TSTP Solution File: GRP654+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP654+3 : 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 11:20:18 EDT 2022
% Result : Theorem 113.10s 113.46s
% Output : Refutation 113.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP654+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 03:30:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.96/4.25 ============================== Prover9 ===============================
% 3.96/4.25 Prover9 (32) version 2009-11A, November 2009.
% 3.96/4.25 Process 16729 was started by sandbox on n017.cluster.edu,
% 3.96/4.25 Tue Jun 14 03:30:54 2022
% 3.96/4.25 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16574_n017.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_16574_n017.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 (6 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 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 3.96/4.25 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 3.96/4.25 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 3.96/4.25 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 3.96/4.25 5 (all C all B all A mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 3.96/4.25 6 -(all X0 all X1 (mult(X0,ld(X1,X1)) = X0 & mult(ld(X1,X1),X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 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 Function symbol KB weights: c1=1. c2=1. mult=1. ld=1. rd=1.
% 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=95.000, iters=3551
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=71.000, iters=3416
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=67.000, iters=3366
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=59.000, iters=3343
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=55.000, iters=3346
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=51.000, iters=3357
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=47.000, iters=3384
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=43.000, iters=3335
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=39.000, iters=3358
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=35.000, iters=3372
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=31.000, iters=3333
% 3.96/4.25
% 3.96/4.25 Low Water (keep): wt=27.000, iters=3373
% 3.96/4.25
% 3.96/4.25 Low Water (displace): id=6061, wt=135.000
% 113.10/113.46
% 113.10/113.46 Low Water (displace): id=7089, wt=119.000
% 113.10/113.46
% 113.10/113.46 Low Water (displace): id=12687, wt=23.000
% 113.10/113.46
% 113.10/113.46 Low Water (displace): id=12930, wt=19.000
% 113.10/113.46
% 113.10/113.46 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 9.93 sec).
% 113.10/113.46
% 113.10/113.46 Low Water (keep): wt=23.000, iters=3339
% 113.10/113.46
% 113.10/113.46 ============================== PROOF =================================
% 113.10/113.46 % SZS status Theorem
% 113.10/113.46 % SZS output start Refutation
% 113.10/113.46
% 113.10/113.46 % Proof 1 at 110.25 (+ 2.22) seconds: goals.
% 113.10/113.46 % Length of proof is 234.
% 113.10/113.46 % Level of proof is 38.
% 113.10/113.46 % Maximum clause weight is 39.000.
% 113.10/113.46 % Given clauses 1568.
% 113.10/113.46
% 113.10/113.46 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 113.10/113.46 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 113.10/113.46 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 113.10/113.46 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 113.10/113.46 5 (all C all B all A mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 113.10/113.46 6 -(all X0 all X1 (mult(X0,ld(X1,X1)) = X0 & mult(ld(X1,X1),X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 113.10/113.46 7 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 113.10/113.46 8 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 113.10/113.46 9 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 113.10/113.46 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 113.10/113.46 11 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f05) # label(axiom). [clausify(5)].
% 113.10/113.46 12 mult(c1,ld(c2,c2)) != c1 | mult(ld(c2,c2),c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)].
% 113.10/113.46 14 rd(A,ld(B,A)) = B. [para(7(a,1),10(a,1,1))].
% 113.10/113.46 15 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C. [para(11(a,1),7(a,1))].
% 113.10/113.46 16 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C). [para(7(a,1),11(a,1,1,1)),flip(a)].
% 113.10/113.46 17 ld(mult(mult(A,B),A),mult(A,mult(B,mult(A,C)))) = C. [para(11(a,1),8(a,1,2))].
% 113.10/113.46 18 mult(rd(A,B),mult(B,mult(rd(A,B),C))) = mult(mult(A,rd(A,B)),C). [para(9(a,1),11(a,1,1,1)),flip(a)].
% 113.10/113.46 19 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A). [para(11(a,1),10(a,1,1))].
% 113.10/113.46 22 mult(A,mult(B,ld(mult(mult(B,A),B),C))) = ld(B,C). [para(15(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 26 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(7(a,1),16(a,1,2,2)),flip(a)].
% 113.10/113.46 27 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)). [para(16(a,1),8(a,1,2))].
% 113.10/113.46 29 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B. [para(16(a,1),10(a,1,1))].
% 113.10/113.46 39 ld(mult(A,mult(ld(A,ld(A,B)),B)),mult(ld(A,B),mult(mult(B,A),C))) = mult(A,C). [para(16(a,1),17(a,1,2,2)),rewrite([26(4)])].
% 113.10/113.46 40 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(9(a,1),18(a,1,2,2)),flip(a)].
% 113.10/113.46 42 mult(rd(A,B),mult(mult(B,mult(rd(A,B),C)),mult(rd(A,B),D))) = mult(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D). [para(18(a,1),11(a,1,1,1)),flip(a)].
% 113.10/113.46 46 rd(mult(A,mult(B,C)),ld(A,C)) = mult(mult(A,B),A). [para(7(a,1),19(a,1,1,2,2))].
% 113.10/113.46 48 mult(mult(A,rd(B,mult(A,C))),A) = rd(mult(A,B),C). [para(9(a,1),19(a,1,1,2)),flip(a)].
% 113.10/113.46 55 mult(ld(A,B),mult(A,ld(mult(B,A),C))) = ld(A,C). [para(7(a,1),22(a,1,2,2,1,1))].
% 113.10/113.46 56 mult(A,ld(mult(mult(A,B),A),C)) = ld(B,ld(A,C)). [para(22(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 63 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C). [para(26(a,1),8(a,1,2))].
% 113.10/113.46 64 mult(A,mult(ld(A,rd(B,A)),C)) = mult(B,ld(A,C)). [para(9(a,1),26(a,1,1)),flip(a)].
% 113.10/113.46 74 mult(ld(A,rd(B,A)),mult(A,C)) = ld(A,mult(B,C)). [para(9(a,1),27(a,1,2,1)),flip(a)].
% 113.10/113.46 130 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A). [para(9(a,1),46(a,1,1,2))].
% 113.10/113.46 147 ld(mult(A,rd(B,mult(A,C))),rd(mult(A,B),C)) = A. [para(48(a,1),8(a,1,2))].
% 113.10/113.46 149 rd(rd(mult(A,B),C),A) = mult(A,rd(B,mult(A,C))). [para(48(a,1),10(a,1,1))].
% 113.10/113.46 151 mult(A,mult(rd(B,mult(A,C)),mult(A,D))) = mult(rd(mult(A,B),C),D). [para(48(a,1),11(a,1,1)),flip(a)].
% 113.10/113.46 168 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)). [para(55(a,1),8(a,1,2))].
% 113.10/113.46 184 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))). [para(56(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 189 mult(rd(A,B),ld(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D)) = ld(mult(B,mult(rd(A,B),C)),ld(rd(A,B),D)). [para(18(a,1),56(a,1,2,1,1))].
% 113.10/113.46 205 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)). [para(7(a,1),63(a,1,2,2))].
% 113.10/113.46 225 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C). [para(64(a,1),8(a,1,2))].
% 113.10/113.46 226 rd(mult(A,ld(B,C)),mult(ld(B,rd(A,B)),C)) = B. [para(64(a,1),10(a,1,1))].
% 113.10/113.46 229 mult(mult(A,B),mult(ld(B,rd(C,B)),D)) = mult(B,mult(ld(B,A),mult(C,ld(B,D)))). [para(64(a,1),16(a,1,2,2)),flip(a)].
% 113.10/113.46 264 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)). [para(7(a,1),130(a,1,1)),flip(a)].
% 113.10/113.46 284 ld(mult(A,rd(B,mult(A,B))),A) = A. [para(10(a,1),147(a,1,2))].
% 113.10/113.46 334 ld(mult(A,rd(ld(A,B),B)),A) = A. [para(7(a,1),284(a,1,1,2,2))].
% 113.10/113.46 337 mult(A,rd(B,mult(A,B))) = rd(A,A). [para(284(a,1),14(a,1,2)),flip(a)].
% 113.10/113.46 350 mult(A,rd(ld(A,B),B)) = rd(A,A). [para(334(a,1),14(a,1,2)),flip(a)].
% 113.10/113.46 353 rd(A,mult(B,A)) = ld(B,rd(B,B)). [para(337(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 354 rd(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [para(9(a,1),337(a,1,2,2)),flip(a)].
% 113.10/113.46 360 mult(rd(A,A),B) = mult(ld(A,A),B). [para(337(a,1),18(a,2,1)),rewrite([353(2),353(5),229(7),7(5),74(6),8(4)]),flip(a)].
% 113.10/113.46 363 mult(ld(A,A),A) = A. [para(337(a,1),19(a,2,1)),rewrite([151(5),10(2),10(2),360(2)]),flip(a)].
% 113.10/113.46 367 mult(ld(A,B),mult(A,rd(C,mult(mult(B,A),C)))) = ld(A,rd(mult(B,A),mult(B,A))). [para(337(a,1),27(a,1,2)),flip(a)].
% 113.10/113.46 390 ld(ld(A,A),A) = A. [para(363(a,1),8(a,1,2))].
% 113.10/113.46 391 rd(A,A) = ld(A,A). [para(363(a,1),10(a,1,1))].
% 113.10/113.46 394 mult(mult(A,ld(mult(A,B),mult(A,B))),A) = rd(mult(A,mult(A,B)),B). [para(363(a,1),19(a,1,1,2)),flip(a)].
% 113.10/113.46 399 mult(ld(A,ld(A,A)),B) = ld(A,B). [para(363(a,1),55(a,1,2,2,1)),rewrite([7(4)])].
% 113.10/113.46 400 mult(mult(A,ld(mult(B,A),B)),ld(A,B)) = ld(A,B). [para(363(a,1),64(a,2)),rewrite([168(3),64(7)])].
% 113.10/113.46 426 mult(ld(A,B),mult(A,rd(C,mult(mult(B,A),C)))) = ld(A,ld(mult(B,A),mult(B,A))). [back_rewrite(367),rewrite([391(9)])].
% 113.10/113.46 433 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [back_rewrite(354),rewrite([391(3)])].
% 113.10/113.46 434 rd(A,mult(B,A)) = ld(B,ld(B,B)). [back_rewrite(353),rewrite([391(3)])].
% 113.10/113.46 435 mult(A,rd(ld(A,B),B)) = ld(A,A). [back_rewrite(350),rewrite([391(4)])].
% 113.10/113.46 436 mult(A,rd(B,mult(A,B))) = ld(A,A). [back_rewrite(337),rewrite([391(4)])].
% 113.10/113.46 464 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)). [para(390(a,1),26(a,2,2,1)),rewrite([7(2)]),flip(a)].
% 113.10/113.46 466 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A). [para(390(a,1),29(a,1,2,1)),rewrite([7(2)])].
% 113.10/113.46 467 mult(A,mult(ld(A,A),ld(A,B))) = ld(ld(A,A),B). [para(390(a,1),55(a,1,1)),rewrite([7(3)])].
% 113.10/113.46 473 rd(ld(A,B),B) = ld(A,ld(A,A)). [para(399(a,1),10(a,1,1))].
% 113.10/113.46 477 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)). [para(399(a,1),19(a,1,1,2,2)),rewrite([399(5),225(3),10(4),399(5)]),flip(a)].
% 113.10/113.46 479 mult(A,mult(ld(A,ld(B,ld(B,B))),C)) = mult(ld(B,A),ld(A,C)). [para(399(a,1),26(a,1,1)),flip(a)].
% 113.10/113.46 489 rd(ld(A,B),ld(ld(A,ld(A,A)),C)) = ld(A,rd(rd(B,C),A)). [para(399(a,1),130(a,1,1)),rewrite([399(9),477(10)])].
% 113.10/113.46 523 ld(ld(A,ld(A,A)),B) = mult(A,B). [para(363(a,1),39(a,1,2,2,1)),rewrite([479(6),477(4),391(1),399(6),8(4)])].
% 113.10/113.46 526 ld(A,mult(ld(A,A),mult(mult(A,A),B))) = mult(A,B). [para(399(a,1),39(a,1,1,2)),rewrite([7(2)])].
% 113.10/113.46 530 rd(ld(A,B),mult(A,C)) = ld(A,rd(rd(B,C),A)). [back_rewrite(489),rewrite([523(4)])].
% 113.10/113.46 552 mult(rd(A,mult(B,A)),C) = ld(B,C). [para(434(a,2),55(a,1,1)),rewrite([363(4),7(4)])].
% 113.10/113.46 558 mult(A,rd(B,mult(C,B))) = mult(A,ld(C,ld(C,C))). [para(434(a,2),64(a,2,2)),rewrite([64(5)]),flip(a)].
% 113.10/113.46 566 rd(A,mult(B,A)) = rd(C,mult(B,C)). [para(434(a,2),434(a,2))].
% 113.10/113.46 582 mult(A,ld(B,rd(ld(ld(B,rd(A,B)),C),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [para(435(a,1),64(a,1,2)),rewrite([168(5),9(2)]),flip(a)].
% 113.10/113.46 612 mult(rd(ld(A,B),B),C) = ld(A,C). [para(473(a,2),55(a,1,1)),rewrite([363(4),7(4)])].
% 113.10/113.46 615 mult(A,rd(ld(B,C),C)) = mult(A,ld(B,ld(B,B))). [para(473(a,2),64(a,2,2)),rewrite([64(5)]),flip(a)].
% 113.10/113.46 618 rd(ld(A,B),B) = rd(C,mult(A,C)). [para(473(a,2),434(a,2)),flip(a)].
% 113.10/113.46 619 rd(ld(A,B),B) = rd(ld(A,C),C). [para(473(a,2),473(a,2))].
% 113.10/113.46 654 ld(rd(A,B),C) = mult(rd(B,A),C). [para(9(a,1),552(a,1,1,2)),flip(a)].
% 113.10/113.46 656 mult(rd(A,mult(B,mult(C,mult(B,A)))),D) = ld(B,ld(C,ld(B,D))). [para(11(a,1),552(a,1,1,2)),rewrite([184(8)])].
% 113.10/113.46 659 mult(ld(A,B),rd(C,mult(A,C))) = ld(A,rd(B,A)). [para(552(a,1),19(a,1,1,2,2)),rewrite([552(5),225(3),10(4),552(5)]),flip(a)].
% 113.10/113.46 664 mult(ld(A,rd(B,mult(C,B))),mult(A,D)) = ld(A,mult(ld(C,A),D)). [para(552(a,1),27(a,1,2,1)),flip(a)].
% 113.10/113.46 670 ld(mult(A,rd(B,mult(A,C))),D) = mult(rd(A,rd(mult(A,B),C)),D). [para(48(a,1),552(a,1,1,2)),flip(a)].
% 113.10/113.46 676 ld(ld(A,rd(B,A)),C) = mult(A,ld(B,mult(A,C))). [para(74(a,1),552(a,1,1,2)),rewrite([130(4),11(5),552(4)]),flip(a)].
% 113.10/113.46 678 ld(ld(A,A),B) = mult(ld(A,A),B). [para(363(a,1),552(a,1,1,2)),rewrite([391(1)]),flip(a)].
% 113.10/113.46 689 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)). [back_rewrite(433),rewrite([654(3)])].
% 113.10/113.46 713 mult(rd(A,B),ld(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D)) = ld(mult(B,mult(rd(A,B),C)),mult(rd(B,A),D)). [back_rewrite(189),rewrite([654(13)])].
% 113.10/113.46 743 mult(A,ld(B,rd(mult(B,ld(A,mult(B,C))),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [back_rewrite(582),rewrite([676(3)])].
% 113.10/113.46 756 mult(A,mult(ld(A,A),ld(A,B))) = mult(ld(A,A),B). [back_rewrite(467),rewrite([678(6)])].
% 113.10/113.46 757 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)). [back_rewrite(464),rewrite([678(5)])].
% 113.10/113.46 765 rd(A,mult(rd(B,C),A)) = rd(C,B). [para(9(a,1),566(a,1,2)),flip(a)].
% 113.10/113.46 773 rd(A,mult(ld(B,B),A)) = ld(B,B). [para(363(a,1),566(a,1,2)),rewrite([391(1)]),flip(a)].
% 113.10/113.46 778 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(7(a,1),42(a,2)),rewrite([713(12),7(11)])].
% 113.10/113.46 807 rd(mult(mult(A,mult(rd(B,A),C)),mult(rd(B,A),D)),mult(mult(mult(mult(B,rd(B,A)),C),rd(B,A)),D)) = mult(rd(A,B),mult(rd(A,B),rd(B,A))). [para(42(a,1),434(a,1,2)),rewrite([654(17),654(18)])].
% 113.10/113.46 817 mult(rd(A,B),mult(rd(A,B),rd(B,A))) = rd(A,B). [para(42(a,1),566(a,1,2)),rewrite([807(13),765(8)])].
% 113.10/113.46 826 mult(ld(A,B),rd(ld(A,C),C)) = ld(A,rd(B,A)). [para(612(a,1),19(a,1,1,2,2)),rewrite([612(5),225(3),10(4),612(5)]),flip(a)].
% 113.10/113.46 845 rd(mult(A,B),mult(C,mult(A,B))) = rd(ld(C,D),D). [para(618(a,2),48(a,2)),rewrite([48(6)])].
% 113.10/113.46 895 mult(ld(A,A),mult(ld(A,A),B)) = B. [para(678(a,1),7(a,1,2))].
% 113.10/113.46 898 mult(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),mult(mult(B,ld(A,A)),C)). [para(678(a,1),27(a,1)),rewrite([678(7)]),flip(a)].
% 113.10/113.46 899 mult(A,mult(ld(A,A),ld(mult(A,A),B))) = ld(A,B). [para(55(a,1),678(a,2)),rewrite([678(5),757(5)])].
% 113.10/113.46 904 rd(A,ld(B,ld(C,ld(B,A)))) = mult(mult(B,C),B). [para(19(a,1),765(a,2)),rewrite([656(5)])].
% 113.10/113.46 914 mult(ld(mult(ld(A,A),B),ld(A,A)),mult(mult(ld(A,A),B),C)) = ld(B,ld(ld(B,ld(A,A)),C)). [para(773(a,1),74(a,1,1,2)),rewrite([205(12)])].
% 113.10/113.46 964 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)). [para(55(a,1),895(a,1,2))].
% 113.10/113.46 971 mult(A,mult(A,ld(mult(A,A),B))) = mult(ld(A,A),B). [back_rewrite(756),rewrite([964(3)])].
% 113.10/113.46 990 mult(A,rd(rd(ld(A,B),B),mult(A,C))) = rd(rd(ld(A,A),C),A). [para(435(a,1),149(a,1,1,1)),flip(a)].
% 113.10/113.46 1029 ld(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),ld(mult(B,ld(A,A)),C)). [para(678(a,1),168(a,1,1)),rewrite([678(4)])].
% 113.10/113.46 1030 rd(A,mult(mult(B,ld(mult(C,B),C)),A)) = mult(B,ld(mult(C,B),C)). [para(168(a,1),773(a,1,2,1)),rewrite([168(8)])].
% 113.10/113.46 1046 mult(A,ld(mult(A,A),mult(ld(A,A),B))) = ld(A,B). [para(363(a,1),184(a,1,1,1)),rewrite([7(2),678(4),678(6),964(6)]),flip(a)].
% 113.10/113.46 1129 mult(ld(mult(A,A),ld(A,A)),B) = ld(mult(A,A),B). [para(205(a,1),399(a,1,1,2)),rewrite([678(3),363(3)])].
% 113.10/113.46 1133 rd(A,mult(mult(B,B),A)) = ld(mult(B,B),ld(B,B)). [para(205(a,1),434(a,2,2)),rewrite([678(6),363(6)])].
% 113.10/113.46 1139 rd(ld(mult(A,A),B),B) = ld(mult(A,A),ld(A,A)). [para(205(a,1),473(a,2,2)),rewrite([678(6),363(6)])].
% 113.10/113.46 1168 mult(ld(A,rd(ld(B,ld(B,B)),A)),C) = ld(A,ld(B,ld(A,C))). [para(399(a,1),225(a,1,2)),flip(a)].
% 113.10/113.46 1213 rd(rd(A,ld(B,C)),B) = mult(B,rd(ld(B,A),C)). [para(264(a,1),10(a,1,1))].
% 113.10/113.46 1241 rd(A,rd(B,mult(C,B))) = rd(A,ld(C,ld(C,C))). [para(434(a,2),264(a,2,2)),rewrite([264(5)]),flip(a)].
% 113.10/113.46 1243 rd(A,rd(ld(B,C),C)) = rd(A,ld(B,ld(B,B))). [para(473(a,2),264(a,2,2)),rewrite([264(5)]),flip(a)].
% 113.10/113.46 1330 mult(mult(A,ld(B,rd(B,A))),ld(A,rd(B,A))) = ld(A,rd(B,A)). [para(9(a,1),400(a,1,1,2,1))].
% 113.10/113.46 1381 rd(mult(A,mult(A,B)),mult(mult(A,A),B)) = ld(A,A). [para(16(a,1),466(a,1,2))].
% 113.10/113.46 1386 rd(mult(A,mult(A,B)),mult(ld(A,A),B)) = mult(A,A). [para(466(a,1),48(a,1,1,2)),rewrite([7(2)]),flip(a)].
% 113.10/113.46 1398 mult(A,ld(mult(A,A),A)) = ld(A,A). [para(435(a,1),466(a,1,1)),rewrite([826(5),391(2),7(4),391(3),678(3),964(3)])].
% 113.10/113.46 1415 ld(mult(A,A),A) = ld(A,ld(A,A)). [para(1398(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 1419 mult(rd(ld(A,ld(A,A)),A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [para(1398(a,1),40(a,2,2)),rewrite([1415(2),1415(4),399(6),1168(5),1415(5)]),flip(a)].
% 113.10/113.46 1428 rd(A,ld(A,ld(A,A))) = mult(A,A). [para(1415(a,1),14(a,1,2))].
% 113.10/113.46 1429 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(mult(A,mult(A,A)),B). [para(1415(a,1),16(a,1,2,1)),rewrite([399(6),27(4),757(4)])].
% 113.10/113.46 1438 rd(ld(A,ld(A,A)),A) = ld(mult(A,A),ld(A,A)). [para(1415(a,1),473(a,1,1)),rewrite([205(7),678(6),363(6)])].
% 113.10/113.46 1446 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [back_rewrite(1419),rewrite([1438(3),1129(5)])].
% 113.10/113.46 1447 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))). [back_rewrite(1438),rewrite([1446(6)])].
% 113.10/113.46 1450 rd(ld(mult(A,A),B),B) = ld(A,ld(A,ld(A,A))). [back_rewrite(1139),rewrite([1446(6)])].
% 113.10/113.46 1451 rd(A,mult(mult(B,B),A)) = ld(B,ld(B,ld(B,B))). [back_rewrite(1133),rewrite([1446(6)])].
% 113.10/113.46 1452 mult(ld(A,ld(A,ld(A,A))),B) = ld(mult(A,A),B). [back_rewrite(1129),rewrite([1446(3)])].
% 113.10/113.46 1504 rd(A,rd(B,mult(A,B))) = mult(A,A). [para(434(a,2),1428(a,1,2))].
% 113.10/113.46 1505 rd(A,rd(ld(A,B),B)) = mult(A,A). [para(473(a,2),1428(a,1,2))].
% 113.10/113.46 1512 mult(mult(A,mult(A,A)),B) = mult(A,mult(A,mult(A,B))). [para(1428(a,1),225(a,2,1,2)),rewrite([523(5),523(5),523(7)]),flip(a)].
% 113.10/113.46 1520 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(A,mult(A,mult(A,B))). [back_rewrite(1429),rewrite([1512(8)])].
% 113.10/113.46 1521 mult(mult(A,A),rd(B,mult(A,B))) = A. [para(1504(a,1),9(a,1,1))].
% 113.10/113.46 1537 mult(mult(A,A),rd(ld(A,B),B)) = A. [para(1505(a,1),9(a,1,1))].
% 113.10/113.46 1550 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1521(a,1),19(a,2,1)),rewrite([552(6),27(4),757(4),1520(5),19(4)])].
% 113.10/113.46 1574 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(mult(A,mult(A,A)),B). [para(1521(a,1),184(a,1,1,1)),rewrite([654(9),10(6),225(8),434(6)]),flip(a)].
% 113.10/113.46 1689 ld(mult(A,mult(A,A)),B) = ld(A,ld(A,ld(A,B))). [para(1550(a,1),184(a,1,1))].
% 113.10/113.46 1699 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1574),rewrite([1689(8)])].
% 113.10/113.46 1707 mult(A,ld(mult(B,A),rd(B,A))) = ld(A,ld(A,A)). [para(477(a,1),8(a,1,2)),rewrite([168(4)])].
% 113.10/113.46 1708 ld(A,rd(mult(A,B),A)) = mult(B,ld(A,ld(A,A))). [para(8(a,1),477(a,1,1)),flip(a)].
% 113.10/113.46 1719 mult(A,ld(B,ld(B,ld(B,B)))) = rd(rd(A,B),B). [para(477(a,1),64(a,1,2)),rewrite([7(4)]),flip(a)].
% 113.10/113.46 1732 mult(A,rd(B,ld(A,ld(A,A)))) = mult(mult(A,B),A). [para(523(a,1),477(a,1,1)),rewrite([168(8),363(5),7(6),168(5),363(3),7(3),523(8)]),flip(a)].
% 113.10/113.46 1739 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,A),A)). [para(619(a,1),477(a,2,2)),rewrite([477(5)]),flip(a)].
% 113.10/113.46 1742 mult(mult(ld(A,A),B),ld(A,A)) = mult(ld(A,A),rd(B,ld(A,A))). [para(678(a,1),477(a,1,1)),rewrite([678(6),964(6),1415(5),7(6),678(5),964(5),1415(4),7(5),678(8)])].
% 113.10/113.46 1757 rd(ld(A,ld(A,ld(A,A))),A) = ld(mult(A,A),ld(A,ld(A,A))). [para(1415(a,1),477(a,1,1)),rewrite([205(6),678(5),363(5),1446(5),1719(6),1447(3),434(7)])].
% 113.10/113.46 1765 ld(mult(A,A),ld(A,ld(A,A))) = ld(A,ld(A,ld(A,ld(A,A)))). [para(477(a,1),1550(a,1,1)),rewrite([473(2),477(6),1447(3),477(11),473(8),1719(10),1447(7),1757(8)]),flip(a)].
% 113.10/113.46 1839 mult(ld(A,ld(A,ld(A,ld(A,A)))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1699),rewrite([1765(4)])].
% 113.10/113.46 1872 ld(A,mult(ld(A,A),B)) = mult(A,ld(mult(A,A),B)). [para(7(a,1),526(a,1,2,2))].
% 113.10/113.46 1944 mult(rd(A,rd(B,mult(C,B))),ld(C,ld(C,C))) = A. [para(558(a,1),9(a,1))].
% 113.10/113.46 2006 mult(A,rd(B,mult(mult(C,C),B))) = rd(rd(A,C),C). [para(205(a,1),558(a,2,2,2)),rewrite([678(7),363(7),1446(7),1719(8)])].
% 113.10/113.46 2188 mult(A,rd(ld(mult(B,B),C),C)) = rd(rd(A,B),B). [para(205(a,1),615(a,2,2,2)),rewrite([678(7),363(7),1446(7),1719(8)])].
% 113.10/113.46 2232 rd(rd(A,mult(B,A)),ld(B,rd(C,B))) = rd(D,mult(ld(B,C),D)). [para(659(a,1),566(a,1,2))].
% 113.10/113.46 2269 rd(A,mult(B,ld(C,mult(B,A)))) = ld(B,rd(C,B)). [para(676(a,1),14(a,1,2))].
% 113.10/113.46 2622 rd(ld(A,B),mult(C,ld(A,B))) = rd(ld(C,D),D). [para(55(a,1),845(a,1,1)),rewrite([55(6)])].
% 113.10/113.46 2669 mult(ld(A,A),ld(mult(A,A),B)) = ld(A,ld(A,B)). [para(899(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 2772 rd(ld(A,A),ld(A,ld(B,rd(C,mult(A,C))))) = mult(mult(A,B),A). [para(434(a,2),904(a,1,2,2,2))].
% 113.10/113.46 2987 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)). [para(1046(a,1),225(a,1,2)),rewrite([434(6),1765(7),1839(10),1872(6),8(7)])].
% 113.10/113.46 3202 rd(rd(A,ld(B,ld(B,B))),mult(B,B)) = mult(mult(B,B),rd(ld(mult(B,B),A),B)). [para(1415(a,1),1213(a,1,1,2))].
% 113.10/113.46 3230 rd(A,rd(ld(B,C),C)) = rd(A,rd(D,mult(B,D))). [para(473(a,2),1241(a,2,2)),flip(a)].
% 113.10/113.46 3345 rd(A,rd(ld(B,C),C)) = rd(A,rd(ld(B,D),D)). [para(473(a,2),1243(a,2,2))].
% 113.10/113.46 3563 rd(ld(A,ld(A,B)),ld(mult(A,A),B)) = ld(A,A). [para(399(a,1),1381(a,1,1,2)),rewrite([399(4),477(7),473(4),1452(6),168(10),363(7),7(8)])].
% 113.10/113.46 3638 rd(mult(ld(A,A),B),ld(A,ld(A,B))) = mult(A,A). [para(971(a,1),1386(a,1,1)),rewrite([2669(6)])].
% 113.10/113.46 3798 rd(A,rd(ld(mult(B,B),C),C)) = mult(mult(A,B),B). [para(1450(a,2),264(a,2,2)),rewrite([1732(5),7(2)]),flip(a)].
% 113.10/113.46 4741 mult(mult(A,B),ld(mult(C,B),rd(C,B))) = rd(A,B). [para(1707(a,1),16(a,1,2,2)),rewrite([477(4),7(3)]),flip(a)].
% 113.10/113.46 4743 mult(rd(A,B),mult(B,rd(B,A))) = rd(A,rd(A,B)). [para(1707(a,1),18(a,1,2,2)),rewrite([654(5),654(6),817(6),4741(12)])].
% 113.10/113.46 5192 ld(A,rd(rd(A,B),B)) = ld(B,ld(B,ld(B,B))). [para(1719(a,1),8(a,1,2))].
% 113.10/113.46 5259 mult(ld(A,A),rd(rd(A,B),B)) = mult(A,rd(rd(ld(A,A),B),B)). [para(1719(a,1),757(a,1,2)),rewrite([1719(9)])].
% 113.10/113.46 5315 rd(A,ld(B,ld(B,B))) = ld(B,mult(mult(B,A),B)). [para(1732(a,1),8(a,1,2)),flip(a)].
% 113.10/113.46 5564 mult(mult(A,A),rd(ld(mult(A,A),B),A)) = mult(B,ld(A,ld(A,A))). [back_rewrite(3202),rewrite([5315(3),530(5),10(3),1708(3)]),flip(a)].
% 113.10/113.46 5756 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,D),D)). [para(619(a,1),1739(a,2,2))].
% 113.10/113.46 5938 mult(A,rd(rd(B,mult(C,B)),D)) = mult(A,rd(ld(C,ld(C,C)),D)). [para(1944(a,1),558(a,1,2,2)),rewrite([654(14),654(15),817(15)]),flip(a)].
% 113.10/113.46 6567 rd(A,mult(mult(B,B),A)) = mult(ld(C,C),rd(rd(ld(C,C),B),B)). [para(2006(a,1),895(a,1,2)),flip(a)].
% 113.10/113.46 7310 rd(ld(mult(A,A),B),B) = mult(ld(C,C),rd(rd(ld(C,C),A),A)). [para(2188(a,1),895(a,1,2)),flip(a)].
% 113.10/113.46 8015 rd(ld(mult(A,A),B),mult(ld(A,A),ld(C,ld(A,ld(A,B))))) = mult(ld(A,A),rd(C,ld(A,A))). [para(2669(a,1),2269(a,1,2,2,2)),rewrite([678(12)])].
% 113.10/113.46 8409 mult(rd(ld(A,rd(B,mult(C,B))),rd(ld(C,D),D)),E) = ld(A,E). [para(3230(a,2),612(a,1,1))].
% 113.10/113.46 8411 rd(ld(A,rd(B,mult(C,B))),rd(ld(C,D),D)) = rd(E,mult(A,E)). [para(3230(a,2),618(a,1))].
% 113.10/113.46 8682 mult(mult(A,A),rd(ld(A,rd(ld(B,C),C)),rd(ld(B,D),D))) = A. [para(3345(a,1),1537(a,1,2))].
% 113.10/113.46 8864 rd(mult(ld(A,ld(A,B)),ld(ld(mult(A,A),B),C)),mult(ld(ld(mult(A,A),B),ld(A,A)),C)) = ld(mult(A,A),B). [para(3563(a,1),226(a,1,2,1,2))].
% 113.10/113.46 8975 mult(mult(ld(A,rd(ld(mult(B,B),C),C)),B),B) = ld(A,ld(A,A)). [para(3798(a,1),473(a,1))].
% 113.10/113.46 8994 mult(mult(A,ld(B,B)),ld(B,B)) = rd(A,ld(B,B)). [para(689(a,1),3798(a,1,2,1,1)),rewrite([391(1),391(2),964(3),1415(2),7(3),678(2),10(3),391(3),391(5)]),flip(a)].
% 113.10/113.46 9657 rd(mult(mult(A,A),B),mult(A,A)) = mult(mult(A,A),rd(rd(B,A),A)). [para(1451(a,1),4743(a,1,2,2)),rewrite([10(3),1719(5),10(9)]),flip(a)].
% 113.10/113.46 9988 rd(ld(A,ld(A,A)),ld(A,ld(B,rd(rd(B,A),A)))) = mult(A,A). [para(5192(a,2),3638(a,1,2,2)),rewrite([964(4),2987(3),1415(2),7(4)])].
% 113.10/113.46 10079 ld(A,mult(mult(A,mult(A,B)),A)) = mult(mult(A,rd(B,ld(A,A))),A). [para(5315(a,1),130(a,1))].
% 113.10/113.46 10664 ld(A,rd(ld(B,C),mult(D,ld(B,C)))) = ld(A,rd(ld(D,E),E)). [para(2622(a,2),5756(a,1,2))].
% 113.10/113.46 11905 rd(ld(A,ld(A,A)),ld(B,B)) = mult(ld(A,ld(B,B)),ld(B,B)). [para(399(a,1),8994(a,1,1)),flip(a)].
% 113.10/113.46 14338 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A). [para(778(a,1),394(a,2,1)),rewrite([391(1),391(2),391(4),1029(6),895(7),391(4),391(6)])].
% 113.10/113.46 14345 rd(ld(mult(A,ld(B,B)),A),ld(B,B)) = mult(ld(A,A),ld(B,B)). [para(394(a,1),8994(a,1,1)),rewrite([895(4),391(1),1029(9),895(10)]),flip(a)].
% 113.10/113.46 14348 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A). [para(14338(a,1),10(a,1,1))].
% 113.10/113.46 14351 ld(ld(mult(A,ld(B,B)),A),C) = mult(ld(mult(B,ld(A,A)),B),C). [para(14338(a,1),552(a,1,1,2)),rewrite([14348(3)]),flip(a)].
% 113.10/113.46 14369 ld(ld(A,ld(B,B)),rd(C,mult(A,C))) = ld(mult(A,ld(B,B)),A). [para(552(a,1),14348(a,2,1)),rewrite([654(5),10(2),436(3),14348(3)]),flip(a)].
% 113.10/113.46 14375 rd(mult(A,ld(mult(B,A),B)),ld(C,C)) = ld(mult(ld(A,B),ld(C,C)),ld(A,B)). [para(168(a,1),14348(a,1,1))].
% 113.10/113.46 14976 mult(mult(ld(A,A),rd(B,mult(C,B))),A) = mult(ld(A,A),mult(ld(C,ld(A,A)),A)). [para(363(a,1),664(a,1,2)),rewrite([678(4),678(10)])].
% 113.10/113.46 14987 ld(mult(A,ld(mult(A,B),mult(A,B))),C) = mult(rd(A,rd(mult(A,mult(A,B)),B)),C). [para(391(a,1),670(a,1,1,2))].
% 113.10/113.46 15491 mult(ld(mult(A,ld(B,B)),A),mult(ld(B,B),ld(A,A))) = ld(A,A). [para(14338(a,1),990(a,1,2,2)),rewrite([14351(7),10(8),14345(8),168(14),14375(16),14338(12),678(12),10(16)])].
% 113.10/113.46 16627 rd(mult(ld(A,A),rd(B,ld(A,A))),mult(ld(B,ld(A,A)),mult(B,ld(A,A)))) = B. [para(1742(a,1),29(a,1,1))].
% 113.10/113.46 20869 rd(rd(rd(A,B),B),mult(A,rd(rd(ld(A,A),B),B))) = ld(A,A). [para(5259(a,1),434(a,1,2)),rewrite([678(11),964(11),1415(10),7(11),678(10),964(10),1415(9),7(10)])].
% 113.10/113.46 20879 rd(ld(A,A),mult(ld(A,A),ld(B,ld(A,A)))) = mult(ld(A,A),rd(B,ld(A,A))). [para(5259(a,1),2772(a,1,2,2,2,2)),rewrite([678(3),964(3),1415(2),7(3),20869(9),678(5),1742(10)])].
% 113.10/113.46 20958 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(mult(B,ld(A,A)),B)). [para(895(a,1),426(a,1,2,2,2,1)),rewrite([914(10),14369(5),895(10),895(10)]),flip(a)].
% 113.10/113.46 22225 mult(mult(A,A),rd(rd(B,mult(mult(A,A),B)),A)) = ld(A,ld(A,A)). [para(5938(a,2),5564(a,1)),rewrite([205(9),678(8),363(8),964(10),2987(9),1415(8),7(10)])].
% 113.10/113.46 26694 mult(mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C),D) = ld(A,D). [para(6567(a,1),8409(a,1,1,1,2)),rewrite([3798(10)])].
% 113.10/113.46 26783 rd(A,mult(B,A)) = mult(mult(ld(B,mult(ld(C,C),rd(rd(ld(C,C),D),D))),D),D). [para(6567(a,1),8411(a,1,1,2)),rewrite([3798(10)]),flip(a)].
% 113.10/113.46 28060 mult(mult(A,A),mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C)) = A. [para(7310(a,1),8682(a,1,2,1,2)),rewrite([3798(11)])].
% 113.10/113.46 28290 mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C) = ld(A,ld(A,A)). [para(7310(a,1),8975(a,1,1,1,2))].
% 113.10/113.46 41618 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = mult(ld(B,B),ld(A,A)). [para(14345(a,1),1330(a,1,1,2,2)),rewrite([14351(8),15491(8),964(3),1415(2),7(3),14345(7),678(6),895(7),14345(9),678(8)]),flip(a)].
% 113.10/113.46 41619 mult(ld(A,A),ld(mult(B,ld(A,A)),B)) = ld(B,B). [para(14345(a,1),2232(a,1,2,2)),rewrite([773(3),678(6),41618(6),773(5),678(6),1030(8)]),flip(a)].
% 113.10/113.46 41621 ld(mult(A,ld(B,B)),A) = mult(ld(B,B),ld(A,A)). [para(14345(a,1),9657(a,2,2,1)),rewrite([964(3),1415(2),7(3),41619(5),964(4),1415(3),7(4),14348(3),964(6),1415(5),7(6),10(9)])].
% 113.10/113.46 41622 mult(ld(A,A),ld(mult(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(14345(a,1),743(a,2,2,2,2)),rewrite([41621(3),41621(8),1029(11),895(12),678(10),898(11),435(10),1029(8),41621(7),678(6),964(6),1415(5),7(6),895(6),964(3),1415(2),7(3),41621(6),205(10),678(7),678(10),895(12)]),flip(a)].
% 113.10/113.46 41626 mult(ld(A,A),ld(B,B)) = ld(B,B). [para(14345(a,1),9988(a,1,2,2,2,1)),rewrite([678(4),964(4),1415(3),7(4),678(3),964(3),1415(2),7(3),41621(5),10(10),678(8),41622(8),14348(3),41621(3),964(6),1415(5),7(6)])].
% 113.10/113.46 41627 mult(mult(A,ld(B,B)),A) = mult(A,A). [para(14345(a,1),10079(a,2,1,2)),rewrite([41621(3),41626(3),10079(5),14348(3),41621(3),41626(3),41626(6),7(5)])].
% 113.10/113.46 41629 ld(A,A) = ld(B,B). [para(10664(a,1),14345(a,1,1,1,2)),rewrite([654(7),10(4),435(3),41621(3),41626(3),654(10),10(5),436(6),14348(3),41621(3),41626(3),654(11),10(6),436(7),41626(4)])].
% 113.10/113.46 41636 mult(mult(A,ld(mult(ld(B,B),A),ld(B,B))),ld(B,B)) = ld(B,B). [para(11905(a,2),14345(a,1,1,1)),rewrite([654(7),5315(4),41627(3),8(2),7(3),391(3),678(3),964(3),1415(2),7(3),168(6)]),flip(a)].
% 113.10/113.46 41640 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(B,B)). [back_rewrite(20958),rewrite([41621(7),41626(7)])].
% 113.10/113.46 41663 ld(mult(A,ld(B,B)),A) = ld(A,A). [back_rewrite(41621),rewrite([41626(6)])].
% 113.10/113.46 41674 rd(mult(A,mult(A,B)),B) = mult(A,A). [back_rewrite(394),rewrite([41627(5)]),flip(a)].
% 113.10/113.46 41675 ld(A,A) = c_0. [new_symbol(41629)].
% 113.10/113.46 41688 ld(mult(A,c_0),B) = mult(ld(A,c_0),B). [back_rewrite(14987),rewrite([41675(3),41674(6),434(5),41675(4)])].
% 113.10/113.46 41701 mult(ld(A,c_0),A) = c_0. [back_rewrite(41663),rewrite([41675(1),41688(3),41675(4)])].
% 113.10/113.46 41718 ld(mult(c_0,A),c_0) = ld(A,c_0). [back_rewrite(41640),rewrite([41675(1),41675(3),41675(5)])].
% 113.10/113.46 41721 mult(c_0,c_0) = c_0. [back_rewrite(41636),rewrite([41675(1),41675(3),41718(4),7(3),41675(2),41675(4)])].
% 113.10/113.46 41989 mult(mult(ld(A,mult(c_0,rd(rd(c_0,B),B))),B),B) = ld(A,c_0). [back_rewrite(28290),rewrite([41675(1),41675(2),41675(9)])].
% 113.10/113.46 41997 mult(A,c_0) = A. [back_rewrite(28060),rewrite([41675(2),41675(3),41989(9),26(4),41675(1),41721(3)])].
% 113.10/113.46 42005 rd(A,mult(B,A)) = ld(B,c_0). [back_rewrite(26783),rewrite([41675(3),41675(4),41989(10)])].
% 113.10/113.46 42006 mult(ld(A,c_0),B) = ld(A,B). [back_rewrite(26694),rewrite([41675(1),41675(2),41989(8)])].
% 113.10/113.46 42083 mult(c_0,ld(A,c_0)) = ld(A,c_0). [back_rewrite(22225),rewrite([42005(4),5564(6),41675(2),41675(5)])].
% 113.10/113.46 42111 mult(c_0,rd(A,c_0)) = A. [back_rewrite(20879),rewrite([41675(1),41675(2),41675(3),42083(5),14(4),41675(1),41675(2)]),flip(a)].
% 113.10/113.46 42267 rd(A,c_0) = A. [back_rewrite(16627),rewrite([41675(1),41675(2),42111(4),41675(1),41675(3),41997(4),41701(3)])].
% 113.10/113.46 42328 mult(c_0,ld(A,B)) = ld(A,B). [back_rewrite(14976),rewrite([41675(1),42005(3),42083(4),42006(3),41675(2),41675(3),42006(5)]),flip(a)].
% 113.10/113.46 42705 ld(mult(A,A),B) = ld(A,ld(A,B)). [back_rewrite(8864),rewrite([41675(9),42006(11),10(10)]),flip(a)].
% 113.10/113.46 42738 mult(c_0,A) = A. [back_rewrite(8015),rewrite([42705(2),41675(3),42328(7),14(6),41675(1),41675(2),42267(3)]),flip(a)].
% 113.10/113.46 42999 $F # answer(goals). [back_rewrite(12),rewrite([41675(4),41997(3),41675(6),42738(6)]),xx(a),xx(b)].
% 113.10/113.46
% 113.10/113.46 % SZS output end Refutation
% 113.10/113.46 ============================== end of proof ==========================
% 113.10/113.46
% 113.10/113.46 ============================== STATISTICS ============================
% 113.10/113.46
% 113.10/113.46 Given=1568. Generated=4044552. Kept=42992. proofs=1.
% 113.10/113.46 Usable=997. Sos=6449. Demods=6424. Limbo=1324, Disabled=34228. Hints=0.
% 113.10/113.46 Megabytes=39.26.
% 113.10/113.46 User_CPU=110.25, System_CPU=2.22, Wall_clock=112.
% 113.10/113.46
% 113.10/113.46 ============================== end of statistics =====================
% 113.10/113.46
% 113.10/113.46 ============================== end of search =========================
% 113.10/113.46
% 113.10/113.46 THEOREM PROVED
% 113.10/113.46 % SZS status Theorem
% 113.10/113.46
% 113.10/113.46 Exiting with 1 proof.
% 113.10/113.46
% 113.10/113.46 Process 16729 exit (max_proofs) Tue Jun 14 03:32:46 2022
% 113.10/113.46 Prover9 interrupted
%------------------------------------------------------------------------------