TSTP Solution File: LAT393-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LAT393-1 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 06:28:36 EDT 2022
% Result : Unsatisfiable 147.38s 147.67s
% Output : Refutation 147.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT393-1 : TPTP v8.1.0. Released v5.4.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.33 % Computer : n021.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jun 30 00:21:27 EDT 2022
% 0.14/0.33 % CPUTime :
% 42.97/43.25 ============================== Prover9 ===============================
% 42.97/43.25 Prover9 (32) version 2009-11A, November 2009.
% 42.97/43.25 Process 5975 was started by sandbox2 on n021.cluster.edu,
% 42.97/43.25 Thu Jun 30 00:21:28 2022
% 42.97/43.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5767_n021.cluster.edu".
% 42.97/43.25 ============================== end of head ===========================
% 42.97/43.25
% 42.97/43.25 ============================== INPUT =================================
% 42.97/43.25
% 42.97/43.25 % Reading from file /tmp/Prover9_5767_n021.cluster.edu
% 42.97/43.25
% 42.97/43.25 set(prolog_style_variables).
% 42.97/43.25 set(auto2).
% 42.97/43.25 % set(auto2) -> set(auto).
% 42.97/43.25 % set(auto) -> set(auto_inference).
% 42.97/43.25 % set(auto) -> set(auto_setup).
% 42.97/43.25 % set(auto_setup) -> set(predicate_elim).
% 42.97/43.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 42.97/43.25 % set(auto) -> set(auto_limits).
% 42.97/43.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 42.97/43.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 42.97/43.25 % set(auto) -> set(auto_denials).
% 42.97/43.25 % set(auto) -> set(auto_process).
% 42.97/43.25 % set(auto2) -> assign(new_constants, 1).
% 42.97/43.25 % set(auto2) -> assign(fold_denial_max, 3).
% 42.97/43.25 % set(auto2) -> assign(max_weight, "200.000").
% 42.97/43.25 % set(auto2) -> assign(max_hours, 1).
% 42.97/43.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 42.97/43.25 % set(auto2) -> assign(max_seconds, 0).
% 42.97/43.25 % set(auto2) -> assign(max_minutes, 5).
% 42.97/43.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 42.97/43.25 % set(auto2) -> set(sort_initial_sos).
% 42.97/43.25 % set(auto2) -> assign(sos_limit, -1).
% 42.97/43.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 42.97/43.25 % set(auto2) -> assign(max_megs, 400).
% 42.97/43.25 % set(auto2) -> assign(stats, some).
% 42.97/43.25 % set(auto2) -> clear(echo_input).
% 42.97/43.25 % set(auto2) -> set(quiet).
% 42.97/43.25 % set(auto2) -> clear(print_initial_clauses).
% 42.97/43.25 % set(auto2) -> clear(print_given).
% 42.97/43.25 assign(lrs_ticks,-1).
% 42.97/43.25 assign(sos_limit,10000).
% 42.97/43.25 assign(order,kbo).
% 42.97/43.25 set(lex_order_vars).
% 42.97/43.25 clear(print_given).
% 42.97/43.25
% 42.97/43.25 % formulas(sos). % not echoed (5 formulas)
% 42.97/43.25
% 42.97/43.25 ============================== end of input ==========================
% 42.97/43.25
% 42.97/43.25 % From the command line: assign(max_seconds, 300).
% 42.97/43.25
% 42.97/43.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 42.97/43.25
% 42.97/43.25 % Formulas that are not ordinary clauses:
% 42.97/43.25
% 42.97/43.25 ============================== end of process non-clausal formulas ===
% 42.97/43.25
% 42.97/43.25 ============================== PROCESS INITIAL CLAUSES ===============
% 42.97/43.25
% 42.97/43.25 ============================== PREDICATE ELIMINATION =================
% 42.97/43.25
% 42.97/43.25 ============================== end predicate elimination =============
% 42.97/43.25
% 42.97/43.25 Auto_denials:
% 42.97/43.25 % copying label goals to answer in negative clause
% 42.97/43.25
% 42.97/43.25 Term ordering decisions:
% 42.97/43.25
% 42.97/43.25 % Assigning unary symbol neg kb_weight 0 and highest precedence (8).
% 42.97/43.25 Function symbol KB weights: x0=1. x1=1. x2=1. f=1. and=1. or=1. neg=0.
% 42.97/43.25
% 42.97/43.25 ============================== end of process initial clauses ========
% 42.97/43.25
% 42.97/43.25 ============================== CLAUSES FOR SEARCH ====================
% 42.97/43.25
% 42.97/43.25 ============================== end of clauses for search =============
% 42.97/43.25
% 42.97/43.25 ============================== SEARCH ================================
% 42.97/43.25
% 42.97/43.25 % Starting search at 0.01 seconds.
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=91.000, iters=3348
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=87.000, iters=3433
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=73.000, iters=3408
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=71.000, iters=3370
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=65.000, iters=3409
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=63.000, iters=3479
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=61.000, iters=3337
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=59.000, iters=3335
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=57.000, iters=3380
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=55.000, iters=3333
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=53.000, iters=3354
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=51.000, iters=3463
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=49.000, iters=3364
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=47.000, iters=3357
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=45.000, iters=3409
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=43.000, iters=3335
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=41.000, iters=3379
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=39.000, iters=3334
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=37.000, iters=3341
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=35.000, iters=3339
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=33.000, iters=3361
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=31.000, iters=3378
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=29.000, iters=3345
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=27.000, iters=3367
% 42.97/43.25
% 42.97/43.25 Low Water (keep): wt=25.000, iters=3350
% 42.97/43.25
% 42.97/43.25 Low Water (displace): id=23409, wt=97.000
% 42.97/43.25
% 42.97/43.25 Low Water (displace): id=21401, wt=85.000
% 42.97/43.25
% 42.97/43.25 Low Water (displace): id=23890, wt=83.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=18665, wt=79.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=23921, wt=75.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=23945, wt=73.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=22031, wt=69.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=23993, wt=63.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=24020, wt=61.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=23980, wt=59.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=24014, wt=57.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=28426, wt=33.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=28452, wt=31.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=28723, wt=29.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=29715, wt=27.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=30986, wt=25.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=33447, wt=23.000
% 147.38/147.67
% 147.38/147.67 Low Water (displace): id=40351, wt=21.000
% 147.38/147.67
% 147.38/147.67 ============================== PROOF =================================
% 147.38/147.67 % SZS status Unsatisfiable
% 147.38/147.67 % SZS output start Refutation
% 147.38/147.67
% 147.38/147.67 % Proof 1 at 144.68 (+ 2.04) seconds: goals.
% 147.38/147.67 % Length of proof is 160.
% 147.38/147.67 % Level of proof is 36.
% 147.38/147.67 % Maximum clause weight is 149.000.
% 147.38/147.67 % Given clauses 1781.
% 147.38/147.67
% 147.38/147.67 2 or(A,B) = f(f(A,A),f(B,B)) # label(sos_001) # label(axiom). [assumption].
% 147.38/147.67 3 and(A,B) = f(f(A,B),f(A,B)) # label(sos_002) # label(axiom). [assumption].
% 147.38/147.67 4 f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))) = B # label(sos) # label(axiom). [assumption].
% 147.38/147.67 5 f(x0,f(f(x1,x2),f(x1,x2))) != f(x1,f(f(x0,x2),f(x0,x2))) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 147.38/147.67 6 f(x1,f(f(x0,x2),f(x0,x2))) != f(x0,f(f(x1,x2),f(x1,x2))) # answer(goals). [copy(5),flip(a)].
% 147.38/147.67 7 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(4(a,1),4(a,1,1,1,1))].
% 147.38/147.67 8 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(4(a,1),4(a,1,1,1,2))].
% 147.38/147.67 10 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(4(a,1),4(a,1,1))].
% 147.38/147.67 11 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(4(a,1),4(a,1,2,2))].
% 147.38/147.67 12 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(7(a,1),4(a,1,1,1,2))].
% 147.38/147.67 23 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(10(a,1),4(a,1,2,2))].
% 147.38/147.67 24 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(10(a,1),4(a,1,2))].
% 147.38/147.67 26 f(f(A,B),f(f(f(A,B),f(B,C)),B)) = f(f(A,B),f(B,C)). [para(4(a,1),10(a,1,2,2))].
% 147.38/147.67 39 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(4(a,1),26(a,1,2,1,2)),rewrite([4(32)])].
% 147.38/147.67 40 f(f(f(f(A,B),f(B,C)),B),f(B,B)) = B. [para(4(a,1),26(a,1,2,1)),rewrite([4(16)])].
% 147.38/147.67 54 f(f(A,A),f(A,A)) = A. [para(4(a,1),40(a,1,1,1))].
% 147.38/147.67 65 f(f(A,B),f(A,f(f(A,f(f(A,A),A)),A))) = A. [para(54(a,1),4(a,1,1,1))].
% 147.38/147.67 105 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(54(a,1),8(a,1,1,1,1,2,1)),rewrite([54(7),54(8),54(20)])].
% 147.38/147.67 140 f(A,f(f(A,B),f(A,B))) = f(A,B). [para(65(a,1),10(a,1,2,2))].
% 147.38/147.67 141 f(A,f(f(A,f(f(A,f(f(A,A),A)),A)),B)) = f(A,A). [para(65(a,1),26(a,1,1)),rewrite([65(7),65(13),65(8)]),flip(a)].
% 147.38/147.67 142 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(65(a,1),26(a,1,2,1,2)),rewrite([65(17)])].
% 147.38/147.67 143 f(A,f(f(A,f(f(A,A),A)),A)) = f(A,A). [para(65(a,1),40(a,1,1,1,1)),rewrite([141(7),65(7),65(11)]),flip(a)].
% 147.38/147.67 163 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(8(a,1),65(a,1,1)),rewrite([143(51)])].
% 147.38/147.67 166 f(A,f(f(A,A),B)) = f(A,A). [back_rewrite(141),rewrite([143(5)])].
% 147.38/147.67 175 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(105),rewrite([166(12),166(12)])].
% 147.38/147.67 176 f(f(A,B),f(A,A)) = A. [back_rewrite(65),rewrite([166(4),166(4)])].
% 147.38/147.67 192 f(f(f(A,A),B),A) = f(A,A). [para(176(a,1),176(a,1,2))].
% 147.38/147.67 196 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(4(a,1),166(a,1,2)),flip(a)].
% 147.38/147.67 221 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(166(a,1),8(a,2)),rewrite([196(10),196(22),196(31),8(41),196(16)])].
% 147.38/147.67 222 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(8(a,1),166(a,1,2)),flip(a)].
% 147.38/147.67 223 f(f(A,A),f(A,B)) = A. [para(176(a,1),166(a,1,2,1)),rewrite([176(6)])].
% 147.38/147.67 267 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(176(a,1),11(a,1,1))].
% 147.38/147.67 278 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(4(a,1),223(a,1,2))].
% 147.38/147.67 289 f(f(f(A,B),f(A,B)),A) = f(A,B). [para(176(a,1),223(a,1,2))].
% 147.38/147.67 293 f(f(f(A,B),f(B,C)),B) = f(B,f(f(A,B),f(B,C))). [para(4(a,1),192(a,1,1)),rewrite([196(11)]),flip(a)].
% 147.38/147.67 306 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(8(a,1),192(a,1,1)),rewrite([222(24)]),flip(a)].
% 147.38/147.67 314 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(267),rewrite([293(8)])].
% 147.38/147.67 336 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(221),rewrite([293(7),293(13)])].
% 147.38/147.67 337 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(196),rewrite([293(11)])].
% 147.38/147.67 359 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(222),rewrite([306(24)])].
% 147.38/147.67 361 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(39),rewrite([306(16)])].
% 147.38/147.67 366 f(f(f(f(A,B),f(B,C)),D),f(B,B)) = B. [para(4(a,1),140(a,1,2,1)),rewrite([4(14),4(16)])].
% 147.38/147.67 384 f(f(A,A),f(f(f(B,A),f(A,C)),D)) = A. [para(4(a,1),289(a,1,1,1)),rewrite([4(10),4(16)])].
% 147.38/147.67 395 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(8(a,1),289(a,1,1,1)),rewrite([8(30),8(43)])].
% 147.38/147.67 449 f(f(A,B),f(B,B)) = B. [para(176(a,1),366(a,1,1))].
% 147.38/147.67 455 f(f(f(f(A,B),f(A,C)),D),f(A,A)) = A. [para(289(a,1),366(a,1,1,1,1))].
% 147.38/147.67 483 f(A,f(f(B,A),f(B,A))) = f(B,A). [para(449(a,1),176(a,1,1))].
% 147.38/147.67 484 f(f(A,f(B,B)),B) = f(B,B). [para(176(a,1),449(a,1,2))].
% 147.38/147.67 486 f(f(A,A),f(B,A)) = A. [para(449(a,1),289(a,1,1,1)),rewrite([449(3),449(6)])].
% 147.38/147.67 516 f(A,f(B,f(A,A))) = f(A,A). [para(486(a,1),8(a,2)),rewrite([223(3),223(9),223(12),166(18),166(18),175(19)])].
% 147.38/147.67 530 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(484(a,1),4(a,1))].
% 147.38/147.67 671 f(f(f(f(A,B),f(C,B)),D),f(B,B)) = B. [para(483(a,1),366(a,1,1,1,2))].
% 147.38/147.67 672 f(f(A,f(f(B,C),f(C,D))),f(C,C)) = C. [para(483(a,1),366(a,1,1))].
% 147.38/147.67 695 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(7(a,1),384(a,1,2,1)),rewrite([530(11)])].
% 147.38/147.67 709 f(f(A,A),f(f(f(A,B),f(A,C)),D)) = A. [para(289(a,1),384(a,1,2,1,1))].
% 147.38/147.67 710 f(f(A,B),f(A,f(f(A,f(f(C,C),C)),D))) = A. [para(384(a,1),12(a,1,2,2,1)),rewrite([695(7),695(12),530(11),695(7),695(12),530(11),223(7),695(8),695(13),530(12),695(8),695(35),695(14),695(19),530(18)])].
% 147.38/147.67 716 f(f(A,A),f(f(f(B,A),f(C,A)),D)) = A. [para(483(a,1),384(a,1,2,1,2))].
% 147.38/147.67 717 f(f(A,A),f(B,f(f(C,A),f(A,D)))) = A. [para(483(a,1),384(a,1,2))].
% 147.38/147.67 816 f(f(f(f(f(A,B),C),B),D),f(f(A,B),f(A,B))) = f(A,B). [para(449(a,1),455(a,1,1,1,2))].
% 147.38/147.67 817 f(f(f(f(A,B),f(C,A)),D),f(A,A)) = A. [para(483(a,1),455(a,1,1,1,2))].
% 147.38/147.67 818 f(f(A,f(f(B,C),f(B,D))),f(B,B)) = B. [para(483(a,1),455(a,1,1))].
% 147.38/147.67 869 f(f(A,f(f(B,f(C,D)),C)),f(f(C,D),f(C,D))) = f(C,D). [para(176(a,1),672(a,1,1,2,2))].
% 147.38/147.67 898 f(f(A,A),f(f(f(A,B),f(C,A)),D)) = A. [para(483(a,1),709(a,1,2,1,2))].
% 147.38/147.67 899 f(f(A,A),f(B,f(f(A,C),f(A,D)))) = A. [para(483(a,1),709(a,1,2))].
% 147.38/147.67 924 f(A,f(f(A,f(f(B,B),B)),C)) = f(A,A). [para(23(a,1),449(a,1,1)),rewrite([710(11)]),flip(a)].
% 147.38/147.67 1020 f(A,f(f(f(B,f(A,A)),f(C,f(A,A))),D)) = f(A,A). [para(176(a,1),716(a,1,1))].
% 147.38/147.67 1049 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(817(a,1),166(a,1,2)),flip(a)].
% 147.38/147.67 1051 f(f(f(A,B),f(C,A)),A) = f(A,f(f(A,B),f(C,A))). [para(817(a,1),192(a,1,1)),rewrite([1049(11)]),flip(a)].
% 147.38/147.67 1053 f(f(A,f(f(B,C),f(D,B))),f(B,B)) = B. [para(483(a,1),817(a,1,1))].
% 147.38/147.67 1102 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(484(a,1),24(a,1,1,1,2,2,1,1)),rewrite([484(55)])].
% 147.38/147.67 1105 f(f(A,B),f(A,f(f(C,C),C))) = A. [para(516(a,1),24(a,1,1,1,2)),rewrite([449(3)])].
% 147.38/147.67 1108 f(A,f(f(B,B),B)) = f(A,A). [para(24(a,1),384(a,1,2,1,1)),rewrite([1105(7),924(5),166(3)]),flip(a)].
% 147.38/147.67 1115 f(f(A,B),f(f(f(C,C),C),f(f(C,C),C))) = f(f(C,C),C). [para(24(a,1),671(a,1,1,1))].
% 147.38/147.67 1122 f(f(f(f(A,A),A),f(f(A,A),A)),f(B,C)) = f(f(A,A),A). [para(24(a,1),716(a,1,2,1))].
% 147.38/147.67 1131 f(f(f(f(A,A),A),f(f(A,A),A)),B) = f(f(A,A),A). [para(24(a,1),24(a,1,1,1,2,2,1,1)),rewrite([483(8),1122(17),1020(32),1122(16),166(9),483(11),1122(20),1020(35),1122(19),483(22),1122(31),1020(46),1122(30),483(29),1122(38),1020(53),1122(37),483(37),1122(46),1020(61),1122(45),1122(40),1122(16),483(9),1122(18),1020(33),1122(17),1122(17),192(12),176(9),483(8),1122(17),1020(32),1122(16)]),flip(a)].
% 147.38/147.67 1134 f(A,f(f(f(B,B),B),f(f(B,B),B))) = f(f(B,B),B). [back_rewrite(1102),rewrite([1131(42),1115(25)]),flip(a)].
% 147.38/147.67 1139 f(f(A,A),f(f(B,B),B)) = A. [para(1108(a,2),2(a,2)),rewrite([2(1),223(3)]),flip(a)].
% 147.38/147.67 1142 f(A,f(B,f(B,B))) = f(A,A). [para(176(a,1),1108(a,1,2,1))].
% 147.38/147.67 1152 f(f(f(A,A),A),B) = f(B,B). [para(1108(a,1),483(a,2)),rewrite([1105(9)])].
% 147.38/147.67 1253 f(f(f(f(A,A),A),B),f(B,C)) = B. [para(1152(a,2),223(a,1,1))].
% 147.38/147.67 1255 f(A,f(f(f(B,B),B),f(A,C))) = f(A,C). [para(1152(a,2),140(a,1,2))].
% 147.38/147.67 1259 f(f(A,f(f(f(B,B),B),C)),C) = f(C,C). [para(1152(a,2),484(a,1,1,2))].
% 147.38/147.67 1276 f(f(f(A,A),A),f(f(A,A),A)) = f(f(f(B,B),B),f(f(B,B),B)). [para(1152(a,1),1108(a,1))].
% 147.38/147.67 1282 f(f(f(A,A),A),f(f(A,A),A)) = f(f(B,f(B,B)),f(B,f(B,B))). [para(1152(a,1),1142(a,1)),flip(a)].
% 147.38/147.67 1288 f(f(f(A,A),A),f(f(A,A),A)) = c_0. [new_symbol(1276)].
% 147.38/147.67 1289 f(f(A,f(A,A)),f(A,f(A,A))) = c_0. [back_rewrite(1282),rewrite([1288(5)]),flip(a)].
% 147.38/147.67 1290 f(f(A,A),A) = f(B,c_0). [back_rewrite(1134),rewrite([1288(5)]),flip(a)].
% 147.38/147.67 1291 f(f(A,A),A) = f(c_0,B). [back_rewrite(1131),rewrite([1288(5)]),flip(a)].
% 147.38/147.67 1631 f(f(A,c_0),f(f(B,B),B)) = c_0. [para(1290(a,1),3(a,2,1)),rewrite([3(2),1288(5)]),flip(a)].
% 147.38/147.67 1633 f(f(A,c_0),B) = f(B,B). [para(1290(a,1),176(a,1,1)),rewrite([223(5)])].
% 147.38/147.67 1635 f(A,f(B,c_0)) = f(A,A). [para(1290(a,1),166(a,1,2))].
% 147.38/147.67 1639 f(f(A,A),c_0) = f(f(A,A),A). [para(1290(a,1),140(a,1,2,1)),rewrite([1631(6)])].
% 147.38/147.67 1643 f(f(A,c_0),f(B,B)) = B. [para(1290(a,1),366(a,1,1))].
% 147.38/147.67 1645 f(f(A,A),f(B,c_0)) = A. [para(1290(a,1),486(a,1,2))].
% 147.38/147.67 1648 f(A,c_0) = f(B,c_0). [para(1290(a,1),483(a,2)),rewrite([1288(5)])].
% 147.38/147.67 1795 f(A,f(c_0,B)) = f(A,A). [para(1291(a,1),166(a,1,2))].
% 147.38/147.67 1911 f(A,f(f(A,B),f(B,A))) = f(A,B). [para(486(a,1),142(a,1,1)),rewrite([486(3),486(7)])].
% 147.38/147.67 1927 f(A,f(f(A,B),f(B,f(f(C,A),f(A,D))))) = f(A,B). [para(717(a,1),142(a,1,1)),rewrite([717(6),717(13)])].
% 147.38/147.67 2101 f(A,f(f(B,c_0),f(C,A))) = f(C,A). [para(1633(a,2),483(a,1,2))].
% 147.38/147.67 2170 f(f(A,B),f(A,f(C,c_0))) = A. [para(1635(a,2),176(a,1,2))].
% 147.38/147.67 2176 f(f(A,B),f(B,f(C,c_0))) = B. [para(1635(a,2),449(a,1,2))].
% 147.38/147.67 2180 f(f(A,c_0),B) = f(B,f(A,c_0)). [para(1635(a,1),483(a,1,2,1)),rewrite([223(7)])].
% 147.38/147.67 2181 f(A,f(f(B,A),f(C,c_0))) = f(B,A). [para(1635(a,2),483(a,1,2))].
% 147.38/147.67 2193 f(f(A,f(B,c_0)),f(f(C,C),C)) = A. [para(1635(a,2),1139(a,1,1))].
% 147.38/147.67 2197 f(f(f(A,f(B,c_0)),A),C) = f(C,C). [para(1635(a,2),1152(a,1,1,1))].
% 147.38/147.67 2496 f(f(f(f(A,B),f(B,C)),D),f(f(f(B,f(f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),D)),c_0)),E),f(f(B,f(f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),D)),c_0)),E))) = f(f(B,B),E). [para(1152(a,1),163(a,2,1)),rewrite([1639(18,R),2180(16),1639(31,R),2180(29)])].
% 147.38/147.67 2516 f(f(f(f(A,B),f(B,C)),D),f(f(f(B,f(E,c_0)),F),f(f(B,f(f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),D)),c_0)),F))) = f(f(B,f(f(f(f(f(A,B),f(B,C)),D),f(f(f(A,B),f(B,C)),D)),c_0)),F). [para(1290(a,1),163(a,1,2,1,1,1)),rewrite([2180(7),1639(22,R),2180(20),1639(37,R),2180(35)])].
% 147.38/147.67 2524 f(f(A,f(f(f(f(f(B,A),f(A,C)),D),f(f(f(B,A),f(A,C)),D)),c_0)),E) = f(f(A,f(F,c_0)),E). [para(1290(a,1),163(a,2,1,1)),rewrite([1639(18,R),2180(16),1639(31,R),2180(29),2516(32),2180(16)])].
% 147.38/147.67 2556 f(f(f(c_0,A),B),C) = f(f(B,f(f(f(f(f(D,B),f(B,E)),F),f(f(f(D,B),f(B,E)),F)),c_0)),C). [para(1291(a,1),163(a,2,1,1)),rewrite([1639(18,R),2180(16),1639(31,R),2180(29),2516(32)]),flip(a)].
% 147.38/147.67 2652 f(f(A,f(f(f(f(f(B,A),f(A,C)),D),f(f(f(B,A),f(A,C)),D)),c_0)),E) = f(f(A,A),E). [back_rewrite(2496),rewrite([2516(32)])].
% 147.38/147.67 2673 f(f(f(c_0,A),B),C) = f(f(B,B),C). [back_rewrite(2556),rewrite([2652(17)])].
% 147.38/147.67 2676 f(f(A,f(B,c_0)),C) = f(f(A,A),C). [back_rewrite(2524),rewrite([2652(13)]),flip(a)].
% 147.38/147.67 2712 f(f(A,c_0),f(B,f(C,c_0))) = B. [para(1635(a,2),1643(a,1,2))].
% 147.38/147.67 3073 f(f(c_0,A),B) = f(B,f(c_0,A)). [para(1795(a,1),483(a,1,2,1)),rewrite([223(7)])].
% 147.38/147.67 3203 f(f(A,f(c_0,B)),C) = f(f(A,A),C). [back_rewrite(2673),rewrite([3073(3)])].
% 147.38/147.67 3265 f(A,f(A,A)) = f(c_0,A). [para(1108(a,1),278(a,1,1)),rewrite([223(3),223(5),1289(5),223(5)]),flip(a)].
% 147.38/147.67 3541 f(A,f(A,f(B,c_0))) = f(c_0,A). [para(1635(a,2),3265(a,1,2))].
% 147.38/147.67 3873 f(f(f(A,B),f(C,c_0)),B) = f(A,B). [para(1648(a,1),293(a,1,1,2)),rewrite([2181(10)])].
% 147.38/147.67 4002 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(818(a,1),2170(a,1,1))].
% 147.38/147.67 4052 f(f(f(f(A,B),f(B,C)),D),f(D,B)) = f(f(D,B),f(f(f(A,B),f(B,C)),D)). [para(486(a,1),306(a,1,1,1)),rewrite([486(16)]),flip(a)].
% 147.38/147.67 4656 f(f(A,c_0),f(B,C)) = f(f(B,C),f(B,C)). [para(1290(a,1),314(a,2,1)),rewrite([1255(10),1259(7)]),flip(a)].
% 147.38/147.67 5665 f(f(A,B),f(f(f(C,B),f(B,D)),A)) = f(f(A,B),f(A,B)). [para(486(a,1),359(a,1,1,1)),rewrite([486(7),486(13),4052(9)]),flip(a)].
% 147.38/147.67 6805 f(f(f(A,B),f(A,B)),f(f(A,A),C)) = f(A,B). [para(166(a,1),395(a,1,2,1,1)),rewrite([223(3),223(4),223(6),223(9)])].
% 147.38/147.67 7258 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(1911(a,1),384(a,1,2,1,1)),rewrite([337(7)])].
% 147.38/147.67 7829 f(f(A,f(B,C)),f(A,f(B,C))) = f(f(c_0,c_0),f(A,f(B,C))). [para(2193(a,1),361(a,1,1,2,1)),rewrite([2180(11),3265(11),2180(10,R),2712(10),2180(12),3265(12),2180(11,R),2712(11),2180(9,R),2101(10),2180(14),3265(14),2180(13,R),2712(13),2180(11,R)])].
% 147.38/147.67 8239 f(f(A,f(c_0,B)),f(f(C,f(A,A)),f(D,c_0))) = f(C,f(A,f(c_0,B))). [para(2197(a,1),306(a,2,2,1,2)),rewrite([2180(3),2180(6,R),2712(6),2180(3),3541(4),3073(3),2180(10),2180(13,R),2712(13),2180(10),3541(11),3073(10),3873(11),2180(7),2180(10,R),2712(10),2180(7),3541(8),3073(7)]),flip(a)].
% 147.38/147.67 9564 f(A,f(B,f(c_0,C))) = f(A,f(B,B)). [para(3203(a,2),2181(a,1)),rewrite([8239(9)])].
% 147.38/147.67 10351 f(A,f(B,f(C,c_0))) = f(A,f(B,B)). [para(483(a,1),9564(a,1,2,2))].
% 147.38/147.67 10510 f(f(A,f(B,c_0)),f(C,C)) = f(f(A,A),f(C,f(D,c_0))). [para(10351(a,1),2676(a,1))].
% 147.38/147.67 10602 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(898(a,1),306(a,1,1,1)),rewrite([898(16)]),flip(a)].
% 147.38/147.67 10609 f(f(A,B),f(f(f(A,B),f(B,A)),C)) = f(f(A,B),f(A,B)). [para(898(a,1),359(a,1,1,1)),rewrite([898(7),898(13),10602(9)]),flip(a)].
% 147.38/147.67 10629 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(7258),rewrite([10609(10)])].
% 147.38/147.67 10653 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(899(a,1),314(a,1,1))].
% 147.38/147.67 10820 f(A,f(f(B,A),f(A,B))) = f(B,A). [para(1053(a,1),336(a,1,2)),rewrite([1051(4),1911(4)]),flip(a)].
% 147.38/147.67 10855 f(f(A,B),f(B,A)) = f(f(A,B),f(A,B)). [back_rewrite(10629),rewrite([10820(4),166(6)]),flip(a)].
% 147.38/147.67 11854 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(816(a,1),1253(a,1,2))].
% 147.38/147.67 12996 f(f(A,c_0),f(f(B,c_0),f(C,D))) = f(C,D). [para(4656(a,2),1643(a,1,2))].
% 147.38/147.67 12997 f(f(f(A,c_0),f(B,C)),f(D,c_0)) = f(B,C). [para(4656(a,2),1645(a,1,1))].
% 147.38/147.67 13735 f(f(A,f(B,C)),f(f(C,B),f(C,B))) = f(C,B). [para(486(a,1),869(a,1,1,2,1))].
% 147.38/147.67 15322 f(A,B) = f(B,A). [para(10855(a,1),486(a,1,2)),rewrite([13735(7)])].
% 147.38/147.67 15433 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(11854),rewrite([15322(2),3265(2),15322(2),15322(4),15322(5),15322(6),15322(9),15322(11),15322(12),15322(13)])].
% 147.38/147.67 15861 f(f(f(A,B),f(A,B)),f(C,f(A,A))) = f(A,B). [back_rewrite(6805),rewrite([15322(5)])].
% 147.38/147.67 16047 f(f(A,B),f(A,f(f(B,C),f(B,D)))) = f(f(A,B),f(A,B)). [back_rewrite(5665),rewrite([15322(2),15322(5)])].
% 147.38/147.67 16413 f(A,f(f(A,B),f(B,f(f(A,C),f(A,D))))) = f(A,B). [back_rewrite(1927),rewrite([15322(2)])].
% 147.38/147.67 17467 f(f(A,A),f(B,f(f(C,A),f(C,A)))) = A. [para(449(a,1),15861(a,1,1,2)),rewrite([449(3),449(9)])].
% 147.38/147.67 17686 f(f(A,A),f(B,A)) = A. [para(17467(a,1),4002(a,1,2,1)),rewrite([2176(5),15322(3),449(7)]),flip(a)].
% 147.38/147.67 18965 f(f(A,f(B,c_0)),f(C,D)) = f(f(A,A),f(C,D)). [para(12997(a,1),10510(a,2,2)),rewrite([7829(12),12996(11)])].
% 147.38/147.67 19434 f(f(A,B),f(C,f(D,c_0))) = f(f(C,C),f(A,B)). [para(18965(a,1),15322(a,1)),flip(a)].
% 147.38/147.67 29421 f(A,f(f(B,A),f(B,C))) = f(B,A). [para(17686(a,1),10653(a,1,2,2,1)),rewrite([16413(7),17686(4)]),flip(a)].
% 147.38/147.67 29544 f(A,f(f(B,C),f(A,B))) = f(A,B). [para(15322(a,1),29421(a,1,2)),rewrite([15322(2),15322(5)])].
% 147.38/147.67 29548 f(A,f(f(A,B),f(C,f(f(B,D),f(B,E))))) = f(A,B). [para(4002(a,1),29421(a,1,2,2)),rewrite([15322(1),15322(8)])].
% 147.38/147.67 29713 f(f(f(A,B),f(A,f(C,C))),f(C,f(D,c_0))) = f(A,f(C,C)). [para(29544(a,1),19434(a,2)),rewrite([15322(3),15322(10)])].
% 147.38/147.67 40152 f(f(f(A,B),f(A,B)),f(f(B,C),f(D,c_0))) = f(A,f(f(B,C),f(B,C))). [para(16047(a,1),29713(a,1,1))].
% 147.38/147.67 40240 f(A,f(f(B,C),f(B,f(D,f(A,B))))) = f(A,B). [para(15433(a,1),29548(a,1,2))].
% 147.38/147.67 40260 f(A,f(f(B,f(C,f(A,B))),f(D,c_0))) = f(A,B). [para(1635(a,2),40240(a,1,2))].
% 147.38/147.67 40345 f(A,f(f(B,f(C,f(B,A))),f(D,c_0))) = f(B,A). [para(40260(a,1),15322(a,2)),rewrite([15322(1),15322(7),15322(8)])].
% 147.38/147.67 40745 f(f(f(A,B),f(A,B)),f(f(B,C),f(D,c_0))) = f(C,f(f(A,B),f(A,B))). [para(17467(a,1),40345(a,1,2,1,2)),rewrite([15322(4)])].
% 147.38/147.67 40790 f(A,f(f(B,C),f(B,C))) = f(C,f(f(A,B),f(A,B))). [back_rewrite(40152),rewrite([40745(8)]),flip(a)].
% 147.38/147.67 41334 f(x2,f(f(x0,x1),f(x0,x1))) != f(x0,f(f(x1,x2),f(x1,x2))) # answer(goals). [para(40790(a,1),6(a,1)),rewrite([15322(4),15322(7)])].
% 147.38/147.67 41335 $F # answer(goals). [resolve(41334,a,40790,a(flip))].
% 147.38/147.67
% 147.38/147.67 % SZS output end Refutation
% 147.38/147.67 ============================== end of proof ==========================
% 147.38/147.67
% 147.38/147.67 ============================== STATISTICS ============================
% 147.38/147.67
% 147.38/147.67 Given=1781. Generated=3597972. Kept=41333. proofs=1.
% 147.38/147.67 Usable=741. Sos=9999. Demods=4198. Limbo=2, Disabled=30595. Hints=0.
% 147.38/147.67 Megabytes=44.77.
% 147.38/147.67 User_CPU=144.68, System_CPU=2.04, Wall_clock=147.
% 147.38/147.67
% 147.38/147.67 ============================== end of statistics =====================
% 147.38/147.67
% 147.38/147.67 ============================== end of search =========================
% 147.38/147.67
% 147.38/147.67 THEOREM PROVED
% 147.38/147.67 % SZS status Unsatisfiable
% 147.38/147.67
% 147.38/147.67 Exiting with 1 proof.
% 147.38/147.67
% 147.38/147.67 Process 5975 exit (max_proofs) Thu Jun 30 00:23:55 2022
% 147.38/147.67 Prover9 interrupted
%------------------------------------------------------------------------------