TSTP Solution File: GRP654+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP654+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 113.11s 113.42s
% Output : Refutation 113.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP654+2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 16:07:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 4.06/4.34 ============================== Prover9 ===============================
% 4.06/4.34 Prover9 (32) version 2009-11A, November 2009.
% 4.06/4.34 Process 23427 was started by sandbox on n029.cluster.edu,
% 4.06/4.34 Mon Jun 13 16:07:55 2022
% 4.06/4.34 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23273_n029.cluster.edu".
% 4.06/4.34 ============================== end of head ===========================
% 4.06/4.34
% 4.06/4.34 ============================== INPUT =================================
% 4.06/4.34
% 4.06/4.34 % Reading from file /tmp/Prover9_23273_n029.cluster.edu
% 4.06/4.34
% 4.06/4.34 set(prolog_style_variables).
% 4.06/4.34 set(auto2).
% 4.06/4.34 % set(auto2) -> set(auto).
% 4.06/4.34 % set(auto) -> set(auto_inference).
% 4.06/4.34 % set(auto) -> set(auto_setup).
% 4.06/4.34 % set(auto_setup) -> set(predicate_elim).
% 4.06/4.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.06/4.34 % set(auto) -> set(auto_limits).
% 4.06/4.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.06/4.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.06/4.34 % set(auto) -> set(auto_denials).
% 4.06/4.34 % set(auto) -> set(auto_process).
% 4.06/4.34 % set(auto2) -> assign(new_constants, 1).
% 4.06/4.34 % set(auto2) -> assign(fold_denial_max, 3).
% 4.06/4.34 % set(auto2) -> assign(max_weight, "200.000").
% 4.06/4.34 % set(auto2) -> assign(max_hours, 1).
% 4.06/4.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.06/4.34 % set(auto2) -> assign(max_seconds, 0).
% 4.06/4.34 % set(auto2) -> assign(max_minutes, 5).
% 4.06/4.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.06/4.34 % set(auto2) -> set(sort_initial_sos).
% 4.06/4.34 % set(auto2) -> assign(sos_limit, -1).
% 4.06/4.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.06/4.34 % set(auto2) -> assign(max_megs, 400).
% 4.06/4.34 % set(auto2) -> assign(stats, some).
% 4.06/4.34 % set(auto2) -> clear(echo_input).
% 4.06/4.34 % set(auto2) -> set(quiet).
% 4.06/4.34 % set(auto2) -> clear(print_initial_clauses).
% 4.06/4.34 % set(auto2) -> clear(print_given).
% 4.06/4.34 assign(lrs_ticks,-1).
% 4.06/4.34 assign(sos_limit,10000).
% 4.06/4.34 assign(order,kbo).
% 4.06/4.34 set(lex_order_vars).
% 4.06/4.34 clear(print_given).
% 4.06/4.34
% 4.06/4.34 % formulas(sos). % not echoed (6 formulas)
% 4.06/4.34
% 4.06/4.34 ============================== end of input ==========================
% 4.06/4.34
% 4.06/4.34 % From the command line: assign(max_seconds, 300).
% 4.06/4.34
% 4.06/4.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.06/4.34
% 4.06/4.34 % Formulas that are not ordinary clauses:
% 4.06/4.34 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 4.06/4.34 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 4.06/4.34 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 4.06/4.34 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 4.06/4.34 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].
% 4.06/4.34 6 -(all X0 all X1 (mult(X0,rd(X1,X1)) = X0 & mult(rd(X1,X1),X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 4.06/4.34
% 4.06/4.34 ============================== end of process non-clausal formulas ===
% 4.06/4.34
% 4.06/4.34 ============================== PROCESS INITIAL CLAUSES ===============
% 4.06/4.34
% 4.06/4.34 ============================== PREDICATE ELIMINATION =================
% 4.06/4.34
% 4.06/4.34 ============================== end predicate elimination =============
% 4.06/4.34
% 4.06/4.34 Auto_denials:
% 4.06/4.34 % copying label goals to answer in negative clause
% 4.06/4.34
% 4.06/4.34 Term ordering decisions:
% 4.06/4.34 Function symbol KB weights: c1=1. c2=1. mult=1. ld=1. rd=1.
% 4.06/4.34
% 4.06/4.34 ============================== end of process initial clauses ========
% 4.06/4.34
% 4.06/4.34 ============================== CLAUSES FOR SEARCH ====================
% 4.06/4.34
% 4.06/4.34 ============================== end of clauses for search =============
% 4.06/4.34
% 4.06/4.34 ============================== SEARCH ================================
% 4.06/4.34
% 4.06/4.34 % Starting search at 0.01 seconds.
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=95.000, iters=3551
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=71.000, iters=3416
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=67.000, iters=3366
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=59.000, iters=3343
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=55.000, iters=3346
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=51.000, iters=3357
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=47.000, iters=3384
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=43.000, iters=3335
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=39.000, iters=3358
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=35.000, iters=3372
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=31.000, iters=3333
% 4.06/4.34
% 4.06/4.34 Low Water (keep): wt=27.000, iters=3373
% 4.06/4.34
% 4.06/4.34 Low Water (displace): id=6063, wt=135.000
% 113.11/113.42
% 113.11/113.42 Low Water (displace): id=7091, wt=119.000
% 113.11/113.42
% 113.11/113.42 Low Water (displace): id=12689, wt=23.000
% 113.11/113.42
% 113.11/113.42 Low Water (displace): id=12932, wt=19.000
% 113.11/113.42
% 113.11/113.42 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 10.07 sec).
% 113.11/113.42
% 113.11/113.42 Low Water (keep): wt=23.000, iters=3336
% 113.11/113.42
% 113.11/113.42 ============================== PROOF =================================
% 113.11/113.42 % SZS status Theorem
% 113.11/113.42 % SZS output start Refutation
% 113.11/113.42
% 113.11/113.42 % Proof 1 at 110.13 (+ 2.29) seconds: goals.
% 113.11/113.42 % Length of proof is 236.
% 113.11/113.42 % Level of proof is 38.
% 113.11/113.42 % Maximum clause weight is 39.000.
% 113.11/113.42 % Given clauses 1570.
% 113.11/113.42
% 113.11/113.42 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 113.11/113.42 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 113.11/113.42 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 113.11/113.42 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 113.11/113.42 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].
% 113.11/113.42 6 -(all X0 all X1 (mult(X0,rd(X1,X1)) = X0 & mult(rd(X1,X1),X0) = X0)) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 113.11/113.42 7 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 113.11/113.42 8 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 113.11/113.42 9 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 113.11/113.42 10 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 113.11/113.42 11 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f05) # label(axiom). [clausify(5)].
% 113.11/113.42 12 mult(c1,rd(c2,c2)) != c1 | mult(rd(c2,c2),c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals). [clausify(6)].
% 113.11/113.42 14 rd(A,ld(B,A)) = B. [para(7(a,1),10(a,1,1))].
% 113.11/113.42 15 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C. [para(11(a,1),7(a,1))].
% 113.11/113.42 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)].
% 113.11/113.42 17 ld(mult(mult(A,B),A),mult(A,mult(B,mult(A,C)))) = C. [para(11(a,1),8(a,1,2))].
% 113.11/113.42 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)].
% 113.11/113.42 19 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A). [para(11(a,1),10(a,1,1))].
% 113.11/113.42 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)].
% 113.11/113.42 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)].
% 113.11/113.42 27 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)). [para(16(a,1),8(a,1,2))].
% 113.11/113.42 29 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B. [para(16(a,1),10(a,1,1))].
% 113.11/113.42 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)])].
% 113.11/113.42 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)].
% 113.11/113.42 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)].
% 113.11/113.42 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))].
% 113.11/113.42 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)].
% 113.11/113.42 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))].
% 113.11/113.42 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)].
% 113.11/113.42 63 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C). [para(26(a,1),8(a,1,2))].
% 113.11/113.42 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)].
% 113.11/113.42 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)].
% 113.11/113.42 130 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A). [para(9(a,1),46(a,1,1,2))].
% 113.11/113.42 147 ld(mult(A,rd(B,mult(A,C))),rd(mult(A,B),C)) = A. [para(48(a,1),8(a,1,2))].
% 113.11/113.42 149 rd(rd(mult(A,B),C),A) = mult(A,rd(B,mult(A,C))). [para(48(a,1),10(a,1,1))].
% 113.11/113.42 151 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)].
% 113.11/113.42 168 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)). [para(55(a,1),8(a,1,2))].
% 113.11/113.42 184 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))). [para(56(a,1),8(a,1,2)),flip(a)].
% 113.11/113.42 189 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))].
% 113.11/113.42 205 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)). [para(7(a,1),63(a,1,2,2))].
% 113.11/113.42 225 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C). [para(64(a,1),8(a,1,2))].
% 113.11/113.42 226 rd(mult(A,ld(B,C)),mult(ld(B,rd(A,B)),C)) = B. [para(64(a,1),10(a,1,1))].
% 113.11/113.42 229 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)].
% 113.11/113.42 264 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)). [para(7(a,1),130(a,1,1)),flip(a)].
% 113.11/113.42 284 ld(mult(A,rd(B,mult(A,B))),A) = A. [para(10(a,1),147(a,1,2))].
% 113.11/113.42 334 ld(mult(A,rd(ld(A,B),B)),A) = A. [para(7(a,1),284(a,1,1,2,2))].
% 113.11/113.42 337 mult(A,rd(B,mult(A,B))) = rd(A,A). [para(284(a,1),14(a,1,2)),flip(a)].
% 113.11/113.42 350 mult(A,rd(ld(A,B),B)) = rd(A,A). [para(334(a,1),14(a,1,2)),flip(a)].
% 113.11/113.42 353 rd(A,mult(B,A)) = ld(B,rd(B,B)). [para(337(a,1),8(a,1,2)),flip(a)].
% 113.11/113.42 354 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)].
% 113.11/113.42 360 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)].
% 113.11/113.42 363 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)].
% 113.11/113.42 367 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)].
% 113.11/113.42 390 mult(c1,rd(c2,c2)) != c1 | mult(ld(c2,c2),c1) != c1 # answer(goals). [back_rewrite(12),rewrite([360(12)])].
% 113.11/113.42 391 ld(ld(A,A),A) = A. [para(363(a,1),8(a,1,2))].
% 113.11/113.42 392 rd(A,A) = ld(A,A). [para(363(a,1),10(a,1,1))].
% 113.11/113.42 395 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)].
% 113.11/113.42 400 mult(ld(A,ld(A,A)),B) = ld(A,B). [para(363(a,1),55(a,1,2,2,1)),rewrite([7(4)])].
% 113.11/113.42 401 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)])].
% 113.11/113.42 409 mult(c1,ld(c2,c2)) != c1 | mult(ld(c2,c2),c1) != c1 # answer(goals). [back_rewrite(390),rewrite([392(4)])].
% 113.11/113.42 428 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([392(9)])].
% 113.11/113.42 435 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [back_rewrite(354),rewrite([392(3)])].
% 113.11/113.42 436 rd(A,mult(B,A)) = ld(B,ld(B,B)). [back_rewrite(353),rewrite([392(3)])].
% 113.11/113.42 437 mult(A,rd(ld(A,B),B)) = ld(A,A). [back_rewrite(350),rewrite([392(4)])].
% 113.11/113.42 438 mult(A,rd(B,mult(A,B))) = ld(A,A). [back_rewrite(337),rewrite([392(4)])].
% 113.11/113.42 466 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)). [para(391(a,1),26(a,2,2,1)),rewrite([7(2)]),flip(a)].
% 113.11/113.42 468 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A). [para(391(a,1),29(a,1,2,1)),rewrite([7(2)])].
% 113.11/113.42 469 mult(A,mult(ld(A,A),ld(A,B))) = ld(ld(A,A),B). [para(391(a,1),55(a,1,1)),rewrite([7(3)])].
% 113.11/113.42 475 rd(ld(A,B),B) = ld(A,ld(A,A)). [para(400(a,1),10(a,1,1))].
% 113.11/113.42 479 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)). [para(400(a,1),19(a,1,1,2,2)),rewrite([400(5),225(3),10(4),400(5)]),flip(a)].
% 113.11/113.42 481 mult(A,mult(ld(A,ld(B,ld(B,B))),C)) = mult(ld(B,A),ld(A,C)). [para(400(a,1),26(a,1,1)),flip(a)].
% 113.11/113.42 491 rd(ld(A,B),ld(ld(A,ld(A,A)),C)) = ld(A,rd(rd(B,C),A)). [para(400(a,1),130(a,1,1)),rewrite([400(9),479(10)])].
% 113.11/113.42 525 ld(ld(A,ld(A,A)),B) = mult(A,B). [para(363(a,1),39(a,1,2,2,1)),rewrite([481(6),479(4),392(1),400(6),8(4)])].
% 113.11/113.42 528 ld(A,mult(ld(A,A),mult(mult(A,A),B))) = mult(A,B). [para(400(a,1),39(a,1,1,2)),rewrite([7(2)])].
% 113.11/113.42 532 rd(ld(A,B),mult(A,C)) = ld(A,rd(rd(B,C),A)). [back_rewrite(491),rewrite([525(4)])].
% 113.11/113.42 554 mult(rd(A,mult(B,A)),C) = ld(B,C). [para(436(a,2),55(a,1,1)),rewrite([363(4),7(4)])].
% 113.11/113.42 560 mult(A,rd(B,mult(C,B))) = mult(A,ld(C,ld(C,C))). [para(436(a,2),64(a,2,2)),rewrite([64(5)]),flip(a)].
% 113.11/113.42 568 rd(A,mult(B,A)) = rd(C,mult(B,C)). [para(436(a,2),436(a,2))].
% 113.11/113.42 584 mult(A,ld(B,rd(ld(ld(B,rd(A,B)),C),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [para(437(a,1),64(a,1,2)),rewrite([168(5),9(2)]),flip(a)].
% 113.11/113.42 614 mult(rd(ld(A,B),B),C) = ld(A,C). [para(475(a,2),55(a,1,1)),rewrite([363(4),7(4)])].
% 113.11/113.42 617 mult(A,rd(ld(B,C),C)) = mult(A,ld(B,ld(B,B))). [para(475(a,2),64(a,2,2)),rewrite([64(5)]),flip(a)].
% 113.11/113.42 620 rd(ld(A,B),B) = rd(C,mult(A,C)). [para(475(a,2),436(a,2)),flip(a)].
% 113.11/113.42 621 rd(ld(A,B),B) = rd(ld(A,C),C). [para(475(a,2),475(a,2))].
% 113.11/113.42 656 ld(rd(A,B),C) = mult(rd(B,A),C). [para(9(a,1),554(a,1,1,2)),flip(a)].
% 113.11/113.42 658 mult(rd(A,mult(B,mult(C,mult(B,A)))),D) = ld(B,ld(C,ld(B,D))). [para(11(a,1),554(a,1,1,2)),rewrite([184(8)])].
% 113.11/113.42 661 mult(ld(A,B),rd(C,mult(A,C))) = ld(A,rd(B,A)). [para(554(a,1),19(a,1,1,2,2)),rewrite([554(5),225(3),10(4),554(5)]),flip(a)].
% 113.11/113.42 666 mult(ld(A,rd(B,mult(C,B))),mult(A,D)) = ld(A,mult(ld(C,A),D)). [para(554(a,1),27(a,1,2,1)),flip(a)].
% 113.11/113.42 672 ld(mult(A,rd(B,mult(A,C))),D) = mult(rd(A,rd(mult(A,B),C)),D). [para(48(a,1),554(a,1,1,2)),flip(a)].
% 113.11/113.42 678 ld(ld(A,rd(B,A)),C) = mult(A,ld(B,mult(A,C))). [para(74(a,1),554(a,1,1,2)),rewrite([130(4),11(5),554(4)]),flip(a)].
% 113.11/113.42 680 ld(ld(A,A),B) = mult(ld(A,A),B). [para(363(a,1),554(a,1,1,2)),rewrite([392(1)]),flip(a)].
% 113.11/113.42 691 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)). [back_rewrite(435),rewrite([656(3)])].
% 113.11/113.42 715 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([656(13)])].
% 113.11/113.42 745 mult(A,ld(B,rd(mult(B,ld(A,mult(B,C))),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [back_rewrite(584),rewrite([678(3)])].
% 113.11/113.42 758 mult(A,mult(ld(A,A),ld(A,B))) = mult(ld(A,A),B). [back_rewrite(469),rewrite([680(6)])].
% 113.11/113.42 759 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)). [back_rewrite(466),rewrite([680(5)])].
% 113.11/113.42 767 rd(A,mult(rd(B,C),A)) = rd(C,B). [para(9(a,1),568(a,1,2)),flip(a)].
% 113.11/113.42 775 rd(A,mult(ld(B,B),A)) = ld(B,B). [para(363(a,1),568(a,1,2)),rewrite([392(1)]),flip(a)].
% 113.11/113.42 780 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(7(a,1),42(a,2)),rewrite([715(12),7(11)])].
% 113.11/113.42 809 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),436(a,1,2)),rewrite([656(17),656(18)])].
% 113.11/113.42 819 mult(rd(A,B),mult(rd(A,B),rd(B,A))) = rd(A,B). [para(42(a,1),568(a,1,2)),rewrite([809(13),767(8)])].
% 113.11/113.42 828 mult(ld(A,B),rd(ld(A,C),C)) = ld(A,rd(B,A)). [para(614(a,1),19(a,1,1,2,2)),rewrite([614(5),225(3),10(4),614(5)]),flip(a)].
% 113.11/113.42 847 rd(mult(A,B),mult(C,mult(A,B))) = rd(ld(C,D),D). [para(620(a,2),48(a,2)),rewrite([48(6)])].
% 113.11/113.42 897 mult(ld(A,A),mult(ld(A,A),B)) = B. [para(680(a,1),7(a,1,2))].
% 113.11/113.42 900 mult(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),mult(mult(B,ld(A,A)),C)). [para(680(a,1),27(a,1)),rewrite([680(7)]),flip(a)].
% 113.11/113.42 901 mult(A,mult(ld(A,A),ld(mult(A,A),B))) = ld(A,B). [para(55(a,1),680(a,2)),rewrite([680(5),759(5)])].
% 113.11/113.42 906 rd(A,ld(B,ld(C,ld(B,A)))) = mult(mult(B,C),B). [para(19(a,1),767(a,2)),rewrite([658(5)])].
% 113.11/113.42 916 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(775(a,1),74(a,1,1,2)),rewrite([205(12)])].
% 113.11/113.42 966 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)). [para(55(a,1),897(a,1,2))].
% 113.11/113.42 973 mult(A,mult(A,ld(mult(A,A),B))) = mult(ld(A,A),B). [back_rewrite(758),rewrite([966(3)])].
% 113.11/113.42 992 mult(A,rd(rd(ld(A,B),B),mult(A,C))) = rd(rd(ld(A,A),C),A). [para(437(a,1),149(a,1,1,1)),flip(a)].
% 113.11/113.42 1031 ld(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),ld(mult(B,ld(A,A)),C)). [para(680(a,1),168(a,1,1)),rewrite([680(4)])].
% 113.11/113.42 1032 rd(A,mult(mult(B,ld(mult(C,B),C)),A)) = mult(B,ld(mult(C,B),C)). [para(168(a,1),775(a,1,2,1)),rewrite([168(8)])].
% 113.11/113.42 1048 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),680(4),680(6),966(6)]),flip(a)].
% 113.11/113.42 1131 mult(ld(mult(A,A),ld(A,A)),B) = ld(mult(A,A),B). [para(205(a,1),400(a,1,1,2)),rewrite([680(3),363(3)])].
% 113.11/113.42 1135 rd(A,mult(mult(B,B),A)) = ld(mult(B,B),ld(B,B)). [para(205(a,1),436(a,2,2)),rewrite([680(6),363(6)])].
% 113.11/113.42 1141 rd(ld(mult(A,A),B),B) = ld(mult(A,A),ld(A,A)). [para(205(a,1),475(a,2,2)),rewrite([680(6),363(6)])].
% 113.11/113.42 1170 mult(ld(A,rd(ld(B,ld(B,B)),A)),C) = ld(A,ld(B,ld(A,C))). [para(400(a,1),225(a,1,2)),flip(a)].
% 113.11/113.42 1215 rd(rd(A,ld(B,C)),B) = mult(B,rd(ld(B,A),C)). [para(264(a,1),10(a,1,1))].
% 113.11/113.42 1243 rd(A,rd(B,mult(C,B))) = rd(A,ld(C,ld(C,C))). [para(436(a,2),264(a,2,2)),rewrite([264(5)]),flip(a)].
% 113.11/113.42 1245 rd(A,rd(ld(B,C),C)) = rd(A,ld(B,ld(B,B))). [para(475(a,2),264(a,2,2)),rewrite([264(5)]),flip(a)].
% 113.11/113.42 1332 mult(mult(A,ld(B,rd(B,A))),ld(A,rd(B,A))) = ld(A,rd(B,A)). [para(9(a,1),401(a,1,1,2,1))].
% 113.11/113.42 1383 rd(mult(A,mult(A,B)),mult(mult(A,A),B)) = ld(A,A). [para(16(a,1),468(a,1,2))].
% 113.11/113.42 1388 rd(mult(A,mult(A,B)),mult(ld(A,A),B)) = mult(A,A). [para(468(a,1),48(a,1,1,2)),rewrite([7(2)]),flip(a)].
% 113.11/113.42 1400 mult(A,ld(mult(A,A),A)) = ld(A,A). [para(437(a,1),468(a,1,1)),rewrite([828(5),392(2),7(4),392(3),680(3),966(3)])].
% 113.11/113.42 1417 ld(mult(A,A),A) = ld(A,ld(A,A)). [para(1400(a,1),8(a,1,2)),flip(a)].
% 113.11/113.42 1421 mult(rd(ld(A,ld(A,A)),A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [para(1400(a,1),40(a,2,2)),rewrite([1417(2),1417(4),400(6),1170(5),1417(5)]),flip(a)].
% 113.11/113.42 1430 rd(A,ld(A,ld(A,A))) = mult(A,A). [para(1417(a,1),14(a,1,2))].
% 113.11/113.42 1431 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(mult(A,mult(A,A)),B). [para(1417(a,1),16(a,1,2,1)),rewrite([400(6),27(4),759(4)])].
% 113.11/113.42 1440 rd(ld(A,ld(A,A)),A) = ld(mult(A,A),ld(A,A)). [para(1417(a,1),475(a,1,1)),rewrite([205(7),680(6),363(6)])].
% 113.11/113.42 1448 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [back_rewrite(1421),rewrite([1440(3),1131(5)])].
% 113.11/113.42 1449 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))). [back_rewrite(1440),rewrite([1448(6)])].
% 113.11/113.42 1452 rd(ld(mult(A,A),B),B) = ld(A,ld(A,ld(A,A))). [back_rewrite(1141),rewrite([1448(6)])].
% 113.11/113.42 1453 rd(A,mult(mult(B,B),A)) = ld(B,ld(B,ld(B,B))). [back_rewrite(1135),rewrite([1448(6)])].
% 113.11/113.42 1454 mult(ld(A,ld(A,ld(A,A))),B) = ld(mult(A,A),B). [back_rewrite(1131),rewrite([1448(3)])].
% 113.11/113.42 1506 rd(A,rd(B,mult(A,B))) = mult(A,A). [para(436(a,2),1430(a,1,2))].
% 113.11/113.42 1507 rd(A,rd(ld(A,B),B)) = mult(A,A). [para(475(a,2),1430(a,1,2))].
% 113.11/113.42 1514 mult(mult(A,mult(A,A)),B) = mult(A,mult(A,mult(A,B))). [para(1430(a,1),225(a,2,1,2)),rewrite([525(5),525(5),525(7)]),flip(a)].
% 113.11/113.42 1522 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(A,mult(A,mult(A,B))). [back_rewrite(1431),rewrite([1514(8)])].
% 113.11/113.42 1523 mult(mult(A,A),rd(B,mult(A,B))) = A. [para(1506(a,1),9(a,1,1))].
% 113.11/113.42 1539 mult(mult(A,A),rd(ld(A,B),B)) = A. [para(1507(a,1),9(a,1,1))].
% 113.11/113.42 1552 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1523(a,1),19(a,2,1)),rewrite([554(6),27(4),759(4),1522(5),19(4)])].
% 113.11/113.42 1576 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(mult(A,mult(A,A)),B). [para(1523(a,1),184(a,1,1,1)),rewrite([656(9),10(6),225(8),436(6)]),flip(a)].
% 113.11/113.42 1691 ld(mult(A,mult(A,A)),B) = ld(A,ld(A,ld(A,B))). [para(1552(a,1),184(a,1,1))].
% 113.11/113.42 1701 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1576),rewrite([1691(8)])].
% 113.11/113.42 1709 mult(A,ld(mult(B,A),rd(B,A))) = ld(A,ld(A,A)). [para(479(a,1),8(a,1,2)),rewrite([168(4)])].
% 113.11/113.42 1710 ld(A,rd(mult(A,B),A)) = mult(B,ld(A,ld(A,A))). [para(8(a,1),479(a,1,1)),flip(a)].
% 113.11/113.42 1721 mult(A,ld(B,ld(B,ld(B,B)))) = rd(rd(A,B),B). [para(479(a,1),64(a,1,2)),rewrite([7(4)]),flip(a)].
% 113.11/113.42 1734 mult(A,rd(B,ld(A,ld(A,A)))) = mult(mult(A,B),A). [para(525(a,1),479(a,1,1)),rewrite([168(8),363(5),7(6),168(5),363(3),7(3),525(8)]),flip(a)].
% 113.11/113.42 1741 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,A),A)). [para(621(a,1),479(a,2,2)),rewrite([479(5)]),flip(a)].
% 113.11/113.42 1744 mult(mult(ld(A,A),B),ld(A,A)) = mult(ld(A,A),rd(B,ld(A,A))). [para(680(a,1),479(a,1,1)),rewrite([680(6),966(6),1417(5),7(6),680(5),966(5),1417(4),7(5),680(8)])].
% 113.11/113.42 1759 rd(ld(A,ld(A,ld(A,A))),A) = ld(mult(A,A),ld(A,ld(A,A))). [para(1417(a,1),479(a,1,1)),rewrite([205(6),680(5),363(5),1448(5),1721(6),1449(3),436(7)])].
% 113.11/113.42 1767 ld(mult(A,A),ld(A,ld(A,A))) = ld(A,ld(A,ld(A,ld(A,A)))). [para(479(a,1),1552(a,1,1)),rewrite([475(2),479(6),1449(3),479(11),475(8),1721(10),1449(7),1759(8)]),flip(a)].
% 113.11/113.42 1841 mult(ld(A,ld(A,ld(A,ld(A,A)))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1701),rewrite([1767(4)])].
% 113.11/113.42 1874 ld(A,mult(ld(A,A),B)) = mult(A,ld(mult(A,A),B)). [para(7(a,1),528(a,1,2,2))].
% 113.11/113.42 1946 mult(rd(A,rd(B,mult(C,B))),ld(C,ld(C,C))) = A. [para(560(a,1),9(a,1))].
% 113.11/113.42 2008 mult(A,rd(B,mult(mult(C,C),B))) = rd(rd(A,C),C). [para(205(a,1),560(a,2,2,2)),rewrite([680(7),363(7),1448(7),1721(8)])].
% 113.11/113.42 2190 mult(A,rd(ld(mult(B,B),C),C)) = rd(rd(A,B),B). [para(205(a,1),617(a,2,2,2)),rewrite([680(7),363(7),1448(7),1721(8)])].
% 113.11/113.42 2234 rd(rd(A,mult(B,A)),ld(B,rd(C,B))) = rd(D,mult(ld(B,C),D)). [para(661(a,1),568(a,1,2))].
% 113.11/113.42 2271 rd(A,mult(B,ld(C,mult(B,A)))) = ld(B,rd(C,B)). [para(678(a,1),14(a,1,2))].
% 113.11/113.42 2624 rd(ld(A,B),mult(C,ld(A,B))) = rd(ld(C,D),D). [para(55(a,1),847(a,1,1)),rewrite([55(6)])].
% 113.11/113.42 2671 mult(ld(A,A),ld(mult(A,A),B)) = ld(A,ld(A,B)). [para(901(a,1),8(a,1,2)),flip(a)].
% 113.11/113.42 2774 rd(ld(A,A),ld(A,ld(B,rd(C,mult(A,C))))) = mult(mult(A,B),A). [para(436(a,2),906(a,1,2,2,2))].
% 113.11/113.42 2989 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)). [para(1048(a,1),225(a,1,2)),rewrite([436(6),1767(7),1841(10),1874(6),8(7)])].
% 113.11/113.42 3204 rd(rd(A,ld(B,ld(B,B))),mult(B,B)) = mult(mult(B,B),rd(ld(mult(B,B),A),B)). [para(1417(a,1),1215(a,1,1,2))].
% 113.11/113.42 3232 rd(A,rd(ld(B,C),C)) = rd(A,rd(D,mult(B,D))). [para(475(a,2),1243(a,2,2)),flip(a)].
% 113.11/113.42 3347 rd(A,rd(ld(B,C),C)) = rd(A,rd(ld(B,D),D)). [para(475(a,2),1245(a,2,2))].
% 113.11/113.42 3565 rd(ld(A,ld(A,B)),ld(mult(A,A),B)) = ld(A,A). [para(400(a,1),1383(a,1,1,2)),rewrite([400(4),479(7),475(4),1454(6),168(10),363(7),7(8)])].
% 113.11/113.42 3640 rd(mult(ld(A,A),B),ld(A,ld(A,B))) = mult(A,A). [para(973(a,1),1388(a,1,1)),rewrite([2671(6)])].
% 113.11/113.42 3800 rd(A,rd(ld(mult(B,B),C),C)) = mult(mult(A,B),B). [para(1452(a,2),264(a,2,2)),rewrite([1734(5),7(2)]),flip(a)].
% 113.11/113.42 4743 mult(mult(A,B),ld(mult(C,B),rd(C,B))) = rd(A,B). [para(1709(a,1),16(a,1,2,2)),rewrite([479(4),7(3)]),flip(a)].
% 113.11/113.42 4745 mult(rd(A,B),mult(B,rd(B,A))) = rd(A,rd(A,B)). [para(1709(a,1),18(a,1,2,2)),rewrite([656(5),656(6),819(6),4743(12)])].
% 113.11/113.42 5194 ld(A,rd(rd(A,B),B)) = ld(B,ld(B,ld(B,B))). [para(1721(a,1),8(a,1,2))].
% 113.11/113.42 5261 mult(ld(A,A),rd(rd(A,B),B)) = mult(A,rd(rd(ld(A,A),B),B)). [para(1721(a,1),759(a,1,2)),rewrite([1721(9)])].
% 113.11/113.42 5317 rd(A,ld(B,ld(B,B))) = ld(B,mult(mult(B,A),B)). [para(1734(a,1),8(a,1,2)),flip(a)].
% 113.11/113.42 5566 mult(mult(A,A),rd(ld(mult(A,A),B),A)) = mult(B,ld(A,ld(A,A))). [back_rewrite(3204),rewrite([5317(3),532(5),10(3),1710(3)]),flip(a)].
% 113.11/113.42 5758 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,D),D)). [para(621(a,1),1741(a,2,2))].
% 113.11/113.42 5940 mult(A,rd(rd(B,mult(C,B)),D)) = mult(A,rd(ld(C,ld(C,C)),D)). [para(1946(a,1),560(a,1,2,2)),rewrite([656(14),656(15),819(15)]),flip(a)].
% 113.11/113.42 6569 rd(A,mult(mult(B,B),A)) = mult(ld(C,C),rd(rd(ld(C,C),B),B)). [para(2008(a,1),897(a,1,2)),flip(a)].
% 113.11/113.42 7312 rd(ld(mult(A,A),B),B) = mult(ld(C,C),rd(rd(ld(C,C),A),A)). [para(2190(a,1),897(a,1,2)),flip(a)].
% 113.11/113.42 8017 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(2671(a,1),2271(a,1,2,2,2)),rewrite([680(12)])].
% 113.11/113.42 8411 mult(rd(ld(A,rd(B,mult(C,B))),rd(ld(C,D),D)),E) = ld(A,E). [para(3232(a,2),614(a,1,1))].
% 113.11/113.42 8413 rd(ld(A,rd(B,mult(C,B))),rd(ld(C,D),D)) = rd(E,mult(A,E)). [para(3232(a,2),620(a,1))].
% 113.11/113.42 8684 mult(mult(A,A),rd(ld(A,rd(ld(B,C),C)),rd(ld(B,D),D))) = A. [para(3347(a,1),1539(a,1,2))].
% 113.11/113.42 8866 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(3565(a,1),226(a,1,2,1,2))].
% 113.11/113.42 8977 mult(mult(ld(A,rd(ld(mult(B,B),C),C)),B),B) = ld(A,ld(A,A)). [para(3800(a,1),475(a,1))].
% 113.11/113.42 8996 mult(mult(A,ld(B,B)),ld(B,B)) = rd(A,ld(B,B)). [para(691(a,1),3800(a,1,2,1,1)),rewrite([392(1),392(2),966(3),1417(2),7(3),680(2),10(3),392(3),392(5)]),flip(a)].
% 113.11/113.42 9659 rd(mult(mult(A,A),B),mult(A,A)) = mult(mult(A,A),rd(rd(B,A),A)). [para(1453(a,1),4745(a,1,2,2)),rewrite([10(3),1721(5),10(9)]),flip(a)].
% 113.11/113.42 9990 rd(ld(A,ld(A,A)),ld(A,ld(B,rd(rd(B,A),A)))) = mult(A,A). [para(5194(a,2),3640(a,1,2,2)),rewrite([966(4),2989(3),1417(2),7(4)])].
% 113.11/113.42 10081 ld(A,mult(mult(A,mult(A,B)),A)) = mult(mult(A,rd(B,ld(A,A))),A). [para(5317(a,1),130(a,1))].
% 113.11/113.42 10666 ld(A,rd(ld(B,C),mult(D,ld(B,C)))) = ld(A,rd(ld(D,E),E)). [para(2624(a,2),5758(a,1,2))].
% 113.11/113.42 11907 rd(ld(A,ld(A,A)),ld(B,B)) = mult(ld(A,ld(B,B)),ld(B,B)). [para(400(a,1),8996(a,1,1)),flip(a)].
% 113.11/113.42 14340 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A). [para(780(a,1),395(a,2,1)),rewrite([392(1),392(2),392(4),1031(6),897(7),392(4),392(6)])].
% 113.11/113.42 14347 rd(ld(mult(A,ld(B,B)),A),ld(B,B)) = mult(ld(A,A),ld(B,B)). [para(395(a,1),8996(a,1,1)),rewrite([897(4),392(1),1031(9),897(10)]),flip(a)].
% 113.11/113.42 14350 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A). [para(14340(a,1),10(a,1,1))].
% 113.11/113.42 14353 ld(ld(mult(A,ld(B,B)),A),C) = mult(ld(mult(B,ld(A,A)),B),C). [para(14340(a,1),554(a,1,1,2)),rewrite([14350(3)]),flip(a)].
% 113.11/113.42 14371 ld(ld(A,ld(B,B)),rd(C,mult(A,C))) = ld(mult(A,ld(B,B)),A). [para(554(a,1),14350(a,2,1)),rewrite([656(5),10(2),438(3),14350(3)]),flip(a)].
% 113.11/113.42 14377 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),14350(a,1,1))].
% 113.11/113.42 14978 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),666(a,1,2)),rewrite([680(4),680(10)])].
% 113.11/113.42 14989 ld(mult(A,ld(mult(A,B),mult(A,B))),C) = mult(rd(A,rd(mult(A,mult(A,B)),B)),C). [para(392(a,1),672(a,1,1,2))].
% 113.11/113.42 15493 mult(ld(mult(A,ld(B,B)),A),mult(ld(B,B),ld(A,A))) = ld(A,A). [para(14340(a,1),992(a,1,2,2)),rewrite([14353(7),10(8),14347(8),168(14),14377(16),14340(12),680(12),10(16)])].
% 113.11/113.42 16629 rd(mult(ld(A,A),rd(B,ld(A,A))),mult(ld(B,ld(A,A)),mult(B,ld(A,A)))) = B. [para(1744(a,1),29(a,1,1))].
% 113.11/113.42 20871 rd(rd(rd(A,B),B),mult(A,rd(rd(ld(A,A),B),B))) = ld(A,A). [para(5261(a,1),436(a,1,2)),rewrite([680(11),966(11),1417(10),7(11),680(10),966(10),1417(9),7(10)])].
% 113.11/113.42 20881 rd(ld(A,A),mult(ld(A,A),ld(B,ld(A,A)))) = mult(ld(A,A),rd(B,ld(A,A))). [para(5261(a,1),2774(a,1,2,2,2,2)),rewrite([680(3),966(3),1417(2),7(3),20871(9),680(5),1744(10)])].
% 113.11/113.42 20960 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(mult(B,ld(A,A)),B)). [para(897(a,1),428(a,1,2,2,2,1)),rewrite([916(10),14371(5),897(10),897(10)]),flip(a)].
% 113.11/113.42 22228 mult(mult(A,A),rd(rd(B,mult(mult(A,A),B)),A)) = ld(A,ld(A,A)). [para(5940(a,2),5566(a,1)),rewrite([205(9),680(8),363(8),966(10),2989(9),1417(8),7(10)])].
% 113.11/113.42 26699 mult(mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C),D) = ld(A,D). [para(6569(a,1),8411(a,1,1,1,2)),rewrite([3800(10)])].
% 113.11/113.42 26788 rd(A,mult(B,A)) = mult(mult(ld(B,mult(ld(C,C),rd(rd(ld(C,C),D),D))),D),D). [para(6569(a,1),8413(a,1,1,2)),rewrite([3800(10)]),flip(a)].
% 113.11/113.42 28094 mult(mult(A,A),mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C)) = A. [para(7312(a,1),8684(a,1,2,1,2)),rewrite([3800(11)])].
% 113.11/113.42 28329 mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C) = ld(A,ld(A,A)). [para(7312(a,1),8977(a,1,1,1,2))].
% 113.11/113.42 41616 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = mult(ld(B,B),ld(A,A)). [para(14347(a,1),1332(a,1,1,2,2)),rewrite([14353(8),15493(8),966(3),1417(2),7(3),14347(7),680(6),897(7),14347(9),680(8)]),flip(a)].
% 113.11/113.42 41617 mult(ld(A,A),ld(mult(B,ld(A,A)),B)) = ld(B,B). [para(14347(a,1),2234(a,1,2,2)),rewrite([775(3),680(6),41616(6),775(5),680(6),1032(8)]),flip(a)].
% 113.11/113.42 41619 ld(mult(A,ld(B,B)),A) = mult(ld(B,B),ld(A,A)). [para(14347(a,1),9659(a,2,2,1)),rewrite([966(3),1417(2),7(3),41617(5),966(4),1417(3),7(4),14350(3),966(6),1417(5),7(6),10(9)])].
% 113.11/113.42 41620 mult(ld(A,A),ld(mult(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(14347(a,1),745(a,2,2,2,2)),rewrite([41619(3),41619(8),1031(11),897(12),680(10),900(11),437(10),1031(8),41619(7),680(6),966(6),1417(5),7(6),897(6),966(3),1417(2),7(3),41619(6),205(10),680(7),680(10),897(12)]),flip(a)].
% 113.11/113.42 41624 mult(ld(A,A),ld(B,B)) = ld(B,B). [para(14347(a,1),9990(a,1,2,2,2,1)),rewrite([680(4),966(4),1417(3),7(4),680(3),966(3),1417(2),7(3),41619(5),10(10),680(8),41620(8),14350(3),41619(3),966(6),1417(5),7(6)])].
% 113.11/113.42 41625 mult(mult(A,ld(B,B)),A) = mult(A,A). [para(14347(a,1),10081(a,2,1,2)),rewrite([41619(3),41624(3),10081(5),14350(3),41619(3),41624(3),41624(6),7(5)])].
% 113.11/113.42 41627 ld(A,A) = ld(B,B). [para(10666(a,1),14347(a,1,1,1,2)),rewrite([656(7),10(4),437(3),41619(3),41624(3),656(10),10(5),438(6),14350(3),41619(3),41624(3),656(11),10(6),438(7),41624(4)])].
% 113.11/113.42 41634 mult(mult(A,ld(mult(ld(B,B),A),ld(B,B))),ld(B,B)) = ld(B,B). [para(11907(a,2),14347(a,1,1,1)),rewrite([656(7),5317(4),41625(3),8(2),7(3),392(3),680(3),966(3),1417(2),7(3),168(6)]),flip(a)].
% 113.11/113.42 41638 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(B,B)). [back_rewrite(20960),rewrite([41619(7),41624(7)])].
% 113.11/113.42 41661 ld(mult(A,ld(B,B)),A) = ld(A,A). [back_rewrite(41619),rewrite([41624(6)])].
% 113.11/113.42 41672 rd(mult(A,mult(A,B)),B) = mult(A,A). [back_rewrite(395),rewrite([41625(5)]),flip(a)].
% 113.11/113.42 41673 ld(A,A) = c_0. [new_symbol(41627)].
% 113.11/113.42 41686 ld(mult(A,c_0),B) = mult(ld(A,c_0),B). [back_rewrite(14989),rewrite([41673(3),41672(6),436(5),41673(4)])].
% 113.11/113.42 41699 mult(ld(A,c_0),A) = c_0. [back_rewrite(41661),rewrite([41673(1),41686(3),41673(4)])].
% 113.11/113.43 41716 ld(mult(c_0,A),c_0) = ld(A,c_0). [back_rewrite(41638),rewrite([41673(1),41673(3),41673(5)])].
% 113.11/113.43 41719 mult(c_0,c_0) = c_0. [back_rewrite(41634),rewrite([41673(1),41673(3),41716(4),7(3),41673(2),41673(4)])].
% 113.11/113.43 41974 mult(mult(ld(A,mult(c_0,rd(rd(c_0,B),B))),B),B) = ld(A,c_0). [back_rewrite(28329),rewrite([41673(1),41673(2),41673(9)])].
% 113.11/113.43 41982 mult(A,c_0) = A. [back_rewrite(28094),rewrite([41673(2),41673(3),41974(9),26(4),41673(1),41719(3)])].
% 113.11/113.43 41991 rd(A,mult(B,A)) = ld(B,c_0). [back_rewrite(26788),rewrite([41673(3),41673(4),41974(10)])].
% 113.11/113.43 41992 mult(ld(A,c_0),B) = ld(A,B). [back_rewrite(26699),rewrite([41673(1),41673(2),41974(8)])].
% 113.11/113.43 42069 mult(c_0,ld(A,c_0)) = ld(A,c_0). [back_rewrite(22228),rewrite([41991(4),5566(6),41673(2),41673(5)])].
% 113.11/113.43 42097 mult(c_0,rd(A,c_0)) = A. [back_rewrite(20881),rewrite([41673(1),41673(2),41673(3),42069(5),14(4),41673(1),41673(2)]),flip(a)].
% 113.11/113.43 42253 rd(A,c_0) = A. [back_rewrite(16629),rewrite([41673(1),41673(2),42097(4),41673(1),41673(3),41982(4),41699(3)])].
% 113.11/113.43 42314 mult(c_0,ld(A,B)) = ld(A,B). [back_rewrite(14978),rewrite([41673(1),41991(3),42069(4),41992(3),41673(2),41673(3),41992(5)]),flip(a)].
% 113.11/113.43 42691 ld(mult(A,A),B) = ld(A,ld(A,B)). [back_rewrite(8866),rewrite([41673(9),41992(11),10(10)]),flip(a)].
% 113.11/113.43 42724 mult(c_0,A) = A. [back_rewrite(8017),rewrite([42691(2),41673(3),42314(7),14(6),41673(1),41673(2),42253(3)]),flip(a)].
% 113.11/113.43 42984 $F # answer(goals). [back_rewrite(409),rewrite([41673(4),41982(3),41673(6),42724(6)]),xx(a),xx(b)].
% 113.11/113.43
% 113.11/113.43 % SZS output end Refutation
% 113.11/113.43 ============================== end of proof ==========================
% 113.11/113.43
% 113.11/113.43 ============================== STATISTICS ============================
% 113.11/113.43
% 113.11/113.43 Given=1570. Generated=4051332. Kept=42977. proofs=1.
% 113.11/113.43 Usable=1001. Sos=6462. Demods=6429. Limbo=1311, Disabled=34209. Hints=0.
% 113.11/113.43 Megabytes=39.25.
% 113.11/113.43 User_CPU=110.14, System_CPU=2.29, Wall_clock=113.
% 113.11/113.43
% 113.11/113.43 ============================== end of statistics =====================
% 113.11/113.43
% 113.11/113.43 ============================== end of search =========================
% 113.11/113.43
% 113.11/113.43 THEOREM PROVED
% 113.11/113.43 % SZS status Theorem
% 113.11/113.43
% 113.11/113.43 Exiting with 1 proof.
% 113.11/113.43
% 113.11/113.43 Process 23427 exit (max_proofs) Mon Jun 13 16:09:48 2022
% 113.11/113.43 Prover9 interrupted
%------------------------------------------------------------------------------