TSTP Solution File: GRP400-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP400-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 : Sat Jul 16 11:18:56 EDT 2022
% Result : Unsatisfiable 7.90s 8.16s
% Output : Refutation 7.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP400-1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 04:09:11 EDT 2022
% 0.14/0.35 % CPUTime :
% 5.28/5.59 ============================== Prover9 ===============================
% 5.28/5.59 Prover9 (32) version 2009-11A, November 2009.
% 5.28/5.59 Process 10056 was started by sandbox on n012.cluster.edu,
% 5.28/5.59 Mon Jun 13 04:09:11 2022
% 5.28/5.59 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9902_n012.cluster.edu".
% 5.28/5.59 ============================== end of head ===========================
% 5.28/5.59
% 5.28/5.59 ============================== INPUT =================================
% 5.28/5.59
% 5.28/5.59 % Reading from file /tmp/Prover9_9902_n012.cluster.edu
% 5.28/5.59
% 5.28/5.59 set(prolog_style_variables).
% 5.28/5.59 set(auto2).
% 5.28/5.59 % set(auto2) -> set(auto).
% 5.28/5.59 % set(auto) -> set(auto_inference).
% 5.28/5.59 % set(auto) -> set(auto_setup).
% 5.28/5.59 % set(auto_setup) -> set(predicate_elim).
% 5.28/5.59 % set(auto_setup) -> assign(eq_defs, unfold).
% 5.28/5.59 % set(auto) -> set(auto_limits).
% 5.28/5.59 % set(auto_limits) -> assign(max_weight, "100.000").
% 5.28/5.59 % set(auto_limits) -> assign(sos_limit, 20000).
% 5.28/5.59 % set(auto) -> set(auto_denials).
% 5.28/5.59 % set(auto) -> set(auto_process).
% 5.28/5.59 % set(auto2) -> assign(new_constants, 1).
% 5.28/5.59 % set(auto2) -> assign(fold_denial_max, 3).
% 5.28/5.59 % set(auto2) -> assign(max_weight, "200.000").
% 5.28/5.59 % set(auto2) -> assign(max_hours, 1).
% 5.28/5.59 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 5.28/5.59 % set(auto2) -> assign(max_seconds, 0).
% 5.28/5.59 % set(auto2) -> assign(max_minutes, 5).
% 5.28/5.59 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 5.28/5.59 % set(auto2) -> set(sort_initial_sos).
% 5.28/5.59 % set(auto2) -> assign(sos_limit, -1).
% 5.28/5.59 % set(auto2) -> assign(lrs_ticks, 3000).
% 5.28/5.59 % set(auto2) -> assign(max_megs, 400).
% 5.28/5.59 % set(auto2) -> assign(stats, some).
% 5.28/5.59 % set(auto2) -> clear(echo_input).
% 5.28/5.59 % set(auto2) -> set(quiet).
% 5.28/5.59 % set(auto2) -> clear(print_initial_clauses).
% 5.28/5.59 % set(auto2) -> clear(print_given).
% 5.28/5.59 assign(lrs_ticks,-1).
% 5.28/5.59 assign(sos_limit,10000).
% 5.28/5.59 assign(order,kbo).
% 5.28/5.59 set(lex_order_vars).
% 5.28/5.59 clear(print_given).
% 5.28/5.59
% 5.28/5.59 % formulas(sos). % not echoed (6 formulas)
% 5.28/5.59
% 5.28/5.59 ============================== end of input ==========================
% 5.28/5.59
% 5.28/5.59 % From the command line: assign(max_seconds, 300).
% 5.28/5.59
% 5.28/5.59 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 5.28/5.59
% 5.28/5.59 % Formulas that are not ordinary clauses:
% 5.28/5.59
% 5.28/5.59 ============================== end of process non-clausal formulas ===
% 5.28/5.59
% 5.28/5.59 ============================== PROCESS INITIAL CLAUSES ===============
% 5.28/5.59
% 5.28/5.59 ============================== PREDICATE ELIMINATION =================
% 5.28/5.59
% 5.28/5.59 ============================== end predicate elimination =============
% 5.28/5.59
% 5.28/5.59 Auto_denials:
% 5.28/5.59 % copying label prove_commutator_distributes_over_product to answer in negative clause
% 5.28/5.59
% 5.28/5.59 Term ordering decisions:
% 5.28/5.59 Function symbol KB weights: a=1. b=1. c=1. multiply=1. commutator=1.
% 5.28/5.59
% 5.28/5.59 ============================== end of process initial clauses ========
% 5.28/5.59
% 5.28/5.59 ============================== CLAUSES FOR SEARCH ====================
% 5.28/5.59
% 5.28/5.59 ============================== end of clauses for search =============
% 5.28/5.59
% 5.28/5.59 ============================== SEARCH ================================
% 5.28/5.59
% 5.28/5.59 % Starting search at 0.01 seconds.
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=59.000, iters=3349
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=53.000, iters=3470
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=51.000, iters=3372
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=49.000, iters=3333
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=47.000, iters=3380
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=45.000, iters=3411
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=43.000, iters=3514
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=41.000, iters=3340
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=39.000, iters=3334
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=37.000, iters=3348
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=35.000, iters=3372
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=34.000, iters=3366
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=33.000, iters=3398
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=32.000, iters=3364
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=31.000, iters=3433
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=30.000, iters=3336
% 5.28/5.59
% 5.28/5.59 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 4.04 sec).
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=29.000, iters=3343
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=28.000, iters=3350
% 5.28/5.59
% 5.28/5.59 Low Water (keep): wt=27.000, iters=3391
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7451, wt=81.000
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7448, wt=79.000
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7450, wt=75.000
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7453, wt=73.000
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7452, wt=71.000
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7449, wt=67.000
% 5.28/5.59
% 5.28/5.59 Low Water (displace): id=7162, wt=65.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=7531, wt=63.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=7530, wt=61.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=7529, wt=59.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=8192, wt=55.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=7048, wt=54.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=9974, wt=53.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=9984, wt=51.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=8197, wt=50.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=9928, wt=49.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=7913, wt=48.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=10294, wt=47.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=8206, wt=46.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=8140, wt=45.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=10286, wt=44.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=13453, wt=29.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=13455, wt=25.000
% 7.90/8.16
% 7.90/8.16 Low Water (keep): wt=26.000, iters=3370
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=13994, wt=21.000
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=14454, wt=19.000
% 7.90/8.16
% 7.90/8.16 Low Water (keep): wt=25.000, iters=3391
% 7.90/8.16
% 7.90/8.16 Low Water (displace): id=14725, wt=17.000
% 7.90/8.16
% 7.90/8.16 Low Water (keep): wt=24.000, iters=3333
% 7.90/8.16
% 7.90/8.16 ============================== PROOF =================================
% 7.90/8.16 % SZS status Unsatisfiable
% 7.90/8.16 % SZS output start Refutation
% 7.90/8.16
% 7.90/8.16 % Proof 1 at 7.07 (+ 0.10) seconds: prove_commutator_distributes_over_product.
% 7.90/8.16 % Length of proof is 107.
% 7.90/8.16 % Level of proof is 23.
% 7.90/8.16 % Maximum clause weight is 29.000.
% 7.90/8.16 % Given clauses 797.
% 7.90/8.16
% 7.90/8.16 1 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity_of_multiply) # label(axiom). [assumption].
% 7.90/8.16 2 multiply(A,B) = multiply(B,multiply(A,commutator(A,B))) # label(commutator) # label(axiom). [assumption].
% 7.90/8.16 3 multiply(A,multiply(B,commutator(B,A))) = multiply(B,A). [copy(2),flip(a)].
% 7.90/8.16 4 commutator(commutator(A,B),C) = commutator(A,commutator(B,C)) # label(associativity_of_commutator) # label(axiom). [assumption].
% 7.90/8.16 5 commutator(multiply(a,b),c) != multiply(commutator(a,c),commutator(b,c)) # label(prove_commutator_distributes_over_product) # label(negated_conjecture) # answer(prove_commutator_distributes_over_product). [assumption].
% 7.90/8.16 6 multiply(commutator(a,c),commutator(b,c)) != commutator(multiply(a,b),c) # answer(prove_commutator_distributes_over_product). [copy(5),flip(a)].
% 7.90/8.16 7 multiply(A,B) != multiply(C,B) | A = C # label(right_cancellation) # label(axiom). [assumption].
% 7.90/8.16 8 multiply(A,B) != multiply(A,C) | B = C # label(left_cancellation) # label(axiom). [assumption].
% 7.90/8.16 9 multiply(A,multiply(B,multiply(commutator(B,A),C))) = multiply(B,multiply(A,C)). [para(3(a,1),1(a,1,1)),rewrite([1(2),1(5)]),flip(a)].
% 7.90/8.16 10 multiply(A,multiply(B,multiply(C,commutator(C,multiply(A,B))))) = multiply(C,multiply(A,B)). [para(3(a,1),1(a,1)),flip(a)].
% 7.90/8.16 12 multiply(A,multiply(commutator(B,C),commutator(B,commutator(C,A)))) = multiply(commutator(B,C),A). [para(4(a,1),3(a,1,2,2))].
% 7.90/8.16 13 multiply(commutator(a,c),multiply(commutator(b,c),A)) != multiply(commutator(multiply(a,b),c),A) # answer(prove_commutator_distributes_over_product). [ur(7,b,6,a),rewrite([1(8)])].
% 7.90/8.16 14 multiply(A,multiply(B,C)) != multiply(D,C) | multiply(A,B) = D. [para(1(a,1),7(a,1))].
% 7.90/8.16 17 multiply(A,commutator(A,A)) = A. [hyper(8,a,3,a)].
% 7.90/8.16 19 multiply(A,multiply(B,C)) != multiply(A,multiply(B,D)) | C = D. [para(1(a,1),8(a,1)),rewrite([1(4)])].
% 7.90/8.16 20 multiply(A,B) != multiply(C,A) | multiply(C,commutator(C,A)) = B. [para(3(a,1),8(a,1)),flip(a)].
% 7.90/8.16 21 multiply(A,multiply(commutator(A,A),B)) = multiply(A,B). [hyper(8,a,9,a)].
% 7.90/8.16 23 multiply(A,multiply(B,multiply(C,multiply(commutator(multiply(B,C),A),D)))) = multiply(B,multiply(C,multiply(A,D))). [para(1(a,1),9(a,1,2)),rewrite([1(9)])].
% 7.90/8.16 24 multiply(A,multiply(B,multiply(C,commutator(C,commutator(A,B))))) = multiply(B,multiply(A,multiply(C,commutator(A,B)))). [para(3(a,1),9(a,1,2,2)),flip(a)].
% 7.90/8.16 29 multiply(A,multiply(B,C)) != multiply(B,D) | multiply(A,multiply(commutator(A,B),C)) = D. [para(9(a,1),8(a,1))].
% 7.90/8.16 30 multiply(A,multiply(B,multiply(C,multiply(commutator(C,commutator(A,B)),D)))) = multiply(B,multiply(A,multiply(C,multiply(commutator(A,B),D)))). [para(9(a,1),9(a,1,2,2)),flip(a)].
% 7.90/8.16 34 multiply(commutator(multiply(a,b),c),commutator(b,commutator(c,commutator(a,c)))) != multiply(commutator(b,c),commutator(a,c)) # answer(prove_commutator_distributes_over_product). [para(3(a,1),13(a,1)),rewrite([4(19)]),flip(a)].
% 7.90/8.16 53 multiply(A,B) != A | commutator(A,A) = B. [para(17(a,1),8(a,1)),flip(a)].
% 7.90/8.16 73 multiply(A,multiply(B,commutator(B,multiply(B,A)))) = multiply(B,A). [hyper(8,a,10,a)].
% 7.90/8.16 81 multiply(A,multiply(B,multiply(C,commutator(C,multiply(A,commutator(A,B)))))) = multiply(B,multiply(C,multiply(A,commutator(A,B)))). [para(10(a,1),9(a,1,2)),flip(a)].
% 7.90/8.16 108 multiply(commutator(A,A),B) = B. [hyper(8,a,21,a)].
% 7.90/8.16 122 multiply(A,commutator(B,commutator(B,A))) = A. [para(108(a,1),3(a,1,2)),rewrite([4(2),108(5)])].
% 7.90/8.16 124 multiply(commutator(A,commutator(B,commutator(A,B))),C) = C. [para(4(a,1),108(a,1,1))].
% 7.90/8.16 125 multiply(A,B) != B | commutator(C,C) = A. [para(108(a,1),7(a,1)),flip(a)].
% 7.90/8.16 131 commutator(A,commutator(A,B)) = commutator(B,B). [hyper(53,a,122,a),flip(a)].
% 7.90/8.16 141 commutator(A,commutator(A,commutator(B,B))) = commutator(B,B). [para(122(a,1),108(a,1)),flip(a)].
% 7.90/8.16 147 multiply(commutator(A,B),multiply(A,C)) = multiply(A,multiply(commutator(A,B),C)). [para(131(a,1),9(a,1,2,2,1)),rewrite([108(3)])].
% 7.90/8.16 148 multiply(commutator(A,commutator(A,B)),C) = C. [para(131(a,2),108(a,1,1))].
% 7.90/8.16 151 commutator(A,commutator(B,commutator(A,B))) = commutator(A,commutator(B,B)). [para(131(a,1),131(a,1,2)),rewrite([4(5)]),flip(a)].
% 7.90/8.16 157 multiply(commutator(A,commutator(B,B)),C) = C. [back_rewrite(124),rewrite([151(3)])].
% 7.90/8.16 231 commutator(A,commutator(B,commutator(B,commutator(A,commutator(B,B))))) = commutator(A,commutator(B,B)). [hyper(53,a,157,a),rewrite([4(5),4(4)])].
% 7.90/8.16 240 commutator(A,commutator(A,commutator(B,commutator(C,C)))) = commutator(B,commutator(C,C)). [para(157(a,1),122(a,1))].
% 7.90/8.16 244 commutator(A,commutator(B,B)) = commutator(B,B). [back_rewrite(231),rewrite([240(4),141(3)]),flip(a)].
% 7.90/8.16 261 commutator(A,commutator(A,B)) = commutator(C,C). [hyper(125,a,148,a),flip(a)].
% 7.90/8.16 262 commutator(A,A) = commutator(B,B). [hyper(125,a,108,a)].
% 7.90/8.16 269 commutator(A,A) = c_0. [new_symbol(262)].
% 7.90/8.16 276 commutator(A,commutator(A,B)) = c_0. [back_rewrite(261),rewrite([269(3)])].
% 7.90/8.16 280 commutator(A,c_0) = c_0. [back_rewrite(244),rewrite([269(1),269(3)])].
% 7.90/8.16 289 multiply(c_0,A) = A. [back_rewrite(108),rewrite([269(1)])].
% 7.90/8.16 300 multiply(A,B) != A | c_0 = B. [back_rewrite(53),rewrite([269(3)])].
% 7.90/8.16 304 multiply(A,c_0) = A. [back_rewrite(17),rewrite([269(1)])].
% 7.90/8.16 344 multiply(commutator(A,B),B) = multiply(B,commutator(A,B)). [para(269(a,1),12(a,1,2,2,2)),rewrite([280(3),304(3)]),flip(a)].
% 7.90/8.16 352 multiply(A,multiply(B,commutator(B,C))) != multiply(D,multiply(B,C)) | multiply(D,C) = A. [para(3(a,1),14(a,1,2)),flip(a)].
% 7.90/8.16 390 multiply(commutator(A,B),A) = multiply(A,commutator(A,B)). [para(276(a,1),3(a,1,2,2)),rewrite([304(3)])].
% 7.90/8.16 391 multiply(commutator(A,B),commutator(C,A)) = multiply(commutator(C,A),commutator(A,B)). [para(276(a,1),12(a,1,2,2,2)),rewrite([280(4),304(4)])].
% 7.90/8.16 511 multiply(commutator(A,B),multiply(B,C)) = multiply(B,multiply(commutator(A,B),C)). [para(344(a,1),1(a,1,1)),rewrite([1(3)]),flip(a)].
% 7.90/8.16 618 multiply(A,multiply(B,multiply(commutator(multiply(a,b),c),commutator(b,commutator(c,commutator(a,c)))))) != multiply(A,multiply(B,multiply(commutator(b,c),commutator(a,c)))) # answer(prove_commutator_distributes_over_product). [ur(19,b,34,a)].
% 7.90/8.16 623 multiply(A,multiply(B,C)) != multiply(B,A) | commutator(B,A) = C. [para(3(a,1),19(a,1)),flip(a)].
% 7.90/8.16 678 multiply(A,commutator(A,commutator(B,A))) = A. [hyper(20,a,344,a)].
% 7.90/8.16 751 commutator(A,commutator(B,A)) = c_0. [hyper(300,a,678,a),flip(a)].
% 7.90/8.16 755 multiply(A,multiply(B,multiply(commutator(b,c),commutator(a,c)))) != multiply(A,multiply(B,commutator(multiply(a,b),c))) # answer(prove_commutator_distributes_over_product). [back_rewrite(618),rewrite([751(11),280(8),304(7)]),flip(a)].
% 7.90/8.16 907 multiply(A,multiply(B,multiply(C,commutator(multiply(A,B),commutator(C,B))))) = multiply(C,multiply(A,multiply(commutator(multiply(A,B),C),B))). [para(3(a,1),23(a,1,2,2)),rewrite([4(8)]),flip(a)].
% 7.90/8.16 944 multiply(commutator(multiply(A,B),C),multiply(A,multiply(B,D))) = multiply(A,multiply(B,multiply(commutator(multiply(A,B),C),D))). [para(276(a,1),23(a,1,2,2,2,1)),rewrite([289(4)])].
% 7.90/8.16 1004 multiply(c,multiply(b,commutator(multiply(a,b),c))) != multiply(b,multiply(c,commutator(a,c))) # answer(prove_commutator_distributes_over_product). [para(9(a,1),755(a,1)),flip(a)].
% 7.90/8.16 1017 multiply(c,multiply(b,multiply(commutator(multiply(a,b),c),A))) != multiply(b,multiply(c,multiply(commutator(a,c),A))) # answer(prove_commutator_distributes_over_product). [ur(14,b,1004,a),rewrite([1(9),1(18),1(17)])].
% 7.90/8.16 1224 multiply(A,commutator(A,multiply(A,B))) = multiply(A,commutator(A,B)). [hyper(20,a,73,a),flip(a)].
% 7.90/8.16 1419 multiply(c,multiply(b,multiply(commutator(multiply(a,b),c),a))) != multiply(b,multiply(a,c)) # answer(prove_commutator_distributes_over_product). [para(390(a,1),1017(a,2,2,2)),rewrite([3(19)])].
% 7.90/8.16 1442 multiply(c,multiply(b,multiply(commutator(multiply(a,b),c),multiply(a,A)))) != multiply(b,multiply(a,multiply(c,A))) # answer(prove_commutator_distributes_over_product). [ur(14,b,1419,a),rewrite([1(11),1(10),1(18),1(17)])].
% 7.90/8.16 1703 commutator(A,multiply(A,B)) = commutator(A,B). [hyper(8,a,1224,a)].
% 7.90/8.16 1754 commutator(A,multiply(B,commutator(B,A))) = commutator(A,multiply(B,A)). [para(3(a,1),1703(a,1,2)),flip(a)].
% 7.90/8.16 1755 commutator(A,commutator(multiply(A,B),C)) = commutator(A,commutator(B,C)). [para(1703(a,1),4(a,1,1)),rewrite([4(2)]),flip(a)].
% 7.90/8.16 1757 commutator(A,multiply(B,multiply(commutator(B,A),C))) = commutator(A,multiply(B,multiply(A,C))). [para(9(a,1),1703(a,1,2)),flip(a)].
% 7.90/8.16 1923 multiply(A,multiply(commutator(A,B),commutator(B,A))) = A. [hyper(29,a,3,a)].
% 7.90/8.16 2054 multiply(commutator(A,B),commutator(B,A)) = c_0. [hyper(300,a,1923,a),flip(a)].
% 7.90/8.16 2105 multiply(commutator(A,B),multiply(commutator(B,A),C)) = C. [para(2054(a,1),1(a,1,1)),rewrite([289(2)]),flip(a)].
% 7.90/8.16 2106 multiply(commutator(A,commutator(B,C)),commutator(C,commutator(A,B))) = c_0. [para(4(a,1),2054(a,1,1))].
% 7.90/8.16 2109 multiply(commutator(A,B),C) != c_0 | commutator(B,A) = C. [para(2054(a,1),8(a,1)),flip(a)].
% 7.90/8.16 2118 multiply(A,commutator(B,C)) != D | multiply(D,commutator(C,B)) = A. [para(2054(a,1),14(a,1,2)),rewrite([304(2)]),flip(a)].
% 7.90/8.16 2122 multiply(A,multiply(commutator(B,C),D)) != A | commutator(C,B) = D. [para(2054(a,1),19(a,1,2)),rewrite([304(2)]),flip(a)].
% 7.90/8.16 2137 multiply(commutator(A,B),commutator(multiply(A,B),A)) = c_0. [para(1703(a,1),2054(a,1,1))].
% 7.90/8.16 2212 multiply(A,multiply(B,multiply(C,multiply(commutator(B,commutator(A,C)),commutator(C,B))))) = multiply(C,multiply(A,multiply(B,commutator(A,C)))). [para(24(a,1),30(a,1,2)),rewrite([4(12),4(11),276(10),280(10),280(10),304(10)])].
% 7.90/8.16 2319 multiply(A,multiply(commutator(B,C),D)) != D | commutator(C,B) = A. [para(2105(a,1),7(a,1)),flip(a)].
% 7.90/8.16 2320 multiply(commutator(A,B),C) != D | multiply(commutator(B,A),D) = C. [para(2105(a,1),8(a,1)),flip(a)].
% 7.90/8.16 2499 commutator(multiply(A,B),A) = commutator(B,A). [para(2137(a,1),2105(a,1,2)),rewrite([304(3)]),flip(a)].
% 7.90/8.16 2538 commutator(multiply(commutator(A,B),C),commutator(B,A)) = commutator(C,commutator(B,A)). [para(2105(a,1),2499(a,1,1)),flip(a)].
% 7.90/8.16 3643 commutator(A,commutator(B,multiply(A,multiply(B,C)))) = commutator(A,commutator(B,C)). [para(1703(a,1),1755(a,1,2)),rewrite([1755(3),1(4)]),flip(a)].
% 7.90/8.16 4313 commutator(A,commutator(B,C)) = commutator(C,commutator(A,B)). [hyper(2109,a,2106,a),rewrite([4(2)]),flip(a)].
% 7.90/8.16 4328 multiply(A,multiply(commutator(B,C),commutator(A,commutator(B,C)))) = multiply(commutator(B,C),A). [para(2106(a,1),24(a,2,2,2)),rewrite([4313(3),4313(5),269(8),304(5),304(8)])].
% 7.90/8.16 4754 commutator(A,commutator(multiply(commutator(A,B),C),B)) = commutator(A,commutator(C,B)). [back_rewrite(2538),rewrite([4313(4),4313(6)])].
% 7.90/8.16 4835 multiply(A,multiply(B,multiply(C,commutator(A,commutator(B,C))))) = multiply(B,multiply(A,multiply(C,commutator(A,B)))). [back_rewrite(2212),rewrite([4313(2,R),344(4),9(6)])].
% 7.90/8.16 5099 multiply(A,multiply(B,multiply(C,commutator(B,commutator(multiply(A,B),C))))) = multiply(C,multiply(A,multiply(commutator(multiply(A,B),C),B))). [back_rewrite(907),rewrite([4313(3)])].
% 7.90/8.16 5469 multiply(b,multiply(a,multiply(c,commutator(a,multiply(b,commutator(b,commutator(multiply(a,b),c))))))) != multiply(c,multiply(a,multiply(commutator(multiply(a,b),c),b))) # answer(prove_commutator_distributes_over_product). [para(81(a,1),1442(a,1,2)),rewrite([944(18),4328(17)]),flip(a)].
% 7.90/8.16 6312 commutator(A,commutator(B,multiply(A,C))) = commutator(A,commutator(B,C)). [para(147(a,1),1703(a,1,2)),rewrite([4(5),1757(4),3643(4),4(5)]),flip(a)].
% 7.90/8.16 8985 multiply(commutator(A,B),multiply(commutator(C,B),commutator(B,A))) = commutator(C,B). [hyper(2320,a,391,a)].
% 7.90/8.16 8986 multiply(commutator(A,B),multiply(commutator(B,C),commutator(B,A))) = commutator(B,C). [hyper(2118,a,391,a),rewrite([1(5)])].
% 7.90/8.16 13595 multiply(A,multiply(B,commutator(multiply(B,commutator(C,A)),A))) = multiply(B,A). [para(8985(a,1),23(a,1,2,2)),rewrite([511(9),2054(8),304(7)])].
% 7.90/8.16 13619 commutator(A,B) != commutator(C,B) | commutator(B,A) = commutator(B,C). [para(8985(a,1),2122(a,1))].
% 7.90/8.16 13752 commutator(A,B) != commutator(A,C) | commutator(B,A) = commutator(C,A). [para(8986(a,1),2319(a,1))].
% 7.90/8.16 15305 multiply(A,B) != multiply(C,A) | multiply(B,commutator(A,B)) = C. [para(3(a,1),352(a,2)),rewrite([276(2),304(2)]),flip(a)].
% 7.90/8.16 15535 multiply(A,multiply(commutator(A,B),commutator(B,multiply(A,B)))) = A. [hyper(15305,a,3,a),rewrite([1754(5),1(5)])].
% 7.90/8.16 15683 commutator(A,multiply(B,A)) = commutator(A,B). [hyper(2122,a,15535,a),flip(a)].
% 7.90/8.16 15779 commutator(multiply(A,B),B) = commutator(A,B). [hyper(13752,a,15683,a)].
% 7.90/8.16 15780 commutator(A,multiply(B,multiply(C,A))) = commutator(A,multiply(B,C)). [para(1(a,1),15683(a,1,2))].
% 7.90/8.16 15787 commutator(A,commutator(B,C)) = commutator(A,commutator(C,B)). [para(2105(a,1),15683(a,1,2)),rewrite([15779(3),4(2),4313(6),4754(6)])].
% 7.90/8.16 15788 commutator(A,commutator(B,multiply(C,A))) = commutator(A,commutator(B,C)). [para(15683(a,1),1755(a,1,2)),rewrite([15787(3),6312(3),15787(2),15780(5)]),flip(a)].
% 7.90/8.16 15889 multiply(b,multiply(a,multiply(c,commutator(a,multiply(b,commutator(a,commutator(b,c))))))) != multiply(c,multiply(a,multiply(commutator(multiply(a,b),c),b))) # answer(prove_commutator_distributes_over_product). [back_rewrite(5469),rewrite([15787(12),15788(12),4313(10)])].
% 7.90/8.16 15890 multiply(A,multiply(B,multiply(commutator(multiply(B,C),A),C))) = multiply(C,multiply(B,multiply(A,commutator(B,C)))). [back_rewrite(5099),rewrite([15787(3),15788(3),4313(2),4835(5)]),flip(a)].
% 7.90/8.16 16404 multiply(b,multiply(a,multiply(c,commutator(a,multiply(b,commutator(a,commutator(b,c))))))) != multiply(b,multiply(a,multiply(c,commutator(a,b)))) # answer(prove_commutator_distributes_over_product). [back_rewrite(15889),rewrite([15890(26)])].
% 7.90/8.16 17615 commutator(multiply(A,commutator(B,C)),C) = commutator(A,C). [hyper(623,a,13595,a),flip(a)].
% 7.90/8.16 17661 commutator(A,multiply(B,commutator(C,A))) = commutator(A,B). [hyper(13619,a,17615,a)].
% 7.90/8.16 17794 commutator(A,multiply(B,commutator(A,commutator(C,D)))) = commutator(A,B). [para(4(a,1),17661(a,1,2,2)),rewrite([4313(2)])].
% 7.90/8.16 17860 $F # answer(prove_commutator_distributes_over_product). [back_rewrite(16404),rewrite([17794(12)]),xx(a)].
% 7.90/8.16
% 7.90/8.16 % SZS output end Refutation
% 7.90/8.16 ============================== end of proof ==========================
% 7.90/8.16
% 7.90/8.16 ============================== STATISTICS ============================
% 7.90/8.16
% 7.90/8.16 Given=797. Generated=135473. Kept=17857. proofs=1.
% 7.90/8.16 Usable=526. Sos=8683. Demods=1744. Limbo=66, Disabled=8588. Hints=0.
% 7.90/8.16 Megabytes=20.07.
% 7.90/8.16 User_CPU=7.07, System_CPU=0.10, Wall_clock=7.
% 7.90/8.16
% 7.90/8.16 ============================== end of statistics =====================
% 7.90/8.16
% 7.90/8.16 ============================== end of search =========================
% 7.90/8.16
% 7.90/8.16 THEOREM PROVED
% 7.90/8.16 % SZS status Unsatisfiable
% 7.90/8.16
% 7.90/8.16 Exiting with 1 proof.
% 7.90/8.16
% 7.90/8.16 Process 10056 exit (max_proofs) Mon Jun 13 04:09:18 2022
% 7.90/8.16 Prover9 interrupted
%------------------------------------------------------------------------------