TSTP Solution File: GRP705-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP705-1 : 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 11:20:43 EDT 2022
% Result : Unsatisfiable 10.51s 10.81s
% Output : Refutation 10.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP705-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 10:49:36 EDT 2022
% 0.13/0.35 % CPUTime :
% 10.51/10.81 ============================== Prover9 ===============================
% 10.51/10.81 Prover9 (32) version 2009-11A, November 2009.
% 10.51/10.81 Process 346 was started by sandbox2 on n026.cluster.edu,
% 10.51/10.81 Tue Jun 14 10:49:37 2022
% 10.51/10.81 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32661_n026.cluster.edu".
% 10.51/10.81 ============================== end of head ===========================
% 10.51/10.81
% 10.51/10.81 ============================== INPUT =================================
% 10.51/10.81
% 10.51/10.81 % Reading from file /tmp/Prover9_32661_n026.cluster.edu
% 10.51/10.81
% 10.51/10.81 set(prolog_style_variables).
% 10.51/10.81 set(auto2).
% 10.51/10.81 % set(auto2) -> set(auto).
% 10.51/10.81 % set(auto) -> set(auto_inference).
% 10.51/10.81 % set(auto) -> set(auto_setup).
% 10.51/10.81 % set(auto_setup) -> set(predicate_elim).
% 10.51/10.81 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.51/10.81 % set(auto) -> set(auto_limits).
% 10.51/10.81 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.51/10.81 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.51/10.81 % set(auto) -> set(auto_denials).
% 10.51/10.81 % set(auto) -> set(auto_process).
% 10.51/10.81 % set(auto2) -> assign(new_constants, 1).
% 10.51/10.81 % set(auto2) -> assign(fold_denial_max, 3).
% 10.51/10.81 % set(auto2) -> assign(max_weight, "200.000").
% 10.51/10.81 % set(auto2) -> assign(max_hours, 1).
% 10.51/10.81 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.51/10.81 % set(auto2) -> assign(max_seconds, 0).
% 10.51/10.81 % set(auto2) -> assign(max_minutes, 5).
% 10.51/10.81 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.51/10.81 % set(auto2) -> set(sort_initial_sos).
% 10.51/10.81 % set(auto2) -> assign(sos_limit, -1).
% 10.51/10.81 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.51/10.81 % set(auto2) -> assign(max_megs, 400).
% 10.51/10.81 % set(auto2) -> assign(stats, some).
% 10.51/10.81 % set(auto2) -> clear(echo_input).
% 10.51/10.81 % set(auto2) -> set(quiet).
% 10.51/10.81 % set(auto2) -> clear(print_initial_clauses).
% 10.51/10.81 % set(auto2) -> clear(print_given).
% 10.51/10.81 assign(lrs_ticks,-1).
% 10.51/10.81 assign(sos_limit,10000).
% 10.51/10.81 assign(order,kbo).
% 10.51/10.81 set(lex_order_vars).
% 10.51/10.81 clear(print_given).
% 10.51/10.81
% 10.51/10.81 % formulas(sos). % not echoed (10 formulas)
% 10.51/10.81
% 10.51/10.81 ============================== end of input ==========================
% 10.51/10.81
% 10.51/10.81 % From the command line: assign(max_seconds, 300).
% 10.51/10.81
% 10.51/10.81 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.51/10.81
% 10.51/10.81 % Formulas that are not ordinary clauses:
% 10.51/10.81
% 10.51/10.81 ============================== end of process non-clausal formulas ===
% 10.51/10.81
% 10.51/10.81 ============================== PROCESS INITIAL CLAUSES ===============
% 10.51/10.81
% 10.51/10.81 ============================== PREDICATE ELIMINATION =================
% 10.51/10.81
% 10.51/10.81 ============================== end predicate elimination =============
% 10.51/10.81
% 10.51/10.81 Auto_denials:
% 10.51/10.81 % copying label goals to answer in negative clause
% 10.51/10.81
% 10.51/10.81 Term ordering decisions:
% 10.51/10.81 Function symbol KB weights: op_b=1. op_a=1. unit=1. a=1. mult=1. ld=1. rd=1.
% 10.51/10.81
% 10.51/10.81 ============================== end of process initial clauses ========
% 10.51/10.81
% 10.51/10.81 ============================== CLAUSES FOR SEARCH ====================
% 10.51/10.81
% 10.51/10.81 ============================== end of clauses for search =============
% 10.51/10.81
% 10.51/10.81 ============================== SEARCH ================================
% 10.51/10.81
% 10.51/10.81 % Starting search at 0.01 seconds.
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=183.000, iters=3348
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=175.000, iters=3363
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=155.000, iters=3391
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=139.000, iters=3363
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=131.000, iters=3341
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=123.000, iters=3358
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=119.000, iters=3337
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=111.000, iters=3393
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=103.000, iters=3359
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=99.000, iters=3340
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=91.000, iters=3342
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=87.000, iters=3378
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=83.000, iters=3401
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=79.000, iters=3385
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=75.000, iters=3340
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=71.000, iters=3379
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=67.000, iters=3409
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=63.000, iters=3410
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=59.000, iters=3366
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=55.000, iters=3357
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=51.000, iters=3441
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=47.000, iters=3356
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=43.000, iters=3336
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=39.000, iters=3350
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=35.000, iters=3373
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=31.000, iters=3346
% 10.51/10.81
% 10.51/10.81 Low Water (keep): wt=27.000, iters=3394
% 10.51/10.81
% 10.51/10.81 ============================== PROOF =================================
% 10.51/10.81 % SZS status Unsatisfiable
% 10.51/10.81 % SZS output start Refutation
% 10.51/10.81
% 10.51/10.81 % Proof 1 at 9.67 (+ 0.09) seconds: goals.
% 10.51/10.81 % Length of proof is 157.
% 10.51/10.81 % Level of proof is 26.
% 10.51/10.81 % Maximum clause weight is 63.000.
% 10.51/10.81 % Given clauses 371.
% 10.51/10.81
% 10.51/10.81 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 10.51/10.81 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 10.51/10.81 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 10.51/10.81 4 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 10.51/10.81 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 10.51/10.81 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 10.51/10.81 8 mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) # label(c07) # label(axiom). [assumption].
% 10.51/10.81 9 mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))). [copy(8),flip(a)].
% 10.51/10.81 10 mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit # label(c09) # label(axiom). [assumption].
% 10.51/10.81 11 mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 10.51/10.81 12 mult(mult(op_a,op_b),a) != mult(op_a,mult(op_b,a)) # answer(goals). [copy(11),flip(a)].
% 10.51/10.81 14 ld(A,A) = unit. [para(1(a,1),4(a,1,2))].
% 10.51/10.81 16 ld(rd(A,B),A) = B. [para(5(a,1),4(a,1,2))].
% 10.51/10.81 17 rd(A,A) = unit. [para(2(a,1),6(a,1,1))].
% 10.51/10.81 18 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 10.51/10.81 20 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(9(a,1),1(a,1)),rewrite([1(2)]),flip(a)].
% 10.51/10.81 21 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(2(a,1),9(a,1,1,1)),rewrite([2(6)])].
% 10.51/10.81 22 mult(A,mult(B,mult(B,ld(mult(A,mult(B,B)),C)))) = C. [para(9(a,1),3(a,1)),rewrite([20(2)])].
% 10.51/10.81 23 mult(A,mult(ld(A,B),mult(ld(A,B),C))) = mult(mult(B,ld(A,B)),C). [para(3(a,1),9(a,1,1,1)),flip(a)].
% 10.51/10.81 25 ld(mult(A,mult(B,B)),mult(A,mult(B,mult(B,C)))) = C. [para(9(a,1),4(a,1,2)),rewrite([20(2)])].
% 10.51/10.81 26 mult(rd(A,B),mult(B,mult(B,C))) = mult(mult(A,B),C). [para(5(a,1),9(a,1,1,1)),flip(a)].
% 10.51/10.81 29 rd(mult(A,mult(B,mult(B,C))),C) = mult(A,mult(B,B)). [para(9(a,1),6(a,1,1)),rewrite([20(6)])].
% 10.51/10.81 31 mult(mult(A,mult(B,mult(B,B))),C) = mult(mult(A,B),mult(B,mult(B,C))). [para(9(a,1),9(a,1,1))].
% 10.51/10.81 32 mult(mult(A,mult(mult(B,mult(C,C)),mult(B,mult(C,C)))),D) = mult(A,mult(mult(B,mult(C,C)),mult(B,mult(C,mult(C,D))))). [para(9(a,1),9(a,2,2,2)),rewrite([20(2),20(5),20(6),20(9)])].
% 10.51/10.81 34 mult(mult(mult(A,mult(B,B)),mult(C,C)),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))). [para(9(a,1),9(a,2)),rewrite([20(2),20(4)])].
% 10.51/10.81 35 mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))). [back_rewrite(9),rewrite([20(2)])].
% 10.51/10.81 36 mult(mult(A,mult(B,mult(C,mult(C,mult(B,mult(C,C)))))),D) = mult(A,mult(B,mult(C,mult(C,mult(B,mult(C,mult(C,D))))))). [back_rewrite(32),rewrite([35(5),35(13)])].
% 10.51/10.81 37 mult(mult(A,mult(B,mult(B,mult(C,C)))),D) = mult(A,mult(B,mult(B,mult(C,mult(C,D))))). [back_rewrite(34),rewrite([35(4)])].
% 10.51/10.81 39 mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))) = ld(op_b,unit). [para(10(a,1),4(a,1,2)),flip(a)].
% 10.51/10.81 44 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(5(a,1),20(a,1,1)),flip(a)].
% 10.51/10.81 45 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(20(a,1),6(a,1,1))].
% 10.51/10.81 49 mult(A,mult(A,ld(mult(A,A),B))) = B. [para(21(a,1),3(a,1))].
% 10.51/10.81 50 ld(mult(A,A),mult(A,mult(A,B))) = B. [para(21(a,1),4(a,1,2))].
% 10.51/10.81 52 mult(mult(A,mult(A,B)),B) = mult(A,mult(A,mult(B,B))). [para(21(a,1),20(a,1,1)),rewrite([21(6)])].
% 10.51/10.81 60 mult(A,mult(A,ld(mult(B,mult(A,A)),C))) = ld(B,C). [para(22(a,1),4(a,1,2)),flip(a)].
% 10.51/10.81 70 mult(mult(A,ld(B,A)),ld(ld(B,A),C)) = mult(B,mult(ld(B,A),C)). [para(3(a,1),23(a,1,2,2)),flip(a)].
% 10.51/10.81 71 ld(A,mult(mult(B,ld(A,B)),C)) = mult(ld(A,B),mult(ld(A,B),C)). [para(23(a,1),4(a,1,2))].
% 10.51/10.81 89 ld(mult(A,mult(B,B)),mult(A,mult(B,C))) = ld(B,C). [para(3(a,1),25(a,1,2,2,2))].
% 10.51/10.81 100 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(44(a,1),4(a,1,2))].
% 10.51/10.81 101 rd(mult(A,B),mult(B,B)) = rd(A,B). [para(44(a,1),6(a,1,1))].
% 10.51/10.81 105 mult(rd(A,B),mult(B,C)) = mult(mult(A,B),ld(B,C)). [para(3(a,1),26(a,1,2,2))].
% 10.51/10.81 106 ld(rd(A,B),mult(mult(A,B),C)) = mult(B,mult(B,C)). [para(26(a,1),4(a,1,2))].
% 10.51/10.81 129 mult(rd(A,mult(B,mult(B,C))),mult(B,B)) = rd(A,C). [para(5(a,1),29(a,1,1)),flip(a)].
% 10.51/10.81 138 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(5(a,1),45(a,1,1)),flip(a)].
% 10.51/10.81 141 mult(A,ld(mult(A,A),B)) = ld(A,B). [para(49(a,1),4(a,1,2)),flip(a)].
% 10.51/10.81 144 ld(mult(A,A),mult(A,B)) = ld(A,B). [para(3(a,1),50(a,1,2,2))].
% 10.51/10.81 146 mult(mult(A,mult(A,mult(B,B))),C) = mult(A,mult(A,mult(B,mult(B,C)))). [para(50(a,1),23(a,1,2,1)),rewrite([144(5),4(3),21(4),144(10),4(8),52(7)]),flip(a)].
% 10.51/10.81 184 mult(mult(A,mult(B,mult(B,C))),C) = mult(A,mult(B,mult(B,mult(C,C)))). [para(35(a,1),20(a,1,1)),rewrite([35(8)])].
% 10.51/10.81 195 mult(mult(A,mult(B,mult(B,mult(C,mult(C,C))))),D) = mult(mult(A,mult(B,mult(B,C))),mult(C,mult(C,D))). [para(35(a,1),31(a,1,1)),rewrite([35(9)])].
% 10.51/10.81 204 ld(rd(unit,A),A) = mult(A,A). [para(2(a,1),100(a,1,2))].
% 10.51/10.81 217 rd(A,mult(A,A)) = rd(unit,A). [para(204(a,1),18(a,1,2))].
% 10.51/10.81 240 mult(mult(A,mult(B,mult(C,mult(C,mult(B,mult(C,mult(C,mult(D,mult(D,D))))))))),E) = mult(mult(A,mult(B,mult(C,mult(C,mult(B,mult(C,mult(C,D))))))),mult(D,mult(D,E))). [para(36(a,1),31(a,1,1)),rewrite([36(17)])].
% 10.51/10.81 247 mult(mult(A,mult(B,mult(C,mult(D,mult(D,mult(C,mult(D,mult(D,mult(B,mult(C,mult(D,mult(D,mult(C,mult(D,D)))))))))))))),E) = mult(A,mult(B,mult(C,mult(D,mult(D,mult(C,mult(D,mult(D,mult(B,mult(C,mult(D,mult(D,mult(C,mult(D,mult(D,E))))))))))))))). [para(36(a,1),35(a,1,1,2)),rewrite([36(28),36(29)])].
% 10.51/10.81 249 mult(mult(A,mult(B,mult(C,mult(C,mult(D,mult(D,mult(B,mult(C,mult(C,mult(D,D)))))))))),E) = mult(A,mult(B,mult(C,mult(C,mult(D,mult(D,mult(B,mult(C,mult(C,mult(D,mult(D,E))))))))))). [para(35(a,1),36(a,1,1,2,2,2,2)),rewrite([35(9),35(18),35(21)])].
% 10.51/10.81 262 rd(rd(A,B),B) = rd(A,mult(B,B)). [para(5(a,1),101(a,1,1)),flip(a)].
% 10.51/10.81 339 mult(rd(A,mult(mult(B,mult(B,C)),mult(B,mult(B,C)))),mult(B,B)) = rd(rd(A,mult(B,mult(B,C))),C). [para(138(a,1),29(a,1,1)),flip(a)].
% 10.51/10.81 357 ld(mult(A,A),B) = ld(A,ld(A,B)). [para(141(a,1),4(a,1,2)),flip(a)].
% 10.51/10.81 359 mult(A,mult(ld(A,unit),B)) = B. [para(141(a,1),23(a,2,1)),rewrite([357(3),14(2),357(5),14(4),21(8),23(7),2(4),14(5),2(6)])].
% 10.51/10.81 367 ld(ld(A,unit),B) = mult(A,B). [para(3(a,1),359(a,1,2)),flip(a)].
% 10.51/10.81 368 mult(ld(A,unit),B) = ld(A,B). [para(359(a,1),4(a,1,2)),flip(a)].
% 10.51/10.81 372 rd(ld(A,B),B) = ld(A,unit). [para(359(a,1),29(a,1,1)),rewrite([368(3),368(7),3(6)])].
% 10.51/10.81 375 mult(mult(A,mult(A,ld(B,mult(A,A)))),C) = mult(A,mult(A,ld(B,mult(A,mult(A,C))))). [para(359(a,1),36(a,1,1)),rewrite([368(4),368(12),368(13),3(12)])].
% 10.51/10.81 376 ld(A,mult(B,mult(B,C))) = mult(ld(A,mult(B,B)),C). [para(359(a,1),37(a,1,1)),rewrite([368(4),368(10),368(9),3(8)]),flip(a)].
% 10.51/10.81 379 mult(mult(A,mult(A,ld(B,mult(A,A)))),C) = mult(A,mult(A,mult(ld(B,mult(A,A)),C))). [back_rewrite(375),rewrite([376(8)])].
% 10.51/10.81 383 mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = ld(op_b,ld(op_b,unit)). [para(39(a,1),4(a,1,2)),flip(a)].
% 10.51/10.81 386 rd(ld(op_b,unit),mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(op_b,mult(op_b,op_b)). [para(39(a,1),29(a,1,1))].
% 10.51/10.81 393 rd(A,mult(B,A)) = ld(B,unit). [para(367(a,1),18(a,1,2))].
% 10.51/10.81 395 rd(unit,A) = ld(A,unit). [back_rewrite(217),rewrite([393(2)]),flip(a)].
% 10.51/10.81 401 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(368(a,1),20(a,1,1)),rewrite([368(6)]),flip(a)].
% 10.51/10.81 414 rd(ld(A,B),mult(B,B)) = rd(ld(A,unit),B). [para(368(a,1),101(a,1,1))].
% 10.51/10.81 423 mult(mult(A,mult(A,mult(ld(B,A),A))),C) = mult(A,mult(A,mult(mult(ld(B,A),A),C))). [back_rewrite(379),rewrite([401(2),401(7)])].
% 10.51/10.81 424 ld(A,mult(B,mult(B,C))) = mult(mult(ld(A,B),B),C). [back_rewrite(376),rewrite([401(5)])].
% 10.51/10.81 429 ld(rd(A,B),unit) = rd(B,A). [para(16(a,1),372(a,1,1)),flip(a)].
% 10.51/10.81 456 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))). [para(393(a,1),100(a,1,1)),rewrite([367(5)]),flip(a)].
% 10.51/10.81 460 rd(mult(A,A),B) = rd(A,rd(B,A)). [para(138(a,1),393(a,1,2)),rewrite([429(6)]),flip(a)].
% 10.51/10.81 464 mult(rd(A,mult(B,mult(mult(B,C),mult(B,mult(B,C))))),mult(B,B)) = rd(rd(A,mult(B,mult(B,C))),C). [back_rewrite(339),rewrite([456(5)])].
% 10.51/10.81 477 ld(rd(A,B),C) = mult(rd(B,A),C). [para(429(a,1),367(a,1,1))].
% 10.51/10.81 490 mult(rd(A,B),mult(mult(B,A),C)) = mult(A,mult(A,C)). [back_rewrite(106),rewrite([477(4)])].
% 10.51/10.81 491 mult(mult(A,B),ld(B,A)) = mult(A,A). [back_rewrite(100),rewrite([477(3),105(3)])].
% 10.51/10.81 623 ld(mult(A,mult(B,mult(B,mult(A,mult(B,B))))),C) = ld(mult(A,mult(B,B)),ld(mult(A,mult(B,B)),C)). [para(35(a,1),357(a,1,1))].
% 10.51/10.81 653 mult(mult(A,mult(A,mult(A,mult(A,B)))),B) = mult(A,mult(A,mult(A,mult(A,mult(B,B))))). [para(21(a,1),52(a,1,1,2)),rewrite([21(4),21(9),21(10)])].
% 10.51/10.81 726 mult(rd(A,rd(B,A)),C) = mult(A,mult(A,ld(B,C))). [para(5(a,1),60(a,1,2,2,1)),rewrite([477(6),460(5)]),flip(a)].
% 10.51/10.81 806 mult(A,mult(mult(ld(A,B),B),C)) = mult(B,mult(B,C)). [para(21(a,1),70(a,1,1)),rewrite([401(2),401(6),423(8),3(6),401(4)]),flip(a)].
% 10.51/10.81 849 rd(A,ld(B,unit)) = mult(A,B). [para(491(a,1),6(a,1,1)),rewrite([460(3),372(2)])].
% 10.51/10.81 871 rd(ld(A,unit),B) = ld(mult(B,A),unit). [para(491(a,1),393(a,1,2)),rewrite([414(3)])].
% 10.51/10.81 877 mult(A,mult(mult(A,B),mult(A,mult(A,B)))) = mult(A,mult(A,mult(B,mult(A,mult(A,B))))). [para(52(a,1),491(a,1,1)),rewrite([424(6),146(7),806(4),456(10)]),flip(a)].
% 10.51/10.81 912 ld(mult(op_b,mult(op_b,op_b)),ld(mult(op_b,mult(op_b,op_b)),unit)) = mult(op_b,mult(op_b,op_b)). [back_rewrite(386),rewrite([871(13),653(11),623(13)])].
% 10.51/10.81 942 rd(rd(A,mult(B,mult(B,C))),C) = rd(A,mult(C,mult(B,mult(B,C)))). [back_rewrite(464),rewrite([877(5),129(8)]),flip(a)].
% 10.51/10.81 952 mult(mult(A,mult(B,mult(B,ld(C,unit)))),C) = mult(A,mult(B,B)). [para(849(a,1),29(a,1))].
% 10.51/10.81 955 mult(A,ld(B,unit)) = rd(A,B). [para(367(a,1),849(a,1,2)),rewrite([1(2)]),flip(a)].
% 10.51/10.81 956 mult(ld(A,ld(B,unit)),B) = ld(A,unit). [para(849(a,1),372(a,1))].
% 10.51/10.81 960 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(477(a,1),849(a,1,2)),rewrite([1(3)])].
% 10.51/10.81 962 mult(mult(A,mult(B,rd(B,C))),C) = mult(A,mult(B,B)). [back_rewrite(952),rewrite([955(3)])].
% 10.51/10.81 985 mult(mult(A,rd(A,B)),C) = mult(A,mult(A,ld(B,C))). [back_rewrite(726),rewrite([960(2)])].
% 10.51/10.81 991 rd(mult(A,A),B) = mult(A,rd(A,B)). [back_rewrite(460),rewrite([960(4)])].
% 10.51/10.81 1023 mult(ld(A,ld(B,unit)),mult(ld(A,ld(B,unit)),C)) = ld(A,mult(ld(B,ld(A,ld(B,unit))),C)). [para(368(a,1),71(a,1,2,1)),flip(a)].
% 10.51/10.81 1038 ld(A,rd(A,B)) = ld(B,unit). [para(955(a,1),4(a,1,2))].
% 10.51/10.81 1039 mult(A,ld(B,ld(B,unit))) = rd(A,mult(B,B)). [para(955(a,1),20(a,1,1)),rewrite([955(4),262(2),955(7),871(5),357(5)]),flip(a)].
% 10.51/10.81 1045 mult(rd(A,mult(B,B)),C) = mult(A,ld(B,ld(B,C))). [para(955(a,1),35(a,1,1,2)),rewrite([871(3),357(3),1039(4),368(8),368(7)])].
% 10.51/10.81 1051 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(955(a,1),368(a,1)),rewrite([871(3)])].
% 10.51/10.81 1078 ld(mult(op_b,mult(op_b,op_b)),ld(op_b,ld(op_b,ld(op_b,unit)))) = mult(op_b,mult(op_b,op_b)). [back_rewrite(912),rewrite([1051(12),357(12)])].
% 10.51/10.81 1083 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [back_rewrite(871),rewrite([1051(6)])].
% 10.51/10.81 1114 ld(mult(A,B),A) = ld(B,unit). [para(6(a,1),1038(a,1,2))].
% 10.51/10.81 1115 ld(ld(A,B),unit) = ld(B,A). [para(18(a,1),1038(a,1,2)),flip(a)].
% 10.51/10.81 1191 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1115(a,1),367(a,1,1))].
% 10.51/10.81 1299 ld(mult(A,mult(B,B)),mult(A,C)) = ld(B,ld(B,C)). [para(3(a,1),89(a,1,2,2))].
% 10.51/10.81 1301 ld(mult(rd(A,mult(B,C)),mult(B,B)),A) = ld(B,C). [para(5(a,1),89(a,1,2))].
% 10.51/10.81 1354 mult(ld(A,ld(B,ld(A,unit))),A) = mult(B,rd(ld(B,ld(A,unit)),B)). [para(956(a,1),23(a,1,2,2)),rewrite([955(6),368(11)]),flip(a)].
% 10.51/10.81 1380 ld(A,mult(ld(B,ld(A,ld(B,unit))),B)) = rd(ld(A,ld(B,unit)),A). [para(956(a,1),71(a,2,2)),rewrite([368(6),955(12)])].
% 10.51/10.81 1397 ld(mult(A,rd(B,C)),D) = mult(rd(rd(C,B),A),D). [para(960(a,1),477(a,1,1))].
% 10.51/10.81 1444 ld(mult(A,B),ld(A,unit)) = ld(B,ld(A,ld(A,unit))). [para(21(a,1),1051(a,1,1)),rewrite([1051(4),357(7)])].
% 10.51/10.81 1448 ld(mult(A,mult(A,B)),ld(C,unit)) = ld(B,ld(A,ld(A,ld(C,unit)))). [para(35(a,1),1051(a,1,1)),rewrite([1051(5),1051(9),357(9)])].
% 10.51/10.81 1450 ld(mult(A,mult(A,B)),ld(C,ld(C,ld(D,unit)))) = ld(B,ld(A,ld(A,ld(C,ld(C,ld(D,unit)))))). [para(37(a,1),1051(a,1,1)),rewrite([1051(7),1448(7),1051(13),1448(13),357(13)])].
% 10.51/10.81 1451 mult(ld(A,ld(B,unit)),C) = ld(mult(B,A),C). [para(1051(a,1),368(a,1,1))].
% 10.51/10.81 1454 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(1051(a,1),955(a,1,2))].
% 10.51/10.81 1476 ld(op_b,ld(op_b,ld(op_b,ld(op_b,ld(op_b,ld(op_b,unit)))))) = mult(op_b,mult(op_b,op_b)). [back_rewrite(1078),rewrite([1450(13)])].
% 10.51/10.81 1486 ld(A,mult(ld(B,ld(A,ld(B,unit))),C)) = ld(mult(B,A),ld(mult(B,A),C)). [back_rewrite(1023),rewrite([1451(7),1451(6)]),flip(a)].
% 10.51/10.81 1501 rd(ld(A,ld(B,unit)),A) = ld(mult(B,A),ld(A,unit)). [back_rewrite(1380),rewrite([1486(6),1114(3)]),flip(a)].
% 10.51/10.82 1510 rd(A,mult(A,mult(B,A))) = mult(ld(B,ld(A,ld(B,unit))),B). [back_rewrite(1354),rewrite([1501(9),1454(10)]),flip(a)].
% 10.51/10.82 1514 rd(ld(A,ld(B,unit)),C) = ld(mult(B,A),ld(C,unit)). [para(1051(a,1),1083(a,1,1))].
% 10.51/10.82 1534 mult(mult(A,mult(A,B)),ld(B,C)) = mult(A,mult(A,C)). [para(21(a,1),105(a,2,1)),rewrite([991(2),985(4),4(2)]),flip(a)].
% 10.51/10.82 1557 ld(mult(A,B),mult(A,C)) = mult(ld(B,A),ld(A,C)). [para(368(a,1),105(a,2,1)),rewrite([1083(3),1451(5)])].
% 10.51/10.82 1619 mult(ld(A,ld(A,B)),ld(B,C)) = ld(A,ld(A,C)). [back_rewrite(1299),rewrite([1557(4),357(2)])].
% 10.51/10.82 1661 ld(mult(rd(A,B),C),D) = mult(ld(C,rd(B,A)),D). [para(477(a,1),1191(a,1,1))].
% 10.51/10.82 1673 mult(ld(A,ld(A,rd(mult(A,B),C))),C) = ld(A,B). [back_rewrite(1301),rewrite([1661(5),357(4)])].
% 10.51/10.82 1952 rd(rd(A,B),mult(C,C)) = rd(A,mult(C,mult(C,B))). [para(129(a,1),6(a,1,1))].
% 10.51/10.82 1962 mult(rd(A,mult(B,mult(B,C))),mult(B,mult(B,D))) = mult(rd(A,C),D). [para(129(a,1),35(a,1,1)),flip(a)].
% 10.51/10.82 1983 mult(rd(A,mult(B,mult(B,C))),D) = mult(rd(A,C),ld(B,ld(B,D))). [para(129(a,1),105(a,2,1)),rewrite([1952(5),21(7),1962(8),357(7)])].
% 10.51/10.82 2239 mult(ld(A,ld(B,ld(C,unit))),D) = ld(mult(mult(C,B),A),D). [para(1051(a,1),1451(a,1,1,2))].
% 10.51/10.82 2260 rd(A,mult(A,mult(B,A))) = ld(mult(mult(B,A),B),B). [back_rewrite(1510),rewrite([2239(8)])].
% 10.51/10.82 2261 ld(mult(A,B),ld(mult(A,B),C)) = ld(B,ld(mult(mult(A,B),A),C)). [back_rewrite(1486),rewrite([2239(5)]),flip(a)].
% 10.51/10.82 2299 mult(A,ld(B,ld(C,ld(D,unit)))) = rd(A,mult(mult(D,C),B)). [para(1051(a,1),1454(a,1,2,2))].
% 10.51/10.82 2911 mult(A,mult(A,ld(mult(B,A),C))) = mult(rd(A,B),C). [para(3(a,1),490(a,1,2)),flip(a)].
% 10.51/10.82 2956 mult(rd(A,B),rd(mult(B,A),C)) = mult(A,rd(A,C)). [para(955(a,1),490(a,1,2)),rewrite([955(7)])].
% 10.51/10.82 3934 rd(rd(A,mult(B,B)),C) = rd(A,mult(C,mult(B,B))). [para(962(a,1),393(a,1,2)),rewrite([1051(8),1397(8),262(5),955(8)]),flip(a)].
% 10.51/10.82 4031 rd(ld(A,B),mult(C,C)) = ld(A,rd(B,mult(C,C))). [para(985(a,1),1051(a,1,1)),rewrite([1051(5),1444(5),1191(5),1454(5),1051(7),477(7),955(7),262(5)])].
% 10.51/10.82 5930 mult(mult(A,mult(A,B)),C) = mult(A,mult(A,mult(B,C))). [para(4(a,1),1534(a,1,2))].
% 10.51/10.82 5963 mult(ld(A,ld(mult(mult(B,A),B),C)),ld(C,D)) = ld(A,ld(mult(mult(B,A),B),D)). [para(1451(a,1),1534(a,1,1,2)),rewrite([1451(6),2261(4),1451(13),1451(12),2261(10)])].
% 10.51/10.82 6868 rd(ld(A,ld(A,B)),C) = ld(A,ld(A,rd(B,C))). [para(1038(a,1),1619(a,1,2)),rewrite([955(5)])].
% 10.51/10.82 6869 ld(A,ld(mult(mult(B,A),B),B)) = ld(mult(B,A),ld(A,unit)). [para(1114(a,1),1619(a,2,2)),rewrite([2261(4),5963(6)])].
% 10.51/10.82 7428 ld(A,ld(A,rd(mult(A,B),C))) = rd(ld(A,B),C). [para(1673(a,1),6(a,1,1)),flip(a)].
% 10.51/10.82 11860 mult(A,rd(A,mult(B,mult(C,A)))) = rd(rd(A,C),B). [para(955(a,1),2911(a,2)),rewrite([1454(5)])].
% 10.51/10.82 12262 mult(A,ld(mult(mult(B,A),B),B)) = rd(rd(A,B),A). [para(2260(a,1),2956(a,2,2)),rewrite([2956(6),11860(4)]),flip(a)].
% 10.51/10.82 13957 rd(rd(A,mult(B,mult(B,C))),D) = rd(rd(A,C),mult(D,mult(B,B))). [para(1952(a,1),3934(a,1,1))].
% 10.51/10.82 13967 rd(rd(A,B),mult(B,mult(C,C))) = rd(A,mult(B,mult(C,mult(C,B)))). [back_rewrite(942),rewrite([13957(4)])].
% 10.51/10.82 15748 ld(A,rd(mult(A,B),C)) = mult(A,rd(ld(A,B),C)). [para(7428(a,1),3(a,1,2)),flip(a)].
% 10.51/10.82 18066 rd(A,mult(B,mult(A,mult(C,A)))) = ld(A,rd(rd(rd(A,C),A),B)). [para(12262(a,1),15748(a,1,2,1)),rewrite([6869(8),1514(9),1454(10)]),flip(a)].
% 10.51/10.82 19572 mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = ld(op_b,ld(op_b,ld(op_b,unit))). [para(383(a,1),4(a,1,2)),flip(a)].
% 10.51/10.82 19573 ld(op_b,ld(op_b,ld(op_b,ld(op_b,ld(op_b,unit))))) = mult(op_b,mult(op_b,mult(op_b,op_b))). [para(383(a,1),20(a,1,1)),rewrite([19572(16),2299(13),21(10),6868(11),395(9),1051(9),357(9),19572(23),19572(30),2299(27),21(24),6868(25),1083(23),1051(22),357(22),1476(25)])].
% 10.51/10.82 19574 mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,A))))))) = ld(op_b,ld(op_b,A)). [para(383(a,1),36(a,1,1)),rewrite([1451(6),357(4)]),flip(a)].
% 10.51/10.82 19575 ld(op_b,ld(op_b,ld(op_b,ld(op_b,unit)))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))). [para(383(a,1),456(a,1,1)),rewrite([19572(17),3(14),1454(11),4031(9),4031(8),395(7),357(7),19572(21),19572(29),3(26),1454(23),4031(21),4031(20),4031(19),395(18),357(18),19573(21)])].
% 10.51/10.82 19576 mult(A,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = rd(A,mult(op_b,mult(op_b,mult(op_b,op_b)))). [para(383(a,1),184(a,1,1,2,2)),rewrite([3(7),955(4),19572(13),2299(10),21(7),13967(8),19572(21),19572(28),2299(25),21(22),6868(23),1083(21),1051(20),357(20),19575(21),4(22),4(19)]),flip(a)].
% 10.51/10.82 19579 mult(rd(A,op_b),B) = mult(A,ld(op_b,B)). [para(383(a,1),195(a,2,1,2)),rewrite([19576(30),6(28),5930(13),5930(11),19576(13),18066(11),17(6),395(6),1083(8),3(10),3(7),955(4),1454(9),5930(26),5930(24),5930(27),5930(25),19574(24),3(15),3(12),1045(10),4(8)])].
% 10.51/10.82 19584 mult(A,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,B))))))) = mult(A,ld(op_b,ld(op_b,ld(op_b,B)))). [para(383(a,1),240(a,2,1,2,2,2)),rewrite([456(22),21(21),19576(22),18066(20),17(15),395(15),1083(17),2299(19),21(16),17(17),1(8),19576(11),18066(9),17(4),395(4),1083(6),2299(8),21(5),1983(7),19579(7),3(15),3(12),1(9),5930(18),5930(19)]),flip(a)].
% 10.51/10.82 19585 mult(A,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,B)))))) = mult(A,ld(op_b,ld(op_b,ld(op_b,ld(op_b,B))))). [para(383(a,1),247(a,1,1,2,2,2,2,2,2,2,2)),rewrite([3(13),3(10),1(7),19576(10),1983(9),1045(9),19584(30),3(24),3(21),3(18)]),flip(a)].
% 10.51/10.82 19586 mult(mult(A,op_b),B) = mult(A,mult(op_b,B)). [para(383(a,1),249(a,1,1,2,2,2,2)),rewrite([3(9),3(6),1(3),19585(19),3(17),3(14),3(11),3(8)])].
% 10.51/10.82 19587 $F # answer(goals). [resolve(19586,a,12,a)].
% 10.51/10.82
% 10.51/10.82 % SZS output end Refutation
% 10.51/10.82 ============================== end of proof ==========================
% 10.51/10.82
% 10.51/10.82 ============================== STATISTICS ============================
% 10.51/10.82
% 10.51/10.82 Given=371. Generated=134122. Kept=19584. proofs=1.
% 10.51/10.82 Usable=245. Sos=9951. Demods=9729. Limbo=14, Disabled=9383. Hints=0.
% 10.51/10.82 Megabytes=29.36.
% 10.51/10.82 User_CPU=9.67, System_CPU=0.09, Wall_clock=10.
% 10.51/10.82
% 10.51/10.82 ============================== end of statistics =====================
% 10.51/10.82
% 10.51/10.82 ============================== end of search =========================
% 10.51/10.82
% 10.51/10.82 THEOREM PROVED
% 10.51/10.82 % SZS status Unsatisfiable
% 10.51/10.82
% 10.51/10.82 Exiting with 1 proof.
% 10.51/10.82
% 10.51/10.82 Process 346 exit (max_proofs) Tue Jun 14 10:49:47 2022
% 10.51/10.82 Prover9 interrupted
%------------------------------------------------------------------------------