TSTP Solution File: GRP667-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP667-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:20:28 EDT 2022
% Result : Unsatisfiable 7.43s 7.76s
% Output : Refutation 7.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP667-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 23:04:25 EDT 2022
% 0.13/0.35 % CPUTime :
% 3.05/3.35 ============================== Prover9 ===============================
% 3.05/3.35 Prover9 (32) version 2009-11A, November 2009.
% 3.05/3.35 Process 14614 was started by sandbox2 on n019.cluster.edu,
% 3.05/3.35 Mon Jun 13 23:04:25 2022
% 3.05/3.35 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14334_n019.cluster.edu".
% 3.05/3.35 ============================== end of head ===========================
% 3.05/3.35
% 3.05/3.35 ============================== INPUT =================================
% 3.05/3.35
% 3.05/3.35 % Reading from file /tmp/Prover9_14334_n019.cluster.edu
% 3.05/3.35
% 3.05/3.35 set(prolog_style_variables).
% 3.05/3.35 set(auto2).
% 3.05/3.35 % set(auto2) -> set(auto).
% 3.05/3.35 % set(auto) -> set(auto_inference).
% 3.05/3.35 % set(auto) -> set(auto_setup).
% 3.05/3.35 % set(auto_setup) -> set(predicate_elim).
% 3.05/3.35 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.05/3.35 % set(auto) -> set(auto_limits).
% 3.05/3.35 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.05/3.35 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.05/3.35 % set(auto) -> set(auto_denials).
% 3.05/3.35 % set(auto) -> set(auto_process).
% 3.05/3.35 % set(auto2) -> assign(new_constants, 1).
% 3.05/3.35 % set(auto2) -> assign(fold_denial_max, 3).
% 3.05/3.35 % set(auto2) -> assign(max_weight, "200.000").
% 3.05/3.35 % set(auto2) -> assign(max_hours, 1).
% 3.05/3.35 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.05/3.35 % set(auto2) -> assign(max_seconds, 0).
% 3.05/3.35 % set(auto2) -> assign(max_minutes, 5).
% 3.05/3.35 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.05/3.35 % set(auto2) -> set(sort_initial_sos).
% 3.05/3.35 % set(auto2) -> assign(sos_limit, -1).
% 3.05/3.35 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.05/3.35 % set(auto2) -> assign(max_megs, 400).
% 3.05/3.35 % set(auto2) -> assign(stats, some).
% 3.05/3.35 % set(auto2) -> clear(echo_input).
% 3.05/3.35 % set(auto2) -> set(quiet).
% 3.05/3.35 % set(auto2) -> clear(print_initial_clauses).
% 3.05/3.35 % set(auto2) -> clear(print_given).
% 3.05/3.35 assign(lrs_ticks,-1).
% 3.05/3.35 assign(sos_limit,10000).
% 3.05/3.35 assign(order,kbo).
% 3.05/3.35 set(lex_order_vars).
% 3.05/3.35 clear(print_given).
% 3.05/3.35
% 3.05/3.35 % formulas(sos). % not echoed (14 formulas)
% 3.05/3.35
% 3.05/3.35 ============================== end of input ==========================
% 3.05/3.35
% 3.05/3.35 % From the command line: assign(max_seconds, 300).
% 3.05/3.35
% 3.05/3.35 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.05/3.35
% 3.05/3.35 % Formulas that are not ordinary clauses:
% 3.05/3.35
% 3.05/3.35 ============================== end of process non-clausal formulas ===
% 3.05/3.35
% 3.05/3.35 ============================== PROCESS INITIAL CLAUSES ===============
% 3.05/3.35
% 3.05/3.35 ============================== PREDICATE ELIMINATION =================
% 3.05/3.35
% 3.05/3.35 ============================== end predicate elimination =============
% 3.05/3.35
% 3.05/3.35 Auto_denials:
% 3.05/3.35 % copying label goals to answer in negative clause
% 3.05/3.35
% 3.05/3.35 Term ordering decisions:
% 3.05/3.35
% 3.05/3.35 % Assigning unary symbol f kb_weight 0 and highest precedence (10).
% 3.05/3.35 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. ifeq=1. f=0.
% 3.05/3.35
% 3.05/3.35 ============================== end of process initial clauses ========
% 3.05/3.35
% 3.05/3.35 ============================== CLAUSES FOR SEARCH ====================
% 3.05/3.35
% 3.05/3.35 ============================== end of clauses for search =============
% 3.05/3.35
% 3.05/3.35 ============================== SEARCH ================================
% 3.05/3.35
% 3.05/3.35 % Starting search at 0.01 seconds.
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=157.000, iters=3416
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=153.000, iters=3386
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=147.000, iters=3376
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% 3.05/3.35 Low Water (keep): wt=145.000, iters=3346
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=139.000, iters=3336
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=137.000, iters=3376
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=127.000, iters=3338
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=117.000, iters=3371
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% 3.05/3.35 Low Water (keep): wt=107.000, iters=3354
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=100.000, iters=3342
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% 3.05/3.35 Low Water (keep): wt=99.000, iters=3338
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=97.000, iters=3361
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% 3.05/3.35 Low Water (keep): wt=96.000, iters=3397
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% 3.05/3.35 Low Water (keep): wt=92.000, iters=3335
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=90.000, iters=3460
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=87.000, iters=3437
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=85.000, iters=3341
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=82.000, iters=3343
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=81.000, iters=3342
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=79.000, iters=3353
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=78.000, iters=3351
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=77.000, iters=3340
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=76.000, iters=3353
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=75.000, iters=3340
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=73.000, iters=3336
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=72.000, iters=3338
% 3.05/3.35
% 3.05/3.35 Low Water (keep): wt=71.000, iters=3444
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=69.000, iters=3385
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=67.000, iters=3374
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=63.000, iters=3336
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=62.000, iters=3343
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=61.000, iters=3341
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=60.000, iters=3372
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=59.000, iters=3341
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=58.000, iters=3335
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=57.000, iters=3347
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=55.000, iters=3340
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=54.000, iters=3384
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=53.000, iters=3350
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=52.000, iters=3361
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=51.000, iters=3391
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=50.000, iters=3377
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=49.000, iters=3339
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=47.000, iters=3368
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=45.000, iters=3430
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=43.000, iters=3411
% 7.43/7.75
% 7.43/7.75 Low Water (displace): id=10067, wt=197.000
% 7.43/7.75
% 7.43/7.75 Low Water (displace): id=8287, wt=195.000
% 7.43/7.75
% 7.43/7.75 Low Water (displace): id=16191, wt=39.000
% 7.43/7.75
% 7.43/7.75 Low Water (keep): wt=41.000, iters=3350
% 7.43/7.75
% 7.43/7.75 Low Water (displace): id=16233, wt=31.000
% 7.43/7.75
% 7.43/7.75 Low Water (displace): id=16236, wt=23.000
% 7.43/7.76
% 7.43/7.76 Low Water (displace): id=16248, wt=21.000
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=39.000, iters=3411
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=37.000, iters=3351
% 7.43/7.76
% 7.43/7.76 Low Water (displace): id=16529, wt=20.000
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=35.000, iters=3342
% 7.43/7.76
% 7.43/7.76 Low Water (displace): id=16645, wt=19.000
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=31.000, iters=3336
% 7.43/7.76
% 7.43/7.76 Low Water (displace): id=17392, wt=17.000
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=29.000, iters=3339
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=27.000, iters=3363
% 7.43/7.76
% 7.43/7.76 Low Water (keep): wt=25.000, iters=3338
% 7.43/7.76
% 7.43/7.76 ============================== PROOF =================================
% 7.43/7.76 % SZS status Unsatisfiable
% 7.43/7.76 % SZS output start Refutation
% 7.43/7.76
% 7.43/7.76 % Proof 1 at 6.65 (+ 0.11) seconds: goals.
% 7.43/7.76 % Length of proof is 94.
% 7.43/7.76 % Level of proof is 21.
% 7.43/7.76 % Maximum clause weight is 45.000.
% 7.43/7.76 % Given clauses 430.
% 7.43/7.76
% 7.43/7.76 1 mult(A,unit) = A # label(f05) # label(axiom). [assumption].
% 7.43/7.76 2 mult(unit,A) = A # label(f06) # label(axiom). [assumption].
% 7.43/7.76 3 ifeq(A,A,B,C) = B # label(ifeq_axiom) # label(axiom). [assumption].
% 7.43/7.76 4 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 7.43/7.76 5 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 7.43/7.76 6 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 7.43/7.76 7 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 7.43/7.76 8 mult(f(A),f(A)) = A # label(f09) # label(axiom). [assumption].
% 7.43/7.76 9 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [assumption].
% 7.43/7.76 10 mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C) # label(f07) # label(axiom). [assumption].
% 7.43/7.76 11 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(10),rewrite([9(3),9(6)]),flip(a)].
% 7.43/7.76 12 ifeq(mult(A,mult(B,mult(C,B))),mult(mult(mult(A,B),C),B),mult(B,mult(A,mult(B,C))),mult(mult(mult(B,A),B),C)) = mult(mult(mult(B,A),B),C) # label(f10) # label(axiom). [assumption].
% 7.43/7.76 13 ifeq(mult(A,mult(B,mult(C,B))),mult(mult(mult(A,B),C),B),mult(B,mult(A,mult(B,C))),mult(mult(B,mult(A,B)),C)) = mult(mult(B,mult(A,B)),C). [copy(12),rewrite([9(11),9(15)])].
% 7.43/7.76 14 ifeq(mult(mult(A,B),mult(C,A)),mult(mult(A,mult(B,C)),A),mult(A,mult(B,mult(A,C))),mult(mult(mult(A,B),A),C)) = mult(mult(mult(A,B),A),C) # label(f11) # label(axiom). [assumption].
% 7.43/7.76 15 ifeq(mult(mult(A,B),mult(C,A)),mult(A,mult(mult(B,C),A)),mult(A,mult(B,mult(A,C))),mult(mult(A,mult(B,A)),C)) = mult(mult(A,mult(B,A)),C). [copy(14),rewrite([9(6),9(11),9(15)])].
% 7.43/7.76 17 mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 7.43/7.76 18 mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))) # answer(goals). [copy(17),rewrite([9(12)]),flip(a)].
% 7.43/7.76 20 ld(A,A) = unit. [para(1(a,1),5(a,1,2))].
% 7.43/7.76 22 ld(rd(A,B),A) = B. [para(6(a,1),5(a,1,2))].
% 7.43/7.76 24 rd(A,ld(B,A)) = B. [para(4(a,1),7(a,1,1))].
% 7.43/7.76 27 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(4(a,1),9(a,1,1)),flip(a)].
% 7.43/7.76 29 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(6(a,1),9(a,1,1)),flip(a)].
% 7.43/7.76 30 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(9(a,1),7(a,1,1))].
% 7.43/7.76 31 mult(f(A),A) = mult(A,f(A)). [para(8(a,1),9(a,1,1)),rewrite([8(6)]),flip(a)].
% 7.43/7.76 33 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(11(a,1),1(a,1)),rewrite([1(4),2(3),2(4)])].
% 7.43/7.76 34 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(2(a,1),11(a,1,1)),rewrite([2(5)])].
% 7.43/7.76 36 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(4(a,1),11(a,2,2,2)),rewrite([27(3)])].
% 7.43/7.76 39 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(6(a,1),11(a,1,1)),flip(a)].
% 7.43/7.76 50 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(2(a,1),13(a,1,1)),rewrite([2(4),9(4),2(7),2(8),3(9),2(4)]),flip(a)].
% 7.43/7.76 58 ifeq(mult(rd(A,B),mult(B,mult(C,B))),mult(mult(A,C),B),mult(B,mult(rd(A,B),mult(B,C))),mult(mult(B,A),C)) = mult(mult(B,A),C). [para(6(a,1),13(a,1,2,1,1)),rewrite([6(12),6(15)])].
% 7.43/7.76 90 ifeq(mult(A,mult(B,f(A))),mult(f(A),mult(f(A),mult(B,f(A)))),mult(f(A),mult(f(A),mult(f(A),B))),mult(mult(A,f(A)),B)) = mult(mult(A,f(A)),B). [para(8(a,1),15(a,1,1,1)),rewrite([9(8),8(19),31(17),8(23),31(21)])].
% 7.43/7.76 111 rd(mult(A,f(A)),A) = f(A). [para(31(a,1),7(a,1,1))].
% 7.43/7.76 127 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(27(a,1),5(a,1,2))].
% 7.43/7.76 129 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(27(a,1),9(a,1,1)),rewrite([33(2),33(5)]),flip(a)].
% 7.43/7.76 159 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(6(a,1),30(a,1,1,2))].
% 7.43/7.76 162 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(27(a,1),30(a,2)),rewrite([33(3),129(4)])].
% 7.43/7.76 163 mult(A,rd(f(A),A)) = f(A). [back_rewrite(111),rewrite([159(3)])].
% 7.43/7.76 164 rd(f(A),A) = ld(A,f(A)). [para(163(a,1),5(a,1,2)),flip(a)].
% 7.43/7.76 165 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(163(a,1),11(a,2,2,2)),rewrite([164(2),27(4),31(2),164(5),164(9)])].
% 7.43/7.76 186 mult(ld(A,f(A)),A) = f(A). [para(164(a,1),6(a,1,1))].
% 7.43/7.76 188 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(164(a,1),29(a,1,1)),rewrite([164(4),4(5),164(7)])].
% 7.43/7.76 189 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(165),rewrite([188(11)])].
% 7.43/7.76 294 mult(A,mult(A,ld(mult(A,A),B))) = B. [para(50(a,1),4(a,1))].
% 7.43/7.76 296 rd(mult(A,mult(A,B)),B) = mult(A,A). [para(50(a,1),7(a,1,1))].
% 7.43/7.76 297 mult(f(A),mult(f(A),B)) = mult(A,B). [para(8(a,1),50(a,1,1)),flip(a)].
% 7.43/7.76 314 mult(mult(A,f(A)),B) = mult(f(A),mult(A,B)). [back_rewrite(90),rewrite([297(9),297(11),3(13)]),flip(a)].
% 7.43/7.76 342 mult(ld(A,unit),A) = unit. [para(2(a,1),127(a,1,2)),rewrite([20(1)]),flip(a)].
% 7.43/7.76 355 rd(unit,A) = ld(A,unit). [para(342(a,1),7(a,1,1))].
% 7.43/7.76 368 mult(ld(A,unit),mult(A,A)) = A. [para(342(a,1),33(a,1,1)),rewrite([2(2)]),flip(a)].
% 7.43/7.76 374 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(6(a,1),34(a,2,2,2)),rewrite([29(4)])].
% 7.43/7.76 412 ld(ld(A,unit),A) = mult(A,A). [para(368(a,1),5(a,1,2))].
% 7.43/7.76 413 rd(A,mult(A,A)) = ld(A,unit). [para(368(a,1),7(a,1,1))].
% 7.43/7.76 414 mult(ld(f(A),unit),A) = f(A). [para(8(a,1),368(a,1,2))].
% 7.43/7.76 430 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(22(a,1),412(a,1,1)),rewrite([355(2),355(5),355(7)]),flip(a)].
% 7.43/7.76 471 ld(f(A),unit) = ld(A,f(A)). [para(8(a,1),413(a,1,2)),rewrite([164(2)]),flip(a)].
% 7.43/7.76 478 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(414(a,1),9(a,1,1)),rewrite([4(5)]),flip(a)].
% 7.43/7.76 494 mult(ld(f(A),unit),mult(A,f(A))) = A. [para(414(a,1),34(a,2,2,2)),rewrite([478(8),2(2)]),flip(a)].
% 7.43/7.76 495 mult(f(A),ld(A,f(A))) = unit. [para(471(a,1),4(a,1,2))].
% 7.43/7.76 497 ld(ld(A,f(A)),unit) = f(A). [para(471(a,1),24(a,1,2)),rewrite([355(4)])].
% 7.43/7.76 504 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(189),rewrite([495(11),1(9)])].
% 7.43/7.76 505 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(188),rewrite([495(8)])].
% 7.43/7.76 582 mult(ld(A,f(A)),ld(A,f(A))) = ld(f(A),ld(A,f(A))). [para(497(a,1),412(a,1,1)),flip(a)].
% 7.43/7.76 585 mult(ld(f(A),ld(A,f(A))),f(A)) = ld(A,f(A)). [para(505(a,1),50(a,2,2)),rewrite([582(5),1(10)])].
% 7.43/7.76 769 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(6(a,1),162(a,1,1)),flip(a)].
% 7.43/7.76 882 mult(A,ld(mult(A,A),B)) = ld(A,B). [para(294(a,1),5(a,1,2)),flip(a)].
% 7.43/7.76 894 rd(mult(A,B),ld(A,B)) = mult(A,A). [para(4(a,1),296(a,1,1,2))].
% 7.43/7.76 900 ld(f(A),ld(A,f(A))) = ld(A,unit). [para(186(a,1),296(a,1,1,2)),rewrite([505(4),355(2),582(7)]),flip(a)].
% 7.43/7.76 907 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(414(a,1),296(a,1,1,2)),rewrite([342(5),355(2),430(9)]),flip(a)].
% 7.43/7.76 934 mult(ld(A,unit),f(A)) = ld(A,f(A)). [back_rewrite(585),rewrite([900(4)])].
% 7.43/7.76 942 mult(A,ld(f(A),B)) = mult(f(A),B). [para(4(a,1),297(a,1,2)),flip(a)].
% 7.43/7.76 945 mult(mult(A,B),f(A)) = mult(A,mult(B,f(A))). [para(297(a,1),9(a,1,1)),rewrite([9(8),297(9)])].
% 7.43/7.76 953 mult(f(A),mult(A,B)) = mult(A,mult(f(A),B)). [para(297(a,1),13(a,1,3)),rewrite([297(6),8(6),945(6),8(13),31(11),314(12),3(13),8(7),31(5),314(6)]),flip(a)].
% 7.43/7.76 1000 mult(mult(A,f(A)),B) = mult(A,mult(f(A),B)). [back_rewrite(314),rewrite([953(6)])].
% 7.43/7.76 1232 mult(ld(A,unit),mult(A,f(A))) = f(A). [para(494(a,1),50(a,2,2)),rewrite([430(7),907(5),414(9)])].
% 7.43/7.76 1807 mult(f(A),ld(A,B)) = ld(f(A),B). [para(8(a,1),882(a,1,2,1))].
% 7.43/7.76 2719 mult(A,ld(B,unit)) = rd(A,B). [para(1232(a,1),39(a,1,1,1,2,2)),rewrite([33(4),8(3),1000(12),1807(11),942(11),1(10),934(9),504(8),769(3)]),flip(a)].
% 7.43/7.76 3104 ld(A,rd(A,B)) = ld(B,unit). [para(2719(a,1),5(a,1,2))].
% 7.43/7.76 3116 rd(A,ld(B,unit)) = mult(A,B). [para(22(a,1),2719(a,1,2)),rewrite([355(3)]),flip(a)].
% 7.43/7.76 3128 mult(mult(A,rd(B,C)),ld(ld(C,unit),B)) = mult(rd(A,C),mult(ld(ld(C,unit),B),B)). [para(2719(a,1),36(a,1,1,2)),rewrite([2719(9)])].
% 7.43/7.76 3137 mult(rd(A,B),mult(B,A)) = mult(A,A). [para(2719(a,1),296(a,1,1,2)),rewrite([3116(5),374(3)])].
% 7.43/7.76 3138 mult(f(A),rd(f(A),B)) = rd(A,B). [para(2719(a,1),297(a,1,2)),rewrite([2719(7)])].
% 7.43/7.76 3235 ld(ld(A,B),unit) = ld(B,A). [para(24(a,1),3104(a,1,2)),flip(a)].
% 7.43/7.76 3242 ld(mult(A,B),mult(A,A)) = ld(B,A). [para(894(a,1),3104(a,1,2)),rewrite([3235(6)])].
% 7.43/7.76 4365 ld(rd(A,B),mult(A,A)) = mult(B,A). [para(3137(a,1),5(a,1,2))].
% 7.43/7.76 4690 mult(mult(A,rd(f(B),C)),mult(C,f(B))) = mult(mult(A,rd(B,C)),C). [para(3138(a,1),36(a,1,1,2)),rewrite([22(6),22(10)]),flip(a)].
% 7.43/7.76 4784 ifeq(mult(rd(A,B),mult(B,mult(C,mult(B,B)))),mult(mult(A,mult(C,B)),B),mult(B,mult(rd(A,B),mult(B,mult(C,B)))),mult(mult(B,A),mult(C,B))) = mult(mult(B,A),mult(C,B)). [para(33(a,1),58(a,1,1,2,2))].
% 7.43/7.76 5127 ld(ld(A,unit),B) = mult(A,B). [para(2719(a,1),3242(a,1,1)),rewrite([4365(3)]),flip(a)].
% 7.43/7.76 5162 mult(mult(A,rd(B,C)),mult(C,B)) = mult(rd(A,C),mult(C,mult(B,B))). [back_rewrite(3128),rewrite([5127(5),5127(8),33(7)])].
% 7.43/7.76 5184 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [back_rewrite(4690),rewrite([5162(6),8(4)]),flip(a)].
% 7.43/7.76 21591 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(7(a,1),5184(a,1,1,2)),flip(a)].
% 7.43/7.76 21604 mult(rd(A,B),mult(B,mult(C,mult(B,B)))) = mult(mult(A,mult(C,B)),B). [para(162(a,1),5184(a,1,1,2)),flip(a)].
% 7.43/7.76 21759 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(4784),rewrite([21604(5),21591(10),3(13)]),flip(a)].
% 7.43/7.76 22140 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [back_rewrite(15),rewrite([21759(3),3(13)]),flip(a)].
% 7.43/7.76 22141 $F # answer(goals). [resolve(22140,a,18,a)].
% 7.43/7.76
% 7.43/7.76 % SZS output end Refutation
% 7.43/7.76 ============================== end of proof ==========================
% 7.43/7.76
% 7.43/7.76 ============================== STATISTICS ============================
% 7.43/7.76
% 7.43/7.76 Given=430. Generated=156668. Kept=22135. proofs=1.
% 7.43/7.76 Usable=279. Sos=8754. Demods=8906. Limbo=381, Disabled=12734. Hints=0.
% 7.43/7.76 Megabytes=37.34.
% 7.43/7.76 User_CPU=6.65, System_CPU=0.11, Wall_clock=7.
% 7.43/7.76
% 7.43/7.76 ============================== end of statistics =====================
% 7.43/7.76
% 7.43/7.76 ============================== end of search =========================
% 7.43/7.76
% 7.43/7.76 THEOREM PROVED
% 7.43/7.76 % SZS status Unsatisfiable
% 7.43/7.76
% 7.43/7.76 Exiting with 1 proof.
% 7.43/7.76
% 7.43/7.76 Process 14614 exit (max_proofs) Mon Jun 13 23:04:32 2022
% 7.43/7.76 Prover9 interrupted
%------------------------------------------------------------------------------