TSTP Solution File: LAT070-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT070-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 06:25:24 EDT 2022
% Result : Unsatisfiable 138.91s 139.22s
% Output : Refutation 138.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT070-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 30 03:00:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 42.53/42.85 ============================== Prover9 ===============================
% 42.53/42.85 Prover9 (32) version 2009-11A, November 2009.
% 42.53/42.85 Process 27846 was started by sandbox on n029.cluster.edu,
% 42.53/42.85 Thu Jun 30 03:00:53 2022
% 42.53/42.85 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27692_n029.cluster.edu".
% 42.53/42.85 ============================== end of head ===========================
% 42.53/42.85
% 42.53/42.85 ============================== INPUT =================================
% 42.53/42.85
% 42.53/42.85 % Reading from file /tmp/Prover9_27692_n029.cluster.edu
% 42.53/42.85
% 42.53/42.85 set(prolog_style_variables).
% 42.53/42.85 set(auto2).
% 42.53/42.85 % set(auto2) -> set(auto).
% 42.53/42.85 % set(auto) -> set(auto_inference).
% 42.53/42.85 % set(auto) -> set(auto_setup).
% 42.53/42.85 % set(auto_setup) -> set(predicate_elim).
% 42.53/42.85 % set(auto_setup) -> assign(eq_defs, unfold).
% 42.53/42.85 % set(auto) -> set(auto_limits).
% 42.53/42.85 % set(auto_limits) -> assign(max_weight, "100.000").
% 42.53/42.85 % set(auto_limits) -> assign(sos_limit, 20000).
% 42.53/42.85 % set(auto) -> set(auto_denials).
% 42.53/42.85 % set(auto) -> set(auto_process).
% 42.53/42.85 % set(auto2) -> assign(new_constants, 1).
% 42.53/42.85 % set(auto2) -> assign(fold_denial_max, 3).
% 42.53/42.85 % set(auto2) -> assign(max_weight, "200.000").
% 42.53/42.85 % set(auto2) -> assign(max_hours, 1).
% 42.53/42.85 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 42.53/42.85 % set(auto2) -> assign(max_seconds, 0).
% 42.53/42.85 % set(auto2) -> assign(max_minutes, 5).
% 42.53/42.85 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 42.53/42.85 % set(auto2) -> set(sort_initial_sos).
% 42.53/42.85 % set(auto2) -> assign(sos_limit, -1).
% 42.53/42.85 % set(auto2) -> assign(lrs_ticks, 3000).
% 42.53/42.85 % set(auto2) -> assign(max_megs, 400).
% 42.53/42.85 % set(auto2) -> assign(stats, some).
% 42.53/42.85 % set(auto2) -> clear(echo_input).
% 42.53/42.85 % set(auto2) -> set(quiet).
% 42.53/42.85 % set(auto2) -> clear(print_initial_clauses).
% 42.53/42.85 % set(auto2) -> clear(print_given).
% 42.53/42.85 assign(lrs_ticks,-1).
% 42.53/42.85 assign(sos_limit,10000).
% 42.53/42.85 assign(order,kbo).
% 42.53/42.85 set(lex_order_vars).
% 42.53/42.85 clear(print_given).
% 42.53/42.85
% 42.53/42.85 % formulas(sos). % not echoed (2 formulas)
% 42.53/42.85
% 42.53/42.85 ============================== end of input ==========================
% 42.53/42.85
% 42.53/42.85 % From the command line: assign(max_seconds, 300).
% 42.53/42.85
% 42.53/42.85 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 42.53/42.85
% 42.53/42.85 % Formulas that are not ordinary clauses:
% 42.53/42.85
% 42.53/42.85 ============================== end of process non-clausal formulas ===
% 42.53/42.85
% 42.53/42.85 ============================== PROCESS INITIAL CLAUSES ===============
% 42.53/42.85
% 42.53/42.85 ============================== PREDICATE ELIMINATION =================
% 42.53/42.85
% 42.53/42.85 ============================== end predicate elimination =============
% 42.53/42.85
% 42.53/42.85 Auto_denials:
% 42.53/42.85 % copying label associativity to answer in negative clause
% 42.53/42.85
% 42.53/42.85 Term ordering decisions:
% 42.53/42.85 Function symbol KB weights: a=1. b=1. c=1. f=1.
% 42.53/42.85
% 42.53/42.85 ============================== end of process initial clauses ========
% 42.53/42.85
% 42.53/42.85 ============================== CLAUSES FOR SEARCH ====================
% 42.53/42.85
% 42.53/42.85 ============================== end of clauses for search =============
% 42.53/42.85
% 42.53/42.85 ============================== SEARCH ================================
% 42.53/42.85
% 42.53/42.85 % Starting search at 0.01 seconds.
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=91.000, iters=3344
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=87.000, iters=3430
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=73.000, iters=3405
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=71.000, iters=3367
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=65.000, iters=3406
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=63.000, iters=3476
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=61.000, iters=3334
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=59.000, iters=3414
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=57.000, iters=3377
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=55.000, iters=3362
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=53.000, iters=3349
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=51.000, iters=3456
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=49.000, iters=3357
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=47.000, iters=3348
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=45.000, iters=3399
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=43.000, iters=3362
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=41.000, iters=3368
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=39.000, iters=3336
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=37.000, iters=3353
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=35.000, iters=3384
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=33.000, iters=3341
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=31.000, iters=3343
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=29.000, iters=3344
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=27.000, iters=3372
% 42.53/42.85
% 42.53/42.85 Low Water (keep): wt=25.000, iters=3367
% 42.53/42.85
% 42.53/42.85 Low Water (displace): id=23581, wt=97.000
% 42.53/42.85
% 42.53/42.85 Low Water (displace): id=21492, wt=85.000
% 42.53/42.85
% 42.53/42.85 Low Water (displace): id=24022, wt=83.000
% 42.53/42.85
% 42.53/42.85 Low Water (displace): id=18366, wt=79.000
% 42.53/42.85
% 42.53/42.85 Low Water (displace): id=24051, wt=75.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=24076, wt=73.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=23128, wt=69.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=24123, wt=63.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=24149, wt=61.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=24110, wt=59.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=24144, wt=57.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=28288, wt=31.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=28661, wt=29.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=30486, wt=27.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=31492, wt=25.000
% 138.91/139.22
% 138.91/139.22 Low Water (displace): id=35934, wt=23.000
% 138.91/139.22
% 138.91/139.22 ============================== PROOF =================================
% 138.91/139.22 % SZS status Unsatisfiable
% 138.91/139.22 % SZS output start Refutation
% 138.91/139.22
% 138.91/139.22 % Proof 1 at 136.35 (+ 1.91) seconds: associativity.
% 138.91/139.22 % Length of proof is 155.
% 138.91/139.22 % Level of proof is 32.
% 138.91/139.22 % Maximum clause weight is 149.000.
% 138.91/139.22 % Given clauses 1740.
% 138.91/139.22
% 138.91/139.22 1 f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))) = B # label(ol_23A) # label(axiom). [assumption].
% 138.91/139.22 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].
% 138.91/139.22 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)].
% 138.91/139.22 4 f(f(f(A,f(f(A,f(f(A,f(f(B,B),B)),C)),D)),E),f(f(A,f(f(A,f(f(B,B),B)),C)),f(f(f(A,f(f(A,f(f(B,B),B)),C)),f(f(f(f(f(B,A),f(A,C)),F),f(f(f(B,A),f(A,C)),F)),f(f(f(B,A),f(A,C)),F))),D))) = f(A,f(f(A,f(f(B,B),B)),C)). [para(1(a,1),1(a,1,1,1,1))].
% 138.91/139.22 5 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(f(f(B,C),f(C,D)),E),f(f(A,A),A)),f(C,f(f(C,f(f(B,B),B)),D))))) = f(f(f(B,C),f(C,D)),E). [para(1(a,1),1(a,1,1,1,2))].
% 138.91/139.22 7 f(A,f(f(A,B),f(f(f(A,B),f(f(f(C,A),f(C,A)),f(C,A))),D))) = f(A,B). [para(1(a,1),1(a,1,1))].
% 138.91/139.22 8 f(f(f(f(A,f(f(B,C),f(C,D))),f(f(f(B,C),f(C,D)),f(C,f(f(C,f(f(B,B),B)),D)))),E),f(f(f(B,C),f(C,D)),C)) = f(f(B,C),f(C,D)). [para(1(a,1),1(a,1,2,2))].
% 138.91/139.22 9 f(f(f(f(A,f(f(B,f(f(B,f(f(B,f(f(C,C),C)),D)),E)),F)),f(B,f(f(B,f(f(C,C),C)),D))),V6),f(f(f(B,f(f(B,f(f(B,f(f(C,C),C)),D)),E)),F),f(f(f(f(B,f(f(B,f(f(B,f(f(C,C),C)),D)),E)),F),f(f(A,A),A)),f(f(B,f(f(B,f(f(C,C),C)),D)),f(f(f(B,f(f(B,f(f(C,C),C)),D)),f(f(f(f(f(C,B),f(B,D)),V7),f(f(f(C,B),f(B,D)),V7)),f(f(f(C,B),f(B,D)),V7))),E))))) = f(f(B,f(f(B,f(f(B,f(f(C,C),C)),D)),E)),F). [para(4(a,1),1(a,1,1,1,2))].
% 138.91/139.22 20 f(f(f(f(A,B),f(B,f(f(f(B,f(f(A,A),A)),C),f(f(f(f(B,f(f(A,A),A)),C),f(f(f(D,f(B,f(f(A,A),A))),f(D,f(B,f(f(A,A),A)))),f(D,f(B,f(f(A,A),A))))),E)))),F),f(B,f(f(B,f(f(A,A),A)),C))) = B. [para(7(a,1),1(a,1,2,2))].
% 138.91/139.22 21 f(f(f(f(A,B),f(B,f(f(f(B,f(f(A,A),A)),f(f(f(C,B),f(C,B)),f(C,B))),D))),E),f(B,f(f(A,A),A))) = B. [para(7(a,1),1(a,1,2))].
% 138.91/139.22 23 f(f(A,B),f(f(f(A,B),f(B,C)),B)) = f(f(A,B),f(B,C)). [para(1(a,1),7(a,1,2,2))].
% 138.91/139.22 36 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(1(a,1),23(a,1,2,1,2)),rewrite([1(32)])].
% 138.91/139.22 37 f(f(f(f(A,B),f(B,C)),B),f(B,B)) = B. [para(1(a,1),23(a,1,2,1)),rewrite([1(16)])].
% 138.91/139.22 51 f(f(A,A),f(A,A)) = A. [para(1(a,1),37(a,1,1,1))].
% 138.91/139.22 62 f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))) = A. [para(51(a,1),1(a,1,1,1))].
% 138.91/139.22 102 f(f(f(f(A,f(B,C)),B),D),f(f(B,C),f(f(f(B,C),f(f(A,A),A)),f(B,f(f(B,f(f(B,B),B)),B))))) = f(B,C). [para(51(a,1),5(a,1,1,1,1,2,1)),rewrite([51(7),51(8),51(20)])].
% 138.91/139.22 137 f(A,f(f(A,B),f(A,B))) = f(A,B). [para(62(a,1),7(a,1,2,2))].
% 138.91/139.22 138 f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),B)) = f(A,A). [para(62(a,1),23(a,1,1)),rewrite([62(7),62(13),62(8)]),flip(a)].
% 138.91/139.22 139 f(f(A,f(B,C)),f(f(f(A,f(B,C)),B),f(B,C))) = f(f(A,f(B,C)),B). [para(62(a,1),23(a,1,2,1,2)),rewrite([62(17)])].
% 138.91/139.22 140 f(A,f(f(A,f(f(A,A),A)),A)) = f(A,A). [para(62(a,1),37(a,1,1,1,1)),rewrite([138(7),62(7),62(11)]),flip(a)].
% 138.91/139.22 163 f(A,f(f(A,A),B)) = f(A,A). [back_rewrite(138),rewrite([140(5)])].
% 138.91/139.22 172 f(f(f(f(A,f(B,C)),B),D),f(f(B,C),f(f(f(B,C),f(f(A,A),A)),f(B,B)))) = f(B,C). [back_rewrite(102),rewrite([163(12),163(12)])].
% 138.91/139.22 173 f(f(A,B),f(A,A)) = A. [back_rewrite(62),rewrite([163(4),163(4)])].
% 138.91/139.22 189 f(f(f(A,A),B),A) = f(A,A). [para(173(a,1),173(a,1,2))].
% 138.91/139.22 193 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(1(a,1),163(a,1,2)),flip(a)].
% 138.91/139.22 218 f(f(f(A,B),f(B,C)),f(f(f(f(A,B),f(B,C)),B),D)) = f(f(f(A,B),f(B,C)),B). [para(163(a,1),5(a,2)),rewrite([193(10),193(22),193(31),5(41),193(16)])].
% 138.91/139.22 219 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(A,f(f(f(B,C),f(C,D)),E)),C),f(f(f(B,C),f(C,D)),E)). [para(5(a,1),163(a,1,2)),flip(a)].
% 138.91/139.22 220 f(f(A,A),f(A,B)) = A. [para(173(a,1),163(a,1,2,1)),rewrite([173(6)])].
% 138.91/139.22 264 f(f(A,f(f(B,C),f(C,D))),f(f(f(B,C),f(C,D)),C)) = f(f(B,C),f(C,D)). [para(173(a,1),8(a,1,1))].
% 138.91/139.22 275 f(f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),D)),B) = f(f(f(A,B),f(B,C)),D). [para(1(a,1),220(a,1,2))].
% 138.91/139.22 286 f(f(f(A,B),f(A,B)),A) = f(A,B). [para(173(a,1),220(a,1,2))].
% 138.91/139.22 290 f(f(f(A,B),f(B,C)),B) = f(B,f(f(A,B),f(B,C))). [para(1(a,1),189(a,1,1)),rewrite([193(11)]),flip(a)].
% 138.91/139.22 303 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(f(f(B,C),f(C,D)),E),f(f(A,f(f(f(B,C),f(C,D)),E)),C)). [para(5(a,1),189(a,1,1)),rewrite([219(24)]),flip(a)].
% 138.91/139.22 311 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)). [back_rewrite(264),rewrite([290(8)])].
% 138.91/139.22 333 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))). [back_rewrite(218),rewrite([290(7),290(13)])].
% 138.91/139.22 334 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(193),rewrite([290(11)])].
% 138.91/139.22 356 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)). [back_rewrite(219),rewrite([303(24)])].
% 138.91/139.22 358 f(f(A,f(f(f(B,C),f(C,D)),E)),f(f(f(f(B,C),f(C,D)),E),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). [back_rewrite(36),rewrite([303(16)])].
% 138.91/139.22 363 f(f(f(f(A,B),f(B,C)),D),f(B,B)) = B. [para(1(a,1),137(a,1,2,1)),rewrite([1(14),1(16)])].
% 138.91/139.22 381 f(f(A,A),f(f(f(B,A),f(A,C)),D)) = A. [para(1(a,1),286(a,1,1,1)),rewrite([1(10),1(16)])].
% 138.91/139.22 392 f(f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),D)),f(f(f(E,f(f(f(A,B),f(B,C)),D)),B),F)) = f(f(f(A,B),f(B,C)),D). [para(5(a,1),286(a,1,1,1)),rewrite([5(30),5(43)])].
% 138.91/139.22 446 f(f(A,B),f(B,B)) = B. [para(173(a,1),363(a,1,1))].
% 138.91/139.22 452 f(f(f(f(A,B),f(A,C)),D),f(A,A)) = A. [para(286(a,1),363(a,1,1,1,1))].
% 138.91/139.22 480 f(A,f(f(B,A),f(B,A))) = f(B,A). [para(446(a,1),173(a,1,1))].
% 138.91/139.22 481 f(f(A,f(B,B)),B) = f(B,B). [para(173(a,1),446(a,1,2))].
% 138.91/139.22 483 f(f(A,A),f(B,A)) = A. [para(446(a,1),286(a,1,1,1)),rewrite([446(3),446(6)])].
% 138.91/139.22 513 f(A,f(B,f(A,A))) = f(A,A). [para(483(a,1),5(a,2)),rewrite([220(3),220(9),220(12),163(18),163(18),172(19)])].
% 138.91/139.22 519 f(f(f(A,f(f(B,A),C)),D),f(f(B,A),f(B,A))) = f(B,A). [para(483(a,1),363(a,1,1,1,1))].
% 138.91/139.22 527 f(f(A,f(f(A,f(f(B,B),B)),C)),f(A,f(f(A,f(f(B,B),B)),C))) = A. [para(481(a,1),1(a,1))].
% 138.91/139.22 668 f(f(f(f(A,B),f(C,B)),D),f(B,B)) = B. [para(480(a,1),363(a,1,1,1,2))].
% 138.91/139.22 669 f(f(A,f(f(B,C),f(C,D))),f(C,C)) = C. [para(480(a,1),363(a,1,1))].
% 138.91/139.22 692 f(A,f(f(A,f(f(A,f(f(B,B),B)),C)),D)) = f(A,f(f(A,f(f(B,B),B)),C)). [para(4(a,1),381(a,1,2,1)),rewrite([527(11)])].
% 138.91/139.22 706 f(f(A,A),f(f(f(A,B),f(A,C)),D)) = A. [para(286(a,1),381(a,1,2,1,1))].
% 138.91/139.22 707 f(f(A,B),f(A,f(f(A,f(f(C,C),C)),D))) = A. [para(381(a,1),9(a,1,2,2,1)),rewrite([692(7),692(12),527(11),692(7),692(12),527(11),220(7),692(8),692(13),527(12),692(8),692(35),692(14),692(19),527(18)])].
% 138.91/139.22 713 f(f(A,A),f(f(f(B,A),f(C,A)),D)) = A. [para(480(a,1),381(a,1,2,1,2))].
% 138.91/139.22 714 f(f(A,A),f(B,f(f(C,A),f(A,D)))) = A. [para(480(a,1),381(a,1,2))].
% 138.91/139.22 799 f(f(A,B),f(f(f(A,B),f(A,C)),A)) = f(f(A,B),f(A,C)). [para(452(a,1),7(a,1,2,2))].
% 138.91/139.22 809 f(f(f(A,B),f(A,C)),f(f(A,B),f(A,C))) = f(f(f(A,B),f(A,C)),A). [para(452(a,1),163(a,1,2)),flip(a)].
% 138.91/139.22 811 f(f(f(A,B),f(A,C)),A) = f(A,f(f(A,B),f(A,C))). [para(452(a,1),189(a,1,1)),rewrite([809(11)]),flip(a)].
% 138.91/139.22 813 f(f(f(f(f(A,B),C),B),D),f(f(A,B),f(A,B))) = f(A,B). [para(446(a,1),452(a,1,1,1,2))].
% 138.91/139.22 814 f(f(f(f(A,B),f(C,A)),D),f(A,A)) = A. [para(480(a,1),452(a,1,1,1,2))].
% 138.91/139.22 815 f(f(A,f(f(B,C),f(B,D))),f(B,B)) = B. [para(480(a,1),452(a,1,1))].
% 138.91/139.22 822 f(f(A,B),f(A,f(f(A,B),f(A,C)))) = f(f(A,B),f(A,C)). [back_rewrite(799),rewrite([811(5)])].
% 138.91/139.22 866 f(f(A,f(f(B,f(C,D)),C)),f(f(C,D),f(C,D))) = f(C,D). [para(173(a,1),669(a,1,1,2,2))].
% 138.91/139.22 895 f(f(A,A),f(f(f(A,B),f(C,A)),D)) = A. [para(480(a,1),706(a,1,2,1,2))].
% 138.91/139.22 896 f(f(A,A),f(B,f(f(A,C),f(A,D)))) = A. [para(480(a,1),706(a,1,2))].
% 138.91/139.22 921 f(A,f(f(A,f(f(B,B),B)),C)) = f(A,A). [para(20(a,1),446(a,1,1)),rewrite([707(11)]),flip(a)].
% 138.91/139.22 1017 f(A,f(f(f(B,f(A,A)),f(C,f(A,A))),D)) = f(A,A). [para(173(a,1),713(a,1,1))].
% 138.91/139.22 1046 f(f(f(A,B),f(C,A)),f(f(A,B),f(C,A))) = f(f(f(A,B),f(C,A)),A). [para(814(a,1),163(a,1,2)),flip(a)].
% 138.91/139.22 1048 f(f(f(A,B),f(C,A)),A) = f(A,f(f(A,B),f(C,A))). [para(814(a,1),189(a,1,1)),rewrite([1046(11)]),flip(a)].
% 138.91/139.22 1050 f(f(A,f(f(B,C),f(D,B))),f(B,B)) = B. [para(480(a,1),814(a,1,1))].
% 138.91/139.22 1099 f(f(f(f(A,f(B,f(f(f(A,A),A),f(f(A,A),A)))),f(f(B,f(f(f(A,A),A),f(f(A,A),A))),f(f(f(f(f(A,A),A),f(f(A,A),A)),f(f(f(C,f(B,f(f(f(A,A),A),f(f(A,A),A)))),f(C,f(B,f(f(f(A,A),A),f(f(A,A),A))))),f(C,f(B,f(f(f(A,A),A),f(f(A,A),A)))))),D))),E),f(f(f(A,A),A),f(f(A,A),A))) = f(B,f(f(f(A,A),A),f(f(A,A),A))). [para(481(a,1),21(a,1,1,1,2,2,1,1)),rewrite([481(55)])].
% 138.91/139.22 1102 f(f(A,B),f(A,f(f(C,C),C))) = A. [para(513(a,1),21(a,1,1,1,2)),rewrite([446(3)])].
% 138.91/139.22 1105 f(A,f(f(B,B),B)) = f(A,A). [para(21(a,1),381(a,1,2,1,1)),rewrite([1102(7),921(5),163(3)]),flip(a)].
% 138.91/139.22 1112 f(f(A,B),f(f(f(C,C),C),f(f(C,C),C))) = f(f(C,C),C). [para(21(a,1),668(a,1,1,1))].
% 138.91/139.22 1119 f(f(f(f(A,A),A),f(f(A,A),A)),f(B,C)) = f(f(A,A),A). [para(21(a,1),713(a,1,2,1))].
% 138.91/139.22 1128 f(f(f(f(A,A),A),f(f(A,A),A)),B) = f(f(A,A),A). [para(21(a,1),21(a,1,1,1,2,2,1,1)),rewrite([480(8),1119(17),1017(32),1119(16),163(9),480(11),1119(20),1017(35),1119(19),480(22),1119(31),1017(46),1119(30),480(29),1119(38),1017(53),1119(37),480(37),1119(46),1017(61),1119(45),1119(40),1119(16),480(9),1119(18),1017(33),1119(17),1119(17),189(12),173(9),480(8),1119(17),1017(32),1119(16)]),flip(a)].
% 138.91/139.22 1131 f(A,f(f(f(B,B),B),f(f(B,B),B))) = f(f(B,B),B). [back_rewrite(1099),rewrite([1128(42),1112(25)]),flip(a)].
% 138.91/139.22 1134 f(c,f(f(b,a),f(f(A,A),A))) != f(a,f(f(b,c),f(b,c))) # answer(associativity). [para(1105(a,2),3(a,1,2))].
% 138.91/139.22 1136 f(f(A,A),f(f(B,B),B)) = A. [para(1105(a,2),173(a,1))].
% 138.91/139.22 1137 f(A,f(B,f(B,B))) = f(A,A). [para(173(a,1),1105(a,1,2,1))].
% 138.91/139.22 1147 f(f(f(A,A),A),B) = f(B,B). [para(1105(a,1),480(a,2)),rewrite([1102(9)])].
% 138.91/139.22 1242 f(f(f(f(A,A),A),B),f(B,C)) = B. [para(1147(a,2),220(a,1,1))].
% 138.91/139.22 1244 f(A,f(f(f(B,B),B),f(A,C))) = f(A,C). [para(1147(a,2),137(a,1,2))].
% 138.91/139.22 1248 f(f(A,f(f(f(B,B),B),C)),C) = f(C,C). [para(1147(a,2),481(a,1,1,2))].
% 138.91/139.22 1265 f(f(f(A,A),A),f(f(A,A),A)) = f(f(f(B,B),B),f(f(B,B),B)). [para(1147(a,1),1105(a,1))].
% 138.91/139.22 1271 f(f(f(A,A),A),f(f(A,A),A)) = f(f(B,f(B,B)),f(B,f(B,B))). [para(1147(a,1),1137(a,1)),flip(a)].
% 138.91/139.22 1277 f(f(f(A,A),A),f(f(A,A),A)) = c_0. [new_symbol(1265)].
% 138.91/139.22 1278 f(f(A,f(A,A)),f(A,f(A,A))) = c_0. [back_rewrite(1271),rewrite([1277(5)]),flip(a)].
% 138.91/139.22 1279 f(f(A,A),A) = f(B,c_0). [back_rewrite(1131),rewrite([1277(5)]),flip(a)].
% 138.91/139.22 1617 f(f(A,c_0),B) = f(B,B). [para(1279(a,1),173(a,1,1)),rewrite([220(5)])].
% 138.91/139.22 1620 f(A,f(B,c_0)) = f(A,A). [para(1279(a,1),163(a,1,2))].
% 138.91/139.22 1627 f(f(f(f(A,c_0),f(B,C)),D),f(B,B)) = B. [para(1279(a,1),363(a,1,1,1,1))].
% 138.91/139.22 1629 f(f(A,c_0),f(B,B)) = B. [para(1279(a,1),363(a,1,1))].
% 138.91/139.22 1632 f(f(A,A),f(B,c_0)) = A. [para(1279(a,1),483(a,1,2))].
% 138.91/139.22 1636 f(A,c_0) = f(B,c_0). [para(1279(a,1),480(a,2)),rewrite([1277(5)])].
% 138.91/139.22 1656 f(f(A,A),f(B,f(f(C,c_0),f(A,D)))) = A. [para(1279(a,1),714(a,1,2,2,1))].
% 138.91/139.22 1657 f(A,f(B,f(f(C,f(A,A)),f(D,c_0)))) = f(A,A). [para(1279(a,1),714(a,1,2,2,2)),rewrite([220(3)])].
% 138.91/139.22 1752 f(f(A,f(f(B,C),f(D,c_0))),f(C,C)) = C. [para(1636(a,1),669(a,1,1,2,2))].
% 138.91/139.22 1902 f(A,f(f(A,B),f(B,A))) = f(A,B). [para(483(a,1),139(a,1,1)),rewrite([483(3),483(7)])].
% 138.91/139.22 1918 f(A,f(f(A,B),f(B,f(f(C,A),f(A,D))))) = f(A,B). [para(714(a,1),139(a,1,1)),rewrite([714(6),714(13)])].
% 138.91/139.22 2006 f(f(f(f(A,c_0),B),C),B) = f(B,B). [para(1617(a,2),189(a,1,1,1))].
% 138.91/139.22 2013 f(A,f(f(B,c_0),f(C,A))) = f(C,A). [para(1617(a,2),480(a,1,2))].
% 138.91/139.22 2068 f(f(f(A,c_0),f(B,C)),B) = f(B,C). [para(1617(a,1),139(a,1,1)),rewrite([2006(10),220(7)]),flip(a)].
% 138.91/139.22 2157 f(f(A,B),f(A,f(C,c_0))) = A. [para(1620(a,2),173(a,1,2))].
% 138.91/139.22 2163 f(f(A,B),f(B,f(C,c_0))) = B. [para(1620(a,2),446(a,1,2))].
% 138.91/139.22 2167 f(f(A,c_0),B) = f(B,f(A,c_0)). [para(1620(a,1),480(a,1,2,1)),rewrite([220(7)])].
% 138.91/139.22 2180 f(f(A,f(B,c_0)),f(f(C,C),C)) = A. [para(1620(a,2),1136(a,1,1))].
% 138.91/139.22 2240 f(f(f(A,B),f(C,c_0)),A) = f(A,B). [para(1620(a,2),139(a,2,1)),rewrite([811(7),137(7),220(7)]),flip(a)].
% 138.91/139.22 2697 f(f(A,c_0),f(B,f(C,c_0))) = B. [para(1620(a,2),1629(a,1,2))].
% 138.91/139.22 3241 f(A,f(A,A)) = f(c_0,A). [para(1105(a,1),275(a,1,1)),rewrite([220(3),220(5),1278(5),220(5)]),flip(a)].
% 138.91/139.22 3980 f(A,f(f(B,f(f(A,C),f(A,D))),f(E,c_0))) = f(B,f(f(A,C),f(A,D))). [para(815(a,1),2157(a,1,1))].
% 138.91/139.22 4633 f(f(A,c_0),f(B,C)) = f(f(B,C),f(B,C)). [para(1279(a,1),311(a,2,1)),rewrite([1244(10),1248(7)]),flip(a)].
% 138.91/139.22 6780 f(f(f(A,B),f(A,B)),f(f(A,A),C)) = f(A,B). [para(163(a,1),392(a,1,2,1,1)),rewrite([220(3),220(4),220(6),220(9)])].
% 138.91/139.22 7237 f(f(A,f(f(B,A),f(A,B))),f(f(f(B,A),f(f(f(B,A),f(A,B)),C)),D)) = f(f(B,A),f(A,B)). [para(1902(a,1),381(a,1,2,1,1)),rewrite([334(7)])].
% 138.91/139.22 7808 f(f(A,f(B,C)),f(A,f(B,C))) = f(f(c_0,c_0),f(A,f(B,C))). [para(2180(a,1),358(a,1,1,2,1)),rewrite([2167(11),3241(11),2167(10,R),2697(10),2167(12),3241(12),2167(11,R),2697(11),2167(9,R),2013(10),2167(14),3241(14),2167(13,R),2697(13),2167(11,R)])].
% 138.91/139.22 8730 f(f(f(f(A,c_0),f(B,C)),D),f(B,C)) = f(f(B,C),f(A,c_0)). [para(2240(a,1),519(a,1,1,1,2)),rewrite([2157(14)])].
% 138.91/139.22 10626 f(f(f(f(A,B),f(B,A)),C),f(A,B)) = f(f(A,B),f(f(f(A,B),f(B,A)),C)). [para(895(a,1),303(a,1,1,1)),rewrite([895(16)]),flip(a)].
% 138.91/139.22 10633 f(f(A,B),f(f(f(A,B),f(B,A)),C)) = f(f(A,B),f(A,B)). [para(895(a,1),356(a,1,1,1)),rewrite([895(7),895(13),10626(9)]),flip(a)].
% 138.91/139.22 10653 f(f(A,f(f(B,A),f(A,B))),f(f(f(B,A),f(B,A)),C)) = f(f(B,A),f(A,B)). [back_rewrite(7237),rewrite([10633(10)])].
% 138.91/139.22 10677 f(A,f(f(A,B),f(f(C,f(A,B)),f(f(A,B),f(A,D))))) = f(f(C,f(A,B)),f(f(A,B),f(A,D))). [para(896(a,1),311(a,1,1))].
% 138.91/139.22 10844 f(A,f(f(B,A),f(A,B))) = f(B,A). [para(1050(a,1),333(a,1,2)),rewrite([1048(4),1902(4)]),flip(a)].
% 138.91/139.22 10879 f(f(A,B),f(B,A)) = f(f(A,B),f(A,B)). [back_rewrite(10653),rewrite([10844(4),163(6)]),flip(a)].
% 138.91/139.22 11505 f(f(c_0,c_0),f(f(A,c_0),f(B,C))) = f(B,C). [para(1627(a,1),163(a,1,2)),rewrite([2068(5),7808(10)]),flip(a)].
% 138.91/139.22 11524 f(f(A,c_0),f(B,C)) = f(f(B,C),f(D,c_0)). [para(2068(a,1),1627(a,1,1,1,2)),rewrite([7808(14),11505(13),8730(7)]),flip(a)].
% 138.91/139.22 11816 f(f(A,f(f(B,C),f(D,c_0))),f(C,f(E,c_0))) = C. [para(1620(a,2),1752(a,1,2))].
% 138.91/139.22 11867 f(f(f(f(A,A),A),f(f(f(f(B,C),D),C),E)),f(B,C)) = f(f(f(f(B,C),D),C),E). [para(813(a,1),1242(a,1,2))].
% 138.91/139.22 12999 f(f(A,c_0),f(f(B,c_0),f(C,D))) = f(C,D). [para(4633(a,2),1629(a,1,2))].
% 138.91/139.22 13751 f(f(A,f(B,C)),f(f(C,B),f(C,B))) = f(C,B). [para(483(a,1),866(a,1,1,2,1))].
% 138.91/139.22 15335 f(A,B) = f(B,A). [para(10879(a,1),483(a,1,2)),rewrite([13751(7)])].
% 138.91/139.22 15336 f(c,f(f(a,b),f(A,c_0))) != f(a,f(f(b,c),f(b,c))) # answer(associativity). [para(10879(a,1),1134(a,1,2,2,1)),rewrite([15335(4),220(7),3241(6),15335(6)])].
% 138.91/139.22 15485 f(f(A,B),f(f(C,c_0),f(D,f(B,f(E,f(A,B)))))) = f(D,f(B,f(E,f(A,B)))). [back_rewrite(11867),rewrite([15335(2),3241(2),15335(2),15335(4),15335(5),15335(6),15335(9),15335(11),15335(12),15335(13)])].
% 138.91/139.22 15944 f(f(f(A,B),f(A,B)),f(C,f(A,A))) = f(A,B). [back_rewrite(6780),rewrite([15335(5)])].
% 138.91/139.22 16505 f(A,f(f(A,B),f(B,f(f(A,C),f(A,D))))) = f(A,B). [back_rewrite(1918),rewrite([15335(2)])].
% 138.91/139.22 16599 f(f(f(A,c_0),f(B,C)),f(D,f(B,f(E,c_0)))) = f(B,C). [para(1656(a,1),1657(a,1,2,2,1)),rewrite([7808(18),12999(17)])].
% 138.91/139.22 16603 f(f(f(A,f(B,B)),f(C,c_0)),f(B,D)) = f(A,f(B,B)). [para(1657(a,1),1657(a,1,2,2,1)),rewrite([1632(9),15335(6),2157(18)])].
% 138.91/139.22 16830 f(f(A,B),f(f(C,f(B,B)),f(D,c_0))) = f(C,f(B,B)). [para(513(a,1),11816(a,1,1,2,1)),rewrite([1632(4)])].
% 138.91/139.22 17266 f(f(A,A),f(B,f(f(C,A),f(C,A)))) = A. [para(446(a,1),15944(a,1,1,2)),rewrite([446(3),446(9)])].
% 138.91/139.22 17534 f(f(A,A),f(B,A)) = A. [para(17266(a,1),3980(a,1,2,1)),rewrite([2163(5),15335(3),446(7)]),flip(a)].
% 138.91/139.22 25091 f(f(A,f(B,c_0)),f(C,f(f(D,A),f(E,c_0)))) = A. [para(446(a,1),16599(a,2)),rewrite([446(5),15335(3)])].
% 138.91/139.22 25714 f(A,f(f(A,f(B,C)),f(A,f(C,C)))) = f(A,f(B,C)). [para(16830(a,1),16505(a,1,2,2))].
% 138.91/139.22 29561 f(f(A,f(B,C)),f(A,f(C,C))) = f(f(c_0,c_0),f(A,f(B,C))). [para(25714(a,1),822(a,1,2)),rewrite([7808(5)]),flip(a)].
% 138.91/139.22 29640 f(A,f(f(B,A),f(B,C))) = f(B,A). [para(17534(a,1),10677(a,1,2,2,1)),rewrite([16505(7),17534(4)]),flip(a)].
% 138.91/139.22 29759 f(A,f(f(B,C),f(A,B))) = f(A,B). [para(15335(a,1),29640(a,1,2)),rewrite([15335(2),15335(5)])].
% 138.91/139.23 29763 f(A,f(f(A,B),f(C,f(f(B,D),f(B,E))))) = f(A,B). [para(3980(a,1),29640(a,1,2,2)),rewrite([15335(1),15335(8)])].
% 138.91/139.23 29904 f(A,f(f(B,C),f(B,A))) = f(B,A). [para(29759(a,1),15335(a,2)),rewrite([15335(2),15335(4),15335(5)])].
% 138.91/139.23 39266 f(f(A,A),f(f(c_0,c_0),f(B,f(A,C)))) = f(B,f(A,A)). [para(29561(a,1),29904(a,1,2)),rewrite([15335(5)])].
% 138.91/139.23 39322 f(f(A,A),f(f(B,f(A,C)),f(D,c_0))) = f(B,f(A,A)). [para(11524(a,1),39266(a,1,2))].
% 138.91/139.23 39660 f(f(f(A,f(B,C)),f(D,c_0)),f(B,B)) = f(A,f(B,B)). [para(39322(a,1),15335(a,1)),flip(a)].
% 138.91/139.23 39699 f(A,f(f(B,C),f(B,f(D,f(A,B))))) = f(A,B). [para(15485(a,1),29763(a,1,2))].
% 138.91/139.23 39736 f(A,f(f(B,C),f(C,f(D,f(A,C))))) = f(A,C). [para(15335(a,1),39699(a,1,2,1))].
% 138.91/139.23 39804 f(A,f(f(B,C),f(C,f(D,f(A,A))))) = f(A,C). [para(16603(a,1),39736(a,1,2,2,2))].
% 138.91/139.23 39958 f(f(f(A,B),f(C,c_0)),f(f(D,E),f(B,E))) = f(E,f(f(A,B),f(C,c_0))). [para(25091(a,1),39804(a,1,2,2,2)),rewrite([15335(6),15335(13)])].
% 138.91/139.23 40448 f(A,f(f(B,C),f(D,c_0))) = f(B,f(f(C,A),f(C,A))). [para(173(a,1),39660(a,1,1,1,2)),rewrite([39958(8)])].
% 138.91/139.23 40449 $F # answer(associativity). [resolve(40448,a,15336,a)].
% 138.91/139.23
% 138.91/139.23 % SZS output end Refutation
% 138.91/139.23 ============================== end of proof ==========================
% 138.91/139.23
% 138.91/139.23 ============================== STATISTICS ============================
% 138.91/139.23
% 138.91/139.23 Given=1740. Generated=3385987. Kept=40447. proofs=1.
% 138.91/139.23 Usable=729. Sos=9999. Demods=4180. Limbo=0, Disabled=29720. Hints=0.
% 138.91/139.23 Megabytes=43.95.
% 138.91/139.23 User_CPU=136.35, System_CPU=1.91, Wall_clock=139.
% 138.91/139.23
% 138.91/139.23 ============================== end of statistics =====================
% 138.91/139.23
% 138.91/139.23 ============================== end of search =========================
% 138.91/139.23
% 138.91/139.23 THEOREM PROVED
% 138.91/139.23 % SZS status Unsatisfiable
% 138.91/139.23
% 138.91/139.23 Exiting with 1 proof.
% 138.91/139.23
% 138.91/139.23 Process 27846 exit (max_proofs) Thu Jun 30 03:03:12 2022
% 138.91/139.23 Prover9 interrupted
%------------------------------------------------------------------------------