TSTP Solution File: GRP667-5 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP667-5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:20:29 EDT 2022
% Result : Unsatisfiable 35.70s 36.00s
% Output : Refutation 35.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667-5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.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 07:17:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.96/4.25 ============================== Prover9 ===============================
% 3.96/4.25 Prover9 (32) version 2009-11A, November 2009.
% 3.96/4.25 Process 14498 was started by sandbox2 on n026.cluster.edu,
% 3.96/4.25 Mon Jun 13 07:17:51 2022
% 3.96/4.25 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14089_n026.cluster.edu".
% 3.96/4.25 ============================== end of head ===========================
% 3.96/4.25
% 3.96/4.25 ============================== INPUT =================================
% 3.96/4.25
% 3.96/4.25 % Reading from file /tmp/Prover9_14089_n026.cluster.edu
% 3.96/4.25
% 3.96/4.25 set(prolog_style_variables).
% 3.96/4.25 set(auto2).
% 3.96/4.25 % set(auto2) -> set(auto).
% 3.96/4.25 % set(auto) -> set(auto_inference).
% 3.96/4.25 % set(auto) -> set(auto_setup).
% 3.96/4.25 % set(auto_setup) -> set(predicate_elim).
% 3.96/4.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.96/4.25 % set(auto) -> set(auto_limits).
% 3.96/4.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.96/4.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.96/4.25 % set(auto) -> set(auto_denials).
% 3.96/4.25 % set(auto) -> set(auto_process).
% 3.96/4.25 % set(auto2) -> assign(new_constants, 1).
% 3.96/4.25 % set(auto2) -> assign(fold_denial_max, 3).
% 3.96/4.25 % set(auto2) -> assign(max_weight, "200.000").
% 3.96/4.25 % set(auto2) -> assign(max_hours, 1).
% 3.96/4.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.96/4.25 % set(auto2) -> assign(max_seconds, 0).
% 3.96/4.25 % set(auto2) -> assign(max_minutes, 5).
% 3.96/4.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.96/4.25 % set(auto2) -> set(sort_initial_sos).
% 3.96/4.25 % set(auto2) -> assign(sos_limit, -1).
% 3.96/4.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.96/4.25 % set(auto2) -> assign(max_megs, 400).
% 3.96/4.25 % set(auto2) -> assign(stats, some).
% 3.96/4.25 % set(auto2) -> clear(echo_input).
% 3.96/4.25 % set(auto2) -> set(quiet).
% 3.96/4.25 % set(auto2) -> clear(print_initial_clauses).
% 3.96/4.25 % set(auto2) -> clear(print_given).
% 3.96/4.25 assign(lrs_ticks,-1).
% 3.96/4.25 assign(sos_limit,10000).
% 3.96/4.25 assign(order,kbo).
% 3.96/4.25 set(lex_order_vars).
% 3.96/4.25 clear(print_given).
% 3.96/4.25
% 3.96/4.25 % formulas(sos). % not echoed (10 formulas)
% 3.96/4.25
% 3.96/4.25 ============================== end of input ==========================
% 3.96/4.25
% 3.96/4.25 % From the command line: assign(max_seconds, 300).
% 3.96/4.25
% 3.96/4.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.96/4.25
% 3.96/4.25 % Formulas that are not ordinary clauses:
% 3.96/4.25
% 3.96/4.25 ============================== end of process non-clausal formulas ===
% 3.96/4.25
% 3.96/4.25 ============================== PROCESS INITIAL CLAUSES ===============
% 3.96/4.25
% 3.96/4.25 ============================== PREDICATE ELIMINATION =================
% 3.96/4.25
% 3.96/4.25 ============================== end predicate elimination =============
% 3.96/4.25
% 3.96/4.25 Auto_denials:
% 3.96/4.25 % copying label goals to answer in negative clause
% 3.96/4.25
% 3.96/4.25 Term ordering decisions:
% 3.96/4.25
% 3.96/4.25 % Assigning unary symbol f kb_weight 0 and highest precedence (9).
% 3.96/4.25 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. f=0.
% 3.96/4.25
% 3.96/4.25 ============================== end of process initial clauses ========
% 3.96/4.25
% 3.96/4.25 ============================== CLAUSES FOR SEARCH ====================
% 3.96/4.25
% 3.96/4.25 ============================== end of clauses for search =============
% 3.96/4.25
% 3.96/4.25 ============================== SEARCH ================================
% 3.96/4.25
% 3.96/4.25 % Starting search at 0.01 seconds.
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=107.000, iters=3376
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=103.000, iters=3356
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=99.000, iters=3342
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=91.000, iters=3538
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=71.000, iters=3341
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=67.000, iters=3456
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=63.000, iters=3361
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=59.000, iters=3352
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=55.000, iters=3354
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=51.000, iters=3365
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=49.000, iters=3356
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=47.000, iters=3361
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=45.000, iters=3335
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=43.000, iters=3345
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=41.000, iters=3349
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=39.000, iters=3341
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=37.000, iters=3347
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=35.000, iters=3351
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=33.000, iters=3348
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=31.000, iters=3351
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=29.000, iters=3350
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=27.000, iters=3359
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=25.000, iters=3341
% 3.96/4.25
% 3.96/4.25 Low Water (displace): id=8759, wt=191.000
% 3.96/4.25
% 3.96/4.25 Low Water (displace): id=8750, wt=187.000
% 3.96/4.25
% 3.96/4.25 Low Water (displace): id=16620, wt=22.000
% 3.96/4.25
% 3.96/4.25 Low Water (displace): id=16623, wt=19.000
% 35.70/36.00
% 35.70/36.00 Low Water (displace): id=17449, wt=17.000
% 35.70/36.00
% 35.70/36.00 Low Water (keep): wt=23.000, iters=3337
% 35.70/36.00
% 35.70/36.00 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 5.45 sec).
% 35.70/36.00
% 35.70/36.00 Low Water (keep): wt=22.000, iters=3343
% 35.70/36.00
% 35.70/36.00 Low Water (keep): wt=21.000, iters=3343
% 35.70/36.00
% 35.70/36.00 Low Water (displace): id=23016, wt=15.000
% 35.70/36.00
% 35.70/36.00 ============================== PROOF =================================
% 35.70/36.00 % SZS status Unsatisfiable
% 35.70/36.00 % SZS output start Refutation
% 35.70/36.00
% 35.70/36.00 % Proof 1 at 34.36 (+ 0.54) seconds: goals.
% 35.70/36.00 % Length of proof is 113.
% 35.70/36.00 % Level of proof is 24.
% 35.70/36.00 % Maximum clause weight is 29.000.
% 35.70/36.00 % Given clauses 1002.
% 35.70/36.00
% 35.70/36.00 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 35.70/36.00 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 35.70/36.00 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 35.70/36.00 4 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 35.70/36.00 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 35.70/36.00 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 35.70/36.00 7 mult(f(A),f(A)) = A # label(c09) # label(axiom). [assumption].
% 35.70/36.00 8 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(c08) # label(axiom). [assumption].
% 35.70/36.00 9 mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C) # label(c07) # label(axiom). [assumption].
% 35.70/36.00 10 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(9),rewrite([8(3),8(6)]),flip(a)].
% 35.70/36.00 11 mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 35.70/36.00 13 ld(A,A) = unit. [para(1(a,1),4(a,1,2))].
% 35.70/36.00 15 ld(rd(A,B),A) = B. [para(5(a,1),4(a,1,2))].
% 35.70/36.00 17 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 35.70/36.00 20 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(3(a,1),8(a,1,1)),flip(a)].
% 35.70/36.00 21 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(8(a,1),4(a,1,2))].
% 35.70/36.00 22 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(5(a,1),8(a,1,1)),flip(a)].
% 35.70/36.00 23 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(8(a,1),6(a,1,1))].
% 35.70/36.00 24 mult(f(A),A) = mult(A,f(A)). [para(7(a,1),8(a,1,1)),rewrite([7(6)]),flip(a)].
% 35.70/36.00 25 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(8(a,1),8(a,1,1))].
% 35.70/36.00 26 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(10(a,1),1(a,1)),rewrite([1(4),2(3),2(4)])].
% 35.70/36.00 27 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(2(a,1),10(a,1,1)),rewrite([2(5)])].
% 35.70/36.00 28 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(3(a,1),10(a,1,1,2,2)),rewrite([20(9)])].
% 35.70/36.00 32 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(5(a,1),10(a,1,1)),flip(a)].
% 35.70/36.00 34 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(10(a,1),6(a,1,1))].
% 35.70/36.00 38 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(8(a,1),10(a,1,1,2,2))].
% 35.70/36.00 44 rd(mult(A,f(A)),A) = f(A). [para(24(a,1),6(a,1,1))].
% 35.70/36.00 45 mult(f(A),mult(A,f(A))) = mult(A,A). [para(24(a,1),8(a,1,1)),rewrite([26(4),7(3)]),flip(a)].
% 35.70/36.00 49 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(20(a,1),4(a,1,2))].
% 35.70/36.00 51 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(20(a,1),8(a,1,1)),rewrite([26(2),26(5)]),flip(a)].
% 35.70/36.00 61 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(24(a,1),21(a,1,1)),rewrite([45(6)])].
% 35.70/36.00 63 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(20(a,1),21(a,1,1)),rewrite([26(4),51(5)])].
% 35.70/36.00 66 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(5(a,1),23(a,1,1,2))].
% 35.70/36.00 69 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(20(a,1),23(a,2)),rewrite([26(3),51(4)])].
% 35.70/36.00 70 mult(A,rd(f(A),A)) = f(A). [back_rewrite(44),rewrite([66(3)])].
% 35.70/36.00 71 rd(f(A),A) = ld(A,f(A)). [para(70(a,1),4(a,1,2)),flip(a)].
% 35.70/36.00 79 mult(ld(A,f(A)),A) = f(A). [para(71(a,1),5(a,1,1))].
% 35.70/36.00 81 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(71(a,1),22(a,1,1)),rewrite([71(4),3(5),71(7)])].
% 35.70/36.00 86 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(5(a,1),26(a,1,1)),flip(a)].
% 35.70/36.00 130 mult(ld(A,unit),A) = unit. [para(2(a,1),49(a,1,2)),rewrite([13(1)]),flip(a)].
% 35.70/36.00 132 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(5(a,1),49(a,1,2)),flip(a)].
% 35.70/36.00 139 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(45(a,1),49(a,1,2)),rewrite([61(4)]),flip(a)].
% 35.70/36.00 140 ld(ld(A,unit),unit) = A. [para(130(a,1),4(a,1,2))].
% 35.70/36.00 141 rd(unit,A) = ld(A,unit). [para(130(a,1),6(a,1,1))].
% 35.70/36.00 143 mult(ld(A,unit),mult(A,A)) = A. [para(130(a,1),26(a,1,1)),rewrite([2(2)]),flip(a)].
% 35.70/36.00 176 ld(ld(A,unit),A) = mult(A,A). [para(143(a,1),4(a,1,2))].
% 35.70/36.00 177 rd(A,mult(A,A)) = ld(A,unit). [para(143(a,1),6(a,1,1))].
% 35.70/36.00 178 mult(ld(f(A),unit),A) = f(A). [para(7(a,1),143(a,1,2))].
% 35.70/36.00 188 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(15(a,1),176(a,1,1)),rewrite([141(2),141(5),141(7)]),flip(a)].
% 35.70/36.00 189 mult(mult(A,A),ld(A,unit)) = A. [para(176(a,1),49(a,2,1)),rewrite([3(5),140(4)]),flip(a)].
% 35.70/36.00 190 ld(f(A),unit) = ld(A,f(A)). [para(7(a,1),177(a,1,2)),rewrite([71(2)]),flip(a)].
% 35.70/36.00 215 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(178(a,1),8(a,1,1)),rewrite([3(5)]),flip(a)].
% 35.70/36.00 216 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(178(a,1),10(a,1,1,2,2)),rewrite([215(16),1(10)])].
% 35.70/36.00 222 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(178(a,1),27(a,1,1,2)),rewrite([215(14),1(8)])].
% 35.70/36.00 226 mult(A,ld(f(A),unit)) = f(A). [para(7(a,1),189(a,1,1))].
% 35.70/36.00 230 mult(f(A),ld(A,f(A))) = unit. [para(190(a,1),3(a,1,2))].
% 35.70/36.00 237 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(81),rewrite([230(8)])].
% 35.70/36.00 279 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(226(a,1),26(a,1,1)),rewrite([3(5),188(8)]),flip(a)].
% 35.70/36.00 417 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(7(a,1),63(a,1,2,2))].
% 35.70/36.00 450 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(5(a,1),69(a,1,1)),flip(a)].
% 35.70/36.00 451 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(7(a,1),69(a,1,1,2))].
% 35.70/36.00 461 ld(mult(rd(A,mult(B,mult(C,B))),B),mult(A,C)) = mult(C,mult(B,C)). [para(32(a,1),4(a,1,2))].
% 35.70/36.00 479 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(79(a,1),32(a,1,1,1,2,2)),rewrite([3(9),237(8),1(6)])].
% 35.70/36.00 496 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(178(a,1),32(a,1,1,1,2,2)),rewrite([479(4),226(10),130(8),1(5)]),flip(a)].
% 35.70/36.00 512 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(86(a,1),4(a,1,2))].
% 35.70/36.00 630 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(222(a,1),6(a,1,1))].
% 35.70/36.00 633 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(222(a,1),26(a,1,1)),rewrite([226(4),188(10)]),flip(a)].
% 35.70/36.00 693 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(130(a,1),34(a,1,1,1)),rewrite([2(4),66(3),6(2)]),flip(a)].
% 35.70/36.00 760 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(279(a,1),4(a,1,2)),flip(a)].
% 35.70/36.00 766 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(633),rewrite([760(7)])].
% 35.70/36.00 1011 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(130(a,1),451(a,1,1)),rewrite([141(3)]),flip(a)].
% 35.70/36.00 1053 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(226(a,1),512(a,1,2)),rewrite([630(4),188(11),760(9)])].
% 35.70/36.00 1074 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(139),rewrite([1053(4)])].
% 35.70/36.00 1607 mult(A,ld(B,unit)) = rd(A,B). [para(766(a,1),32(a,1,2,2)),rewrite([1074(7),26(4),7(3),1011(9),216(9),450(3)]),flip(a)].
% 35.70/36.00 1657 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(496),rewrite([1607(4)]),flip(a)].
% 35.70/36.00 1763 ld(A,rd(A,B)) = ld(B,unit). [para(1607(a,1),4(a,1,2))].
% 35.70/36.00 1848 ld(mult(A,B),A) = ld(B,unit). [para(6(a,1),1763(a,1,2))].
% 35.70/36.00 1849 ld(ld(A,B),unit) = ld(B,A). [para(17(a,1),1763(a,1,2)),flip(a)].
% 35.70/36.00 2053 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1849(a,1),1607(a,1,2)),flip(a)].
% 35.70/36.00 2623 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1657(a,1),28(a,1,1,2)),flip(a)].
% 35.70/36.00 3384 mult(ld(A,unit),mult(A,B)) = B. [para(5(a,1),693(a,1,2,2)),rewrite([5(6)])].
% 35.70/36.00 3391 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(20(a,1),693(a,1,2))].
% 35.70/36.00 3393 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(693(a,1),25(a,1,2)),rewrite([1607(7),66(5),6(4),3384(4),3384(7),3384(10),3391(7)]),flip(a)].
% 35.70/36.00 3405 mult(ld(A,unit),B) = ld(A,B). [para(132(a,1),693(a,1,2,2)),rewrite([3(4),132(6)])].
% 35.70/36.00 3417 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(693(a,1),38(a,1,2)),rewrite([1607(9),66(7),6(6),3405(6),4(4),3405(3),1607(7),3405(10),4(8),3405(13),4(11),3405(10),49(8),3393(9)])].
% 35.70/36.00 3667 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2623),rewrite([3417(8)])].
% 35.70/36.00 4020 rd(ld(A,B),B) = ld(A,unit). [para(3405(a,1),6(a,1,1))].
% 35.70/36.00 4026 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3405(a,1),26(a,1,1)),rewrite([3405(6)]),flip(a)].
% 35.70/36.00 4030 mult(ld(A,f(A)),B) = ld(f(A),B). [para(190(a,1),3405(a,1,1))].
% 35.70/36.00 4042 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3405(a,1),417(a,1,1)),rewrite([3405(5)])].
% 35.70/36.00 4056 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3405(a,1),1607(a,1)),flip(a)].
% 35.70/36.00 4061 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1849(a,1),3405(a,1,1)),flip(a)].
% 35.70/36.00 4092 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3667),rewrite([4030(6),4030(6)]),flip(a)].
% 35.70/36.00 4153 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(4042),rewrite([4061(4)])].
% 35.70/36.00 4337 rd(A,mult(B,A)) = ld(B,unit). [para(4(a,1),4020(a,1,1))].
% 35.70/36.00 4338 ld(rd(A,B),unit) = rd(B,A). [para(15(a,1),4020(a,1,1)),flip(a)].
% 35.70/36.00 4349 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1848(a,1),4020(a,1,1)),rewrite([4056(3)]),flip(a)].
% 35.70/36.00 4677 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4338(a,1),1607(a,1,2)),flip(a)].
% 35.70/36.00 4681 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4338(a,1),3405(a,1,1)),flip(a)].
% 35.70/36.00 5031 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1657(a,1),4026(a,1,2)),rewrite([4020(4),1657(9)]),flip(a)].
% 35.70/36.00 5387 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(4092),rewrite([5031(5)]),flip(a)].
% 35.70/36.00 5853 ld(f(A),ld(f(A),B)) = ld(A,B). [para(4153(a,1),1848(a,1,1)),rewrite([4061(7),1(7)])].
% 35.70/36.00 5871 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5387),rewrite([5853(5)]),flip(a)].
% 35.70/36.00 6068 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4349(a,1),1607(a,1,2))].
% 35.70/36.00 6077 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5871),rewrite([6068(4)])].
% 35.70/36.00 6299 rd(A,mult(B,ld(C,D))) = mult(A,rd(ld(D,C),B)). [para(2053(a,1),4677(a,1,2))].
% 35.70/36.00 6515 ld(mult(rd(A,B),C),D) = mult(ld(C,rd(B,A)),D). [para(4681(a,1),4061(a,1,1))].
% 35.70/36.00 6604 mult(ld(A,rd(mult(A,mult(B,A)),C)),mult(C,B)) = mult(B,mult(A,B)). [back_rewrite(461),rewrite([6515(6)])].
% 35.70/36.00 19996 mult(A,mult(ld(A,B),rd(A,C))) = rd(mult(B,A),C). [para(6077(a,1),4337(a,1,2)),rewrite([6299(4),4677(3),4681(8),1(8)])].
% 35.70/36.00 24321 rd(mult(A,mult(B,A)),C) = mult(A,mult(B,rd(A,C))). [para(4(a,1),19996(a,1,2,1)),rewrite([8(5)]),flip(a)].
% 35.70/36.00 24371 mult(mult(A,rd(B,C)),mult(C,A)) = mult(A,mult(B,A)). [back_rewrite(6604),rewrite([24321(3),4(4)])].
% 35.70/36.00 25791 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(6(a,1),24371(a,1,1,2))].
% 35.70/36.00 25792 $F # answer(goals). [resolve(25791,a,11,a)].
% 35.70/36.00
% 35.70/36.00 % SZS output end Refutation
% 35.70/36.00 ============================== end of proof ==========================
% 35.70/36.00
% 35.70/36.00 ============================== STATISTICS ============================
% 35.70/36.00
% 35.70/36.00 Given=1002. Generated=851016. Kept=25790. proofs=1.
% 35.70/36.00 Usable=693. Sos=9739. Demods=9903. Limbo=1, Disabled=15366. Hints=0.
% 35.70/36.00 Megabytes=27.48.
% 35.70/36.00 User_CPU=34.36, System_CPU=0.54, Wall_clock=35.
% 35.70/36.00
% 35.70/36.00 ============================== end of statistics =====================
% 35.70/36.00
% 35.70/36.00 ============================== end of search =========================
% 35.70/36.00
% 35.70/36.00 THEOREM PROVED
% 35.70/36.00 % SZS status Unsatisfiable
% 35.70/36.00
% 35.70/36.00 Exiting with 1 proof.
% 35.70/36.00
% 35.70/36.00 Process 14498 exit (max_proofs) Mon Jun 13 07:18:26 2022
% 35.70/36.00 Prover9 interrupted
%------------------------------------------------------------------------------