TSTP Solution File: GRP667-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP667-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 37.81s 38.32s
% Output : Refutation 37.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP667-2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 06:43:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.81/4.11 ============================== Prover9 ===============================
% 3.81/4.11 Prover9 (32) version 2009-11A, November 2009.
% 3.81/4.11 Process 13832 was started by sandbox on n016.cluster.edu,
% 3.81/4.11 Mon Jun 13 06:43:14 2022
% 3.81/4.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13679_n016.cluster.edu".
% 3.81/4.11 ============================== end of head ===========================
% 3.81/4.11
% 3.81/4.11 ============================== INPUT =================================
% 3.81/4.11
% 3.81/4.11 % Reading from file /tmp/Prover9_13679_n016.cluster.edu
% 3.81/4.11
% 3.81/4.11 set(prolog_style_variables).
% 3.81/4.11 set(auto2).
% 3.81/4.11 % set(auto2) -> set(auto).
% 3.81/4.11 % set(auto) -> set(auto_inference).
% 3.81/4.11 % set(auto) -> set(auto_setup).
% 3.81/4.11 % set(auto_setup) -> set(predicate_elim).
% 3.81/4.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.81/4.11 % set(auto) -> set(auto_limits).
% 3.81/4.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.81/4.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.81/4.11 % set(auto) -> set(auto_denials).
% 3.81/4.11 % set(auto) -> set(auto_process).
% 3.81/4.11 % set(auto2) -> assign(new_constants, 1).
% 3.81/4.11 % set(auto2) -> assign(fold_denial_max, 3).
% 3.81/4.11 % set(auto2) -> assign(max_weight, "200.000").
% 3.81/4.11 % set(auto2) -> assign(max_hours, 1).
% 3.81/4.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.81/4.11 % set(auto2) -> assign(max_seconds, 0).
% 3.81/4.11 % set(auto2) -> assign(max_minutes, 5).
% 3.81/4.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.81/4.11 % set(auto2) -> set(sort_initial_sos).
% 3.81/4.11 % set(auto2) -> assign(sos_limit, -1).
% 3.81/4.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.81/4.11 % set(auto2) -> assign(max_megs, 400).
% 3.81/4.11 % set(auto2) -> assign(stats, some).
% 3.81/4.11 % set(auto2) -> clear(echo_input).
% 3.81/4.11 % set(auto2) -> set(quiet).
% 3.81/4.11 % set(auto2) -> clear(print_initial_clauses).
% 3.81/4.11 % set(auto2) -> clear(print_given).
% 3.81/4.11 assign(lrs_ticks,-1).
% 3.81/4.11 assign(sos_limit,10000).
% 3.81/4.11 assign(order,kbo).
% 3.81/4.11 set(lex_order_vars).
% 3.81/4.11 clear(print_given).
% 3.81/4.11
% 3.81/4.11 % formulas(sos). % not echoed (10 formulas)
% 3.81/4.11
% 3.81/4.11 ============================== end of input ==========================
% 3.81/4.11
% 3.81/4.11 % From the command line: assign(max_seconds, 300).
% 3.81/4.11
% 3.81/4.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.81/4.11
% 3.81/4.11 % Formulas that are not ordinary clauses:
% 3.81/4.11
% 3.81/4.11 ============================== end of process non-clausal formulas ===
% 3.81/4.11
% 3.81/4.11 ============================== PROCESS INITIAL CLAUSES ===============
% 3.81/4.11
% 3.81/4.11 ============================== PREDICATE ELIMINATION =================
% 3.81/4.11
% 3.81/4.11 ============================== end predicate elimination =============
% 3.81/4.11
% 3.81/4.11 Auto_denials:
% 3.81/4.11 % copying label goals to answer in negative clause
% 3.81/4.11
% 3.81/4.11 Term ordering decisions:
% 3.81/4.11
% 3.81/4.11 % Assigning unary symbol f kb_weight 0 and highest precedence (9).
% 3.81/4.11 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. f=0.
% 3.81/4.11
% 3.81/4.11 ============================== end of process initial clauses ========
% 3.81/4.11
% 3.81/4.11 ============================== CLAUSES FOR SEARCH ====================
% 3.81/4.11
% 3.81/4.11 ============================== end of clauses for search =============
% 3.81/4.11
% 3.81/4.11 ============================== SEARCH ================================
% 3.81/4.11
% 3.81/4.11 % Starting search at 0.01 seconds.
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=107.000, iters=3376
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=103.000, iters=3356
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=99.000, iters=3342
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=91.000, iters=3538
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=71.000, iters=3341
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=67.000, iters=3456
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=63.000, iters=3361
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=59.000, iters=3352
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=55.000, iters=3354
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=51.000, iters=3365
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=49.000, iters=3356
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=47.000, iters=3361
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=45.000, iters=3335
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=43.000, iters=3345
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=41.000, iters=3349
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=39.000, iters=3341
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=37.000, iters=3347
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=35.000, iters=3351
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=33.000, iters=3348
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=31.000, iters=3351
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=29.000, iters=3350
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=27.000, iters=3359
% 3.81/4.11
% 3.81/4.11 Low Water (keep): wt=25.000, iters=3341
% 3.81/4.11
% 3.81/4.11 Low Water (displace): id=8760, wt=191.000
% 3.81/4.11
% 3.81/4.11 Low Water (displace): id=8751, wt=187.000
% 3.81/4.11
% 3.81/4.11 Low Water (displace): id=16621, wt=22.000
% 3.81/4.11
% 3.81/4.11 Low Water (displace): id=16624, wt=19.000
% 37.81/38.32
% 37.81/38.32 Low Water (displace): id=17450, wt=17.000
% 37.81/38.32
% 37.81/38.32 Low Water (keep): wt=23.000, iters=3337
% 37.81/38.32
% 37.81/38.32 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 5.51 sec).
% 37.81/38.32
% 37.81/38.32 Low Water (keep): wt=22.000, iters=3343
% 37.81/38.32
% 37.81/38.32 Low Water (keep): wt=21.000, iters=3343
% 37.81/38.32
% 37.81/38.32 Low Water (displace): id=23017, wt=15.000
% 37.81/38.32
% 37.81/38.32 ============================== PROOF =================================
% 37.81/38.32 % SZS status Unsatisfiable
% 37.81/38.32 % SZS output start Refutation
% 37.81/38.32
% 37.81/38.32 % Proof 1 at 36.59 (+ 0.55) seconds: goals.
% 37.81/38.32 % Length of proof is 164.
% 37.81/38.32 % Level of proof is 26.
% 37.81/38.32 % Maximum clause weight is 43.000.
% 37.81/38.32 % Given clauses 1049.
% 37.81/38.32
% 37.81/38.32 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 37.81/38.32 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 37.81/38.32 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 37.81/38.32 4 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 37.81/38.32 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 37.81/38.32 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 37.81/38.32 7 mult(f(A),f(A)) = A # label(c09) # label(axiom). [assumption].
% 37.81/38.32 8 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(c08) # label(axiom). [assumption].
% 37.81/38.32 9 mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C) # label(c07) # label(axiom). [assumption].
% 37.81/38.32 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)].
% 37.81/38.32 11 mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 37.81/38.32 12 mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))) # answer(goals). [copy(11),rewrite([8(12)]),flip(a)].
% 37.81/38.32 14 ld(A,A) = unit. [para(1(a,1),4(a,1,2))].
% 37.81/38.32 16 ld(rd(A,B),A) = B. [para(5(a,1),4(a,1,2))].
% 37.81/38.32 18 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 37.81/38.32 19 ld(f(A),A) = f(A). [para(7(a,1),4(a,1,2))].
% 37.81/38.32 21 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(3(a,1),8(a,1,1)),flip(a)].
% 37.81/38.32 22 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(8(a,1),4(a,1,2))].
% 37.81/38.32 23 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(5(a,1),8(a,1,1)),flip(a)].
% 37.81/38.32 24 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(8(a,1),6(a,1,1))].
% 37.81/38.32 25 mult(f(A),A) = mult(A,f(A)). [para(7(a,1),8(a,1,1)),rewrite([7(6)]),flip(a)].
% 37.81/38.32 26 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))].
% 37.81/38.32 27 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(10(a,1),1(a,1)),rewrite([1(4),2(3),2(4)])].
% 37.81/38.32 28 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)])].
% 37.81/38.32 29 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([21(9)])].
% 37.81/38.32 30 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(3(a,1),10(a,2,2,2)),rewrite([21(3)])].
% 37.81/38.32 32 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(5(a,1),10(a,1,1,2,2)),rewrite([23(9)])].
% 37.81/38.32 33 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)].
% 37.81/38.32 35 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))].
% 37.81/38.32 36 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(7(a,1),10(a,1,1,2,2)),rewrite([25(2),7(11),25(9)])].
% 37.81/38.32 39 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))].
% 37.81/38.32 45 rd(mult(A,f(A)),A) = f(A). [para(25(a,1),6(a,1,1))].
% 37.81/38.32 46 mult(f(A),mult(A,f(A))) = mult(A,A). [para(25(a,1),8(a,1,1)),rewrite([27(4),7(3)]),flip(a)].
% 37.81/38.32 50 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(21(a,1),4(a,1,2))].
% 37.81/38.32 52 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(21(a,1),8(a,1,1)),rewrite([27(2),27(5)]),flip(a)].
% 37.81/38.32 58 ld(mult(A,mult(B,A)),mult(mult(A,B),mult(A,mult(A,B)))) = mult(A,B). [para(8(a,1),22(a,1,1))].
% 37.81/38.32 62 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(25(a,1),22(a,1,1)),rewrite([46(6)])].
% 37.81/38.32 64 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(21(a,1),22(a,1,1)),rewrite([27(4),52(5)])].
% 37.81/38.32 67 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(5(a,1),24(a,1,1,2))].
% 37.81/38.32 70 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(21(a,1),24(a,2)),rewrite([27(3),52(4)])].
% 37.81/38.32 71 mult(A,rd(f(A),A)) = f(A). [back_rewrite(45),rewrite([67(3)])].
% 37.81/38.32 72 rd(f(A),A) = ld(A,f(A)). [para(71(a,1),4(a,1,2)),flip(a)].
% 37.81/38.32 80 mult(ld(A,f(A)),A) = f(A). [para(72(a,1),5(a,1,1))].
% 37.81/38.32 82 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(72(a,1),23(a,1,1)),rewrite([72(4),3(5),72(7)])].
% 37.81/38.32 87 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(5(a,1),27(a,1,1)),flip(a)].
% 37.81/38.32 131 mult(ld(A,unit),A) = unit. [para(2(a,1),50(a,1,2)),rewrite([14(1)]),flip(a)].
% 37.81/38.32 133 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(5(a,1),50(a,1,2)),flip(a)].
% 37.81/38.32 140 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(46(a,1),50(a,1,2)),rewrite([62(4)]),flip(a)].
% 37.81/38.32 141 ld(ld(A,unit),unit) = A. [para(131(a,1),4(a,1,2))].
% 37.81/38.32 142 rd(unit,A) = ld(A,unit). [para(131(a,1),6(a,1,1))].
% 37.81/38.32 144 mult(ld(A,unit),mult(A,A)) = A. [para(131(a,1),27(a,1,1)),rewrite([2(2)]),flip(a)].
% 37.81/38.32 146 mult(mult(ld(A,B),B),A) = mult(ld(A,B),mult(B,A)). [para(3(a,1),28(a,1,1,2)),rewrite([21(7)])].
% 37.81/38.32 157 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(25(a,1),28(a,1,1,2)),rewrite([36(5),46(9)])].
% 37.81/38.32 177 ld(ld(A,unit),A) = mult(A,A). [para(144(a,1),4(a,1,2))].
% 37.81/38.32 178 rd(A,mult(A,A)) = ld(A,unit). [para(144(a,1),6(a,1,1))].
% 37.81/38.32 179 mult(ld(f(A),unit),A) = f(A). [para(7(a,1),144(a,1,2))].
% 37.81/38.32 189 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(16(a,1),177(a,1,1)),rewrite([142(2),142(5),142(7)]),flip(a)].
% 37.81/38.32 190 mult(mult(A,A),ld(A,unit)) = A. [para(177(a,1),50(a,2,1)),rewrite([3(5),141(4)]),flip(a)].
% 37.81/38.32 191 ld(f(A),unit) = ld(A,f(A)). [para(7(a,1),178(a,1,2)),rewrite([72(2)]),flip(a)].
% 37.81/38.32 193 mult(A,mult(ld(A,B),mult(B,A))) = mult(B,mult(B,A)). [para(3(a,1),29(a,2,1)),rewrite([8(4),146(3)])].
% 37.81/38.32 216 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(179(a,1),8(a,1,1)),rewrite([3(5)]),flip(a)].
% 37.81/38.32 217 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(179(a,1),10(a,1,1,2,2)),rewrite([216(16),1(10)])].
% 37.81/38.32 218 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(179(a,1),10(a,2,2,2)),rewrite([216(8),1(2)]),flip(a)].
% 37.81/38.32 223 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(179(a,1),28(a,1,1,2)),rewrite([216(14),1(8)])].
% 37.81/38.32 227 mult(A,ld(f(A),unit)) = f(A). [para(7(a,1),190(a,1,1))].
% 37.81/38.32 231 mult(f(A),ld(A,f(A))) = unit. [para(191(a,1),3(a,1,2))].
% 37.81/38.32 238 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(82),rewrite([231(8)])].
% 37.81/38.32 280 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(227(a,1),27(a,1,1)),rewrite([3(5),189(8)]),flip(a)].
% 37.81/38.32 408 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(30(a,1),32(a,1,1,2))].
% 37.81/38.32 418 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(7(a,1),64(a,1,2,2))].
% 37.81/38.32 451 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(5(a,1),70(a,1,1)),flip(a)].
% 37.81/38.32 452 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(7(a,1),70(a,1,1,2))].
% 37.81/38.32 462 ld(mult(rd(A,mult(B,mult(C,B))),B),mult(A,C)) = mult(C,mult(B,C)). [para(33(a,1),4(a,1,2))].
% 37.81/38.32 465 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(7(a,1),33(a,1,1,1,2,2)),rewrite([25(2),7(9),25(7)])].
% 37.81/38.32 480 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(80(a,1),33(a,1,1,1,2,2)),rewrite([3(9),238(8),1(6)])].
% 37.81/38.32 494 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(144(a,1),33(a,1,1,1,2,2)),rewrite([8(2),190(11),131(8),1(7)])].
% 37.81/38.32 497 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(179(a,1),33(a,1,1,1,2,2)),rewrite([480(4),227(10),131(8),1(5)]),flip(a)].
% 37.81/38.32 513 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(87(a,1),4(a,1,2))].
% 37.81/38.32 515 mult(rd(A,f(B)),B) = mult(A,f(B)). [para(7(a,1),87(a,1,2))].
% 37.81/38.32 631 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(223(a,1),6(a,1,1))].
% 37.81/38.32 634 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(223(a,1),27(a,1,1)),rewrite([227(4),189(10)]),flip(a)].
% 37.81/38.32 694 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(131(a,1),35(a,1,1,1)),rewrite([2(4),67(3),6(2)]),flip(a)].
% 37.81/38.32 761 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(280(a,1),4(a,1,2)),flip(a)].
% 37.81/38.32 767 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(634),rewrite([761(7)])].
% 37.81/38.32 777 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(36(a,1),27(a,1,1)),rewrite([36(7),27(4),7(3),7(10)]),flip(a)].
% 37.81/38.32 796 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(36(a,1),70(a,2)),rewrite([7(6),777(4)])].
% 37.81/38.32 864 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(451(a,1),4(a,1,2))].
% 37.81/38.32 866 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(7(a,1),451(a,1,1,2))].
% 37.81/38.32 898 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(451(a,1),36(a,1,1)),rewrite([157(10)]),flip(a)].
% 37.81/38.32 1012 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(131(a,1),452(a,1,1)),rewrite([142(3)]),flip(a)].
% 37.81/38.32 1054 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(227(a,1),513(a,1,2)),rewrite([631(4),189(11),761(9)])].
% 37.81/38.32 1075 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(140),rewrite([1054(4)])].
% 37.81/38.32 1608 mult(A,ld(B,unit)) = rd(A,B). [para(767(a,1),33(a,1,2,2)),rewrite([1075(7),27(4),7(3),1012(9),217(9),451(3)]),flip(a)].
% 37.81/38.32 1658 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(497),rewrite([1608(4)]),flip(a)].
% 37.81/38.32 1659 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(494),rewrite([1608(8)])].
% 37.81/38.32 1663 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(218),rewrite([1608(4)])].
% 37.81/38.32 1664 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(217),rewrite([1608(7)])].
% 37.81/38.32 1682 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(796),rewrite([1664(6),27(2)]),flip(a)].
% 37.81/38.32 1706 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(898),rewrite([1682(8),1659(5)]),flip(a)].
% 37.81/38.32 1741 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(465),rewrite([1706(5)])].
% 37.81/38.32 1764 ld(A,rd(A,B)) = ld(B,unit). [para(1608(a,1),4(a,1,2))].
% 37.81/38.32 1849 ld(mult(A,B),A) = ld(B,unit). [para(6(a,1),1764(a,1,2))].
% 37.81/38.32 1850 ld(ld(A,B),unit) = ld(B,A). [para(18(a,1),1764(a,1,2)),flip(a)].
% 37.81/38.32 2024 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(mult(A,B),unit). [para(26(a,1),1849(a,1,1))].
% 37.81/38.32 2054 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1850(a,1),1608(a,1,2)),flip(a)].
% 37.81/38.32 2213 ld(rd(A,B),rd(A,f(B))) = f(B). [para(7(a,1),864(a,1,1,2))].
% 37.81/38.32 2624 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(1658(a,1),29(a,1,1,2)),flip(a)].
% 37.81/38.32 3385 mult(ld(A,unit),mult(A,B)) = B. [para(5(a,1),694(a,1,2,2)),rewrite([5(6)])].
% 37.81/38.32 3392 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(21(a,1),694(a,1,2))].
% 37.81/38.32 3394 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(694(a,1),26(a,1,2)),rewrite([1608(7),67(5),6(4),3385(4),3385(7),3385(10),3392(7)]),flip(a)].
% 37.81/38.32 3406 mult(ld(A,unit),B) = ld(A,B). [para(133(a,1),694(a,1,2,2)),rewrite([3(4),133(6)])].
% 37.81/38.32 3418 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(694(a,1),39(a,1,2)),rewrite([1608(9),67(7),6(6),3406(6),4(4),3406(3),1608(7),3406(10),4(8),3406(13),4(11),3406(10),50(8),3394(9)])].
% 37.81/38.32 3668 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(2624),rewrite([3418(8)])].
% 37.81/38.32 4021 rd(ld(A,B),B) = ld(A,unit). [para(3406(a,1),6(a,1,1))].
% 37.81/38.32 4027 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3406(a,1),27(a,1,1)),rewrite([3406(6)]),flip(a)].
% 37.81/38.32 4031 mult(ld(A,f(A)),B) = ld(f(A),B). [para(191(a,1),3406(a,1,1))].
% 37.81/38.32 4040 rd(mult(ld(A,B),mult(C,mult(B,C))),C) = ld(A,mult(B,mult(C,B))). [para(3406(a,1),35(a,1,1,1)),rewrite([3406(10)])].
% 37.81/38.32 4043 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3406(a,1),418(a,1,1)),rewrite([3406(5)])].
% 37.81/38.32 4057 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3406(a,1),1608(a,1)),flip(a)].
% 37.81/38.32 4062 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1850(a,1),3406(a,1,1)),flip(a)].
% 37.81/38.32 4093 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(3668),rewrite([4031(6),4031(6)]),flip(a)].
% 37.81/38.32 4154 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(4043),rewrite([4062(4)])].
% 37.81/38.32 4338 rd(A,mult(B,A)) = ld(B,unit). [para(4(a,1),4021(a,1,1))].
% 37.81/38.32 4339 ld(rd(A,B),unit) = rd(B,A). [para(16(a,1),4021(a,1,1)),flip(a)].
% 37.81/38.32 4349 mult(ld(A,f(B)),f(B)) = ld(A,B). [para(4021(a,1),515(a,1,1)),rewrite([3406(3)]),flip(a)].
% 37.81/38.32 4350 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1849(a,1),4021(a,1,1)),rewrite([4057(3)]),flip(a)].
% 37.81/38.32 4353 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2213(a,1),4021(a,1,1)),rewrite([4339(7)])].
% 37.81/38.32 4379 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(B,ld(A,unit)). [back_rewrite(2024),rewrite([4350(10)])].
% 37.81/38.32 4678 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4339(a,1),1608(a,1,2)),flip(a)].
% 37.81/38.32 4682 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4339(a,1),3406(a,1,1)),flip(a)].
% 37.81/38.32 4686 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4353),rewrite([4678(4)])].
% 37.81/38.32 5018 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(4027(a,1),21(a,1,2,1)),rewrite([146(3),193(4)]),flip(a)].
% 37.81/38.32 5032 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1658(a,1),4027(a,1,2)),rewrite([4021(4),1658(9)]),flip(a)].
% 37.81/38.32 5388 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(4093),rewrite([5032(5)]),flip(a)].
% 37.81/38.32 5467 mult(ld(A,ld(B,unit)),C) = ld(mult(B,A),C). [para(58(a,1),4062(a,1,1)),rewrite([4379(9)]),flip(a)].
% 37.81/38.32 5854 ld(f(A),ld(f(A),B)) = ld(A,B). [para(4154(a,1),1849(a,1,1)),rewrite([4062(7),1(7)])].
% 37.81/38.32 5872 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5388),rewrite([5854(5)]),flip(a)].
% 37.81/38.32 6069 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4350(a,1),1608(a,1,2))].
% 37.81/38.32 6078 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5872),rewrite([6069(4)])].
% 37.81/38.32 6300 rd(A,mult(B,ld(C,D))) = mult(A,rd(ld(D,C),B)). [para(2054(a,1),4678(a,1,2))].
% 37.81/38.32 6516 ld(mult(rd(A,B),C),D) = mult(ld(C,rd(B,A)),D). [para(4682(a,1),4062(a,1,1))].
% 37.81/38.32 6605 mult(ld(A,rd(mult(A,mult(B,A)),C)),mult(C,B)) = mult(B,mult(A,B)). [back_rewrite(462),rewrite([6516(6)])].
% 37.81/38.32 7126 mult(f(A),mult(f(A),B)) = mult(A,B). [para(7(a,1),5018(a,1,1)),flip(a)].
% 37.81/38.32 8201 rd(mult(A,mult(B,C)),C) = mult(mult(A,C),ld(C,B)). [para(7126(a,1),30(a,1,1,2)),rewrite([1849(6),1608(5),1849(10),3406(10),30(9),4349(8)])].
% 37.81/38.32 13360 mult(ld(A,ld(B,ld(C,unit))),D) = ld(mult(mult(C,B),A),D). [para(4350(a,1),5467(a,1,1,2))].
% 37.81/38.32 19971 mult(rd(mult(A,B),C),mult(rd(C,B),ld(A,B))) = B. [para(6078(a,1),4(a,1,2)),rewrite([4682(6)])].
% 37.81/38.32 19997 mult(A,mult(ld(A,B),rd(A,C))) = rd(mult(B,A),C). [para(6078(a,1),4338(a,1,2)),rewrite([6300(4),4678(3),4682(8),1(8)])].
% 37.81/38.32 19998 ld(mult(mult(A,B),C),B) = ld(mult(B,C),ld(A,B)). [para(4057(a,1),6078(a,1,1)),rewrite([4350(3),13360(5),4057(6),5467(8)])].
% 37.81/38.32 20274 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1741(a,1),408(a,1,2,2)),rewrite([866(3),19(4),25(4),1663(5),19(4),4338(6),1608(5),1741(7),19(8),19(9),1741(12),4338(11),1608(10),32(9),4686(8)])].
% 37.81/38.32 20291 ld(A,mult(B,mult(C,B))) = mult(mult(ld(A,B),C),B). [back_rewrite(4040),rewrite([20274(5),6(4)]),flip(a)].
% 37.81/38.32 21988 mult(ld(A,mult(mult(B,A),ld(A,C))),A) = ld(A,mult(B,mult(C,A))). [para(8201(a,1),133(a,1,1,2))].
% 37.81/38.32 24234 mult(mult(mult(A,B),ld(B,C)),ld(C,ld(A,B))) = B. [para(4021(a,1),19971(a,1,2,1)),rewrite([2054(3),3406(7)])].
% 37.81/38.32 24322 rd(mult(A,mult(B,A)),C) = mult(A,mult(B,rd(A,C))). [para(4(a,1),19997(a,1,2,1)),rewrite([8(5)]),flip(a)].
% 37.81/38.32 24372 mult(mult(A,rd(B,C)),mult(C,A)) = mult(A,mult(B,A)). [back_rewrite(6605),rewrite([24322(3),4(4)])].
% 37.81/38.32 24431 mult(ld(A,mult(mult(B,A),C)),D) = mult(mult(ld(A,B),mult(A,C)),D). [para(19998(a,1),4062(a,1,1)),rewrite([4062(4),4062(3)]),flip(a)].
% 37.81/38.32 24461 ld(A,mult(B,mult(C,A))) = mult(mult(ld(A,B),C),A). [back_rewrite(21988),rewrite([24431(5),3(3)]),flip(a)].
% 37.81/38.32 24564 mult(A,mult(mult(ld(A,B),C),B)) = mult(B,mult(C,B)). [para(20291(a,1),3(a,1,2))].
% 37.81/38.32 24568 mult(A,mult(mult(mult(ld(A,B),C),B),A)) = mult(mult(B,mult(C,B)),A). [para(20291(a,1),21(a,1,2,1))].
% 37.81/38.32 25477 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(24234(a,1),6(a,1,1)),rewrite([2054(3),4062(2)]),flip(a)].
% 37.81/38.32 25792 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(6(a,1),24372(a,1,1,2))].
% 37.81/38.32 25868 mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)). [para(24461(a,1),3(a,1,2))].
% 37.81/38.32 26030 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(4(a,1),24564(a,1,2,1,1)),rewrite([25792(3)]),flip(a)].
% 37.81/38.32 26436 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [para(25477(a,1),8(a,1,1)),rewrite([25792(5),24568(5),26030(8),25868(7)])].
% 37.81/38.32 26437 $F # answer(goals). [resolve(26436,a,12,a)].
% 37.81/38.32
% 37.81/38.32 % SZS output end Refutation
% 37.81/38.32 ============================== end of proof ==========================
% 37.81/38.32
% 37.81/38.32 ============================== STATISTICS ============================
% 37.81/38.32
% 37.81/38.32 Given=1049. Generated=909425. Kept=26434. proofs=1.
% 37.81/38.32 Usable=634. Sos=8849. Demods=8956. Limbo=1, Disabled=16959. Hints=0.
% 37.81/38.32 Megabytes=27.71.
% 37.81/38.32 User_CPU=36.59, System_CPU=0.55, Wall_clock=38.
% 37.81/38.32
% 37.81/38.32 ============================== end of statistics =====================
% 37.81/38.32
% 37.81/38.32 ============================== end of search =========================
% 37.81/38.32
% 37.81/38.32 THEOREM PROVED
% 37.81/38.32 % SZS status Unsatisfiable
% 37.81/38.32
% 37.81/38.32 Exiting with 1 proof.
% 37.81/38.32
% 37.81/38.32 Process 13832 exit (max_proofs) Mon Jun 13 06:43:52 2022
% 37.81/38.32 Prover9 interrupted
%------------------------------------------------------------------------------