1,1,1,1)),rewrite([181(4)])].
% 83.03/83.39 543 f(A,f(f(f(B,A),A),f(B,A))) = f(A,A). [para(235(a,1),352(a,1,2,1,1)),rewrite([181(4)])].
% 83.03/83.39 563 f(A,f(f(f(B,f(A,A)),f(C,f(A,A))),D)) = f(A,A). [para(185(a,1),415(a,1,1))].
% 83.03/83.39 600 f(f(f(f(A,B),f(A,C)),D),f(A,A)) = A. [para(373(a,1),416(a,1,1,1,2))].
% 83.03/83.39 643 f(f(f(f(f(A,B),C),C),B),f(A,B)) = B. [para(170(a,1),241(a,1,1)),rewrite([235(5),181(5),533(8),350(3),235(4),181(4)]),flip(a)].
% 83.03/83.39 660 f(f(f(A,B),B),f(A,B)) = B. [para(352(a,1),241(a,1,1)),rewrite([235(5),181(5),543(6),350(3),235(4),181(4)]),flip(a)].
% 83.03/83.39 679 f(f(A,f(B,A)),A) = f(B,A). [para(343(a,1),660(a,1,1,1)),rewrite([343(5)])].
% 83.03/83.39 681 f(f(A,f(A,B)),A) = f(A,B). [para(350(a,1),660(a,1,1,1)),rewrite([350(5)])].
% 83.03/83.39 682 f(f(f(A,B),A),f(A,B)) = A. [para(373(a,1),660(a,1,1,1)),rewrite([373(6)])].
% 83.03/83.39 696 f(f(A,A),A) = f(A,f(A,A)). [para(228(a,1),681(a,1,1))].
% 83.03/83.39 698 f(A,f(f(f(B,f(B,B)),A),B)) = f(A,A). [para(351(a,1),681(a,1,1,2)),rewrite([681(3),696(3)]),flip(a)].
% 83.03/83.39 762 f(A,f(f(B,A),A)) = f(B,A). [para(660(a,1),682(a,1,1))].
% 83.03/83.39 763 f(f(A,B),f(B,f(A,B))) = B. [para(679(a,1),682(a,1,1))].
% 83.03/83.39 764 f(f(A,B),f(A,f(A,B))) = A. [para(681(a,1),682(a,1,1))].
% 83.03/83.39 810 f(f(f(f(A,f(A,A)),B),B),A) = f(A,A). [para(762(a,1),170(a,1)),rewrite([696(2)])].
% 83.03/83.39 820 f(A,f(f(A,f(f(B,B),A)),B)) = f(A,A). [para(763(a,1),170(a,1,2,1,1,1)),rewrite([681(5)])].
% 83.03/83.39 1045 f(f(A,A),f(B,f(f(A,C),f(A,D)))) = A. [para(373(a,1),477(a,1,2,2,2))].
% 83.03/83.39 1103 f(f(f(A,B),C),f(f(f(f(f(A,D),D),f(A,B)),A),f(f(f(f(f(f(f(A,B),f(f(A,f(A,B)),f(D,f(A,B)))),f(f(f(f(A,D),D),f(A,B)),A)),f(A,B)),f(A,B)),f(f(f(f(A,D),D),f(A,B)),A)),f(f(A,f(A,B)),f(D,f(A,B)))))) = f(f(f(f(A,D),D),f(A,B)),A). [para(350(a,1),276(a,1,2,1,1,1,1,1)),rewrite([350(17),350(27),350(41)])].
% 83.03/83.39 1323 f(A,f(f(f(f(f(f(B,f(f(C,B),f(D,B))),A),E),E),A),f(f(C,B),f(D,B)))) = f(A,A). [para(312(a,1),170(a,1,2,1,1,1,1,1))].
% 83.03/83.39 1327 f(f(f(A,f(B,C)),B),f(f(A,f(B,C)),B)) = f(f(B,C),f(f(A,f(B,C)),B)). [para(350(a,1),312(a,1,1,2)),rewrite([350(8),350(13)])].
% 83.03/83.39 1385 f(f(f(f(A,B),B),f(A,C)),A) = f(A,C). [back_rewrite(1103),rewrite([1323(37),1327(13),374(9),199(6)]),flip(a)].
% 83.03/83.39 1426 f(f(f(A,B),f(A,C)),f(A,A)) = f(A,f(A,A)). [para(600(a,1),762(a,1,2)),rewrite([696(2)]),flip(a)].
% 83.03/83.39 1438 f(f(f(f(f(f(A,B),f(C,B)),D),f(f(f(A,B),f(C,B)),E)),F),f(B,f(f(A,B),f(C,B)))) = f(f(A,B),f(C,B)). [para(312(a,1),600(a,1,2))].
% 83.03/83.39 1441 f(f(f(A,f(A,A)),B),f(A,B)) = B. [para(199(a,1),643(a,1,1,1,1))].
% 83.03/83.39 1461 f(f(A,B),f(f(A,B),B)) = B. [para(660(a,1),643(a,1,1,1,1)),rewrite([679(3)])].
% 83.03/83.39 1476 f(f(A,f(A,B)),f(f(A,C),f(A,B))) = f(A,B). [para(600(a,1),643(a,1,1,1))].
% 83.03/83.39 1477 f(f(A,B),f(f(f(f(A,B),C),C),B)) = B. [para(643(a,1),643(a,1,1,1,1)),rewrite([679(3)])].
% 83.03/83.39 1494 f(f(A,B),B) = f(B,f(A,B)). [para(1461(a,1),681(a,1,1)),flip(a)].
% 83.03/83.39 1511 f(f(A,B),f(f(C,f(f(A,B),C)),B)) = B. [back_rewrite(1477),rewrite([1494(4)])].
% 83.03/83.39 1537 f(f(f(A,f(B,A)),f(B,C)),B) = f(B,C). [back_rewrite(1385),rewrite([1494(2)])].
% 83.03/83.39 1755 f(f(A,f(f(B,f(B,B)),A)),B) = f(B,B). [back_rewrite(810),rewrite([1494(4)])].
% 83.03/83.39 2008 f(f(f(A,f(A,A)),f(A,f(A,A))),B) = f(A,f(A,A)). [para(349(a,1),1441(a,1,1)),rewrite([563(12),1426(7)]),flip(a)].
% 83.03/83.39 2029 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(D,f(A,f(B,f(f(C,D),f(D,E))))). [para(499(a,1),328(a,1,2,2,1)),rewrite([499(23)])].
% 83.03/83.39 2080 f(f(f(A,f(A,A)),f(f(B,B),f(A,f(A,A)))),B) = f(A,f(A,A)). [para(820(a,1),1441(a,1,1)),rewrite([2008(15)]),flip(a)].
% 83.03/83.39 2183 f(A,f(f(B,f(A,B)),f(A,C))) = f(A,C). [para(350(a,1),1511(a,1,1)),rewrite([350(3)])].
% 83.03/83.39 2210 f(f(A,f(f(B,f(B,B)),A)),f(B,B)) = B. [para(1511(a,1),1441(a,1,1)),rewrite([228(8),350(3)]),flip(a)].
% 83.03/83.39 2222 f(A,f(f(B,f(A,B)),f(C,f(f(A,D),f(A,E))))) = f(C,f(f(A,D),f(A,E))). [para(1045(a,1),1511(a,1,1)),rewrite([1045(6)])].
% 83.03/83.39 2338 f(A,B) = f(B,A). [para(1494(a,1),1537(a,1,1)),rewrite([763(4)])].
% 83.03/83.39 2344 f(f(A,f(B,f(B,B))),f(A,f(C,f(C,f(A,f(B,f(B,B))))))) = f(f(B,A),f(A,f(B,f(B,B)))). [para(1441(a,1),1537(a,1,1,2)),rewrite([2338(3),2338(4),2338(6),2338(9),2338(10),2338(13),2338(15)])].
% 83.03/83.39 2352 f(A,f(B,f(A,f(B,f(B,B))))) = f(A,A). [para(698(a,1),1537(a,1,1,2)),rewrite([2338(1),2338(5),228(5),2338(4),2338(5)]),flip(a)].
% 83.03/83.39 2366 f(f(A,B),f(A,f(C,f(C,f(A,B))))) = A. [para(1537(a,1),1511(a,1,1)),rewrite([2338(6),2183(6),2338(3),2338(5)])].
% 83.03/83.39 2369 f(f(A,B),f(f(B,f(B,f(C,f(C,f(A,B))))),f(D,f(A,B)))) = f(D,f(A,B)). [para(1511(a,1),1537(a,1,1,1,2)),rewrite([2338(2),2338(4),2338(5),2338(7),2338(10),2338(12)])].
% 83.03/83.39 2418 f(f(A,A),f(B,f(B,f(A,f(A,A))))) = A. [back_rewrite(2210),rewrite([2338(3),2338(6)])].
% 83.03/83.39 2452 f(A,f(f(B,f(B,B)),f(f(A,A),f(B,f(B,B))))) = f(B,f(B,B)). [back_rewrite(2080),rewrite([2338(8)])].
% 83.03/83.39 2557 f(A,f(B,f(B,f(A,f(A,A))))) = f(A,A). [back_rewrite(1755),rewrite([2338(3),2338(5)])].
% 83.03/83.39 2636 f(f(A,f(f(B,A),f(A,C))),f(D,f(f(E,f(f(B,A),f(A,C))),f(F,f(f(B,A),f(A,C)))))) = f(f(B,A),f(A,C)). [back_rewrite(1438),rewrite([2338(2),2338(4),2338(6),2338(8),2338(10),2338(12),2338(15),2338(17)])].
% 83.03/83.39 2680 f(c,f(f(a,b),f(a,b))) != f(a,f(f(b,c),f(b,c))) # answer(associativity). [back_rewrite(3),rewrite([2338(4),2338(7)])].
% 83.03/83.39 2681 f(f(A,B),f(A,f(B,f(B,B)))) = A. [back_rewrite(2344),rewrite([2366(10),2338(1)]),flip(a)].
% 83.03/83.39 2686 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(391(a,1),764(a,1,1)),rewrite([391(13),2338(7)])].
% 83.03/83.39 2689 f(f(f(A,B),f(A,B)),f(C,f(A,B))) = f(A,B). [para(391(a,1),1045(a,1,2,2))].
% 83.03/83.39 2745 f(A,f(f(B,f(A,B)),f(f(B,f(A,B)),f(B,f(A,B))))) = f(A,A). [para(2352(a,1),2183(a,1)),flip(a)].
% 83.03/83.39 2758 f(A,f(f(A,B),f(f(A,f(C,f(C,f(A,B)))),f(f(A,f(C,f(C,f(A,B)))),f(A,f(C,f(C,f(A,B)))))))) = f(A,B). [para(2366(a,1),2681(a,1,1))].
% 83.03/83.39 2764 f(f(A,f(B,f(C,A))),f(A,f(B,f(C,A)))) = f(f(C,A),f(A,f(B,f(C,A)))). [para(185(a,1),507(a,1,1,2)),rewrite([2338(3),185(8),2338(6),185(13),2338(11)])].
% 83.03/83.39 2800 f(A,f(A,f(B,f(B,B)))) = f(B,f(B,B)). [para(2418(a,1),763(a,1,1)),rewrite([2418(10),2338(5),2557(5)]),flip(a)].
% 83.03/83.39 2801 f(f(f(A,B),f(A,B)),f(A,f(A,A))) = f(A,B). [para(1045(a,1),2418(a,1,2,2)),rewrite([2338(5)])].
% 83.03/83.39 2802 f(f(A,f(A,A)),f(B,f(A,f(A,A)))) = B. [para(2418(a,1),2366(a,1,2,2,2)),rewrite([2800(4),2338(4)])].
% 83.03/83.39 2806 f(A,f(A,A)) = f(B,f(B,B)). [back_rewrite(2452),rewrite([2802(7)])].
% 83.03/83.39 2807 f(A,f(A,A)) = c_0. [new_symbol(2806)].
% 83.03/83.39 2809 f(c_0,f(A,c_0)) = A. [back_rewrite(2802),rewrite([2807(2),2807(3)])].
% 83.03/83.39 2810 f(c_0,f(f(A,B),f(A,B))) = f(A,B). [back_rewrite(2801),rewrite([2807(5),2338(5)])].
% 83.03/83.39 2824 f(A,f(c_0,f(A,B))) = f(A,B). [back_rewrite(2758),rewrite([2807(15),2338(3)])].
% 83.03/83.39 2830 f(A,c_0) = f(A,A). [back_rewrite(2745),rewrite([2807(8)])].
% 83.03/83.39 2957 f(c_0,f(c_0,f(A,B))) = f(A,B). [back_rewrite(2810),rewrite([2830(4,R),2338(4)])].
% 83.03/83.39 2967 f(f(A,B),f(A,f(C,f(A,B)))) = f(c_0,f(A,f(C,f(A,B)))). [back_rewrite(2764),rewrite([2338(1),2338(4),2830(7,R),2338(5),2338(6),2338(7)]),flip(a)].
% 83.03/83.39 2971 f(f(c_0,f(A,B)),f(C,f(A,B))) = f(A,B). [back_rewrite(2689),rewrite([2830(3,R),2338(3)])].
% 83.03/83.39 2976 f(c,f(c_0,f(a,b))) != f(a,f(c_0,f(b,c))) # answer(associativity). [back_rewrite(2680),rewrite([2830(8,R),2338(6),2830(15,R),2338(13)])].
% 83.03/83.39 3089 f(c_0,f(A,A)) = A. [para(2807(a,1),199(a,1,1))].
% 83.03/83.39 3090 f(f(A,A),f(B,f(c_0,f(A,C)))) = A. [para(2807(a,1),1045(a,1,2,2,1))].
% 83.03/83.39 3206 f(f(A,f(B,A)),f(A,f(C,f(B,A)))) = A. [para(185(a,1),1476(a,1,1,2)),rewrite([2338(2),2338(4),185(7),2338(5),185(9)])].
% 83.03/83.39 3208 f(f(A,f(A,B)),f(A,f(C,f(A,B)))) = A. [para(199(a,1),1476(a,1,1,2)),rewrite([2338(2),2338(4),199(7),2338(5),199(9)])].
% 83.03/83.39 3369 f(f(A,f(c_0,f(B,C))),f(B,B)) = B. [para(3090(a,1),2338(a,1)),flip(a)].
% 83.03/83.39 3468 f(f(A,f(c_0,f(B,C))),f(C,C)) = C. [para(2338(a,1),3369(a,1,1,2,2))].
% 83.03/83.39 3544 f(f(A,c_0),f(B,f(c_0,f(C,A)))) = A. [para(2830(a,2),3468(a,1,2)),rewrite([2338(7)])].
% 83.03/83.39 3565 f(f(c_0,f(A,f(B,B))),f(B,C)) = f(A,f(B,B)). [para(228(a,1),3544(a,1,2,2,2)),rewrite([2338(4),3089(7),2338(5)])].
% 83.03/83.39 3723 f(f(c_0,f(A,B)),f(C,f(f(D,f(A,B)),f(E,f(A,B))))) = f(A,B). [para(2369(a,1),1045(a,1,2,2,1)),rewrite([2830(3,R),2338(3),2338(7)])].
% 83.03/83.39 4176 f(A,f(f(B,C),f(A,C))) = f(A,C). [para(3206(a,1),2029(a,1,1)),rewrite([2338(2),2338(5),2338(8),3208(11),2338(5),2338(6),2967(6),2824(7),2338(5),2338(8),3208(11),2338(5)])].
% 83.03/83.39 4180 f(A,f(f(B,C),f(B,A))) = f(B,A). [para(3206(a,1),2222(a,1,2)),flip(a)].
% 83.03/83.39 4214 f(A,f(f(A,B),f(B,C))) = f(A,B). [para(2338(a,1),4176(a,1,2)),rewrite([2338(2)])].
% 83.03/83.39 4311 f(f(A,B),f(B,f(C,f(A,B)))) = f(c_0,f(B,f(C,f(A,B)))). [para(4176(a,1),4180(a,1,2)),rewrite([2338(2),2338(3),2338(5),2338(6),2830(7,R),2338(5),2338(8),2338(9)]),flip(a)].
% 83.03/83.39 12598 f(f(A,c_0),f(B,c_0)) = f(f(A,A),f(B,c_0)). [para(2830(a,1),2636(a,2,1)),rewrite([2338(5),2338(11),2338(17),3723(22),2338(8)])].
% 83.03/83.39 12682 f(f(A,c_0),f(B,c_0)) = f(f(B,B),f(A,c_0)). [para(12598(a,1),2338(a,1)),flip(a)].
% 83.03/83.39 13019 f(f(A,c_0),f(B,c_0)) = f(f(B,B),f(A,A)). [para(2830(a,1),12682(a,2,2))].
% 83.03/83.39 14121 f(f(A,c_0),f(B,C)) = f(f(B,C),f(A,A)). [para(2971(a,1),13019(a,2,1)),rewrite([2338(7),2957(7)])].
% 83.03/83.39 16318 f(A,f(c_0,f(B,f(C,f(A,B))))) = f(A,B). [para(4214(a,1),2686(a,1,2,2)),rewrite([2338(2),2338(4),2338(6),763(7),2338(4),4311(6)]),flip(a)].
% 83.03/83.39 16411 f(A,f(c_0,f(B,f(C,f(B,A))))) = f(B,A). [para(16318(a,1),2338(a,2)),rewrite([2338(2),2338(6),2338(7)])].
% 83.03/83.39 16553 f(A,f(c_0,f(B,f(C,f(A,A))))) = f(A,B). [para(3565(a,1),16318(a,1,2,2,2))].
% 83.03/83.39 16760 f(f(c_0,f(A,B)),f(c_0,f(B,C))) = f(C,f(c_0,f(A,B))). [para(3544(a,1),16411(a,1,2,2,2)),rewrite([2338(5)])].
% 83.03/83.39 16933 f(f(c_0,f(A,f(B,C))),f(B,B)) = f(A,f(B,c_0)). [para(16553(a,1),14121(a,1)),rewrite([2338(3),2830(9,R),2338(8),2809(8),2338(5)]),flip(a)].
% 83.03/83.39 22997 f(A,f(c_0,f(B,C))) = f(C,f(c_0,f(A,B))). [para(185(a,1),16933(a,1,1,2,2)),rewrite([2338(4),2338(5),2830(6,R),2338(6),16760(7),2338(5),2338(7)]),flip(a)].
% 83.03/83.39 22998 $F # answer(associativity). [resolve(22997,a,2976,a(flip))].
% 83.03/83.39
% 83.03/83.39 % SZS output end Refutation
% 83.03/83.39 ============================== end of proof ==========================
% 83.03/83.39
% 83.03/83.39 ============================== STATISTICS ============================
% 83.03/83.39
% 83.03/83.39 Given=568. Generated=830975. Kept=22996. proofs=1.
% 83.03/83.39 Usable=399. Sos=9999. Demods=10064. Limbo=0, Disabled=12599. Hints=0.
% 83.03/83.39 Megabytes=32.37.
% 83.03/83.39 User_CPU=81.96, System_CPU=0.47, Wall_clock=82.
% 83.03/83.39
% 83.03/83.39 ============================== end of statistics =====================
% 83.03/83.39
% 83.03/83.39 ============================== end of search =========================
% 83.03/83.39
% 83.03/83.39 THEOREM PROVED
% 83.03/83.39 % SZS status Unsatisfiable
% 83.03/83.39
% 83.03/83.39 Exiting with 1 proof.
% 83.03/83.39
% 83.03/83.39 Process 3118 exit (max_proofs) Wed Jun 29 10:28:33 2022
% 83.03/83.39 Prover9 interrupted
%------------------------------------------------------------------------------