TSTP Solution File: GRP667+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP667+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 : Theorem 6.23s 6.57s
% Output : Refutation 6.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 13:24:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.00 ============================== Prover9 ===============================
% 0.44/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.00 Process 15036 was started by sandbox2 on n017.cluster.edu,
% 0.44/1.00 Mon Jun 13 13:24:53 2022
% 0.44/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14883_n017.cluster.edu".
% 0.44/1.00 ============================== end of head ===========================
% 0.44/1.00
% 0.44/1.00 ============================== INPUT =================================
% 0.44/1.00
% 0.44/1.00 % Reading from file /tmp/Prover9_14883_n017.cluster.edu
% 0.44/1.00
% 0.44/1.00 set(prolog_style_variables).
% 0.44/1.00 set(auto2).
% 0.44/1.00 % set(auto2) -> set(auto).
% 0.44/1.00 % set(auto) -> set(auto_inference).
% 0.44/1.00 % set(auto) -> set(auto_setup).
% 0.44/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.00 % set(auto) -> set(auto_limits).
% 0.44/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.00 % set(auto) -> set(auto_denials).
% 0.44/1.00 % set(auto) -> set(auto_process).
% 0.44/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.00 % set(auto2) -> assign(stats, some).
% 0.44/1.00 % set(auto2) -> clear(echo_input).
% 0.44/1.00 % set(auto2) -> set(quiet).
% 0.44/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.00 % set(auto2) -> clear(print_given).
% 0.44/1.00 assign(lrs_ticks,-1).
% 0.44/1.00 assign(sos_limit,10000).
% 0.44/1.00 assign(order,kbo).
% 0.44/1.00 set(lex_order_vars).
% 0.44/1.00 clear(print_given).
% 0.44/1.00
% 0.44/1.00 % formulas(sos). % not echoed (13 formulas)
% 0.44/1.00
% 0.44/1.00 ============================== end of input ==========================
% 0.44/1.00
% 0.44/1.00 % From the command line: assign(max_seconds, 300).
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.00
% 0.44/1.00 % Formulas that are not ordinary clauses:
% 0.44/1.00 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 10 (all X0 all X1 all X2 (mult(X0,mult(X1,mult(X2,X1))) = mult(mult(mult(X0,X1),X2),X1) -> mult(X1,mult(X0,mult(X1,X2))) = mult(mult(mult(X1,X0),X1),X2))) # label(f10) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 11 (all X3 all X4 all X5 (mult(mult(X3,X4),mult(X5,X3)) = mult(mult(X3,mult(X4,X5)),X3) -> mult(X3,mult(X4,mult(X3,X5))) = mult(mult(mult(X3,X4),X3),X5))) # label(f11) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00 12 (all X6 all X7 all X8 (mult(mult(X6,X7),mult(X8,X6)) = mult(X6,mult(mult(X7,X8),X6)) -> mult(X6,mult(X7,mult(X6,X8))) = mult(mult(mult(X6,X7),X6),X8))) # label(f12) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.00
% 0.44/1.00 ============================== end of process non-clausal formulas ===
% 0.44/1.00
% 0.44/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.00
% 0.44/1.00 ============================== PREDICATE ELIMINATION =================
% 0.44/1.00
% 0.44/1.00 ============================== end predicate elimination =============
% 0.44/1.00
% 0.44/1.00 Auto_denials:
% 0.44/1.00 % copying label goals to answer in negative clause
% 6.23/6.57
% 6.23/6.57 Term ordering decisions:
% 6.23/6.57
% 6.23/6.57 % Assigning unary symbol f kb_weight 0 and highest precedence (9).
% 6.23/6.57 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. f=0.
% 6.23/6.57
% 6.23/6.57 ============================== end of process initial clauses ========
% 6.23/6.57
% 6.23/6.57 ============================== CLAUSES FOR SEARCH ====================
% 6.23/6.57
% 6.23/6.57 ============================== end of clauses for search =============
% 6.23/6.57
% 6.23/6.57 ============================== SEARCH ================================
% 6.23/6.57
% 6.23/6.57 % Starting search at 0.01 seconds.
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=110.000, iters=3410
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=102.000, iters=3426
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=94.000, iters=3378
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=90.000, iters=3363
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=86.000, iters=3460
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=82.000, iters=3350
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=78.000, iters=3411
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=74.000, iters=3333
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=70.000, iters=3337
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=68.000, iters=3356
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=67.000, iters=3341
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=66.000, iters=3342
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=64.000, iters=3357
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=62.000, iters=3411
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=60.000, iters=3345
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=59.000, iters=3405
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=58.000, iters=3378
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=57.000, iters=3400
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=56.000, iters=3382
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=54.000, iters=3376
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=50.000, iters=3333
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=48.000, iters=3397
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=47.000, iters=3371
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=46.000, iters=3348
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=45.000, iters=3339
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=43.000, iters=3346
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=41.000, iters=3367
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=39.000, iters=3425
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=38.000, iters=3347
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=37.000, iters=3334
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=35.000, iters=3333
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=33.000, iters=3358
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=31.000, iters=3341
% 6.23/6.57
% 6.23/6.57 Low Water (displace): id=8811, wt=198.000
% 6.23/6.57
% 6.23/6.57 Low Water (displace): id=15233, wt=27.000
% 6.23/6.57
% 6.23/6.57 Low Water (displace): id=15237, wt=21.000
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=29.000, iters=3372
% 6.23/6.57
% 6.23/6.57 Low Water (displace): id=15505, wt=19.000
% 6.23/6.57
% 6.23/6.57 Low Water (displace): id=15695, wt=17.000
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=27.000, iters=3341
% 6.23/6.57
% 6.23/6.57 Low Water (keep): wt=25.000, iters=3358
% 6.23/6.57
% 6.23/6.57 ============================== PROOF =================================
% 6.23/6.57 % SZS status Theorem
% 6.23/6.57 % SZS output start Refutation
% 6.23/6.57
% 6.23/6.57 % Proof 1 at 5.52 (+ 0.06) seconds: goals.
% 6.23/6.57 % Length of proof is 103.
% 6.23/6.57 % Level of proof is 21.
% 6.23/6.57 % Maximum clause weight is 38.000.
% 6.23/6.57 % Given clauses 438.
% 6.23/6.57
% 6.23/6.57 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 10 (all X0 all X1 all X2 (mult(X0,mult(X1,mult(X2,X1))) = mult(mult(mult(X0,X1),X2),X1) -> mult(X1,mult(X0,mult(X1,X2))) = mult(mult(mult(X1,X0),X1),X2))) # label(f10) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 11 (all X3 all X4 all X5 (mult(mult(X3,X4),mult(X5,X3)) = mult(mult(X3,mult(X4,X5)),X3) -> mult(X3,mult(X4,mult(X3,X5))) = mult(mult(mult(X3,X4),X3),X5))) # label(f11) # label(axiom) # label(non_clause). [assumption].
% 6.23/6.57 13 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)].
% 6.23/6.57 14 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 6.23/6.57 15 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 6.23/6.57 16 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 6.23/6.57 17 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 6.23/6.57 18 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 6.23/6.57 19 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(9)].
% 6.23/6.57 20 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(8)].
% 6.23/6.57 21 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(7)].
% 6.23/6.57 22 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(21),rewrite([20(2),20(7)])].
% 6.23/6.57 23 mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 6.23/6.57 24 mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))) # answer(goals). [copy(23),rewrite([20(12)]),flip(a)].
% 6.23/6.57 25 mult(mult(mult(A,B),C),B) != mult(A,mult(B,mult(C,B))) | mult(mult(mult(B,A),B),C) = mult(B,mult(A,mult(B,C))) # label(f10) # label(axiom). [clausify(10)].
% 6.23/6.57 26 mult(mult(mult(A,B),C),B) != mult(A,mult(B,mult(C,B))) | mult(mult(B,mult(A,B)),C) = mult(B,mult(A,mult(B,C))). [copy(25),rewrite([20(9)])].
% 6.23/6.57 27 mult(mult(A,mult(B,C)),A) != mult(mult(A,B),mult(C,A)) | mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f11) # label(axiom). [clausify(11)].
% 6.23/6.57 28 mult(mult(A,B),mult(C,A)) != mult(A,mult(mult(B,C),A)) | mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [copy(27),rewrite([20(3),20(9)]),flip(a)].
% 6.23/6.57 31 ld(A,A) = unit. [para(13(a,1),16(a,1,2))].
% 6.23/6.57 33 ld(rd(A,B),A) = B. [para(17(a,1),16(a,1,2))].
% 6.23/6.57 35 rd(A,ld(B,A)) = B. [para(15(a,1),18(a,1,1))].
% 6.23/6.57 38 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(15(a,1),20(a,1,1)),flip(a)].
% 6.23/6.57 40 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(17(a,1),20(a,1,1)),flip(a)].
% 6.23/6.57 41 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(20(a,1),18(a,1,1))].
% 6.23/6.57 42 mult(f(A),A) = mult(A,f(A)). [para(19(a,1),20(a,1,1)),rewrite([19(6)]),flip(a)].
% 6.23/6.57 44 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(22(a,1),13(a,1)),rewrite([13(4),14(3),14(4)])].
% 6.23/6.57 45 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(14(a,1),22(a,1,1)),rewrite([14(5)])].
% 6.23/6.57 47 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(15(a,1),22(a,2,2,2)),rewrite([38(3)])].
% 6.23/6.57 50 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(17(a,1),22(a,1,1)),flip(a)].
% 6.23/6.57 62 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(14(a,1),26(a,1,1,1)),rewrite([20(2),14(6),14(7),14(10)]),xx(a)].
% 6.23/6.57 66 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). [para(17(a,1),26(a,1,1,1)),rewrite([17(9)]),flip(a),flip(b)].
% 6.23/6.57 78 mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)) # answer(goals). [ur(28,b,24,a)].
% 6.23/6.57 86 mult(f(A),mult(f(A),mult(B,f(A)))) != mult(A,mult(B,f(A))) | mult(f(A),mult(f(A),mult(f(A),B))) = mult(mult(A,f(A)),B). [para(19(a,1),28(a,1,1)),rewrite([20(8),19(14),42(12)]),flip(a),flip(b)].
% 6.23/6.57 97 rd(mult(A,f(A)),A) = f(A). [para(42(a,1),18(a,1,1))].
% 6.23/6.57 108 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(38(a,1),16(a,1,2))].
% 6.23/6.57 110 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(38(a,1),20(a,1,1)),rewrite([44(2),44(5)]),flip(a)].
% 6.23/6.57 133 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(17(a,1),41(a,1,1,2))].
% 6.23/6.57 136 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(38(a,1),41(a,2)),rewrite([44(3),110(4)])].
% 6.23/6.57 137 mult(A,rd(f(A),A)) = f(A). [back_rewrite(97),rewrite([133(3)])].
% 6.23/6.57 138 rd(f(A),A) = ld(A,f(A)). [para(137(a,1),16(a,1,2)),flip(a)].
% 6.23/6.57 139 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(ld(B,f(B)),f(B))). [para(137(a,1),22(a,2,2,2)),rewrite([138(2),38(4),42(2),138(5),138(9)])].
% 6.23/6.57 154 mult(ld(A,f(A)),A) = f(A). [para(138(a,1),17(a,1,1))].
% 6.23/6.57 156 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(138(a,1),40(a,1,1)),rewrite([138(4),15(5),138(7)])].
% 6.23/6.57 157 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(mult(A,B),mult(f(B),ld(B,f(B)))). [back_rewrite(139),rewrite([156(11)])].
% 6.23/6.57 216 mult(A,mult(A,ld(mult(A,A),B))) = B. [para(62(a,1),15(a,1))].
% 6.23/6.57 218 rd(mult(A,mult(A,B)),B) = mult(A,A). [para(62(a,1),18(a,1,1))].
% 6.23/6.57 219 mult(f(A),mult(f(A),B)) = mult(A,B). [para(19(a,1),62(a,1,1)),flip(a)].
% 6.23/6.57 238 mult(mult(A,f(A)),B) = mult(f(A),mult(A,B)). [back_rewrite(86),rewrite([219(6),219(12)]),flip(b),xx(a)].
% 6.23/6.57 259 mult(ld(A,unit),A) = unit. [para(14(a,1),108(a,1,2)),rewrite([31(1)]),flip(a)].
% 6.23/6.57 271 rd(unit,A) = ld(A,unit). [para(259(a,1),18(a,1,1))].
% 6.23/6.57 279 mult(ld(A,unit),mult(A,A)) = A. [para(259(a,1),44(a,1,1)),rewrite([14(2)]),flip(a)].
% 6.23/6.57 285 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(17(a,1),45(a,2,2,2)),rewrite([40(4)])].
% 6.23/6.57 348 ld(ld(A,unit),A) = mult(A,A). [para(279(a,1),16(a,1,2))].
% 6.23/6.57 349 rd(A,mult(A,A)) = ld(A,unit). [para(279(a,1),18(a,1,1))].
% 6.23/6.57 350 mult(ld(f(A),unit),A) = f(A). [para(19(a,1),279(a,1,2))].
% 6.23/6.57 362 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(33(a,1),348(a,1,1)),rewrite([271(2),271(5),271(7)]),flip(a)].
% 6.23/6.57 396 ld(f(A),unit) = ld(A,f(A)). [para(19(a,1),349(a,1,2)),rewrite([138(2)]),flip(a)].
% 6.23/6.57 401 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(350(a,1),20(a,1,1)),rewrite([15(5)]),flip(a)].
% 6.23/6.57 414 mult(ld(f(A),unit),mult(A,f(A))) = A. [para(350(a,1),45(a,2,2,2)),rewrite([401(8),14(2)]),flip(a)].
% 6.23/6.57 415 mult(f(A),ld(A,f(A))) = unit. [para(396(a,1),15(a,1,2))].
% 6.23/6.57 417 ld(ld(A,f(A)),unit) = f(A). [para(396(a,1),35(a,1,2)),rewrite([271(4)])].
% 6.23/6.57 423 mult(mult(A,mult(B,f(B))),ld(B,f(B))) = mult(A,B). [back_rewrite(157),rewrite([415(11),13(9)])].
% 6.23/6.57 424 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(156),rewrite([415(8)])].
% 6.23/6.57 492 mult(ld(A,f(A)),ld(A,f(A))) = ld(f(A),ld(A,f(A))). [para(417(a,1),348(a,1,1)),flip(a)].
% 6.23/6.57 498 mult(ld(f(A),ld(A,f(A))),f(A)) = ld(A,f(A)). [para(424(a,1),62(a,2,2)),rewrite([492(5),13(10)])].
% 6.23/6.57 677 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(17(a,1),136(a,1,1)),flip(a)].
% 6.23/6.57 781 mult(A,ld(mult(A,A),B)) = ld(A,B). [para(216(a,1),16(a,1,2)),flip(a)].
% 6.23/6.57 792 rd(mult(A,B),ld(A,B)) = mult(A,A). [para(15(a,1),218(a,1,1,2))].
% 6.23/6.57 798 ld(f(A),ld(A,f(A))) = ld(A,unit). [para(154(a,1),218(a,1,1,2)),rewrite([424(4),271(2),492(7)]),flip(a)].
% 6.23/6.57 805 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(350(a,1),218(a,1,1,2)),rewrite([259(5),271(2),362(9)]),flip(a)].
% 6.23/6.57 827 mult(ld(A,unit),f(A)) = ld(A,f(A)). [back_rewrite(498),rewrite([798(4)])].
% 6.23/6.57 837 mult(A,ld(f(A),B)) = mult(f(A),B). [para(15(a,1),219(a,1,2)),flip(a)].
% 6.23/6.57 854 mult(f(A),mult(A,B)) = mult(A,mult(f(A),B)). [para(219(a,1),62(a,2,2)),rewrite([19(3)]),flip(a)].
% 6.23/6.57 890 mult(mult(A,f(A)),B) = mult(A,mult(f(A),B)). [back_rewrite(238),rewrite([854(6)])].
% 6.23/6.57 1095 mult(ld(A,unit),mult(A,f(A))) = f(A). [para(414(a,1),62(a,2,2)),rewrite([362(7),805(5),350(9)])].
% 6.23/6.57 1637 mult(f(A),ld(A,B)) = ld(f(A),B). [para(19(a,1),781(a,1,2,1))].
% 6.23/6.57 2505 mult(A,ld(B,unit)) = rd(A,B). [para(1095(a,1),50(a,1,1,1,2,2)),rewrite([44(4),19(3),890(12),1637(11),837(11),13(10),827(9),423(8),677(3)]),flip(a)].
% 6.23/6.57 2836 ld(A,rd(A,B)) = ld(B,unit). [para(2505(a,1),16(a,1,2))].
% 6.23/6.57 2848 rd(A,ld(B,unit)) = mult(A,B). [para(33(a,1),2505(a,1,2)),rewrite([271(3)]),flip(a)].
% 6.23/6.57 2860 mult(mult(A,rd(B,C)),ld(ld(C,unit),B)) = mult(rd(A,C),mult(ld(ld(C,unit),B),B)). [para(2505(a,1),47(a,1,1,2)),rewrite([2505(9)])].
% 6.23/6.57 2869 mult(rd(A,B),mult(B,A)) = mult(A,A). [para(2505(a,1),218(a,1,1,2)),rewrite([2848(5),285(3)])].
% 6.23/6.57 2870 mult(f(A),rd(f(A),B)) = rd(A,B). [para(2505(a,1),219(a,1,2)),rewrite([2505(7)])].
% 6.23/6.57 2955 ld(ld(A,B),unit) = ld(B,A). [para(35(a,1),2836(a,1,2)),flip(a)].
% 6.23/6.57 2962 ld(mult(A,B),mult(A,A)) = ld(B,A). [para(792(a,1),2836(a,1,2)),rewrite([2955(6)])].
% 6.23/6.57 3242 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)). [para(44(a,1),66(a,1,2,2))].
% 6.23/6.57 3947 ld(rd(A,B),mult(A,A)) = mult(B,A). [para(2869(a,1),16(a,1,2))].
% 6.23/6.57 4214 mult(mult(A,rd(f(B),C)),mult(C,f(B))) = mult(mult(A,rd(B,C)),C). [para(2870(a,1),47(a,1,1,2)),rewrite([33(6),33(10)]),flip(a)].
% 6.23/6.57 4525 ld(ld(A,unit),B) = mult(A,B). [para(2505(a,1),2962(a,1,1)),rewrite([3947(3)]),flip(a)].
% 6.23/6.57 4554 mult(mult(A,rd(B,C)),mult(C,B)) = mult(rd(A,C),mult(C,mult(B,B))). [back_rewrite(2860),rewrite([4525(5),4525(8),44(7)])].
% 6.23/6.57 4570 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [back_rewrite(4214),rewrite([4554(6),19(4)]),flip(a)].
% 6.23/6.57 20237 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(18(a,1),4570(a,1,1,2)),flip(a)].
% 6.23/6.57 20250 mult(rd(A,B),mult(B,mult(C,mult(B,B)))) = mult(mult(A,mult(C,B)),B). [para(136(a,1),4570(a,1,1,2)),flip(a)].
% 6.23/6.57 20398 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [back_rewrite(3242),rewrite([20250(5),20237(11)]),flip(b),xx(a)].
% 6.23/6.57 20399 $F # answer(goals). [resolve(20398,a,78,a)].
% 6.23/6.57
% 6.23/6.57 % SZS output end Refutation
% 6.23/6.57 ============================== end of proof ==========================
% 6.23/6.57
% 6.23/6.57 ============================== STATISTICS ============================
% 6.23/6.57
% 6.23/6.57 Given=438. Generated=110975. Kept=20381. proofs=1.
% 6.23/6.57 Usable=354. Sos=9932. Demods=8194. Limbo=161, Disabled=9946. Hints=0.
% 6.23/6.57 Megabytes=25.85.
% 6.23/6.57 User_CPU=5.52, System_CPU=0.06, Wall_clock=6.
% 6.23/6.57
% 6.23/6.57 ============================== end of statistics =====================
% 6.23/6.57
% 6.23/6.57 ============================== end of search =========================
% 6.23/6.57
% 6.23/6.57 THEOREM PROVED
% 6.23/6.57 % SZS status Theorem
% 6.23/6.57
% 6.23/6.57 Exiting with 1 proof.
% 6.23/6.57
% 6.23/6.57 Process 15036 exit (max_proofs) Mon Jun 13 13:24:59 2022
% 6.23/6.57 Prover9 interrupted
%------------------------------------------------------------------------------