TSTP Solution File: GRP654-10 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP654-10 : TPTP v8.1.0. Released v8.1.0.
% 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 11:20:17 EDT 2022
% Result : Unsatisfiable 246.84s 247.15s
% Output : Refutation 246.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP654-10 : TPTP v8.1.0. Released v8.1.0.
% 0.13/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 16:10:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.52/7.86 ============================== Prover9 ===============================
% 7.52/7.86 Prover9 (32) version 2009-11A, November 2009.
% 7.52/7.86 Process 29600 was started by sandbox on n029.cluster.edu,
% 7.52/7.86 Mon Jun 13 16:10:40 2022
% 7.52/7.86 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29445_n029.cluster.edu".
% 7.52/7.86 ============================== end of head ===========================
% 7.52/7.86
% 7.52/7.86 ============================== INPUT =================================
% 7.52/7.86
% 7.52/7.86 % Reading from file /tmp/Prover9_29445_n029.cluster.edu
% 7.52/7.86
% 7.52/7.86 set(prolog_style_variables).
% 7.52/7.86 set(auto2).
% 7.52/7.86 % set(auto2) -> set(auto).
% 7.52/7.86 % set(auto) -> set(auto_inference).
% 7.52/7.86 % set(auto) -> set(auto_setup).
% 7.52/7.86 % set(auto_setup) -> set(predicate_elim).
% 7.52/7.86 % set(auto_setup) -> assign(eq_defs, unfold).
% 7.52/7.86 % set(auto) -> set(auto_limits).
% 7.52/7.86 % set(auto_limits) -> assign(max_weight, "100.000").
% 7.52/7.86 % set(auto_limits) -> assign(sos_limit, 20000).
% 7.52/7.86 % set(auto) -> set(auto_denials).
% 7.52/7.86 % set(auto) -> set(auto_process).
% 7.52/7.86 % set(auto2) -> assign(new_constants, 1).
% 7.52/7.86 % set(auto2) -> assign(fold_denial_max, 3).
% 7.52/7.86 % set(auto2) -> assign(max_weight, "200.000").
% 7.52/7.86 % set(auto2) -> assign(max_hours, 1).
% 7.52/7.86 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.52/7.86 % set(auto2) -> assign(max_seconds, 0).
% 7.52/7.86 % set(auto2) -> assign(max_minutes, 5).
% 7.52/7.86 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.52/7.86 % set(auto2) -> set(sort_initial_sos).
% 7.52/7.86 % set(auto2) -> assign(sos_limit, -1).
% 7.52/7.86 % set(auto2) -> assign(lrs_ticks, 3000).
% 7.52/7.86 % set(auto2) -> assign(max_megs, 400).
% 7.52/7.86 % set(auto2) -> assign(stats, some).
% 7.52/7.86 % set(auto2) -> clear(echo_input).
% 7.52/7.86 % set(auto2) -> set(quiet).
% 7.52/7.86 % set(auto2) -> clear(print_initial_clauses).
% 7.52/7.86 % set(auto2) -> clear(print_given).
% 7.52/7.86 assign(lrs_ticks,-1).
% 7.52/7.86 assign(sos_limit,10000).
% 7.52/7.86 assign(order,kbo).
% 7.52/7.86 set(lex_order_vars).
% 7.52/7.86 clear(print_given).
% 7.52/7.86
% 7.52/7.86 % formulas(sos). % not echoed (6 formulas)
% 7.52/7.86
% 7.52/7.86 ============================== end of input ==========================
% 7.52/7.86
% 7.52/7.86 % From the command line: assign(max_seconds, 300).
% 7.52/7.86
% 7.52/7.86 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.52/7.86
% 7.52/7.86 % Formulas that are not ordinary clauses:
% 7.52/7.86
% 7.52/7.86 ============================== end of process non-clausal formulas ===
% 7.52/7.86
% 7.52/7.86 ============================== PROCESS INITIAL CLAUSES ===============
% 7.52/7.86
% 7.52/7.86 ============================== PREDICATE ELIMINATION =================
% 7.52/7.86
% 7.52/7.86 ============================== end predicate elimination =============
% 7.52/7.86
% 7.52/7.86 Auto_denials:
% 7.52/7.86 % copying label goal to answer in negative clause
% 7.52/7.86
% 7.52/7.86 Term ordering decisions:
% 7.52/7.86 Function symbol KB weights: mult=1. ld=1. rd=1. tuple=1. x1=1. x1_2=1.
% 7.52/7.86
% 7.52/7.86 ============================== end of process initial clauses ========
% 7.52/7.86
% 7.52/7.86 ============================== CLAUSES FOR SEARCH ====================
% 7.52/7.86
% 7.52/7.86 ============================== end of clauses for search =============
% 7.52/7.86
% 7.52/7.86 ============================== SEARCH ================================
% 7.52/7.86
% 7.52/7.86 % Starting search at 0.01 seconds.
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=195.000, iters=3391
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=191.000, iters=3345
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=187.000, iters=3382
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=183.000, iters=3350
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=179.000, iters=3435
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=167.000, iters=3399
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=159.000, iters=3453
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=155.000, iters=3442
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=147.000, iters=3508
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=143.000, iters=3461
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=139.000, iters=3616
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=135.000, iters=3538
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=131.000, iters=3434
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=127.000, iters=3417
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=123.000, iters=3399
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=119.000, iters=3519
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=115.000, iters=3366
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=111.000, iters=3574
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=107.000, iters=3407
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=99.000, iters=3335
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=91.000, iters=3503
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=87.000, iters=3418
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=47.000, iters=3363
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=43.000, iters=3441
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=39.000, iters=3408
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=35.000, iters=3349
% 7.52/7.86
% 7.52/7.86 Low Water (keep): wt=31.000, iters=3413
% 7.52/7.86
% 7.52/7.86 Low Water (displace): id=6963, wt=199.000
% 7.52/7.86
% 7.52/7.86 Low Water (displace): id=14376, wt=23.000
% 246.84/247.15
% 246.84/247.15 Low Water (keep): wt=27.000, iters=3394
% 246.84/247.15
% 246.84/247.15 Low Water (displace): id=16232, wt=19.000
% 246.84/247.15
% 246.84/247.15 Low Water (keep): wt=23.000, iters=3398
% 246.84/247.15
% 246.84/247.15 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 55 (0.00 of 11.12 sec).
% 246.84/247.15
% 246.84/247.15 ============================== PROOF =================================
% 246.84/247.15 % SZS status Unsatisfiable
% 246.84/247.15 % SZS output start Refutation
% 246.84/247.15
% 246.84/247.15 % Proof 1 at 242.38 (+ 3.81) seconds: goal.
% 246.84/247.15 % Length of proof is 235.
% 246.84/247.15 % Level of proof is 36.
% 246.84/247.15 % Maximum clause weight is 87.000.
% 246.84/247.15 % Given clauses 2723.
% 246.84/247.15
% 246.84/247.15 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 246.84/247.15 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 246.84/247.15 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 246.84/247.15 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 246.84/247.15 5 mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) # label(f05) # label(axiom). [assumption].
% 246.84/247.15 6 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))). [copy(5),flip(a)].
% 246.84/247.15 7 tuple(mult(A,x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 246.84/247.15 8 ld(rd(A,B),A) = B. [para(3(a,1),2(a,1,2))].
% 246.84/247.15 9 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 246.84/247.15 10 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C. [para(6(a,1),1(a,1))].
% 246.84/247.15 11 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C). [para(1(a,1),6(a,1,1,1)),flip(a)].
% 246.84/247.15 13 mult(rd(A,B),mult(B,mult(rd(A,B),C))) = mult(mult(A,rd(A,B)),C). [para(3(a,1),6(a,1,1,1)),flip(a)].
% 246.84/247.15 14 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A). [para(6(a,1),4(a,1,1))].
% 246.84/247.15 17 tuple(mult(A,mult(B,mult(A,x1(mult(mult(A,B),A))))),mult(x1_2(mult(mult(A,B),A)),mult(mult(A,B),A))) != tuple(x1(mult(mult(A,B),A)),x1_2(mult(mult(A,B),A))) # answer(goal). [para(6(a,1),7(a,1,1))].
% 246.84/247.15 18 tuple(mult(A,mult(B,mult(A,mult(C,mult(A,mult(B,mult(A,x1(mult(mult(A,mult(B,mult(A,C))),mult(mult(A,B),A)))))))))),mult(x1_2(mult(mult(A,mult(B,mult(A,C))),mult(mult(A,B),A))),mult(mult(A,mult(B,mult(A,C))),mult(mult(A,B),A)))) != tuple(x1(mult(mult(A,mult(B,mult(A,C))),mult(mult(A,B),A))),x1_2(mult(mult(A,mult(B,mult(A,C))),mult(mult(A,B),A)))) # answer(goal). [para(6(a,1),17(a,1,1,2,2,2,1,1)),rewrite([6(12),6(14),6(17),6(24),6(32),6(39)])].
% 246.84/247.15 33 mult(A,mult(B,ld(mult(mult(B,A),B),C))) = ld(B,C). [para(10(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 38 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(1(a,1),11(a,1,2,2)),flip(a)].
% 246.84/247.15 39 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)). [para(11(a,1),2(a,1,2))].
% 246.84/247.15 41 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B. [para(11(a,1),4(a,1,1))].
% 246.84/247.15 47 mult(mult(A,B),mult(ld(B,C),mult(B,D))) = mult(B,mult(ld(B,A),mult(mult(C,B),D))). [para(11(a,1),11(a,1,2,2)),flip(a)].
% 246.84/247.15 54 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)). [para(3(a,1),13(a,1,2,2)),flip(a)].
% 246.84/247.15 69 tuple(mult(A,mult(B,mult(mult(C,A),mult(B,mult(A,x1(mult(mult(A,mult(B,C)),mult(mult(A,B),A)))))))),mult(x1_2(mult(mult(A,mult(B,C)),mult(mult(A,B),A))),mult(mult(A,mult(B,C)),mult(mult(A,B),A)))) != tuple(x1(mult(mult(A,mult(B,C)),mult(mult(A,B),A))),x1_2(mult(mult(A,mult(B,C)),mult(mult(A,B),A)))) # answer(goal). [para(1(a,1),18(a,1,1,2,2,2,2,2,2,2,1,1,2,2)),rewrite([11(12),1(14),1(20),1(27),1(33)])].
% 246.84/247.15 79 tuple(mult(A,mult(B,mult(mult(ld(B,C),A),mult(B,mult(A,x1(mult(mult(A,C),mult(mult(A,B),A)))))))),mult(x1_2(mult(mult(A,C),mult(mult(A,B),A))),mult(mult(A,C),mult(mult(A,B),A)))) != tuple(x1(mult(mult(A,C),mult(mult(A,B),A))),x1_2(mult(mult(A,C),mult(mult(A,B),A)))) # answer(goal). [para(1(a,1),69(a,1,1,2,2,2,2,2,1,1,2)),rewrite([1(14),1(19),1(25),1(30)])].
% 246.84/247.15 97 rd(mult(A,mult(B,C)),ld(A,C)) = mult(mult(A,B),A). [para(1(a,1),14(a,1,1,2,2))].
% 246.84/247.15 99 mult(mult(A,rd(B,mult(A,C))),A) = rd(mult(A,B),C). [para(3(a,1),14(a,1,1,2)),flip(a)].
% 246.84/247.15 107 mult(ld(A,B),mult(A,ld(mult(B,A),C))) = ld(A,C). [para(1(a,1),33(a,1,2,2,1,1))].
% 246.84/247.15 108 mult(A,ld(mult(mult(A,B),A),C)) = ld(B,ld(A,C)). [para(33(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 118 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C). [para(38(a,1),2(a,1,2))].
% 246.84/247.15 119 mult(A,mult(ld(A,rd(B,A)),C)) = mult(B,ld(A,C)). [para(3(a,1),38(a,1,1)),flip(a)].
% 246.84/247.15 143 mult(ld(A,rd(B,A)),mult(A,C)) = ld(A,mult(B,C)). [para(3(a,1),39(a,1,2,1)),flip(a)].
% 246.84/247.15 179 tuple(mult(A,mult(B,mult(mult(ld(B,ld(A,C)),A),mult(B,mult(A,x1(mult(C,mult(mult(A,B),A)))))))),mult(x1_2(mult(C,mult(mult(A,B),A))),mult(C,mult(mult(A,B),A)))) != tuple(x1(mult(C,mult(mult(A,B),A))),x1_2(mult(C,mult(mult(A,B),A)))) # answer(goal). [para(1(a,1),79(a,1,1,2,2,2,2,2,1,1)),rewrite([1(14),1(18),1(23),1(27)])].
% 246.84/247.15 196 tuple(mult(A,mult(B,mult(mult(ld(B,ld(A,rd(C,mult(mult(A,B),A)))),A),mult(B,mult(A,x1(C)))))),mult(x1_2(C),C)) != tuple(x1(C),x1_2(C)) # answer(goal). [para(3(a,1),179(a,1,1,2,2,2,2,2,1)),rewrite([3(18),3(19),3(21),3(22)])].
% 246.84/247.15 206 tuple(mult(mult(A,B),mult(ld(B,ld(ld(B,A),ld(B,rd(C,mult(A,B))))),mult(mult(A,B),x1(C)))),mult(x1_2(C),C)) != tuple(x1(C),x1_2(C)) # answer(goal). [para(1(a,1),196(a,1,1,2,2,1,1,2,2,2,1)),rewrite([47(12),11(14)])].
% 246.84/247.15 276 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A). [para(3(a,1),97(a,1,1,2))].
% 246.84/247.15 320 tuple(mult(A,mult(ld(B,ld(ld(B,rd(A,B)),ld(B,rd(C,A)))),mult(A,x1(C)))),mult(x1_2(C),C)) != tuple(x1(C),x1_2(C)) # answer(goal). [para(3(a,1),206(a,1,1,1)),rewrite([3(4),3(8)])].
% 246.84/247.15 336 tuple(mult(A,mult(ld(rd(rd(B,A),C),ld(ld(rd(rd(B,A),C),rd(A,rd(rd(B,A),C))),C)),mult(A,x1(B)))),mult(x1_2(B),B)) != tuple(x1(B),x1_2(B)) # answer(goal). [para(8(a,1),320(a,1,1,2,1,2,2))].
% 246.84/247.15 355 ld(mult(A,rd(B,mult(A,C))),rd(mult(A,B),C)) = A. [para(99(a,1),2(a,1,2))].
% 246.84/247.15 359 mult(A,mult(rd(B,mult(A,C)),mult(A,D))) = mult(rd(mult(A,B),C),D). [para(99(a,1),6(a,1,1)),flip(a)].
% 246.84/247.15 397 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)). [para(107(a,1),2(a,1,2))].
% 246.84/247.15 422 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))). [para(108(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 450 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)). [para(1(a,1),118(a,1,2,2))].
% 246.84/247.15 500 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C). [para(119(a,1),2(a,1,2))].
% 246.84/247.15 509 mult(mult(A,B),mult(ld(B,rd(C,B)),D)) = mult(B,mult(ld(B,A),mult(C,ld(B,D)))). [para(119(a,1),11(a,1,2,2)),flip(a)].
% 246.84/247.15 571 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)). [para(1(a,1),276(a,1,1)),flip(a)].
% 246.84/247.15 591 ld(mult(A,rd(B,mult(A,B))),A) = A. [para(4(a,1),355(a,1,2))].
% 246.84/247.15 661 ld(mult(A,rd(ld(A,B),B)),A) = A. [para(1(a,1),591(a,1,1,2,2))].
% 246.84/247.15 664 mult(A,rd(B,mult(A,B))) = rd(A,A). [para(591(a,1),9(a,1,2)),flip(a)].
% 246.84/247.15 677 mult(A,rd(ld(A,B),B)) = rd(A,A). [para(661(a,1),9(a,1,2)),flip(a)].
% 246.84/247.15 681 rd(A,mult(B,A)) = ld(B,rd(B,B)). [para(664(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 682 rd(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [para(3(a,1),664(a,1,2,2)),flip(a)].
% 246.84/247.15 688 mult(rd(A,A),B) = mult(ld(A,A),B). [para(664(a,1),13(a,2,1)),rewrite([681(2),681(5),509(7),1(5),143(6),2(4)]),flip(a)].
% 246.84/247.15 696 mult(ld(A,A),A) = A. [para(664(a,1),14(a,2,1)),rewrite([359(5),4(2),4(2),688(2)]),flip(a)].
% 246.84/247.15 744 ld(ld(A,A),A) = A. [para(696(a,1),2(a,1,2))].
% 246.84/247.15 745 rd(A,A) = ld(A,A). [para(696(a,1),4(a,1,1))].
% 246.84/247.15 759 mult(mult(A,ld(mult(A,B),mult(A,B))),A) = rd(mult(A,mult(A,B)),B). [para(696(a,1),14(a,1,1,2)),flip(a)].
% 246.84/247.15 767 mult(ld(A,ld(A,A)),B) = ld(A,B). [para(696(a,1),107(a,1,2,2,1)),rewrite([1(4)])].
% 246.84/247.15 816 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [back_rewrite(682),rewrite([745(3)])].
% 246.84/247.15 817 rd(A,mult(B,A)) = ld(B,ld(B,B)). [back_rewrite(681),rewrite([745(3)])].
% 246.84/247.15 819 mult(A,rd(ld(A,B),B)) = ld(A,A). [back_rewrite(677),rewrite([745(4)])].
% 246.84/247.15 821 mult(A,rd(B,mult(A,B))) = ld(A,A). [back_rewrite(664),rewrite([745(4)])].
% 246.84/247.15 864 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)). [para(744(a,1),38(a,2,2,1)),rewrite([1(2)]),flip(a)].
% 246.84/247.15 867 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A). [para(744(a,1),41(a,1,2,1)),rewrite([1(2)])].
% 246.84/247.15 868 mult(A,mult(ld(A,A),ld(A,B))) = ld(ld(A,A),B). [para(744(a,1),107(a,1,1)),rewrite([1(3)])].
% 246.84/247.15 885 rd(ld(A,B),B) = ld(A,ld(A,A)). [para(767(a,1),4(a,1,1))].
% 246.84/247.15 895 mult(ld(A,rd(ld(ld(A,ld(A,A)),B),A)),C) = mult(mult(B,ld(A,ld(A,A))),C). [para(767(a,1),11(a,1,2,2)),rewrite([767(8),500(6)])].
% 246.84/247.15 906 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)). [para(767(a,1),14(a,1,1,2,2)),rewrite([767(5),500(3),4(4),767(5)]),flip(a)].
% 246.84/247.15 1019 ld(ld(A,ld(A,A)),B) = mult(A,B). [para(817(a,1),8(a,1,1))].
% 246.84/247.15 1020 rd(mult(ld(A,B),mult(A,C)),mult(mult(B,A),C)) = ld(A,ld(A,A)). [para(11(a,1),817(a,1,2))].
% 246.84/247.15 1048 mult(rd(A,mult(B,A)),C) = ld(B,C). [para(817(a,2),107(a,1,1)),rewrite([696(4),1(4)])].
% 246.84/247.15 1062 mult(A,rd(B,mult(C,B))) = mult(A,ld(C,ld(C,C))). [para(817(a,2),119(a,2,2)),rewrite([119(5)]),flip(a)].
% 246.84/247.15 1090 rd(A,mult(B,A)) = rd(C,mult(B,C)). [para(817(a,2),817(a,2))].
% 246.84/247.15 1102 mult(ld(A,rd(mult(A,B),A)),C) = mult(mult(B,ld(A,ld(A,A))),C). [back_rewrite(895),rewrite([1019(3)])].
% 246.84/247.15 1155 rd(rd(ld(A,B),B),ld(A,A)) = ld(A,ld(A,A)). [para(819(a,1),817(a,1,2))].
% 246.84/247.15 1192 mult(rd(ld(A,B),B),C) = ld(A,C). [para(885(a,2),107(a,1,1)),rewrite([696(4),1(4)])].
% 246.84/247.15 1204 mult(A,rd(ld(B,C),C)) = mult(A,ld(B,ld(B,B))). [para(885(a,2),119(a,2,2)),rewrite([119(5)]),flip(a)].
% 246.84/247.15 1226 rd(ld(A,B),B) = rd(C,mult(A,C)). [para(885(a,2),817(a,2)),flip(a)].
% 246.84/247.15 1227 rd(ld(A,B),B) = rd(ld(A,C),C). [para(885(a,2),885(a,2))].
% 246.84/247.15 1322 ld(rd(A,B),C) = mult(rd(B,A),C). [para(3(a,1),1048(a,1,1,2)),flip(a)].
% 246.84/247.15 1324 mult(rd(A,mult(B,mult(C,mult(B,A)))),D) = ld(B,ld(C,ld(B,D))). [para(6(a,1),1048(a,1,1,2)),rewrite([422(8)])].
% 246.84/247.15 1341 mult(ld(A,B),rd(C,mult(A,C))) = ld(A,rd(B,A)). [para(1048(a,1),14(a,1,1,2,2)),rewrite([1048(5),500(3),4(4),1048(5)]),flip(a)].
% 246.84/247.15 1357 tuple(mult(ld(A,rd(mult(rd(B,rd(C,rd(D,mult(A,D)))),ld(mult(rd(B,rd(C,rd(D,mult(A,D)))),rd(rd(D,mult(A,D)),rd(rd(C,rd(D,mult(A,D))),B))),B)),A)),x1(C)),mult(x1_2(C),C)) != tuple(x1(C),x1_2(C)) # answer(goal). [para(1048(a,1),336(a,1,1,2,2)),rewrite([1322(18),1322(20),1048(24),500(22)])].
% 246.84/247.15 1363 ld(ld(A,rd(B,A)),C) = mult(A,ld(B,mult(A,C))). [para(143(a,1),1048(a,1,1,2)),rewrite([276(4),6(5),1048(4)]),flip(a)].
% 246.84/247.15 1369 ld(ld(A,A),B) = mult(ld(A,A),B). [para(696(a,1),1048(a,1,1,2)),rewrite([745(1)]),flip(a)].
% 246.84/247.15 1396 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)). [back_rewrite(816),rewrite([1322(3)])].
% 246.84/247.15 1518 mult(A,mult(ld(A,A),ld(A,B))) = mult(ld(A,A),B). [back_rewrite(868),rewrite([1369(6)])].
% 246.84/247.15 1519 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)). [back_rewrite(864),rewrite([1369(5)])].
% 246.84/247.15 1526 rd(A,mult(rd(B,C),A)) = rd(C,B). [para(3(a,1),1090(a,1,2)),flip(a)].
% 246.84/247.15 1599 mult(ld(A,B),rd(ld(A,C),C)) = ld(A,rd(B,A)). [para(1192(a,1),14(a,1,1,2,2)),rewrite([1192(5),500(3),4(4),1192(5)]),flip(a)].
% 246.84/247.15 1658 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(1322(a,1),1(a,1,2))].
% 246.84/247.15 1662 mult(mult(rd(A,B),C),mult(rd(B,A),D)) = mult(rd(A,B),mult(mult(C,rd(B,A)),D)). [para(1322(a,1),39(a,1)),rewrite([1322(7)]),flip(a)].
% 246.84/247.15 1665 mult(rd(A,B),mult(rd(A,B),rd(B,A))) = rd(A,B). [para(1322(a,1),41(a,1,2,1)),rewrite([1662(8),817(9),1322(4),1322(5)])].
% 246.84/247.15 1759 mult(ld(A,A),mult(ld(A,A),B)) = B. [para(1369(a,1),1(a,1,2))].
% 246.84/247.15 1766 mult(A,mult(ld(A,A),ld(mult(A,A),B))) = ld(A,B). [para(107(a,1),1369(a,2)),rewrite([1369(5),1519(5)])].
% 246.84/247.15 1776 rd(A,ld(B,ld(C,ld(B,A)))) = mult(mult(B,C),B). [para(14(a,1),1526(a,2)),rewrite([1324(5)])].
% 246.84/247.15 1908 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)). [para(107(a,1),1759(a,1,2))].
% 246.84/247.15 1923 mult(A,mult(A,ld(mult(A,A),B))) = mult(ld(A,A),B). [back_rewrite(1518),rewrite([1908(3)])].
% 246.84/247.15 1981 ld(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),ld(mult(B,ld(A,A)),C)). [para(1369(a,1),397(a,1,1)),rewrite([1369(4)])].
% 246.84/247.15 1999 mult(A,ld(mult(A,A),mult(ld(A,A),B))) = ld(A,B). [para(696(a,1),422(a,1,1,1)),rewrite([1(2),1369(4),1369(6),1908(6)]),flip(a)].
% 246.84/247.15 2194 mult(rd(A,B),ld(mult(rd(A,B),C),A)) = ld(mult(C,rd(B,A)),B). [para(3(a,1),450(a,1,2)),rewrite([1322(6),1322(8)]),flip(a)].
% 246.84/247.15 2218 mult(ld(A,A),ld(mult(ld(A,A),B),A)) = ld(mult(B,ld(A,A)),A). [para(696(a,1),450(a,1,2)),rewrite([1369(6),1369(8)]),flip(a)].
% 246.84/247.15 2219 mult(ld(mult(A,A),ld(A,A)),B) = ld(mult(A,A),B). [para(450(a,1),767(a,1,1,2)),rewrite([1369(3),696(3)])].
% 246.84/247.15 2229 rd(ld(mult(A,A),B),B) = ld(mult(A,A),ld(A,A)). [para(450(a,1),885(a,2,2)),rewrite([1369(6),696(6)])].
% 246.84/247.15 2256 tuple(mult(mult(rd(A,rd(B,mult(C,B))),ld(C,ld(C,C))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [back_rewrite(1357),rewrite([2194(18),3(12),1322(6),4(2),1102(8)])].
% 246.84/247.15 2266 mult(ld(A,rd(ld(B,ld(B,B)),A)),C) = ld(A,ld(B,ld(A,C))). [para(767(a,1),500(a,1,2)),flip(a)].
% 246.84/247.15 2336 rd(rd(A,ld(B,C)),B) = mult(B,rd(ld(B,A),C)). [para(571(a,1),4(a,1,1))].
% 246.84/247.15 2370 rd(A,rd(B,mult(C,B))) = rd(A,ld(C,ld(C,C))). [para(817(a,2),571(a,2,2)),rewrite([571(5)]),flip(a)].
% 246.84/247.15 2372 rd(A,rd(ld(B,C),C)) = rd(A,ld(B,ld(B,B))). [para(885(a,2),571(a,2,2)),rewrite([571(5)]),flip(a)].
% 246.84/247.15 2517 tuple(mult(mult(rd(A,rd(B,mult(mult(C,C),B))),ld(mult(C,C),ld(C,C))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [para(450(a,1),2256(a,1,1,1,2,2)),rewrite([1369(7),696(7)])].
% 246.84/247.15 2614 rd(mult(A,mult(A,B)),mult(mult(A,A),B)) = ld(A,A). [para(11(a,1),867(a,1,2))].
% 246.84/247.15 2632 mult(A,ld(mult(A,A),A)) = ld(A,A). [para(819(a,1),867(a,1,1)),rewrite([1599(5),745(2),1(4),745(3),1369(3),1908(3)])].
% 246.84/247.15 2649 ld(mult(A,A),A) = ld(A,ld(A,A)). [para(2632(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 2654 mult(rd(ld(A,ld(A,A)),A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [para(2632(a,1),54(a,2,2)),rewrite([2649(2),2649(4),767(6),2266(5),2649(5)]),flip(a)].
% 246.84/247.15 2660 rd(A,ld(A,ld(A,A))) = mult(A,A). [para(2649(a,1),9(a,1,2))].
% 246.84/247.15 2661 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(mult(A,mult(A,A)),B). [para(2649(a,1),11(a,1,2,1)),rewrite([767(6),39(4),1519(4)])].
% 246.84/247.15 2670 rd(ld(A,ld(A,A)),A) = ld(mult(A,A),ld(A,A)). [para(2649(a,1),885(a,1,1)),rewrite([450(7),1369(6),696(6)])].
% 246.84/247.15 2680 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [back_rewrite(2654),rewrite([2670(3),2219(5)])].
% 246.84/247.15 2681 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))). [back_rewrite(2670),rewrite([2680(6)])].
% 246.84/247.15 2684 tuple(mult(mult(rd(A,rd(B,mult(mult(C,C),B))),ld(C,ld(C,ld(C,C)))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [back_rewrite(2517),rewrite([2680(7)])].
% 246.84/247.15 2689 rd(ld(mult(A,A),B),B) = ld(A,ld(A,ld(A,A))). [back_rewrite(2229),rewrite([2680(6)])].
% 246.84/247.15 2691 mult(ld(A,ld(A,ld(A,A))),B) = ld(mult(A,A),B). [back_rewrite(2219),rewrite([2680(3)])].
% 246.84/247.15 2756 rd(A,rd(B,mult(A,B))) = mult(A,A). [para(817(a,2),2660(a,1,2))].
% 246.84/247.15 2757 rd(A,rd(ld(A,B),B)) = mult(A,A). [para(885(a,2),2660(a,1,2))].
% 246.84/247.15 2758 rd(rd(A,mult(B,A)),B) = ld(B,rd(A,mult(B,A))). [para(1048(a,1),2660(a,2)),rewrite([1322(9),4(6),821(7),1322(6),4(4),1(4)])].
% 246.84/247.15 2767 mult(mult(A,mult(A,A)),B) = mult(A,mult(A,mult(A,B))). [para(2660(a,1),500(a,2,1,2)),rewrite([1019(5),1019(5),1019(7)]),flip(a)].
% 246.84/247.15 2779 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(A,mult(A,mult(A,B))). [back_rewrite(2661),rewrite([2767(8)])].
% 246.84/247.15 2782 mult(mult(A,A),rd(B,mult(A,B))) = A. [para(2756(a,1),3(a,1,1))].
% 246.84/247.15 2800 mult(mult(A,A),rd(ld(A,B),B)) = A. [para(2757(a,1),3(a,1,1))].
% 246.84/247.15 2811 mult(mult(rd(A,B),rd(A,B)),rd(B,A)) = rd(A,B). [para(3(a,1),2782(a,1,2,2))].
% 246.84/247.15 2823 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(2782(a,1),14(a,2,1)),rewrite([1048(6),39(4),1519(4),2779(5),14(4)])].
% 246.84/247.15 2849 rd(ld(mult(A,A),B),B) = ld(A,rd(C,mult(A,C))). [para(2782(a,1),1226(a,2,2)),rewrite([2758(6)])].
% 246.84/247.15 2855 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(mult(A,mult(A,A)),B). [para(2782(a,1),422(a,1,1,1)),rewrite([1322(9),4(6),500(8),817(6)]),flip(a)].
% 246.84/247.15 3057 ld(mult(A,mult(A,A)),B) = ld(A,ld(A,ld(A,B))). [para(2823(a,1),422(a,1,1))].
% 246.84/247.15 3070 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(2855),rewrite([3057(8)])].
% 246.84/247.15 3083 mult(A,ld(mult(B,A),rd(B,A))) = ld(A,ld(A,A)). [para(906(a,1),2(a,1,2)),rewrite([397(4)])].
% 246.84/247.15 3084 ld(A,rd(mult(A,B),A)) = mult(B,ld(A,ld(A,A))). [para(2(a,1),906(a,1,1)),flip(a)].
% 246.84/247.15 3085 rd(ld(A,rd(B,A)),ld(A,ld(A,A))) = ld(A,B). [para(906(a,1),4(a,1,1))].
% 246.84/247.15 3104 mult(A,ld(B,ld(B,ld(B,B)))) = rd(rd(A,B),B). [para(906(a,1),119(a,1,2)),rewrite([1(4)]),flip(a)].
% 246.84/247.15 3113 rd(ld(A,ld(A,A)),ld(A,rd(B,A))) = ld(ld(A,B),mult(A,ld(mult(B,A),B))). [para(906(a,1),817(a,1,2)),rewrite([397(9)])].
% 246.84/247.15 3118 mult(A,rd(B,ld(A,ld(A,A)))) = mult(mult(A,B),A). [para(1019(a,1),906(a,1,1)),rewrite([397(8),696(5),1(6),397(5),696(3),1(3),1019(8)]),flip(a)].
% 246.84/247.15 3119 mult(rd(ld(A,ld(A,A)),ld(A,rd(B,A))),C) = ld(ld(A,B),C). [para(906(a,1),1048(a,1,1,2))].
% 246.84/247.15 3137 mult(ld(ld(A,B),C),ld(ld(A,B),mult(A,ld(mult(B,A),B)))) = ld(ld(A,B),rd(C,ld(A,B))). [para(397(a,1),906(a,1,2,2))].
% 246.84/247.15 3157 rd(ld(A,ld(A,ld(A,A))),A) = ld(mult(A,A),ld(A,ld(A,A))). [para(2649(a,1),906(a,1,1)),rewrite([450(6),1369(5),696(5),2680(5),3104(6),2681(3),817(7)])].
% 246.84/247.15 3162 ld(mult(A,A),ld(A,ld(A,A))) = ld(A,ld(A,ld(A,ld(A,A)))). [para(906(a,1),2823(a,1,1)),rewrite([885(2),906(6),2681(3),906(11),885(8),3104(10),2681(7),3157(8)]),flip(a)].
% 246.84/247.15 3174 tuple(mult(rd(rd(rd(A,rd(B,mult(mult(C,C),B))),C),C),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [back_rewrite(2684),rewrite([3104(8)])].
% 246.84/247.15 3230 mult(ld(A,ld(A,ld(A,ld(A,A)))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(3070),rewrite([3162(4)])].
% 246.84/247.15 3295 tuple(mult(rd(mult(A,rd(ld(A,B),rd(C,mult(A,C)))),A),x1(B)),mult(x1_2(B),B)) != tuple(x1(B),x1_2(B)) # answer(goal). [para(2782(a,1),3174(a,1,1,1,1,1,2,2)),rewrite([2758(3),2336(5)])].
% 246.84/247.15 3485 ld(A,rd(B,mult(C,B))) = ld(A,ld(C,ld(C,C))). [para(1062(a,1),767(a,1)),rewrite([767(5)]),flip(a)].
% 246.84/247.15 3720 ld(A,mult(ld(A,A),B)) = mult(A,ld(mult(A,A),B)). [para(1155(a,1),119(a,1,2,1,2)),rewrite([1369(5),1908(5),2680(4),1(5),767(4),1908(3),1369(7),1192(8)]),flip(a)].
% 246.84/247.15 3844 tuple(mult(rd(mult(rd(A,B),rd(mult(rd(B,A),C),rd(B,A))),rd(A,B)),x1(C)),mult(x1_2(C),C)) != tuple(x1(C),x1_2(C)) # answer(goal). [para(3(a,1),3295(a,1,1,1,1,2,2,2)),rewrite([1322(3)])].
% 246.84/247.15 4159 mult(A,rd(ld(mult(B,B),C),C)) = rd(rd(A,B),B). [para(450(a,1),1204(a,2,2,2)),rewrite([1369(7),696(7),2680(7),3104(8)])].
% 246.84/247.15 4243 mult(A,rd(B,rd(C,mult(A,C)))) = mult(mult(A,B),A). [para(1048(a,1),1341(a,1,2,2)),rewrite([1322(3),4(2),9(3),1322(8),4(4)]),flip(a)].
% 246.84/247.15 4311 rd(A,mult(B,ld(C,mult(B,A)))) = ld(B,rd(C,B)). [para(1363(a,1),9(a,1,2))].
% 246.84/247.15 5004 mult(ld(A,A),ld(mult(A,A),B)) = ld(A,ld(A,B)). [para(1766(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 5240 tuple(mult(rd(rd(rd(A,B),B),ld(B,ld(B,ld(B,B)))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [para(2660(a,1),3844(a,1,1,1,1,2,1,1)),rewrite([2681(3),2660(8),2691(8),3084(6),450(4),1369(3),696(3),2680(3),3104(4),2681(5)])].
% 246.84/247.15 5311 mult(mult(A,ld(mult(A,A),B)),ld(A,A)) = mult(ld(A,A),rd(ld(A,B),ld(A,A))). [para(1908(a,1),1776(a,2,1)),rewrite([1369(4),1369(6),4311(7),1369(5)]),flip(a)].
% 246.84/247.15 5392 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)). [para(1999(a,1),500(a,1,2)),rewrite([817(6),3162(7),3230(10),3720(6),2(7)])].
% 246.84/247.15 5489 tuple(mult(rd(rd(rd(A,ld(B,C)),ld(B,C)),ld(ld(B,C),ld(ld(B,C),mult(B,ld(mult(C,B),C))))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [para(397(a,1),5240(a,1,1,1,2,2,2))].
% 246.84/247.15 5939 mult(rd(ld(A,ld(B,ld(B,B))),rd(C,mult(B,C))),D) = ld(A,D). [para(2370(a,2),1192(a,1,1))].
% 246.84/247.15 6075 rd(ld(A,ld(B,ld(B,B))),rd(ld(B,C),C)) = ld(A,ld(A,A)). [para(2372(a,2),885(a,1))].
% 246.84/247.15 6098 rd(A,rd(ld(mult(B,B),C),C)) = rd(A,ld(B,ld(B,ld(B,B)))). [para(450(a,1),2372(a,2,2,2)),rewrite([1369(7),696(7),5392(7),2649(6)])].
% 246.84/247.15 6232 rd(ld(A,ld(A,B)),ld(mult(A,A),B)) = ld(A,A). [para(767(a,1),2614(a,1,1,2)),rewrite([767(4),906(7),885(4),2691(6),397(10),696(7),1(8)])].
% 246.84/247.15 6549 rd(A,rd(ld(mult(B,B),C),C)) = mult(mult(A,B),B). [para(2689(a,2),571(a,2,2)),rewrite([3118(5),1(2)]),flip(a)].
% 246.84/247.15 6589 rd(A,ld(B,ld(B,ld(B,B)))) = mult(mult(A,B),B). [back_rewrite(6098),rewrite([6549(4)]),flip(a)].
% 246.84/247.15 6941 mult(ld(ld(A,B),ld(ld(A,B),mult(A,ld(mult(B,A),B)))),C) = ld(mult(ld(A,B),ld(A,B)),C). [para(397(a,1),2691(a,1,1,2,2))].
% 246.84/247.15 7270 rd(A,mult(B,mult(B,mult(B,A)))) = ld(B,ld(B,ld(B,ld(B,B)))). [para(2767(a,1),817(a,1,2)),rewrite([3057(11),2(9),2(8),3057(8)])].
% 246.84/247.15 8187 rd(ld(mult(ld(A,B),ld(A,B)),C),C) = ld(ld(A,B),rd(ld(A,ld(A,A)),ld(A,rd(B,A)))). [para(906(a,1),2849(a,2,2,2))].
% 246.84/247.15 8556 ld(ld(A,B),mult(A,ld(mult(B,A),B))) = mult(ld(A,B),ld(B,rd(A,ld(A,B)))). [para(1(a,1),3083(a,1,2,1)),rewrite([397(9)]),flip(a)].
% 246.84/247.15 8557 ld(mult(A,B),rd(A,B)) = ld(B,ld(B,ld(B,B))). [para(3083(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 8566 mult(mult(A,B),ld(mult(C,B),rd(C,B))) = rd(A,B). [para(3083(a,1),11(a,1,2,2)),rewrite([906(4),1(3)]),flip(a)].
% 246.84/247.15 8568 mult(rd(A,B),mult(B,rd(B,A))) = rd(A,rd(A,B)). [para(3083(a,1),13(a,1,2,2)),rewrite([1322(5),1322(6),1665(6),8566(12)])].
% 246.84/247.15 8687 ld(mult(ld(A,B),ld(A,B)),C) = mult(ld(B,rd(A,ld(A,B))),C). [back_rewrite(6941),rewrite([8556(6),2(7)]),flip(a)].
% 246.84/247.15 8708 tuple(mult(rd(rd(rd(A,ld(B,C)),ld(B,C)),ld(C,rd(B,ld(B,C)))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [back_rewrite(5489),rewrite([8556(10),2(11)])].
% 246.84/247.15 8728 mult(ld(ld(A,B),C),mult(ld(A,B),ld(B,rd(A,ld(A,B))))) = ld(ld(A,B),rd(C,ld(A,B))). [back_rewrite(3137),rewrite([8556(7)])].
% 246.84/247.15 8730 rd(ld(A,ld(A,A)),ld(A,rd(B,A))) = mult(ld(A,B),ld(B,rd(A,ld(A,B)))). [back_rewrite(3113),rewrite([8556(10)])].
% 246.84/247.15 8761 ld(ld(A,B),rd(ld(A,ld(A,A)),ld(A,rd(B,A)))) = ld(B,rd(A,ld(A,B))). [back_rewrite(8187),rewrite([8687(4),4(5)]),flip(a)].
% 246.84/247.15 8964 rd(ld(A,ld(A,A)),ld(A,rd(B,A))) = mult(ld(B,rd(A,ld(A,B))),ld(A,B)). [para(3085(a,1),2811(a,1,2)),rewrite([3119(11),8761(7)]),flip(a)].
% 246.84/247.15 8986 tuple(mult(rd(rd(rd(A,B),B),ld(mult(C,B),rd(C,B))),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [para(2(a,1),8708(a,1,1,1,1,1,2)),rewrite([2(3),2(5)])].
% 246.84/247.15 9037 tuple(mult(rd(rd(rd(A,ld(B,C)),ld(B,C)),ld(mult(C,ld(B,C)),B)),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [para(9(a,1),8986(a,1,1,1,2,2))].
% 246.84/247.15 9306 rd(rd(ld(A,ld(A,A)),B),B) = ld(A,ld(B,ld(B,ld(B,B)))). [para(3104(a,1),767(a,1))].
% 246.84/247.15 9333 rd(rd(A,ld(B,C)),ld(B,C)) = mult(A,ld(C,rd(B,ld(B,C)))). [para(397(a,1),3104(a,1,2,2,2)),rewrite([8556(6),2(7)]),flip(a)].
% 246.84/247.15 9477 tuple(mult(rd(mult(A,ld(B,rd(C,ld(C,B)))),ld(mult(B,ld(C,B)),C)),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [back_rewrite(9037),rewrite([9333(4)])].
% 246.84/247.15 9516 rd(A,ld(B,ld(B,B))) = ld(B,mult(mult(B,A),B)). [para(3118(a,1),2(a,1,2)),flip(a)].
% 246.84/247.15 12390 mult(A,ld(B,mult(mult(B,ld(mult(C,C),rd(D,mult(B,D)))),B))) = rd(rd(A,C),C). [para(3485(a,2),4159(a,1,2,1)),rewrite([9516(7)])].
% 246.84/247.15 12778 mult(mult(A,ld(mult(B,B),rd(C,mult(A,C)))),A) = rd(rd(A,B),B). [para(2689(a,1),4243(a,1,2)),rewrite([3104(4)]),flip(a)].
% 246.84/247.15 12805 mult(A,ld(B,rd(rd(B,C),C))) = rd(rd(A,C),C). [back_rewrite(12390),rewrite([12778(6)])].
% 246.84/247.15 13179 rd(ld(mult(A,A),B),ld(A,ld(A,B))) = ld(A,A). [para(5004(a,1),817(a,1,2)),rewrite([1369(9),1908(9),2649(8),1(9),1369(8),1908(8),2649(7),1(8)])].
% 246.84/247.15 14920 mult(mult(A,ld(B,B)),ld(B,B)) = rd(A,ld(B,B)). [para(1396(a,1),6549(a,1,2,1,1)),rewrite([745(1),745(2),1908(3),2649(2),1(3),1369(2),4(3),745(3),745(5)]),flip(a)].
% 246.84/247.15 14940 rd(A,ld(B,rd(rd(B,C),C))) = mult(mult(A,C),C). [para(3485(a,2),6549(a,1,2,1)),rewrite([9516(7),12778(6)])].
% 246.84/247.15 15023 rd(ld(A,B),B) = mult(mult(ld(A,ld(C,ld(C,ld(C,C)))),C),C). [para(6589(a,1),1227(a,1)),flip(a)].
% 246.84/247.15 15030 rd(A,ld(B,rd(C,ld(C,B)))) = mult(mult(A,ld(C,B)),ld(C,B)). [para(397(a,1),6589(a,1,2,2,2)),rewrite([8556(6),2(7)])].
% 246.84/247.15 15034 mult(mult(A,A),mult(mult(ld(A,ld(B,ld(B,ld(B,B)))),B),B)) = A. [para(6589(a,1),2800(a,1,2))].
% 246.84/247.15 15532 ld(mult(mult(A,B),B),A) = ld(B,ld(B,ld(B,B))). [para(4(a,1),8557(a,1,2))].
% 246.84/247.15 15534 ld(mult(A,ld(B,A)),B) = ld(A,rd(B,ld(B,A))). [para(9(a,1),8557(a,1,2)),rewrite([397(8),8556(9),2(10)])].
% 246.84/247.15 15557 ld(mult(A,B),rd(A,B)) = ld(B,rd(C,mult(B,C))). [para(817(a,2),8557(a,2,2))].
% 246.84/247.15 15608 rd(ld(mult(A,A),B),B) = ld(mult(C,A),rd(C,A)). [para(8557(a,2),2689(a,2))].
% 246.84/247.15 15678 tuple(mult(mult(mult(mult(A,ld(B,rd(C,ld(C,B)))),ld(C,B)),ld(C,B)),x1(A)),mult(x1_2(A),A)) != tuple(x1(A),x1_2(A)) # answer(goal). [back_rewrite(9477),rewrite([15534(7),15030(8)])].
% 246.84/247.15 15760 mult(ld(A,A),mult(ld(A,ld(A,B)),ld(A,A))) = rd(ld(mult(A,A),B),ld(A,A)). [para(6232(a,1),8568(a,1,2,2)),rewrite([13179(5),13179(13)])].
% 246.84/247.15 20568 rd(ld(A,ld(A,A)),ld(B,B)) = mult(ld(A,ld(B,B)),ld(B,B)). [para(767(a,1),14920(a,1,1)),flip(a)].
% 246.84/247.15 20620 mult(A,mult(mult(ld(A,ld(B,rd(rd(B,C),C))),C),C)) = ld(A,A). [para(14940(a,1),819(a,1,2))].
% 246.84/247.15 21097 mult(mult(A,ld(B,A)),ld(A,rd(B,ld(B,A)))) = B. [para(15534(a,1),1(a,1,2))].
% 246.84/247.15 21312 ld(ld(A,B),rd(ld(A,ld(A,A)),B)) = ld(B,rd(C,mult(B,C))). [para(767(a,1),15557(a,1,1))].
% 246.84/247.15 21934 rd(ld(mult(A,A),B),B) = ld(ld(C,A),rd(ld(C,ld(C,C)),A)). [para(767(a,1),15608(a,2,1))].
% 246.84/247.15 22000 tuple(mult(mult(mult(mult(A,ld(mult(A,A),rd(B,ld(B,A)))),ld(B,A)),ld(B,A)),x1(ld(A,A))),mult(x1_2(ld(A,A)),ld(A,A))) != tuple(x1(ld(A,A)),x1_2(ld(A,A))) # answer(goal). [para(1908(a,1),15678(a,1,1,1,1,1))].
% 246.84/247.15 24743 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A). [para(1658(a,1),759(a,2,1)),rewrite([745(1),745(2),745(4),1981(6),1759(7),745(4),745(6)])].
% 246.84/247.15 24773 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A). [para(24743(a,1),4(a,1,1))].
% 246.84/247.15 24777 rd(A,mult(ld(mult(B,ld(C,C)),B),A)) = ld(mult(C,ld(B,B)),C). [para(24743(a,1),1090(a,1,2)),rewrite([24773(3)]),flip(a)].
% 246.84/247.15 24784 ld(mult(ld(A,A),ld(B,B)),ld(mult(A,ld(B,B)),A)) = ld(B,B). [para(24743(a,1),15532(a,1,1,1)),rewrite([1369(12),1908(12),2649(11),1(12),1369(11),1908(11),2649(10),1(11),1369(10),1908(10),2649(9),1(10)])].
% 246.84/247.15 26019 mult(ld(A,B),ld(B,rd(A,ld(A,B)))) = rd(ld(ld(A,B),A),A). [para(21097(a,1),1020(a,1,2)),rewrite([8728(8),9(3),397(7),8556(8)]),flip(a)].
% 246.84/247.15 26027 rd(ld(A,ld(A,A)),ld(A,rd(B,A))) = rd(ld(ld(A,B),A),A). [back_rewrite(8730),rewrite([26019(10)])].
% 246.84/247.15 26029 mult(ld(A,rd(B,ld(B,A))),ld(B,A)) = rd(ld(ld(B,A),B),B). [back_rewrite(8964),rewrite([26027(5)]),flip(a)].
% 246.84/247.15 43354 mult(ld(A,mult(mult(A,ld(B,ld(A,ld(A,A)))),A)),C) = ld(B,C). [para(11(a,1),5939(a,1,1,2,2)),rewrite([1020(9),9516(6)])].
% 246.84/247.15 44344 ld(A,mult(mult(A,ld(B,ld(A,ld(A,A)))),A)) = ld(B,ld(B,B)). [para(7270(a,2),6075(a,1,2,1)),rewrite([6589(11),1324(8),2691(7),2649(5),9516(6)])].
% 246.84/247.15 44967 rd(ld(A,ld(A,A)),B) = mult(ld(A,ld(B,ld(B,ld(B,B)))),B). [para(9306(a,1),3(a,1,1)),flip(a)].
% 246.84/247.15 152168 ld(ld(A,ld(B,B)),rd(ld(A,ld(A,A)),ld(B,B))) = ld(B,B). [para(1396(a,1),21934(a,1,1,1)),rewrite([745(1),745(2),1908(3),2649(2),1(3),1369(2),4(3),745(2),745(6)]),flip(a)].
% 246.84/247.15 189164 ld(mult(ld(A,A),ld(B,B)),ld(A,A)) = ld(mult(A,ld(B,B)),A). [para(1369(a,1),24777(a,1,2,1,1,2)),rewrite([1908(3),2649(2),1(3),24777(5)]),flip(a)].
% 246.84/247.15 189165 ld(mult(A,ld(B,B)),A) = ld(B,B). [para(20568(a,2),24777(a,1,2)),rewrite([1981(11),189164(10),1981(10),24784(9),1908(4),2649(3),1(4),745(4),1369(4),1908(4),2649(3),1(4),745(3),1369(3),1908(3),2649(2),1(3),1369(4),1908(4),2649(3),1(4)]),flip(a)].
% 246.84/247.15 189166 ld(A,A) = ld(B,B). [para(20620(a,1),24777(a,1,2)),rewrite([189165(3),1369(5),12805(5),3(4),3(3),189165(4),189165(5),1369(4),1908(4),2649(3),1(4),745(3),1369(3),1908(3),2649(2),1(3),189165(4)])].
% 246.84/247.15 189190 mult(ld(A,A),ld(B,B)) = ld(A,A). [para(24777(a,1),21312(a,2,2)),rewrite([189165(3),189165(7),152168(7),189165(4),189165(5),1369(4)]),flip(a)].
% 246.84/247.15 189236 ld(A,A) = c_0. [new_symbol(189166)].
% 246.84/247.15 189257 mult(c_0,c_0) = c_0. [back_rewrite(189190),rewrite([189236(1),189236(2),189236(4)])].
% 246.84/247.15 190480 mult(ld(A,ld(B,ld(B,c_0))),B) = rd(ld(A,c_0),B). [back_rewrite(44967),rewrite([189236(1),189236(4)]),flip(a)].
% 246.84/247.15 190532 ld(A,mult(mult(A,ld(B,ld(A,c_0))),A)) = ld(B,c_0). [back_rewrite(44344),rewrite([189236(1),189236(7)])].
% 246.84/247.15 190571 mult(ld(A,c_0),B) = ld(A,B). [back_rewrite(43354),rewrite([189236(1),190532(6)])].
% 246.84/247.15 191250 tuple(mult(mult(mult(mult(A,ld(mult(A,A),rd(B,ld(B,A)))),ld(B,A)),ld(B,A)),x1(c_0)),mult(x1_2(c_0),c_0)) != tuple(x1(c_0),x1_2(c_0)) # answer(goal). [back_rewrite(22000),rewrite([189236(10),189236(13),189236(15),189236(18),189236(20)])].
% 246.84/247.15 191472 mult(c_0,mult(ld(A,ld(A,B)),c_0)) = rd(ld(mult(A,A),B),c_0). [back_rewrite(15760),rewrite([189236(1),189236(4),189236(9)])].
% 246.84/247.15 191514 mult(A,c_0) = A. [back_rewrite(15034),rewrite([189236(2),190480(6),3(5),38(4),189236(1),189257(3)])].
% 246.84/247.15 191517 rd(ld(A,B),B) = ld(A,c_0). [back_rewrite(15023),rewrite([189236(3),190480(7),3(6)])].
% 246.84/247.15 191537 rd(A,c_0) = A. [back_rewrite(14920),rewrite([189236(1),191514(2),189236(1),191514(2),189236(1)]),flip(a)].
% 246.84/247.15 191741 mult(A,ld(mult(A,A),B)) = mult(c_0,ld(A,B)). [back_rewrite(5311),rewrite([189236(4),191514(5),189236(4),189236(6),191537(7)])].
% 246.84/247.15 191751 ld(A,mult(c_0,B)) = mult(c_0,ld(A,B)). [back_rewrite(3720),rewrite([189236(1),191741(6)])].
% 246.84/247.15 191778 mult(c_0,ld(mult(c_0,A),B)) = ld(A,B). [back_rewrite(2218),rewrite([189236(1),189236(2),189236(6),191514(7)])].
% 246.84/247.15 191781 mult(c_0,ld(A,B)) = ld(A,B). [back_rewrite(1981),rewrite([189236(1),189236(3),191751(5),191778(5),189236(2),189236(3),191514(4)]),flip(a)].
% 246.84/247.15 191783 mult(c_0,A) = A. [back_rewrite(1923),rewrite([191741(3),191781(3),1(2),189236(1)]),flip(a)].
% 246.84/247.15 192497 ld(mult(A,A),B) = ld(A,ld(A,B)). [back_rewrite(191472),rewrite([191514(5),191783(4),191537(6)]),flip(a)].
% 246.84/247.15 192503 $F # answer(goal). [back_rewrite(191250),rewrite([192497(4),1(5),26029(5),191517(3),190571(5),189236(3),191783(4),191514(6)]),xx(a)].
% 246.84/247.15
% 246.84/247.15 % SZS output end Refutation
% 246.84/247.15 ============================== end of proof ==========================
% 246.84/247.15
% 246.84/247.15 ============================== STATISTICS ============================
% 246.84/247.15
% 246.84/247.15 Given=2723. Generated=6245520. Kept=192501. proofs=1.
% 246.84/247.15 Usable=438. Sos=1690. Demods=1009. Limbo=989, Disabled=189390. Hints=0.
% 246.84/247.15 Megabytes=214.92.
% 246.84/247.15 User_CPU=242.38, System_CPU=3.81, Wall_clock=247.
% 246.84/247.15
% 246.84/247.15 ============================== end of statistics =====================
% 246.84/247.15
% 246.84/247.15 ============================== end of search =========================
% 246.84/247.15
% 246.84/247.15 THEOREM PROVED
% 246.84/247.15 % SZS status Unsatisfiable
% 246.84/247.15
% 246.84/247.15 Exiting with 1 proof.
% 246.84/247.15
% 246.84/247.15 Process 29600 exit (max_proofs) Mon Jun 13 16:14:47 2022
% 246.84/247.15 Prover9 interrupted
%------------------------------------------------------------------------------