TSTP Solution File: GRP727-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP727-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:20:49 EDT 2022
% Result : Unsatisfiable 21.14s 21.39s
% Output : Refutation 21.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP727-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n006.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 : Mon Jun 13 22:52:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.47/2.82 ============================== Prover9 ===============================
% 2.47/2.82 Prover9 (32) version 2009-11A, November 2009.
% 2.47/2.82 Process 9642 was started by sandbox2 on n006.cluster.edu,
% 2.47/2.82 Mon Jun 13 22:52:27 2022
% 2.47/2.82 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9489_n006.cluster.edu".
% 2.47/2.82 ============================== end of head ===========================
% 2.47/2.82
% 2.47/2.82 ============================== INPUT =================================
% 2.47/2.82
% 2.47/2.82 % Reading from file /tmp/Prover9_9489_n006.cluster.edu
% 2.47/2.82
% 2.47/2.82 set(prolog_style_variables).
% 2.47/2.82 set(auto2).
% 2.47/2.82 % set(auto2) -> set(auto).
% 2.47/2.82 % set(auto) -> set(auto_inference).
% 2.47/2.82 % set(auto) -> set(auto_setup).
% 2.47/2.82 % set(auto_setup) -> set(predicate_elim).
% 2.47/2.82 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.47/2.82 % set(auto) -> set(auto_limits).
% 2.47/2.82 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.47/2.82 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.47/2.82 % set(auto) -> set(auto_denials).
% 2.47/2.82 % set(auto) -> set(auto_process).
% 2.47/2.82 % set(auto2) -> assign(new_constants, 1).
% 2.47/2.82 % set(auto2) -> assign(fold_denial_max, 3).
% 2.47/2.82 % set(auto2) -> assign(max_weight, "200.000").
% 2.47/2.82 % set(auto2) -> assign(max_hours, 1).
% 2.47/2.82 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.47/2.82 % set(auto2) -> assign(max_seconds, 0).
% 2.47/2.82 % set(auto2) -> assign(max_minutes, 5).
% 2.47/2.82 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.47/2.82 % set(auto2) -> set(sort_initial_sos).
% 2.47/2.82 % set(auto2) -> assign(sos_limit, -1).
% 2.47/2.82 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.47/2.82 % set(auto2) -> assign(max_megs, 400).
% 2.47/2.82 % set(auto2) -> assign(stats, some).
% 2.47/2.82 % set(auto2) -> clear(echo_input).
% 2.47/2.82 % set(auto2) -> set(quiet).
% 2.47/2.82 % set(auto2) -> clear(print_initial_clauses).
% 2.47/2.82 % set(auto2) -> clear(print_given).
% 2.47/2.82 assign(lrs_ticks,-1).
% 2.47/2.82 assign(sos_limit,10000).
% 2.47/2.82 assign(order,kbo).
% 2.47/2.82 set(lex_order_vars).
% 2.47/2.82 clear(print_given).
% 2.47/2.82
% 2.47/2.82 % formulas(sos). % not echoed (21 formulas)
% 2.47/2.82
% 2.47/2.82 ============================== end of input ==========================
% 2.47/2.82
% 2.47/2.82 % From the command line: assign(max_seconds, 300).
% 2.47/2.82
% 2.47/2.82 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.47/2.82
% 2.47/2.82 % Formulas that are not ordinary clauses:
% 2.47/2.82
% 2.47/2.82 ============================== end of process non-clausal formulas ===
% 2.47/2.82
% 2.47/2.82 ============================== PROCESS INITIAL CLAUSES ===============
% 2.47/2.82
% 2.47/2.82 ============================== PREDICATE ELIMINATION =================
% 2.47/2.82
% 2.47/2.82 ============================== end predicate elimination =============
% 2.47/2.82
% 2.47/2.82 Auto_denials:
% 2.47/2.82 % copying label goals to answer in negative clause
% 2.47/2.82
% 2.47/2.82 Term ordering decisions:
% 2.47/2.82
% 2.47/2.82 % Assigning unary symbol i kb_weight 0 and highest precedence (14).
% 2.47/2.82 Function symbol KB weights: unit=1. a=1. b=1. c=1. d=1. e=1. mult=1. op_t=1. rd=1. op_l=1. op_r=1. asoc=1. i=0.
% 2.47/2.82
% 2.47/2.82 ============================== end of process initial clauses ========
% 2.47/2.82
% 2.47/2.82 ============================== CLAUSES FOR SEARCH ====================
% 2.47/2.82
% 2.47/2.82 ============================== end of clauses for search =============
% 2.47/2.82
% 2.47/2.82 ============================== SEARCH ================================
% 2.47/2.82
% 2.47/2.82 % Starting search at 0.01 seconds.
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=158.000, iters=3366
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=156.000, iters=3363
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% 2.47/2.82 Low Water (keep): wt=139.000, iters=3443
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% 2.47/2.82 Low Water (keep): wt=118.000, iters=3380
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=113.000, iters=3350
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% 2.47/2.82 Low Water (keep): wt=112.000, iters=3348
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% 2.47/2.82 Low Water (keep): wt=100.000, iters=3450
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% 2.47/2.82 Low Water (keep): wt=94.000, iters=3406
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% 2.47/2.82 Low Water (keep): wt=88.000, iters=3357
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=82.000, iters=3386
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% 2.47/2.82 Low Water (keep): wt=80.000, iters=3357
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% 2.47/2.82 Low Water (keep): wt=75.000, iters=3478
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% 2.47/2.82 Low Water (keep): wt=71.000, iters=3375
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% 2.47/2.82 Low Water (keep): wt=70.000, iters=3346
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% 2.47/2.82 Low Water (keep): wt=67.000, iters=3337
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=66.000, iters=3338
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=64.000, iters=3407
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% 2.47/2.82 Low Water (keep): wt=62.000, iters=3345
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% 2.47/2.82 Low Water (keep): wt=59.000, iters=3351
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% 2.47/2.82 Low Water (keep): wt=55.000, iters=3378
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% 2.47/2.82 Low Water (keep): wt=54.000, iters=3343
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% 2.47/2.82 Low Water (keep): wt=53.000, iters=3333
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=52.000, iters=3411
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=51.000, iters=3340
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=49.000, iters=3423
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=47.000, iters=3367
% 2.47/2.82
% 2.47/2.82 Low Water (keep): wt=46.000, iters=3377
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=45.000, iters=3368
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=44.000, iters=3358
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% 21.14/21.39 Low Water (keep): wt=43.000, iters=3350
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% 21.14/21.39 Low Water (keep): wt=42.000, iters=3338
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=41.000, iters=3373
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=40.000, iters=3341
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% 21.14/21.39 Low Water (keep): wt=39.000, iters=3340
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% 21.14/21.39 Low Water (keep): wt=38.000, iters=3348
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% 21.14/21.39 Low Water (keep): wt=37.000, iters=3387
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% 21.14/21.39 Low Water (keep): wt=36.000, iters=3361
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% 21.14/21.39 Low Water (keep): wt=35.000, iters=3351
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% 21.14/21.39 Low Water (keep): wt=34.000, iters=3350
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% 21.14/21.39 Low Water (keep): wt=33.000, iters=3373
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% 21.14/21.39 Low Water (keep): wt=32.000, iters=3379
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% 21.14/21.39 Low Water (keep): wt=30.000, iters=3355
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% 21.14/21.39 Low Water (keep): wt=29.000, iters=3342
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=3060, wt=200.000
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=19075, wt=23.000
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=19076, wt=21.000
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=19108, wt=17.000
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=28.000, iters=3343
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=20060, wt=16.000
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=27.000, iters=3335
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=21519, wt=14.000
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=26.000, iters=3333
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=25.000, iters=3344
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% 21.14/21.39 Low Water (keep): wt=24.000, iters=3341
% 21.14/21.39
% 21.14/21.39 Low Water (displace): id=24704, wt=13.000
% 21.14/21.39
% 21.14/21.39 Low Water (keep): wt=23.000, iters=3342
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% 21.14/21.39 Low Water (keep): wt=22.000, iters=3345
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% 21.14/21.39 Low Water (keep): wt=21.000, iters=3342
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% 21.14/21.39 Low Water (keep): wt=20.000, iters=3334
% 21.14/21.39
% 21.14/21.39 ============================== PROOF =================================
% 21.14/21.39 % SZS status Unsatisfiable
% 21.14/21.39 % SZS output start Refutation
% 21.14/21.39
% 21.14/21.39 % Proof 1 at 20.04 (+ 0.38) seconds: goals.
% 21.14/21.39 % Length of proof is 295.
% 21.14/21.39 % Level of proof is 51.
% 21.14/21.39 % Maximum clause weight is 44.000.
% 21.14/21.39 % Given clauses 1385.
% 21.14/21.39
% 21.14/21.39 1 mult(unit,A) = A # label(c01) # label(axiom). [assumption].
% 21.14/21.39 2 mult(A,unit) = A # label(c02) # label(axiom). [assumption].
% 21.14/21.39 3 mult(A,i(A)) = unit # label(c03) # label(axiom). [assumption].
% 21.14/21.39 4 mult(i(A),A) = unit # label(c04) # label(axiom). [assumption].
% 21.14/21.39 5 rd(mult(A,B),B) = A # label(c07) # label(axiom). [assumption].
% 21.14/21.39 6 mult(rd(A,B),B) = A # label(c08) # label(axiom). [assumption].
% 21.14/21.39 7 mult(i(A),mult(A,B)) = B # label(c06) # label(axiom). [assumption].
% 21.14/21.40 8 asoc(asoc(A,B,C),D,E) = unit # label(c20) # label(axiom). [assumption].
% 21.14/21.40 9 i(mult(A,B)) = mult(i(A),i(B)) # label(c05) # label(axiom). [assumption].
% 21.14/21.40 10 op_t(A,B) = mult(i(B),mult(A,B)) # label(c13) # label(axiom). [assumption].
% 21.14/21.40 11 op_t(op_t(A,B),C) = op_t(op_t(A,C),B) # label(c19) # label(axiom). [assumption].
% 21.14/21.40 12 mult(i(A),mult(mult(i(B),mult(C,B)),A)) = mult(i(B),mult(mult(i(A),mult(C,A)),B)). [copy(11),rewrite([10(1),10(4),10(7),10(10)])].
% 21.14/21.40 13 op_t(op_r(A,B,C),D) = op_r(op_t(A,D),B,C) # label(c17) # label(axiom). [assumption].
% 21.14/21.40 14 op_r(mult(i(A),mult(B,A)),C,D) = mult(i(A),mult(op_r(B,C,D),A)). [copy(13),rewrite([10(2),10(5)]),flip(a)].
% 21.14/21.40 17 op_r(A,B,C) = rd(mult(mult(A,B),C),mult(B,C)) # label(c12) # label(axiom). [assumption].
% 21.14/21.40 18 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))) # label(c09) # label(axiom). [assumption].
% 21.14/21.40 27 mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)) # label(c10) # label(axiom). [assumption].
% 21.14/21.40 28 mult(mult(A,mult(B,C)),asoc(A,B,C)) = mult(mult(A,B),C). [copy(27),flip(a)].
% 21.14/21.40 29 asoc(a,b,asoc(c,d,e)) != unit # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 21.14/21.40 30 rd(mult(mult(mult(i(A),mult(B,A)),C),D),mult(C,D)) = mult(i(A),mult(rd(mult(mult(B,C),D),mult(C,D)),A)). [back_rewrite(14),rewrite([17(4),17(9)])].
% 21.14/21.40 32 i(unit) = unit. [para(3(a,1),1(a,1)),flip(a)].
% 21.14/21.40 35 rd(unit,i(A)) = A. [para(3(a,1),5(a,1,1))].
% 21.14/21.40 36 rd(unit,A) = i(A). [para(4(a,1),5(a,1,1))].
% 21.14/21.40 37 i(i(A)) = A. [back_rewrite(35),rewrite([36(3)])].
% 21.14/21.40 38 rd(A,mult(B,A)) = i(B). [para(7(a,1),5(a,1,1))].
% 21.14/21.40 41 mult(mult(A,B),mult(i(A),i(B))) = unit. [para(9(a,1),3(a,1,2))].
% 21.14/21.40 43 mult(i(rd(A,B)),i(B)) = i(A). [para(6(a,1),9(a,1,1)),flip(a)].
% 21.14/21.40 44 mult(mult(i(A),i(B)),mult(mult(A,B),C)) = C. [para(9(a,1),7(a,1,1))].
% 21.14/21.40 51 mult(A,mult(i(B),mult(mult(i(A),mult(C,A)),B))) = mult(mult(i(B),mult(C,B)),A). [para(12(a,1),7(a,1,2)),rewrite([37(2)])].
% 21.14/21.40 59 mult(i(A),mult(mult(i(B),mult(mult(i(C),mult(D,C)),B)),A)) = mult(i(C),mult(mult(i(A),mult(mult(i(B),mult(D,B)),A)),C)). [para(12(a,1),12(a,1,2,1))].
% 21.14/21.40 64 rd(mult(A,mult(B,mult(A,C))),C) = mult(A,mult(B,A)). [para(18(a,1),5(a,1,1))].
% 21.14/21.40 65 mult(A,mult(rd(B,A),mult(A,C))) = mult(mult(A,B),C). [para(6(a,1),18(a,1,1,2)),flip(a)].
% 21.14/21.40 175 mult(A,asoc(A,B,i(B))) = mult(mult(A,B),i(B)). [para(3(a,1),28(a,1,1,2)),rewrite([2(2)])].
% 21.14/21.40 176 mult(A,asoc(A,i(B),B)) = mult(mult(A,i(B)),B). [para(4(a,1),28(a,1,1,2)),rewrite([2(2)])].
% 21.14/21.40 178 mult(A,asoc(i(B),B,A)) = A. [para(4(a,1),28(a,2,1)),rewrite([7(3),1(5)])].
% 21.14/21.40 179 rd(mult(mult(A,B),C),asoc(A,B,C)) = mult(A,mult(B,C)). [para(28(a,1),5(a,1,1))].
% 21.14/21.40 180 mult(mult(A,B),asoc(A,rd(B,C),C)) = mult(mult(A,rd(B,C)),C). [para(6(a,1),28(a,1,1,2))].
% 21.14/21.40 181 mult(A,asoc(rd(A,mult(B,C)),B,C)) = mult(mult(rd(A,mult(B,C)),B),C). [para(6(a,1),28(a,1,1))].
% 21.14/21.40 182 mult(mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = asoc(A,B,C). [para(28(a,1),7(a,1,2)),rewrite([9(3),9(3)])].
% 21.14/21.40 184 mult(mult(asoc(A,B,C),D),E) = mult(asoc(A,B,C),mult(D,E)). [para(8(a,1),28(a,1,2)),rewrite([2(5)]),flip(a)].
% 21.14/21.40 185 mult(mult(i(A),mult(i(B),i(C))),i(asoc(A,B,C))) = mult(mult(i(A),i(B)),i(C)). [para(28(a,1),9(a,1,1)),rewrite([9(3),9(2),9(8),9(8)]),flip(a)].
% 21.14/21.40 186 mult(i(asoc(A,B,C)),mult(mult(i(D),mult(mult(A,mult(B,C)),D)),asoc(A,B,C))) = mult(i(D),mult(mult(i(asoc(A,B,C)),mult(mult(A,B),C)),D)). [para(28(a,1),12(a,1,2,1,2)),flip(a)].
% 21.14/21.40 190 mult(mult(i(A),mult(mult(i(B),mult(C,B)),A)),D) = mult(mult(i(B),mult(mult(i(A),mult(C,A)),B)),D). [para(12(a,1),28(a,2,1)),rewrite([28(14)])].
% 21.14/21.40 357 mult(A,mult(i(A),B)) = B. [para(37(a,1),7(a,1,1))].
% 21.14/21.40 367 i(rd(A,B)) = rd(B,A). [para(6(a,1),38(a,1,2)),flip(a)].
% 21.14/21.40 389 mult(rd(A,B),i(A)) = i(B). [back_rewrite(43),rewrite([367(2)])].
% 21.14/21.40 391 mult(mult(A,i(B)),mult(mult(i(C),mult(A,C)),mult(i(A),B))) = mult(i(C),mult(mult(mult(A,i(B)),B),C)). [para(357(a,1),12(a,1,2,1,2)),rewrite([9(4),37(3),9(9),37(8)]),flip(a)].
% 21.14/21.40 404 mult(mult(A,B),asoc(A,C,mult(i(C),B))) = mult(mult(A,C),mult(i(C),B)). [para(357(a,1),28(a,1,1,2))].
% 21.14/21.40 414 mult(rd(A,B),rd(B,A)) = unit. [para(367(a,1),3(a,1,2))].
% 21.14/21.40 415 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(367(a,1),7(a,1,1))].
% 21.14/21.40 424 rd(mult(A,B),mult(mult(mult(i(C),mult(D,C)),A),B)) = mult(C,mult(rd(mult(A,B),mult(mult(D,A),B)),i(C))). [para(30(a,1),367(a,1,1)),rewrite([9(8),37(2),9(6),367(5)]),flip(a)].
% 21.14/21.40 430 asoc(i(A),A,B) = unit. [para(178(a,1),7(a,1,2)),rewrite([4(2)]),flip(a)].
% 21.14/21.40 460 asoc(mult(i(A),i(B)),mult(A,B),C) = unit. [para(9(a,1),430(a,1,1))].
% 21.14/21.40 461 asoc(A,i(A),B) = unit. [para(37(a,1),430(a,1,1))].
% 21.14/21.40 464 rd(i(A),i(B)) = rd(B,A). [para(389(a,1),5(a,1,1))].
% 21.14/21.40 467 mult(i(A),mult(rd(A,B),mult(i(A),C))) = mult(mult(i(A),i(B)),C). [para(389(a,1),18(a,1,1,2)),flip(a)].
% 21.14/21.40 476 mult(mult(A,i(B)),asoc(A,rd(C,B),i(C))) = mult(mult(A,rd(C,B)),i(C)). [para(389(a,1),28(a,1,1,2))].
% 21.14/21.40 483 mult(rd(i(A),B),A) = i(B). [para(37(a,1),389(a,1,2))].
% 21.14/21.40 524 rd(i(A),mult(i(B),i(C))) = rd(mult(B,C),A). [para(9(a,1),464(a,1,2))].
% 21.14/21.40 529 rd(A,i(B)) = rd(B,i(A)). [para(37(a,1),464(a,1,1))].
% 21.14/21.40 530 rd(i(A),B) = rd(i(B),A). [para(37(a,1),464(a,1,2))].
% 21.14/21.40 531 rd(rd(A,B),C) = rd(i(C),rd(B,A)). [para(367(a,1),464(a,1,2)),flip(a)].
% 21.14/21.40 729 mult(rd(i(A),B),rd(A,i(B))) = unit. [para(529(a,1),414(a,1,2))].
% 21.14/21.40 744 mult(mult(A,i(B)),mult(mult(i(A),B),C)) = C. [para(37(a,1),44(a,1,1,1))].
% 21.14/21.40 774 mult(rd(i(A),B),mult(rd(A,i(B)),C)) = C. [para(529(a,1),415(a,1,2,1))].
% 21.14/21.40 980 asoc(mult(i(A),rd(B,C)),mult(A,rd(C,B)),D) = unit. [para(367(a,1),460(a,1,1,2))].
% 21.14/21.40 1035 rd(rd(i(A),B),C) = rd(i(C),rd(A,i(B))). [para(529(a,1),531(a,2,2))].
% 21.14/21.40 1047 mult(mult(i(A),mult(B,A)),B) = mult(B,mult(i(A),mult(B,A))). [para(7(a,1),51(a,1,2,2,1)),flip(a)].
% 21.14/21.40 1326 mult(i(A),mult(mult(A,B),i(B))) = asoc(A,B,i(B)). [para(175(a,1),7(a,1,2))].
% 21.14/21.40 1341 mult(A,mult(mult(i(A),B),i(B))) = asoc(i(A),B,i(B)). [para(175(a,1),357(a,1,2))].
% 21.14/21.40 1389 mult(A,mult(mult(i(A),i(B)),B)) = asoc(i(A),i(B),B). [para(176(a,1),357(a,1,2))].
% 21.14/21.40 1793 rd(i(A),mult(B,i(C))) = rd(mult(i(B),C),A). [para(37(a,1),524(a,1,2,1))].
% 21.14/21.40 2508 rd(A,mult(i(A),i(B))) = mult(A,mult(B,A)). [para(3(a,1),64(a,1,1,2,2)),rewrite([2(2),529(3),9(2)])].
% 21.14/21.40 2509 rd(mult(i(A),B),A) = mult(i(A),mult(B,i(A))). [para(4(a,1),64(a,1,1,2,2)),rewrite([2(3)])].
% 21.14/21.40 2532 mult(i(A),mult(mult(A,B),i(A))) = rd(B,A). [para(41(a,1),64(a,1,1,2)),rewrite([2(3),529(3),37(2)]),flip(a)].
% 21.14/21.40 2615 rd(A,mult(i(A),B)) = mult(A,mult(i(B),A)). [para(37(a,1),2508(a,1,2,2))].
% 21.14/21.40 2652 mult(mult(A,B),i(A)) = mult(A,rd(B,A)). [para(2532(a,1),7(a,1,2)),rewrite([37(2)]),flip(a)].
% 21.14/21.40 2748 mult(mult(i(A),B),A) = mult(i(A),rd(A,i(B))). [para(37(a,1),2652(a,1,2)),rewrite([529(6)])].
% 21.14/21.40 2749 mult(mult(rd(A,B),C),rd(B,A)) = mult(rd(A,B),rd(C,rd(A,B))). [para(367(a,1),2652(a,1,2))].
% 21.14/21.40 2980 mult(rd(A,B),mult(B,C)) = mult(i(B),mult(mult(B,A),C)). [para(65(a,1),7(a,1,2)),flip(a)].
% 21.14/21.40 2981 mult(mult(i(A),B),mult(A,C)) = mult(i(A),mult(rd(A,i(B)),C)). [para(7(a,1),65(a,1,2,2)),rewrite([529(3)]),flip(a)].
% 21.14/21.40 3006 mult(mult(A,B),mult(i(A),C)) = mult(A,mult(rd(B,A),C)). [para(357(a,1),65(a,1,2,2)),flip(a)].
% 21.14/21.40 3017 mult(mult(rd(i(A),B),C),rd(A,i(B))) = mult(rd(i(A),B),rd(C,rd(i(A),B))). [para(729(a,1),65(a,1,2,2)),rewrite([2(7)]),flip(a)].
% 21.14/21.40 3726 mult(A,mult(i(asoc(i(A),B,i(B))),A)) = rd(A,mult(mult(i(A),B),i(B))). [para(175(a,1),2615(a,1,2)),flip(a)].
% 21.14/21.40 3727 mult(A,mult(i(asoc(i(A),i(B),B)),A)) = rd(A,mult(mult(i(A),i(B)),B)). [para(176(a,1),2615(a,1,2)),flip(a)].
% 21.14/21.40 3935 mult(i(A),rd(A,i(asoc(i(A),B,i(B))))) = mult(mult(mult(i(A),B),i(B)),A). [para(175(a,1),2748(a,1,1)),flip(a)].
% 21.14/21.40 3936 mult(i(A),rd(A,i(asoc(i(A),i(B),B)))) = mult(mult(mult(i(A),i(B)),B),A). [para(176(a,1),2748(a,1,1)),flip(a)].
% 21.14/21.40 4515 asoc(rd(A,B),B,i(B)) = asoc(A,B,i(B)). [para(6(a,1),1326(a,1,2,1)),rewrite([367(2),2980(4),1326(5)]),flip(a)].
% 21.14/21.40 4517 i(asoc(A,B,i(B))) = asoc(i(A),i(B),B). [para(1326(a,1),9(a,1,1)),rewrite([37(5),9(7),9(5),37(8),1389(8)])].
% 21.14/21.40 4526 mult(asoc(A,B,i(B)),asoc(i(A),mult(A,B),i(B))) = unit. [para(1326(a,1),28(a,1,1)),rewrite([7(10),3(9)])].
% 21.14/21.40 4531 asoc(rd(i(A),B),A,i(A)) = asoc(i(B),A,i(A)). [para(483(a,1),1326(a,1,2,1)),rewrite([367(3),529(2),2980(6),37(2),1341(5)]),flip(a)].
% 21.14/21.40 4577 mult(mult(i(A),i(B)),mult(mult(A,rd(B,A)),A)) = asoc(mult(A,B),i(A),A). [para(2652(a,1),1326(a,1,2,1)),rewrite([9(2),37(7),37(11)])].
% 21.14/21.40 4593 mult(i(A),rd(A,asoc(A,i(B),B))) = mult(mult(mult(i(A),B),i(B)),A). [back_rewrite(3935),rewrite([4517(5),37(3)])].
% 21.14/21.40 4596 mult(A,mult(asoc(A,i(B),B),A)) = rd(A,mult(mult(i(A),B),i(B))). [back_rewrite(3726),rewrite([4517(4),37(2)])].
% 21.14/21.40 4799 asoc(mult(A,B),B,i(B)) = asoc(A,B,i(B)). [para(5(a,1),4515(a,1,1)),flip(a)].
% 21.14/21.40 4801 mult(rd(A,B),asoc(A,B,i(B))) = mult(A,i(B)). [para(4515(a,1),28(a,1,2)),rewrite([3(3),2(3),6(6)])].
% 21.14/21.40 4802 asoc(rd(A,i(B)),i(B),B) = asoc(A,i(B),B). [para(37(a,1),4515(a,1,3)),rewrite([37(7)])].
% 21.14/21.40 4869 rd(mult(mult(mult(A,B),i(B)),C),asoc(A,asoc(A,B,i(B)),C)) = mult(A,mult(asoc(A,B,i(B)),C)). [para(175(a,1),179(a,1,1,1))].
% 21.14/21.40 4871 rd(mult(mult(mult(A,i(B)),B),C),asoc(A,asoc(A,i(B),B),C)) = mult(A,mult(asoc(A,i(B),B),C)). [para(176(a,1),179(a,1,1,1))].
% 21.14/21.40 4930 i(asoc(i(A),mult(A,B),i(B))) = asoc(A,B,i(B)). [para(1326(a,1),179(a,2)),rewrite([7(3),3(2),36(6)])].
% 21.14/21.40 4936 rd(mult(A,i(B)),asoc(A,B,i(B))) = rd(A,B). [para(4515(a,1),179(a,1,2)),rewrite([6(2),3(8),2(8)])].
% 21.14/21.40 4953 mult(asoc(A,B,i(B)),asoc(i(A),i(B),B)) = unit. [para(4517(a,1),3(a,1,2))].
% 21.14/21.40 4955 asoc(i(asoc(A,B,C)),i(D),D) = unit. [para(8(a,1),4517(a,1,1)),rewrite([32(2)]),flip(a)].
% 21.14/21.40 4958 i(asoc(A,i(B),B)) = asoc(i(A),B,i(B)). [para(37(a,1),4517(a,1,1,3)),rewrite([37(6)])].
% 21.14/21.40 4963 mult(rd(i(A),asoc(B,C,i(C))),rd(A,asoc(i(B),i(C),C))) = unit. [para(4517(a,1),729(a,1,2,2))].
% 21.14/21.40 5000 rd(asoc(i(A),i(B),B),mult(i(C),i(D))) = rd(mult(C,D),asoc(A,B,i(B))). [para(4517(a,1),524(a,1,1))].
% 21.14/21.40 5042 asoc(mult(asoc(i(A),i(B),B),rd(C,D)),mult(asoc(A,B,i(B)),rd(D,C)),E) = unit. [para(4517(a,1),980(a,1,1,1))].
% 21.14/21.40 5051 asoc(rd(A,B),i(A),A) = asoc(i(B),i(A),A). [para(4515(a,1),4517(a,1,1)),rewrite([4517(3),367(5)]),flip(a)].
% 21.14/21.40 5055 mult(i(A),rd(A,asoc(A,B,i(B)))) = mult(mult(mult(i(A),i(B)),B),A). [back_rewrite(3936),rewrite([4958(5),37(3)])].
% 21.14/21.40 5056 mult(A,mult(asoc(A,B,i(B)),A)) = rd(A,mult(mult(i(A),i(B)),B)). [back_rewrite(3727),rewrite([4958(4),37(2)])].
% 21.14/21.40 5085 asoc(i(asoc(A,B,C)),D,i(D)) = unit. [para(37(a,1),4955(a,1,2))].
% 21.14/21.40 5091 mult(mult(i(A),i(B)),mult(mult(A,rd(B,C)),C)) = asoc(A,rd(B,C),C). [para(180(a,1),7(a,1,2)),rewrite([9(2)])].
% 21.14/21.40 5223 asoc(mult(A,B),i(A),A) = asoc(A,rd(B,A),A). [back_rewrite(4577),rewrite([5091(7)]),flip(a)].
% 21.14/21.40 5228 asoc(mult(A,i(B)),i(B),B) = asoc(A,i(B),B). [para(37(a,1),4799(a,1,3)),rewrite([37(7)])].
% 21.14/21.40 5258 mult(asoc(A,i(B),B),asoc(i(A),B,i(B))) = unit. [para(4958(a,1),3(a,1,2))].
% 21.14/21.40 5270 mult(rd(i(A),asoc(B,i(C),C)),rd(A,asoc(i(B),C,i(C)))) = unit. [para(4958(a,1),729(a,1,2,2))].
% 21.14/21.40 5558 rd(asoc(A,B,C),D) = mult(asoc(A,B,C),i(D)). [para(8(a,1),4801(a,1,2)),rewrite([2(4)])].
% 21.14/21.40 5559 mult(rd(A,B),asoc(i(B),i(A),A)) = mult(i(B),A). [para(4801(a,1),9(a,1,1)),rewrite([9(3),37(3),367(4),4517(6)]),flip(a)].
% 21.14/21.40 5564 mult(rd(A,i(B)),asoc(A,i(B),B)) = mult(A,B). [para(37(a,1),4801(a,1,2,3)),rewrite([37(7)])].
% 21.14/21.40 5565 mult(asoc(A,B,i(B)),mult(i(A),B)) = rd(B,A). [para(4801(a,1),38(a,1,2)),rewrite([5558(5),9(5),37(5),367(7)])].
% 21.14/21.40 5580 mult(rd(i(A),B),mult(A,B)) = asoc(A,i(B),B). [para(4801(a,1),774(a,1,2)),rewrite([37(4),37(7)])].
% 21.14/21.40 5616 rd(i(A),asoc(B,C,D)) = mult(i(asoc(B,C,D)),i(A)). [para(5085(a,1),4801(a,1,2)),rewrite([530(3),2(5)])].
% 21.14/21.40 5647 rd(mult(A,B),asoc(C,D,i(D))) = mult(asoc(i(C),i(D),D),mult(A,B)). [back_rewrite(5000),rewrite([5558(7),9(7),37(5),37(5)]),flip(a)].
% 21.14/21.40 5668 mult(asoc(i(A),B,i(B)),mult(i(C),rd(C,asoc(i(A),B,i(B))))) = unit. [back_rewrite(5270),rewrite([5616(4),4958(3),184(10)])].
% 21.14/21.40 5676 mult(asoc(i(A),i(B),B),mult(i(C),rd(C,asoc(i(A),i(B),B)))) = unit. [back_rewrite(4963),rewrite([5616(4),4517(3),184(10)])].
% 21.14/21.40 5682 mult(asoc(i(A),i(B),B),mult(A,i(B))) = rd(A,B). [back_rewrite(4936),rewrite([5647(5)])].
% 21.14/21.40 5693 asoc(A,rd(B,A),A) = asoc(A,B,A). [para(2509(a,1),4802(a,1,1)),rewrite([37(2),37(2),5223(4),5(2),37(3),5223(4)]),flip(a)].
% 21.14/21.40 5699 asoc(A,mult(B,A),A) = asoc(A,B,A). [para(5(a,1),5693(a,1,2)),flip(a)].
% 21.14/21.40 5728 asoc(A,mult(i(A),mult(B,i(A))),A) = asoc(A,mult(i(A),B),A). [para(2509(a,1),5693(a,1,2))].
% 21.14/21.40 5738 mult(mult(rd(A,B),mult(i(A),i(C))),mult(B,C)) = asoc(rd(B,A),A,C). [para(6(a,1),182(a,1,2,1)),rewrite([367(2)])].
% 21.14/21.40 5739 mult(mult(A,mult(mult(i(A),i(B)),i(C))),mult(B,C)) = asoc(i(A),mult(A,B),C). [para(7(a,1),182(a,1,2,1)),rewrite([37(2),9(2)])].
% 21.14/21.40 5759 mult(mult(i(A),mult(rd(B,C),i(D))),mult(mult(A,rd(C,B)),D)) = asoc(A,rd(C,B),D). [para(367(a,1),182(a,1,1,2,1))].
% 21.14/21.40 5815 asoc(mult(A,B),i(A),C) = asoc(A,rd(B,A),C). [para(2652(a,1),182(a,1,2,1)),rewrite([9(2),37(5),2981(6),37(3),5759(9)]),flip(a)].
% 21.14/21.40 5816 mult(i(A),mult(rd(A,mult(B,i(A))),rd(B,A))) = asoc(A,B,i(A)). [para(2652(a,1),182(a,1,2)),rewrite([37(4),2981(7),9(4),37(3)])].
% 21.14/21.40 5821 mult(A,mult(rd(mult(i(B),i(A)),A),rd(A,i(B)))) = asoc(i(A),B,A). [para(2748(a,1),182(a,1,2)),rewrite([37(2),3006(9)])].
% 21.14/21.40 5874 asoc(i(A),rd(A,B),i(A)) = asoc(i(A),i(B),i(A)). [para(389(a,1),5699(a,1,2)),flip(a)].
% 21.14/21.40 5899 asoc(mult(mult(A,B),C),mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = asoc(mult(mult(A,B),C),asoc(A,B,C),mult(mult(A,B),C)). [para(182(a,1),5699(a,1,2)),flip(a)].
% 21.14/21.40 6059 mult(mult(i(A),mult(asoc(B,C,i(C)),A)),asoc(i(B),i(C),C)) = mult(asoc(i(B),i(C),C),mult(i(A),mult(asoc(B,C,i(C)),A))). [para(4953(a,1),51(a,1,2,2,1,2)),rewrite([4958(8),37(6),2(8)]),flip(a)].
% 21.14/21.40 6091 mult(asoc(A,B,C),mult(mult(i(asoc(A,B,C)),D),E)) = mult(D,E). [para(357(a,1),184(a,1,1)),flip(a)].
% 21.14/21.40 6129 asoc(mult(asoc(A,B,C),D),E,i(E)) = asoc(D,E,i(E)). [para(184(a,1),1326(a,1,2,1)),rewrite([9(3),184(9),2981(10),37(5),5558(4),184(9),1326(8),7(7)]),flip(a)].
% 21.14/21.40 6140 mult(mult(mult(i(asoc(A,B,C)),i(D)),mult(i(E),i(F))),mult(asoc(A,B,C),mult(mult(D,E),F))) = asoc(mult(asoc(A,B,C),D),E,F). [para(184(a,1),182(a,1,2,1)),rewrite([9(3),184(12)])].
% 21.14/21.40 6199 mult(mult(i(A),mult(asoc(B,i(C),C),A)),asoc(i(B),C,i(C))) = mult(asoc(i(B),C,i(C)),mult(i(A),mult(asoc(B,i(C),C),A))). [para(5258(a,1),51(a,1,2,2,1,2)),rewrite([4517(8),37(6),2(8)]),flip(a)].
% 21.14/21.40 6202 mult(asoc(A,i(B),B),mult(mult(i(C),mult(mult(i(D),mult(asoc(A,i(B),B),D)),C)),asoc(i(A),B,i(B)))) = mult(i(C),mult(mult(i(D),mult(asoc(A,i(B),B),D)),C)). [para(5258(a,1),59(a,1,2,1,2,1,2)),rewrite([4517(6),37(4),2(6),4517(12),37(10)]),flip(a)].
% 21.14/21.40 6520 mult(asoc(A,B,i(B)),mult(mult(i(C),mult(asoc(A,B,i(B)),C)),asoc(i(A),mult(A,B),i(B)))) = mult(i(C),mult(asoc(A,B,i(B)),C)). [para(1326(a,1),186(a,1,2,1,2,1)),rewrite([4930(5),4930(19),7(19),3(18),2(18)])].
% 21.14/21.40 6641 rd(A,i(asoc(B,C,D))) = mult(asoc(B,C,D),A). [para(37(a,1),5558(a,2,2)),rewrite([529(3)])].
% 21.14/21.40 6643 rd(A,asoc(B,C,D)) = mult(i(asoc(B,C,D)),A). [para(5558(a,1),367(a,1,1)),rewrite([9(4),37(4)]),flip(a)].
% 21.14/21.40 6664 asoc(mult(asoc(A,B,C),D),i(D),D) = unit. [para(5558(a,1),4802(a,1,1)),rewrite([37(3),8(7)])].
% 21.14/21.40 6665 asoc(A,mult(asoc(B,C,D),i(A)),A) = asoc(A,asoc(B,C,D),A). [para(5558(a,1),5693(a,1,2))].
% 21.14/21.40 6694 mult(asoc(i(A),i(B),B),mult(i(C),mult(asoc(A,B,i(B)),C))) = unit. [back_rewrite(5676),rewrite([6643(8),4958(8),37(6)])].
% 21.14/21.40 6695 mult(asoc(i(A),B,i(B)),mult(i(C),mult(asoc(A,i(B),B),C))) = unit. [back_rewrite(5668),rewrite([6643(8),4517(8),37(6)])].
% 21.14/21.40 6709 mult(i(A),mult(asoc(i(A),i(B),B),A)) = mult(mult(mult(i(A),i(B)),B),A). [back_rewrite(5055),rewrite([6643(4),4517(4)])].
% 21.14/21.40 6742 mult(i(asoc(A,asoc(A,i(B),B),C)),mult(mult(mult(A,i(B)),B),C)) = mult(A,mult(asoc(A,i(B),B),C)). [back_rewrite(4871),rewrite([6643(8)])].
% 21.14/21.40 6744 mult(i(asoc(A,asoc(A,B,i(B)),C)),mult(mult(mult(A,B),i(B)),C)) = mult(A,mult(asoc(A,B,i(B)),C)). [back_rewrite(4869),rewrite([6643(8)])].
% 21.14/21.40 6772 mult(i(A),mult(asoc(i(A),B,i(B)),A)) = mult(mult(mult(i(A),B),i(B)),A). [back_rewrite(4593),rewrite([6643(4),4958(4)])].
% 21.14/21.40 6786 mult(mult(i(A),mult(asoc(B,C,i(C)),A)),asoc(i(B),i(C),C)) = unit. [back_rewrite(6059),rewrite([6694(18)])].
% 21.14/21.40 6788 mult(mult(i(A),mult(asoc(B,i(C),C),A)),asoc(i(B),C,i(C))) = unit. [back_rewrite(6199),rewrite([6695(18)])].
% 21.14/21.40 7189 asoc(rd(A,B),i(B),B) = mult(rd(rd(B,A),B),A). [para(6(a,1),5580(a,1,2)),rewrite([367(2)]),flip(a)].
% 21.14/21.40 7199 asoc(rd(A,B),A,i(A)) = mult(rd(A,rd(A,B)),i(B)). [para(389(a,1),5580(a,1,2)),rewrite([367(2),529(3),367(2),37(7)]),flip(a)].
% 21.14/21.40 7328 asoc(mult(i(A),B),A,C) = asoc(i(A),rd(A,i(B)),C). [para(37(a,1),5815(a,1,2)),rewrite([529(6)])].
% 21.14/21.40 7329 asoc(A,mult(i(A),mult(B,i(A))),C) = asoc(B,i(A),C). [para(357(a,1),5815(a,1,1)),rewrite([2509(5)]),flip(a)].
% 21.14/21.40 7351 asoc(A,mult(asoc(A,B,i(B)),i(A)),C) = asoc(mult(mult(A,B),i(B)),i(A),C). [para(175(a,1),5815(a,1,1)),rewrite([5558(8)]),flip(a)].
% 21.14/21.40 7388 i(asoc(A,B,A)) = asoc(i(A),i(B),i(A)). [para(5815(a,1),4517(a,1,1)),rewrite([37(3),5693(2),9(4),37(7),7328(7),37(5),5874(6)])].
% 21.14/21.40 7393 asoc(rd(A,B),mult(asoc(A,B,i(B)),rd(B,A)),C) = asoc(mult(A,i(B)),rd(B,A),C). [para(4801(a,1),5815(a,1,1)),rewrite([367(4),5558(9),367(9)]),flip(a)].
% 21.14/21.40 7402 asoc(rd(A,B),asoc(i(B),i(A),A),C) = unit. [para(5565(a,1),5815(a,1,1)),rewrite([4517(4),6643(12),4517(10),8(14)])].
% 21.14/21.40 7415 asoc(A,mult(i(A),B),A) = asoc(B,i(A),A). [back_rewrite(5728),rewrite([7329(5)]),flip(a)].
% 21.14/21.40 7536 mult(mult(i(A),mult(asoc(B,C,i(C)),A)),D) = mult(asoc(B,C,i(C)),D). [para(4953(a,1),190(a,1,1,2,1,2)),rewrite([4958(5),37(3),2(5),4958(10),37(8),6786(17),2(10)])].
% 21.14/21.40 7541 mult(mult(i(A),mult(asoc(B,i(C),C),A)),D) = mult(asoc(B,i(C),C),D). [para(5258(a,1),190(a,1,1,2,1,2)),rewrite([4517(5),37(3),2(5),4517(10),37(8),6788(17),2(10)])].
% 21.14/21.40 7563 mult(i(A),mult(asoc(B,C,i(C)),A)) = asoc(B,C,i(C)). [back_rewrite(6520),rewrite([7536(12),4526(9),2(4)]),flip(a)].
% 21.14/21.40 7572 mult(i(A),mult(asoc(B,i(C),C),A)) = asoc(B,i(C),C). [back_rewrite(6202),rewrite([7541(9),7541(11),5258(8),2(4),7541(9)]),flip(a)].
% 21.14/21.40 7579 mult(mult(mult(i(A),B),i(B)),A) = asoc(i(A),B,i(B)). [back_rewrite(6772),rewrite([7563(6)]),flip(a)].
% 21.14/21.40 7580 mult(mult(mult(i(A),i(B)),B),A) = asoc(i(A),i(B),B). [back_rewrite(6709),rewrite([7572(6)]),flip(a)].
% 21.14/21.40 7706 mult(rd(A,B),mult(asoc(i(B),i(A),A),C)) = mult(mult(i(B),A),C). [para(7402(a,1),28(a,1,2)),rewrite([2(8),5559(11)])].
% 21.14/21.40 7709 asoc(i(A),asoc(i(A),i(B),B),C) = unit. [para(38(a,1),7402(a,1,1)),rewrite([9(3),5228(6)])].
% 21.14/21.40 7720 mult(mult(i(A),B),asoc(A,B,i(B))) = rd(B,A). [para(7402(a,1),175(a,1,2)),rewrite([2(3),5559(6),4958(7),37(5)]),flip(a)].
% 21.14/21.40 7749 asoc(A,asoc(A,i(B),B),C) = unit. [para(37(a,1),7709(a,1,1)),rewrite([37(2)])].
% 21.14/21.40 7759 mult(A,mult(asoc(A,i(B),B),C)) = mult(mult(mult(A,i(B)),B),C). [back_rewrite(6742),rewrite([7749(3),32(2),1(6)]),flip(a)].
% 21.14/21.40 7776 rd(A,mult(mult(i(A),B),i(B))) = mult(mult(mult(A,i(B)),B),A). [back_rewrite(4596),rewrite([7759(4)]),flip(a)].
% 21.14/21.40 7941 asoc(A,asoc(A,B,i(B)),C) = unit. [para(37(a,1),7749(a,1,2,2))].
% 21.14/21.40 7948 mult(A,mult(asoc(A,B,i(B)),C)) = mult(mult(mult(A,B),i(B)),C). [back_rewrite(6744),rewrite([7941(3),32(2),1(6)]),flip(a)].
% 21.14/21.40 7949 rd(A,mult(mult(i(A),i(B)),B)) = mult(mult(mult(A,B),i(B)),A). [back_rewrite(5056),rewrite([7948(4)]),flip(a)].
% 21.14/21.40 7956 asoc(mult(mult(A,B),i(B)),i(A),A) = unit. [para(7941(a,1),5693(a,2)),rewrite([5558(3),7351(5)])].
% 21.14/21.40 8171 asoc(mult(A,mult(B,i(A))),i(B),B) = unit. [para(357(a,1),7956(a,1,1,1)),rewrite([9(3),37(2)])].
% 21.14/21.40 8210 asoc(mult(i(A),mult(B,A)),i(B),B) = unit. [para(37(a,1),8171(a,1,1,2,2))].
% 21.14/21.40 8450 rd(A,mult(B,mult(i(A),i(B)))) = mult(A,mult(i(B),mult(A,B))). [para(8210(a,1),5564(a,1,2)),rewrite([529(5),9(4),37(2),9(2),2(7),1047(9)])].
% 21.14/21.40 8456 asoc(A,i(asoc(B,C,D)),asoc(B,C,D)) = unit. [para(7415(a,1),8(a,1))].
% 21.14/21.40 8459 asoc(i(A),mult(A,B),i(A)) = asoc(B,A,i(A)). [para(37(a,1),7415(a,1,2,1)),rewrite([37(6)])].
% 21.14/21.40 8462 asoc(A,mult(mult(i(A),B),i(B)),A) = unit. [para(175(a,1),7415(a,1,2)),rewrite([8(10)])].
% 21.14/21.40 8477 asoc(A,mult(B,mult(i(A),i(B))),A) = unit. [para(7(a,1),8462(a,1,2,1)),rewrite([9(2)])].
% 21.14/21.40 8723 asoc(i(A),mult(i(B),mult(A,B)),i(A)) = unit. [para(8477(a,1),7388(a,1,1)),rewrite([32(2),9(7),9(7),37(5),37(5)]),flip(a)].
% 21.14/21.40 10428 mult(asoc(A,B,C),D) = mult(D,asoc(A,B,C)). [para(8456(a,1),5564(a,1,2)),rewrite([6641(3),2(4)])].
% 21.14/21.40 10726 asoc(mult(i(A),mult(B,A)),B,i(B)) = unit. [para(8723(a,1),5693(a,2)),rewrite([529(6),9(5),37(3),9(3),8450(6),8459(7)])].
% 21.14/21.40 10749 asoc(mult(mult(A,i(B)),B),A,i(A)) = unit. [para(357(a,1),10726(a,1,1,2)),rewrite([9(3),37(2)])].
% 21.14/21.40 10764 asoc(mult(mult(A,B),i(B)),A,i(A)) = unit. [para(175(a,1),10726(a,1,1,2)),rewrite([4517(3),6129(9)])].
% 21.14/21.40 10875 mult(mult(mult(mult(A,i(B)),B),A),i(A)) = mult(mult(A,i(B)),B). [para(10749(a,1),28(a,1,2)),rewrite([3(5),2(5),2(5)]),flip(a)].
% 21.14/21.40 10880 rd(mult(mult(A,i(B)),B),A) = mult(mult(mult(A,i(B)),B),i(A)). [para(10749(a,1),4801(a,1,2)),rewrite([2(6)])].
% 21.14/21.40 10894 mult(mult(mult(mult(A,B),i(B)),A),i(A)) = mult(mult(A,B),i(B)). [para(10764(a,1),28(a,1,2)),rewrite([3(5),2(5),2(5)]),flip(a)].
% 21.14/21.40 10917 rd(mult(mult(A,B),i(B)),A) = mult(mult(mult(A,B),i(B)),i(A)). [para(10764(a,1),4801(a,1,2)),rewrite([2(6)])].
% 21.14/21.40 11232 mult(asoc(A,B,i(B)),mult(i(C),mult(mult(mult(A,i(B)),rd(B,A)),mult(asoc(i(A),i(B),B),C)))) = mult(mult(A,i(B)),rd(B,A)). [para(5565(a,1),391(a,1,2,1,2)),rewrite([9(7),37(6),4517(11),184(14),9(17),37(16),184(21),4(20),2(20),5565(21)])].
% 21.14/21.40 11691 rd(mult(A,asoc(B,C,D)),A) = asoc(B,C,D). [para(10428(a,1),5(a,1,1))].
% 21.14/21.40 11693 mult(i(A),mult(asoc(B,C,D),A)) = asoc(B,C,D). [para(10428(a,2),7(a,1,2))].
% 21.14/21.40 11703 mult(mult(A,asoc(B,C,D)),E) = mult(asoc(B,C,D),mult(A,E)). [para(10428(a,1),28(a,2,1)),rewrite([8(5),2(5)]),flip(a)].
% 21.14/21.40 11705 rd(A,mult(A,asoc(B,C,D))) = i(asoc(B,C,D)). [para(10428(a,1),38(a,1,2))].
% 21.14/21.40 11706 mult(A,mult(asoc(B,C,D),i(A))) = asoc(B,C,D). [para(10428(a,2),357(a,1,2))].
% 21.14/21.40 11738 mult(asoc(A,i(B),B),A) = mult(mult(A,i(B)),B). [para(10428(a,2),176(a,1))].
% 21.14/21.40 11786 mult(A,asoc(rd(A,mult(B,asoc(C,D,E))),asoc(C,D,E),B)) = mult(asoc(C,D,E),mult(rd(A,mult(asoc(C,D,E),B)),B)). [para(10428(a,1),181(a,1,2,1,2)),rewrite([11703(12)])].
% 21.14/21.40 11788 mult(asoc(A,B,C),mult(rd(D,mult(asoc(A,B,C),E)),E)) = mult(asoc(A,B,C),mult(rd(D,mult(E,asoc(A,B,C))),E)). [para(10428(a,1),181(a,2,1,1,2)),rewrite([181(6),11703(6),11703(12)])].
% 21.14/21.40 11789 mult(A,asoc(rd(A,mult(asoc(B,C,D),E)),E,asoc(B,C,D))) = mult(mult(rd(A,mult(E,asoc(B,C,D))),E),asoc(B,C,D)). [para(10428(a,2),181(a,1,2,1,2))].
% 21.14/21.40 11792 mult(mult(rd(A,mult(B,asoc(C,D,E))),B),asoc(C,D,E)) = mult(asoc(C,D,E),mult(rd(A,mult(B,asoc(C,D,E))),B)). [para(10428(a,2),181(a,2)),rewrite([181(6)])].
% 21.14/21.40 11806 asoc(A,asoc(B,C,D),A) = unit. [para(10428(a,1),6664(a,1,1)),rewrite([5815(4),5558(2),6665(4)])].
% 21.14/21.40 11811 asoc(mult(asoc(A,B,C),D),i(D),E) = asoc(D,mult(asoc(A,B,C),i(D)),E). [para(10428(a,2),5815(a,1,1)),rewrite([5558(6)])].
% 21.14/21.40 11952 mult(A,asoc(rd(A,mult(asoc(B,C,D),E)),E,asoc(B,C,D))) = mult(asoc(B,C,D),mult(rd(A,mult(E,asoc(B,C,D))),E)). [back_rewrite(11789),rewrite([11792(12)])].
% 21.14/21.40 11955 asoc(mult(mult(A,B),C),mult(i(A),mult(i(B),i(C))),mult(mult(A,B),C)) = unit. [back_rewrite(5899),rewrite([11806(16)])].
% 21.14/21.40 12371 rd(mult(A,B),mult(mult(mult(mult(C,i(D)),rd(D,C)),A),B)) = mult(mult(i(C),D),rd(C,D)). [para(5565(a,1),424(a,1,2,1,1,2)),rewrite([9(4),37(3),184(15),38(16),4517(13),9(16),37(15),5682(16)])].
% 21.14/21.40 12774 mult(mult(mult(A,B),i(B)),i(A)) = asoc(A,B,i(B)). [para(175(a,1),11691(a,1,1)),rewrite([10917(4)])].
% 21.14/21.40 12775 mult(mult(mult(A,i(B)),B),i(A)) = asoc(A,i(B),B). [para(176(a,1),11691(a,1,1)),rewrite([10880(4)])].
% 21.14/21.40 12794 rd(mult(mult(A,B),i(B)),A) = asoc(A,B,i(B)). [back_rewrite(10917),rewrite([12774(9)])].
% 21.14/21.40 12795 rd(mult(mult(A,i(B)),B),A) = asoc(A,i(B),B). [back_rewrite(10880),rewrite([12775(9)])].
% 21.14/21.40 12803 mult(rd(A,B),mult(i(A),C)) = mult(A,mult(mult(i(A),i(B)),C)). [para(467(a,1),7(a,1,2)),rewrite([37(2)]),flip(a)].
% 21.14/21.40 12825 mult(mult(i(asoc(A,B,C)),i(D)),E) = mult(i(asoc(A,B,C)),mult(i(D),E)). [para(5558(a,1),467(a,1,2,1)),rewrite([3006(9),6643(6),6091(9)]),flip(a)].
% 21.14/21.40 12851 asoc(rd(A,B),B,C) = asoc(i(B),mult(B,A),C). [back_rewrite(5738),rewrite([12803(5),5739(8)]),flip(a)].
% 21.14/21.40 12878 asoc(mult(asoc(A,B,C),D),E,F) = asoc(D,E,F). [back_rewrite(6140),rewrite([12825(8),2981(13),9(9),37(5),9(7),37(5),37(5),5558(6),9(6),9(6),184(12),182(11),7(6)]),flip(a)].
% 21.14/21.40 12931 asoc(A,mult(asoc(B,C,D),i(A)),E) = unit. [back_rewrite(11811),rewrite([12878(4),461(2)]),flip(a)].
% 21.14/21.40 12982 asoc(rd(A,B),mult(asoc(C,D,i(D)),rd(B,A)),E) = unit. [back_rewrite(5042),rewrite([12878(10)])].
% 21.14/21.40 12992 asoc(mult(A,i(B)),rd(B,A),C) = unit. [back_rewrite(7393),rewrite([12982(6)]),flip(a)].
% 21.14/21.40 13097 asoc(A,rd(B,rd(A,i(B))),C) = unit. [para(6(a,1),12992(a,1,1))].
% 21.14/21.40 13100 mult(mult(mult(A,i(B)),rd(B,A)),C) = mult(mult(A,i(B)),mult(rd(B,A),C)). [para(12992(a,1),28(a,1,2)),rewrite([2(7)]),flip(a)].
% 21.14/21.40 13103 asoc(i(A),rd(B,rd(B,A)),C) = unit. [para(389(a,1),12992(a,1,1))].
% 21.14/21.40 13137 rd(mult(A,B),mult(mult(mult(C,i(D)),mult(rd(D,C),A)),B)) = mult(mult(i(C),D),rd(C,D)). [back_rewrite(12371),rewrite([13100(6)])].
% 21.14/21.40 13143 mult(mult(A,i(B)),rd(B,A)) = asoc(A,B,i(B)). [back_rewrite(11232),rewrite([13100(12),7706(11),744(9),4(4),2(4)]),flip(a)].
% 21.14/21.40 13151 mult(mult(A,i(B)),mult(rd(B,A),C)) = mult(asoc(A,B,i(B)),C). [back_rewrite(13100),rewrite([13143(4)]),flip(a)].
% 21.14/21.40 13154 mult(mult(i(A),B),rd(A,B)) = asoc(i(A),i(B),B). [back_rewrite(13137),rewrite([13151(6),184(5),38(6),4517(3)]),flip(a)].
% 21.14/21.40 13161 asoc(A,rd(rd(B,A),B),C) = unit. [para(530(a,1),13097(a,1,2)),rewrite([37(2),367(2)])].
% 21.14/21.40 13175 asoc(A,rd(B,mult(B,A)),C) = unit. [para(5(a,1),13161(a,1,2,1))].
% 21.14/21.40 13195 rd(A,rd(rd(B,A),B)) = mult(A,rd(B,rd(B,A))). [para(13161(a,1),4801(a,1,2)),rewrite([2(5),367(6)])].
% 21.14/21.40 13203 asoc(mult(i(A),B),rd(A,B),C) = unit. [para(357(a,1),13175(a,1,2,2))].
% 21.14/21.40 13389 asoc(rd(A,rd(A,B)),B,i(B)) = unit. [para(13103(a,1),5693(a,2)),rewrite([529(5),367(4),13195(4),8459(6)])].
% 21.14/21.40 13435 mult(mult(i(A),i(B)),B) = mult(mult(i(A),B),i(B)). [para(13203(a,1),476(a,1,2)),rewrite([2(6),13154(8),11738(9)]),flip(a)].
% 21.14/21.40 13492 mult(mult(mult(A,i(B)),B),A) = mult(mult(mult(A,B),i(B)),A). [back_rewrite(7949),rewrite([13435(4),7776(5)])].
% 21.14/21.40 13500 asoc(i(A),i(B),B) = asoc(i(A),B,i(B)). [back_rewrite(7580),rewrite([13435(4),7579(5)]),flip(a)].
% 21.14/21.40 13533 mult(mult(A,i(B)),B) = mult(mult(A,B),i(B)). [back_rewrite(10875),rewrite([13492(4),10894(6)]),flip(a)].
% 21.14/21.40 13606 asoc(rd(A,B),i(A),A) = asoc(i(B),A,i(A)). [back_rewrite(5051),rewrite([13500(6)])].
% 21.14/21.40 13645 asoc(A,i(B),B) = asoc(A,B,i(B)). [back_rewrite(12795),rewrite([13533(3),12794(4)]),flip(a)].
% 21.14/21.40 13813 asoc(rd(A,B),A,i(A)) = asoc(i(B),A,i(A)). [back_rewrite(13606),rewrite([13645(3)])].
% 21.14/21.40 13892 mult(rd(rd(A,B),A),B) = asoc(B,A,i(A)). [back_rewrite(7189),rewrite([13645(3),12851(3),8459(4)]),flip(a)].
% 21.14/21.40 13945 mult(rd(A,rd(A,B)),i(B)) = asoc(i(B),A,i(A)). [back_rewrite(7199),rewrite([13813(3)]),flip(a)].
% 21.14/21.40 14060 asoc(rd(A,rd(A,i(B))),B,i(B)) = unit. [para(37(a,1),13389(a,1,3)),rewrite([13645(5)])].
% 21.14/21.40 14085 asoc(rd(rd(A,B),A),B,i(B)) = unit. [para(1035(a,2),13389(a,1,1)),rewrite([37(2),37(5),13645(4)])].
% 21.14/21.40 14100 rd(A,rd(B,rd(B,A))) = asoc(A,B,i(B)). [para(13389(a,1),5565(a,1,1)),rewrite([367(4),13892(4),1(4)]),flip(a)].
% 21.14/21.40 14108 asoc(mult(A,B),A,i(A)) = asoc(A,B,A). [para(13645(a,1),5815(a,1)),rewrite([5693(5)])].
% 21.14/21.40 14364 mult(asoc(i(A),B,i(B)),A) = rd(B,rd(B,A)). [para(14085(a,1),185(a,1,2,1)),rewrite([367(3),37(5),4(4),2(4),32(4),2(4),367(5),13945(6),37(7)]),flip(a)].
% 21.14/21.40 14403 asoc(i(A),mult(asoc(B,C,D),A),E) = unit. [para(37(a,1),12931(a,1,2,2))].
% 21.14/21.40 14607 rd(rd(A,i(B)),A) = rd(A,rd(A,B)). [para(14060(a,1),185(a,1,2,1)),rewrite([367(4),37(6),4(5),2(5),32(5),2(5),367(7),13892(8),37(8),14364(7)])].
% 21.14/21.40 14843 asoc(i(A),mult(A,asoc(B,C,D)),E) = unit. [para(10428(a,1),14403(a,1,2))].
% 21.14/21.40 14876 rd(rd(A,B),A) = rd(A,rd(A,i(B))). [para(37(a,1),14607(a,1,1,2))].
% 21.14/21.40 14879 rd(i(A),rd(i(A),B)) = rd(A,rd(A,B)). [para(14607(a,1),529(a,1)),rewrite([529(7),37(6),367(6)])].
% 21.14/21.40 14977 mult(rd(A,rd(A,i(B))),B) = asoc(B,A,i(A)). [back_rewrite(13892),rewrite([14876(2)])].
% 21.14/21.40 15094 asoc(rd(A,B),mult(B,i(A)),C) = unit. [para(4801(a,1),14843(a,1,2)),rewrite([367(2)])].
% 21.14/21.40 15112 asoc(rd(A,rd(A,i(B))),B,C) = unit. [para(6(a,1),15094(a,1,2)),rewrite([529(2)])].
% 21.14/21.40 15177 mult(asoc(A,B,i(B)),mult(i(A),C)) = mult(rd(B,rd(B,i(A))),C). [para(15112(a,1),404(a,1,2)),rewrite([2(6),14977(8)]),flip(a)].
% 21.14/21.40 15189 mult(rd(A,rd(B,i(A))),A) = rd(A,B). [back_rewrite(5565),rewrite([15177(5),529(2)])].
% 21.14/21.40 15674 rd(A,mult(B,i(A))) = mult(rd(A,B),A). [para(5(a,1),15189(a,1,1,2)),flip(a)].
% 21.14/21.40 15719 mult(i(A),mult(rd(A,B),rd(A,rd(A,B)))) = asoc(A,B,i(A)). [back_rewrite(5816),rewrite([15674(4),2749(5)])].
% 21.14/21.40 15819 rd(mult(A,i(B)),B) = mult(rd(A,B),i(B)). [para(15674(a,1),367(a,1,1)),rewrite([9(3),367(2)]),flip(a)].
% 21.14/21.40 15928 mult(A,mult(rd(i(A),B),rd(A,rd(A,B)))) = asoc(i(A),B,A). [back_rewrite(5821),rewrite([15819(4),530(2),3017(7),14879(6)])].
% 21.14/21.40 16241 mult(asoc(A,B,i(B)),rd(B,rd(B,A))) = A. [para(14100(a,1),6(a,1,1))].
% 21.14/21.40 17062 mult(asoc(A,B,i(B)),B) = mult(A,rd(B,A)). [para(16241(a,1),180(a,2,1)),rewrite([8(9),2(5)])].
% 21.14/21.40 17087 mult(i(A),mult(B,rd(A,B))) = asoc(B,A,i(A)). [para(17062(a,1),10(a,2,2)),rewrite([10(3),11693(5)]),flip(a)].
% 21.14/21.40 17260 asoc(A,B,i(B)) = asoc(B,A,B). [para(17062(a,2),14108(a,1,1)),rewrite([12878(5),5693(4)])].
% 21.14/21.40 17293 mult(rd(i(A),B),rd(A,rd(A,B))) = mult(asoc(i(B),A,i(A)),i(A)). [para(14879(a,1),17062(a,2,2)),rewrite([37(5),13645(4),4531(4)]),flip(a)].
% 21.14/21.40 17304 asoc(i(A),B,i(B)) = asoc(B,A,i(B)). [back_rewrite(15719),rewrite([17087(6),13813(3)])].
% 21.14/21.40 17314 asoc(i(A),B,i(B)) = asoc(i(B),A,B). [back_rewrite(15928),rewrite([17293(5),11706(6)])].
% 21.14/21.40 17355 mult(rd(A,B),asoc(B,A,B)) = mult(A,i(B)). [para(17260(a,1),4801(a,1,2))].
% 21.14/21.40 17706 asoc(A,i(B),A) = asoc(A,B,i(A)). [para(17304(a,1),17260(a,1)),flip(a)].
% 21.14/21.40 17810 asoc(i(A),rd(A,B),i(A)) = asoc(i(A),B,A). [back_rewrite(5874),rewrite([17706(8),37(7)])].
% 21.14/21.40 17867 asoc(A,i(B),i(A)) = asoc(A,B,A). [para(37(a,1),17706(a,1,2)),flip(a)].
% 21.14/21.40 17938 asoc(i(A),i(B),A) = asoc(i(A),B,i(A)). [para(37(a,1),17867(a,1,3))].
% 21.14/21.40 18067 asoc(i(A),B,A) = asoc(A,B,i(A)). [para(17314(a,1),17260(a,1)),rewrite([17706(4)])].
% 21.14/21.40 18077 asoc(i(A),B,i(A)) = asoc(A,B,A). [back_rewrite(17938),rewrite([18067(3),17867(3)]),flip(a)].
% 21.14/21.40 18084 asoc(A,rd(A,B),A) = asoc(A,B,i(A)). [back_rewrite(17810),rewrite([18077(4),18067(4)])].
% 21.14/21.40 18771 asoc(A,mult(i(B),C),A) = asoc(A,mult(B,i(C)),i(A)). [para(1793(a,1),18084(a,1,2)),rewrite([18077(6),5693(4),37(8),18067(7)])].
% 21.14/21.40 18808 asoc(mult(mult(A,B),C),mult(A,mult(B,C)),mult(mult(i(A),i(B)),i(C))) = unit. [back_rewrite(11955),rewrite([18771(10),9(6),37(4),37(4),9(7),9(6)])].
% 21.14/21.40 19605 mult(rd(A,i(B)),asoc(B,A,B)) = mult(A,B). [para(37(a,1),17355(a,2,2)),rewrite([18077(5)])].
% 21.14/21.40 20832 rd(mult(i(A),mult(i(B),i(C))),mult(mult(i(A),i(B)),i(C))) = asoc(A,B,C). [para(182(a,1),19605(a,2)),rewrite([9(8),9(7),18771(21),9(17),37(15),37(15),9(18),9(17),18808(21),2(13)])].
% 21.14/21.40 27809 rd(mult(A,mult(B,C)),mult(mult(A,B),C)) = i(asoc(A,B,C)). [para(28(a,1),11705(a,1,2))].
% 21.14/21.40 27820 i(asoc(i(A),i(B),i(C))) = asoc(A,B,C). [back_rewrite(20832),rewrite([27809(11)])].
% 21.14/21.40 27827 i(asoc(A,B,C)) = asoc(i(A),i(B),i(C)). [para(27820(a,1),37(a,1,1))].
% 21.14/21.40 27848 asoc(A,asoc(B,C,D),E) = unit. [para(27820(a,1),5815(a,1,2)),rewrite([12878(7),6643(11),27827(11),37(8),37(8),37(8),8(9)])].
% 21.14/21.40 27931 mult(asoc(A,B,C),mult(rd(D,mult(asoc(A,B,C),E)),E)) = D. [back_rewrite(11786),rewrite([27848(5),2(2)]),flip(a)].
% 21.14/21.40 27932 mult(asoc(A,B,C),mult(rd(D,mult(E,asoc(A,B,C))),E)) = D. [back_rewrite(11788),rewrite([27931(6)]),flip(a)].
% 21.14/21.40 27933 mult(A,asoc(rd(A,mult(asoc(B,C,D),E)),E,asoc(B,C,D))) = A. [back_rewrite(11952),rewrite([27932(12)])].
% 21.14/21.40 28760 rd(A,mult(asoc(B,C,D),E)) = mult(asoc(i(B),i(C),i(D)),rd(A,E)). [para(12878(a,1),7720(a,1,2)),rewrite([9(3),27827(2),184(7),184(10),7720(9)]),flip(a)].
% 21.14/21.40 28986 mult(A,asoc(i(B),mult(B,A),asoc(C,D,E))) = A. [back_rewrite(27933),rewrite([28760(3),12878(8),12851(3)])].
% 21.14/21.40 35799 asoc(i(A),mult(A,B),asoc(C,D,E)) = unit. [para(28986(a,1),7(a,1,2)),rewrite([4(2)]),flip(a)].
% 21.14/21.40 35809 asoc(A,B,asoc(C,D,E)) = unit. [para(7(a,1),35799(a,1,2)),rewrite([37(2)])].
% 21.14/21.40 35810 $F # answer(goals). [resolve(35809,a,29,a)].
% 21.14/21.40
% 21.14/21.40 % SZS output end Refutation
% 21.14/21.40 ============================== end of proof ==========================
% 21.14/21.40
% 21.14/21.40 ============================== STATISTICS ============================
% 21.14/21.40
% 21.14/21.40 Given=1385. Generated=651257. Kept=35801. proofs=1.
% 21.14/21.40 Usable=829. Sos=9559. Demods=9471. Limbo=0, Disabled=25433. Hints=0.
% 21.14/21.40 Megabytes=35.95.
% 21.14/21.40 User_CPU=20.05, System_CPU=0.38, Wall_clock=20.
% 21.14/21.40
% 21.14/21.40 ============================== end of statistics =====================
% 21.14/21.40
% 21.14/21.40 ============================== end of search =========================
% 21.14/21.40
% 21.14/21.40 THEOREM PROVED
% 21.14/21.40 % SZS status Unsatisfiable
% 21.14/21.40
% 21.14/21.40 Exiting with 1 proof.
% 21.14/21.40
% 21.14/21.40 Process 9642 exit (max_proofs) Mon Jun 13 22:52:47 2022
% 21.14/21.40 Prover9 interrupted
%------------------------------------------------------------------------------