TSTP Solution File: GRP654-12 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP654-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 115.06s 115.38s
% Output : Refutation 115.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP654-12 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n013.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 : Tue Jun 14 12:58:59 EDT 2022
% 0.12/0.34 % CPUTime :
% 115.06/115.38 ============================== Prover9 ===============================
% 115.06/115.38 Prover9 (32) version 2009-11A, November 2009.
% 115.06/115.38 Process 32229 was started by sandbox2 on n013.cluster.edu,
% 115.06/115.38 Tue Jun 14 12:58:59 2022
% 115.06/115.38 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_32076_n013.cluster.edu".
% 115.06/115.38 ============================== end of head ===========================
% 115.06/115.38
% 115.06/115.38 ============================== INPUT =================================
% 115.06/115.38
% 115.06/115.38 % Reading from file /tmp/Prover9_32076_n013.cluster.edu
% 115.06/115.38
% 115.06/115.38 set(prolog_style_variables).
% 115.06/115.38 set(auto2).
% 115.06/115.38 % set(auto2) -> set(auto).
% 115.06/115.38 % set(auto) -> set(auto_inference).
% 115.06/115.38 % set(auto) -> set(auto_setup).
% 115.06/115.38 % set(auto_setup) -> set(predicate_elim).
% 115.06/115.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 115.06/115.38 % set(auto) -> set(auto_limits).
% 115.06/115.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 115.06/115.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 115.06/115.38 % set(auto) -> set(auto_denials).
% 115.06/115.38 % set(auto) -> set(auto_process).
% 115.06/115.38 % set(auto2) -> assign(new_constants, 1).
% 115.06/115.38 % set(auto2) -> assign(fold_denial_max, 3).
% 115.06/115.38 % set(auto2) -> assign(max_weight, "200.000").
% 115.06/115.38 % set(auto2) -> assign(max_hours, 1).
% 115.06/115.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 115.06/115.38 % set(auto2) -> assign(max_seconds, 0).
% 115.06/115.38 % set(auto2) -> assign(max_minutes, 5).
% 115.06/115.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 115.06/115.38 % set(auto2) -> set(sort_initial_sos).
% 115.06/115.38 % set(auto2) -> assign(sos_limit, -1).
% 115.06/115.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 115.06/115.38 % set(auto2) -> assign(max_megs, 400).
% 115.06/115.38 % set(auto2) -> assign(stats, some).
% 115.06/115.38 % set(auto2) -> clear(echo_input).
% 115.06/115.38 % set(auto2) -> set(quiet).
% 115.06/115.38 % set(auto2) -> clear(print_initial_clauses).
% 115.06/115.38 % set(auto2) -> clear(print_given).
% 115.06/115.38 assign(lrs_ticks,-1).
% 115.06/115.38 assign(sos_limit,10000).
% 115.06/115.38 assign(order,kbo).
% 115.06/115.38 set(lex_order_vars).
% 115.06/115.38 clear(print_given).
% 115.06/115.38
% 115.06/115.38 % formulas(sos). % not echoed (6 formulas)
% 115.06/115.38
% 115.06/115.38 ============================== end of input ==========================
% 115.06/115.38
% 115.06/115.38 % From the command line: assign(max_seconds, 300).
% 115.06/115.38
% 115.06/115.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 115.06/115.38
% 115.06/115.38 % Formulas that are not ordinary clauses:
% 115.06/115.38
% 115.06/115.38 ============================== end of process non-clausal formulas ===
% 115.06/115.38
% 115.06/115.38 ============================== PROCESS INITIAL CLAUSES ===============
% 115.06/115.38
% 115.06/115.38 ============================== PREDICATE ELIMINATION =================
% 115.06/115.38
% 115.06/115.38 ============================== end predicate elimination =============
% 115.06/115.38
% 115.06/115.38 Auto_denials:
% 115.06/115.38 % copying label goal to answer in negative clause
% 115.06/115.38
% 115.06/115.38 Term ordering decisions:
% 115.06/115.38 Function symbol KB weights: x0=1. x1=1. mult=1. ld=1. rd=1.
% 115.06/115.38
% 115.06/115.38 ============================== end of process initial clauses ========
% 115.06/115.38
% 115.06/115.38 ============================== CLAUSES FOR SEARCH ====================
% 115.06/115.38
% 115.06/115.38 ============================== end of clauses for search =============
% 115.06/115.38
% 115.06/115.38 ============================== SEARCH ================================
% 115.06/115.38
% 115.06/115.38 % Starting search at 0.01 seconds.
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=95.000, iters=3551
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=71.000, iters=3416
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=67.000, iters=3366
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=59.000, iters=3343
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=55.000, iters=3346
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=51.000, iters=3357
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=47.000, iters=3384
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=43.000, iters=3335
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=39.000, iters=3358
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=35.000, iters=3372
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=31.000, iters=3333
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=27.000, iters=3373
% 115.06/115.38
% 115.06/115.38 Low Water (displace): id=6057, wt=135.000
% 115.06/115.38
% 115.06/115.38 Low Water (displace): id=7085, wt=119.000
% 115.06/115.38
% 115.06/115.38 Low Water (displace): id=12683, wt=23.000
% 115.06/115.38
% 115.06/115.38 Low Water (displace): id=12926, wt=19.000
% 115.06/115.38
% 115.06/115.38 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 9.42 sec).
% 115.06/115.38
% 115.06/115.38 Low Water (keep): wt=23.000, iters=3336
% 115.06/115.38
% 115.06/115.38 ============================== PROOF =================================
% 115.06/115.38 % SZS status Unsatisfiable
% 115.06/115.38 % SZS output start Refutation
% 115.06/115.38
% 115.06/115.38 % Proof 1 at 112.08 (+ 2.32) seconds: goal.
% 115.06/115.38 % Length of proof is 230.
% 115.06/115.38 % Level of proof is 38.
% 115.06/115.38 % Maximum clause weight is 39.000.
% 115.06/115.38 % Given clauses 1570.
% 115.06/115.38
% 115.06/115.38 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 115.06/115.38 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 115.06/115.38 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 115.06/115.38 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 115.06/115.38 5 mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) # label(f05) # label(axiom). [assumption].
% 115.06/115.38 6 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))). [copy(5),flip(a)].
% 115.06/115.38 7 mult(rd(x1,x1),x0) != x0 # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 115.06/115.38 9 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 115.06/115.38 10 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C. [para(6(a,1),1(a,1))].
% 115.06/115.38 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)].
% 115.06/115.38 12 ld(mult(mult(A,B),A),mult(A,mult(B,mult(A,C)))) = C. [para(6(a,1),2(a,1,2))].
% 115.06/115.38 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)].
% 115.06/115.38 14 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A). [para(6(a,1),4(a,1,1))].
% 115.06/115.38 17 mult(A,mult(B,ld(mult(mult(B,A),B),C))) = ld(B,C). [para(10(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 21 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)].
% 115.06/115.38 22 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)). [para(11(a,1),2(a,1,2))].
% 115.06/115.38 24 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B. [para(11(a,1),4(a,1,1))].
% 115.06/115.38 34 ld(mult(A,mult(ld(A,ld(A,B)),B)),mult(ld(A,B),mult(mult(B,A),C))) = mult(A,C). [para(11(a,1),12(a,1,2,2)),rewrite([21(4)])].
% 115.06/115.38 35 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)].
% 115.06/115.38 37 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(13(a,1),6(a,1,1,1)),flip(a)].
% 115.06/115.38 41 rd(mult(A,mult(B,C)),ld(A,C)) = mult(mult(A,B),A). [para(1(a,1),14(a,1,1,2,2))].
% 115.06/115.38 43 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)].
% 115.06/115.38 50 mult(ld(A,B),mult(A,ld(mult(B,A),C))) = ld(A,C). [para(1(a,1),17(a,1,2,2,1,1))].
% 115.06/115.38 51 mult(A,ld(mult(mult(A,B),A),C)) = ld(B,ld(A,C)). [para(17(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 58 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C). [para(21(a,1),2(a,1,2))].
% 115.06/115.38 59 mult(A,mult(ld(A,rd(B,A)),C)) = mult(B,ld(A,C)). [para(3(a,1),21(a,1,1)),flip(a)].
% 115.06/115.38 69 mult(ld(A,rd(B,A)),mult(A,C)) = ld(A,mult(B,C)). [para(3(a,1),22(a,1,2,1)),flip(a)].
% 115.06/115.38 125 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A). [para(3(a,1),41(a,1,1,2))].
% 115.06/115.38 142 ld(mult(A,rd(B,mult(A,C))),rd(mult(A,B),C)) = A. [para(43(a,1),2(a,1,2))].
% 115.06/115.38 144 rd(rd(mult(A,B),C),A) = mult(A,rd(B,mult(A,C))). [para(43(a,1),4(a,1,1))].
% 115.06/115.38 146 mult(A,mult(rd(B,mult(A,C)),mult(A,D))) = mult(rd(mult(A,B),C),D). [para(43(a,1),6(a,1,1)),flip(a)].
% 115.06/115.38 163 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)). [para(50(a,1),2(a,1,2))].
% 115.06/115.38 179 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))). [para(51(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 184 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(13(a,1),51(a,1,2,1,1))].
% 115.06/115.38 200 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)). [para(1(a,1),58(a,1,2,2))].
% 115.06/115.38 220 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C). [para(59(a,1),2(a,1,2))].
% 115.06/115.38 221 rd(mult(A,ld(B,C)),mult(ld(B,rd(A,B)),C)) = B. [para(59(a,1),4(a,1,1))].
% 115.06/115.38 224 mult(mult(A,B),mult(ld(B,rd(C,B)),D)) = mult(B,mult(ld(B,A),mult(C,ld(B,D)))). [para(59(a,1),11(a,1,2,2)),flip(a)].
% 115.06/115.38 259 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)). [para(1(a,1),125(a,1,1)),flip(a)].
% 115.06/115.38 279 ld(mult(A,rd(B,mult(A,B))),A) = A. [para(4(a,1),142(a,1,2))].
% 115.06/115.38 329 ld(mult(A,rd(ld(A,B),B)),A) = A. [para(1(a,1),279(a,1,1,2,2))].
% 115.06/115.38 332 mult(A,rd(B,mult(A,B))) = rd(A,A). [para(279(a,1),9(a,1,2)),flip(a)].
% 115.06/115.38 345 mult(A,rd(ld(A,B),B)) = rd(A,A). [para(329(a,1),9(a,1,2)),flip(a)].
% 115.06/115.38 348 rd(A,mult(B,A)) = ld(B,rd(B,B)). [para(332(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 349 rd(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [para(3(a,1),332(a,1,2,2)),flip(a)].
% 115.06/115.38 355 mult(rd(A,A),B) = mult(ld(A,A),B). [para(332(a,1),13(a,2,1)),rewrite([348(2),348(5),224(7),1(5),69(6),2(4)]),flip(a)].
% 115.06/115.38 358 mult(ld(A,A),A) = A. [para(332(a,1),14(a,2,1)),rewrite([146(5),4(2),4(2),355(2)]),flip(a)].
% 115.06/115.38 362 mult(ld(A,B),mult(A,rd(C,mult(mult(B,A),C)))) = ld(A,rd(mult(B,A),mult(B,A))). [para(332(a,1),22(a,1,2)),flip(a)].
% 115.06/115.38 385 mult(ld(x1,x1),x0) != x0 # answer(goal). [back_rewrite(7),rewrite([355(5)])].
% 115.06/115.38 386 ld(ld(A,A),A) = A. [para(358(a,1),2(a,1,2))].
% 115.06/115.38 387 rd(A,A) = ld(A,A). [para(358(a,1),4(a,1,1))].
% 115.06/115.38 390 mult(mult(A,ld(mult(A,B),mult(A,B))),A) = rd(mult(A,mult(A,B)),B). [para(358(a,1),14(a,1,1,2)),flip(a)].
% 115.06/115.38 395 mult(ld(A,ld(A,A)),B) = ld(A,B). [para(358(a,1),50(a,1,2,2,1)),rewrite([1(4)])].
% 115.06/115.38 396 mult(mult(A,ld(mult(B,A),B)),ld(A,B)) = ld(A,B). [para(358(a,1),59(a,2)),rewrite([163(3),59(7)])].
% 115.06/115.38 422 mult(ld(A,B),mult(A,rd(C,mult(mult(B,A),C)))) = ld(A,ld(mult(B,A),mult(B,A))). [back_rewrite(362),rewrite([387(9)])].
% 115.06/115.38 429 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [back_rewrite(349),rewrite([387(3)])].
% 115.06/115.38 430 rd(A,mult(B,A)) = ld(B,ld(B,B)). [back_rewrite(348),rewrite([387(3)])].
% 115.06/115.38 431 mult(A,rd(ld(A,B),B)) = ld(A,A). [back_rewrite(345),rewrite([387(4)])].
% 115.06/115.38 432 mult(A,rd(B,mult(A,B))) = ld(A,A). [back_rewrite(332),rewrite([387(4)])].
% 115.06/115.38 460 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)). [para(386(a,1),21(a,2,2,1)),rewrite([1(2)]),flip(a)].
% 115.06/115.38 462 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A). [para(386(a,1),24(a,1,2,1)),rewrite([1(2)])].
% 115.06/115.38 463 mult(A,mult(ld(A,A),ld(A,B))) = ld(ld(A,A),B). [para(386(a,1),50(a,1,1)),rewrite([1(3)])].
% 115.06/115.38 469 rd(ld(A,B),B) = ld(A,ld(A,A)). [para(395(a,1),4(a,1,1))].
% 115.06/115.38 473 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)). [para(395(a,1),14(a,1,1,2,2)),rewrite([395(5),220(3),4(4),395(5)]),flip(a)].
% 115.06/115.38 475 mult(A,mult(ld(A,ld(B,ld(B,B))),C)) = mult(ld(B,A),ld(A,C)). [para(395(a,1),21(a,1,1)),flip(a)].
% 115.06/115.38 485 rd(ld(A,B),ld(ld(A,ld(A,A)),C)) = ld(A,rd(rd(B,C),A)). [para(395(a,1),125(a,1,1)),rewrite([395(9),473(10)])].
% 115.06/115.38 519 ld(ld(A,ld(A,A)),B) = mult(A,B). [para(358(a,1),34(a,1,2,2,1)),rewrite([475(6),473(4),387(1),395(6),2(4)])].
% 115.06/115.38 522 ld(A,mult(ld(A,A),mult(mult(A,A),B))) = mult(A,B). [para(395(a,1),34(a,1,1,2)),rewrite([1(2)])].
% 115.06/115.38 526 rd(ld(A,B),mult(A,C)) = ld(A,rd(rd(B,C),A)). [back_rewrite(485),rewrite([519(4)])].
% 115.06/115.38 548 mult(rd(A,mult(B,A)),C) = ld(B,C). [para(430(a,2),50(a,1,1)),rewrite([358(4),1(4)])].
% 115.06/115.38 554 mult(A,rd(B,mult(C,B))) = mult(A,ld(C,ld(C,C))). [para(430(a,2),59(a,2,2)),rewrite([59(5)]),flip(a)].
% 115.06/115.38 562 rd(A,mult(B,A)) = rd(C,mult(B,C)). [para(430(a,2),430(a,2))].
% 115.06/115.38 578 mult(A,ld(B,rd(ld(ld(B,rd(A,B)),C),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [para(431(a,1),59(a,1,2)),rewrite([163(5),3(2)]),flip(a)].
% 115.06/115.38 608 mult(rd(ld(A,B),B),C) = ld(A,C). [para(469(a,2),50(a,1,1)),rewrite([358(4),1(4)])].
% 115.06/115.38 611 mult(A,rd(ld(B,C),C)) = mult(A,ld(B,ld(B,B))). [para(469(a,2),59(a,2,2)),rewrite([59(5)]),flip(a)].
% 115.06/115.38 614 rd(ld(A,B),B) = rd(C,mult(A,C)). [para(469(a,2),430(a,2)),flip(a)].
% 115.06/115.38 615 rd(ld(A,B),B) = rd(ld(A,C),C). [para(469(a,2),469(a,2))].
% 115.06/115.38 650 ld(rd(A,B),C) = mult(rd(B,A),C). [para(3(a,1),548(a,1,1,2)),flip(a)].
% 115.06/115.38 652 mult(rd(A,mult(B,mult(C,mult(B,A)))),D) = ld(B,ld(C,ld(B,D))). [para(6(a,1),548(a,1,1,2)),rewrite([179(8)])].
% 115.06/115.38 655 mult(ld(A,B),rd(C,mult(A,C))) = ld(A,rd(B,A)). [para(548(a,1),14(a,1,1,2,2)),rewrite([548(5),220(3),4(4),548(5)]),flip(a)].
% 115.06/115.38 660 mult(ld(A,rd(B,mult(C,B))),mult(A,D)) = ld(A,mult(ld(C,A),D)). [para(548(a,1),22(a,1,2,1)),flip(a)].
% 115.06/115.38 666 ld(mult(A,rd(B,mult(A,C))),D) = mult(rd(A,rd(mult(A,B),C)),D). [para(43(a,1),548(a,1,1,2)),flip(a)].
% 115.06/115.38 672 ld(ld(A,rd(B,A)),C) = mult(A,ld(B,mult(A,C))). [para(69(a,1),548(a,1,1,2)),rewrite([125(4),6(5),548(4)]),flip(a)].
% 115.06/115.38 674 ld(ld(A,A),B) = mult(ld(A,A),B). [para(358(a,1),548(a,1,1,2)),rewrite([387(1)]),flip(a)].
% 115.06/115.38 685 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)). [back_rewrite(429),rewrite([650(3)])].
% 115.06/115.38 709 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(184),rewrite([650(13)])].
% 115.06/115.38 739 mult(A,ld(B,rd(mult(B,ld(A,mult(B,C))),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [back_rewrite(578),rewrite([672(3)])].
% 115.06/115.38 752 mult(A,mult(ld(A,A),ld(A,B))) = mult(ld(A,A),B). [back_rewrite(463),rewrite([674(6)])].
% 115.06/115.38 753 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)). [back_rewrite(460),rewrite([674(5)])].
% 115.06/115.38 761 rd(A,mult(rd(B,C),A)) = rd(C,B). [para(3(a,1),562(a,1,2)),flip(a)].
% 115.06/115.38 769 rd(A,mult(ld(B,B),A)) = ld(B,B). [para(358(a,1),562(a,1,2)),rewrite([387(1)]),flip(a)].
% 115.06/115.38 774 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(1(a,1),37(a,2)),rewrite([709(12),1(11)])].
% 115.06/115.38 803 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(37(a,1),430(a,1,2)),rewrite([650(17),650(18)])].
% 115.06/115.38 813 mult(rd(A,B),mult(rd(A,B),rd(B,A))) = rd(A,B). [para(37(a,1),562(a,1,2)),rewrite([803(13),761(8)])].
% 115.06/115.38 822 mult(ld(A,B),rd(ld(A,C),C)) = ld(A,rd(B,A)). [para(608(a,1),14(a,1,1,2,2)),rewrite([608(5),220(3),4(4),608(5)]),flip(a)].
% 115.06/115.38 841 rd(mult(A,B),mult(C,mult(A,B))) = rd(ld(C,D),D). [para(614(a,2),43(a,2)),rewrite([43(6)])].
% 115.06/115.38 891 mult(ld(A,A),mult(ld(A,A),B)) = B. [para(674(a,1),1(a,1,2))].
% 115.06/115.38 894 mult(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),mult(mult(B,ld(A,A)),C)). [para(674(a,1),22(a,1)),rewrite([674(7)]),flip(a)].
% 115.06/115.38 895 mult(A,mult(ld(A,A),ld(mult(A,A),B))) = ld(A,B). [para(50(a,1),674(a,2)),rewrite([674(5),753(5)])].
% 115.06/115.38 900 rd(A,ld(B,ld(C,ld(B,A)))) = mult(mult(B,C),B). [para(14(a,1),761(a,2)),rewrite([652(5)])].
% 115.06/115.38 910 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(769(a,1),69(a,1,1,2)),rewrite([200(12)])].
% 115.06/115.38 960 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)). [para(50(a,1),891(a,1,2))].
% 115.06/115.38 967 mult(A,mult(A,ld(mult(A,A),B))) = mult(ld(A,A),B). [back_rewrite(752),rewrite([960(3)])].
% 115.06/115.38 986 mult(A,rd(rd(ld(A,B),B),mult(A,C))) = rd(rd(ld(A,A),C),A). [para(431(a,1),144(a,1,1,1)),flip(a)].
% 115.06/115.38 1025 ld(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),ld(mult(B,ld(A,A)),C)). [para(674(a,1),163(a,1,1)),rewrite([674(4)])].
% 115.06/115.38 1026 rd(A,mult(mult(B,ld(mult(C,B),C)),A)) = mult(B,ld(mult(C,B),C)). [para(163(a,1),769(a,1,2,1)),rewrite([163(8)])].
% 115.06/115.38 1042 mult(A,ld(mult(A,A),mult(ld(A,A),B))) = ld(A,B). [para(358(a,1),179(a,1,1,1)),rewrite([1(2),674(4),674(6),960(6)]),flip(a)].
% 115.06/115.38 1125 mult(ld(mult(A,A),ld(A,A)),B) = ld(mult(A,A),B). [para(200(a,1),395(a,1,1,2)),rewrite([674(3),358(3)])].
% 115.06/115.38 1129 rd(A,mult(mult(B,B),A)) = ld(mult(B,B),ld(B,B)). [para(200(a,1),430(a,2,2)),rewrite([674(6),358(6)])].
% 115.06/115.38 1135 rd(ld(mult(A,A),B),B) = ld(mult(A,A),ld(A,A)). [para(200(a,1),469(a,2,2)),rewrite([674(6),358(6)])].
% 115.06/115.38 1164 mult(ld(A,rd(ld(B,ld(B,B)),A)),C) = ld(A,ld(B,ld(A,C))). [para(395(a,1),220(a,1,2)),flip(a)].
% 115.06/115.38 1209 rd(rd(A,ld(B,C)),B) = mult(B,rd(ld(B,A),C)). [para(259(a,1),4(a,1,1))].
% 115.06/115.38 1237 rd(A,rd(B,mult(C,B))) = rd(A,ld(C,ld(C,C))). [para(430(a,2),259(a,2,2)),rewrite([259(5)]),flip(a)].
% 115.06/115.38 1239 rd(A,rd(ld(B,C),C)) = rd(A,ld(B,ld(B,B))). [para(469(a,2),259(a,2,2)),rewrite([259(5)]),flip(a)].
% 115.06/115.38 1326 mult(mult(A,ld(B,rd(B,A))),ld(A,rd(B,A))) = ld(A,rd(B,A)). [para(3(a,1),396(a,1,1,2,1))].
% 115.06/115.38 1377 rd(mult(A,mult(A,B)),mult(mult(A,A),B)) = ld(A,A). [para(11(a,1),462(a,1,2))].
% 115.06/115.38 1382 rd(mult(A,mult(A,B)),mult(ld(A,A),B)) = mult(A,A). [para(462(a,1),43(a,1,1,2)),rewrite([1(2)]),flip(a)].
% 115.06/115.38 1394 mult(A,ld(mult(A,A),A)) = ld(A,A). [para(431(a,1),462(a,1,1)),rewrite([822(5),387(2),1(4),387(3),674(3),960(3)])].
% 115.06/115.38 1411 ld(mult(A,A),A) = ld(A,ld(A,A)). [para(1394(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 1415 mult(rd(ld(A,ld(A,A)),A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [para(1394(a,1),35(a,2,2)),rewrite([1411(2),1411(4),395(6),1164(5),1411(5)]),flip(a)].
% 115.06/115.38 1424 rd(A,ld(A,ld(A,A))) = mult(A,A). [para(1411(a,1),9(a,1,2))].
% 115.06/115.38 1425 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(mult(A,mult(A,A)),B). [para(1411(a,1),11(a,1,2,1)),rewrite([395(6),22(4),753(4)])].
% 115.06/115.38 1434 rd(ld(A,ld(A,A)),A) = ld(mult(A,A),ld(A,A)). [para(1411(a,1),469(a,1,1)),rewrite([200(7),674(6),358(6)])].
% 115.06/115.38 1442 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [back_rewrite(1415),rewrite([1434(3),1125(5)])].
% 115.06/115.38 1443 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))). [back_rewrite(1434),rewrite([1442(6)])].
% 115.06/115.38 1446 rd(ld(mult(A,A),B),B) = ld(A,ld(A,ld(A,A))). [back_rewrite(1135),rewrite([1442(6)])].
% 115.06/115.38 1447 rd(A,mult(mult(B,B),A)) = ld(B,ld(B,ld(B,B))). [back_rewrite(1129),rewrite([1442(6)])].
% 115.06/115.38 1448 mult(ld(A,ld(A,ld(A,A))),B) = ld(mult(A,A),B). [back_rewrite(1125),rewrite([1442(3)])].
% 115.06/115.38 1500 rd(A,rd(B,mult(A,B))) = mult(A,A). [para(430(a,2),1424(a,1,2))].
% 115.06/115.38 1501 rd(A,rd(ld(A,B),B)) = mult(A,A). [para(469(a,2),1424(a,1,2))].
% 115.06/115.38 1508 mult(mult(A,mult(A,A)),B) = mult(A,mult(A,mult(A,B))). [para(1424(a,1),220(a,2,1,2)),rewrite([519(5),519(5),519(7)]),flip(a)].
% 115.06/115.38 1516 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(A,mult(A,mult(A,B))). [back_rewrite(1425),rewrite([1508(8)])].
% 115.06/115.38 1517 mult(mult(A,A),rd(B,mult(A,B))) = A. [para(1500(a,1),3(a,1,1))].
% 115.06/115.38 1533 mult(mult(A,A),rd(ld(A,B),B)) = A. [para(1501(a,1),3(a,1,1))].
% 115.06/115.38 1546 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1517(a,1),14(a,2,1)),rewrite([548(6),22(4),753(4),1516(5),14(4)])].
% 115.06/115.38 1570 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(mult(A,mult(A,A)),B). [para(1517(a,1),179(a,1,1,1)),rewrite([650(9),4(6),220(8),430(6)]),flip(a)].
% 115.06/115.38 1685 ld(mult(A,mult(A,A)),B) = ld(A,ld(A,ld(A,B))). [para(1546(a,1),179(a,1,1))].
% 115.06/115.38 1695 mult(ld(mult(A,A),ld(A,ld(A,A))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1570),rewrite([1685(8)])].
% 115.06/115.38 1703 mult(A,ld(mult(B,A),rd(B,A))) = ld(A,ld(A,A)). [para(473(a,1),2(a,1,2)),rewrite([163(4)])].
% 115.06/115.38 1704 ld(A,rd(mult(A,B),A)) = mult(B,ld(A,ld(A,A))). [para(2(a,1),473(a,1,1)),flip(a)].
% 115.06/115.38 1715 mult(A,ld(B,ld(B,ld(B,B)))) = rd(rd(A,B),B). [para(473(a,1),59(a,1,2)),rewrite([1(4)]),flip(a)].
% 115.06/115.38 1728 mult(A,rd(B,ld(A,ld(A,A)))) = mult(mult(A,B),A). [para(519(a,1),473(a,1,1)),rewrite([163(8),358(5),1(6),163(5),358(3),1(3),519(8)]),flip(a)].
% 115.06/115.38 1735 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,A),A)). [para(615(a,1),473(a,2,2)),rewrite([473(5)]),flip(a)].
% 115.06/115.38 1738 mult(mult(ld(A,A),B),ld(A,A)) = mult(ld(A,A),rd(B,ld(A,A))). [para(674(a,1),473(a,1,1)),rewrite([674(6),960(6),1411(5),1(6),674(5),960(5),1411(4),1(5),674(8)])].
% 115.06/115.38 1753 rd(ld(A,ld(A,ld(A,A))),A) = ld(mult(A,A),ld(A,ld(A,A))). [para(1411(a,1),473(a,1,1)),rewrite([200(6),674(5),358(5),1442(5),1715(6),1443(3),430(7)])].
% 115.06/115.38 1761 ld(mult(A,A),ld(A,ld(A,A))) = ld(A,ld(A,ld(A,ld(A,A)))). [para(473(a,1),1546(a,1,1)),rewrite([469(2),473(6),1443(3),473(11),469(8),1715(10),1443(7),1753(8)]),flip(a)].
% 115.06/115.38 1835 mult(ld(A,ld(A,ld(A,ld(A,A)))),B) = ld(A,ld(A,ld(A,B))). [back_rewrite(1695),rewrite([1761(4)])].
% 115.06/115.38 1868 ld(A,mult(ld(A,A),B)) = mult(A,ld(mult(A,A),B)). [para(1(a,1),522(a,1,2,2))].
% 115.06/115.38 1940 mult(rd(A,rd(B,mult(C,B))),ld(C,ld(C,C))) = A. [para(554(a,1),3(a,1))].
% 115.06/115.38 2002 mult(A,rd(B,mult(mult(C,C),B))) = rd(rd(A,C),C). [para(200(a,1),554(a,2,2,2)),rewrite([674(7),358(7),1442(7),1715(8)])].
% 115.06/115.38 2184 mult(A,rd(ld(mult(B,B),C),C)) = rd(rd(A,B),B). [para(200(a,1),611(a,2,2,2)),rewrite([674(7),358(7),1442(7),1715(8)])].
% 115.06/115.38 2228 rd(rd(A,mult(B,A)),ld(B,rd(C,B))) = rd(D,mult(ld(B,C),D)). [para(655(a,1),562(a,1,2))].
% 115.06/115.38 2265 rd(A,mult(B,ld(C,mult(B,A)))) = ld(B,rd(C,B)). [para(672(a,1),9(a,1,2))].
% 115.06/115.38 2618 rd(ld(A,B),mult(C,ld(A,B))) = rd(ld(C,D),D). [para(50(a,1),841(a,1,1)),rewrite([50(6)])].
% 115.06/115.38 2665 mult(ld(A,A),ld(mult(A,A),B)) = ld(A,ld(A,B)). [para(895(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 2768 rd(ld(A,A),ld(A,ld(B,rd(C,mult(A,C))))) = mult(mult(A,B),A). [para(430(a,2),900(a,1,2,2,2))].
% 115.06/115.38 2983 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)). [para(1042(a,1),220(a,1,2)),rewrite([430(6),1761(7),1835(10),1868(6),2(7)])].
% 115.06/115.38 3198 rd(rd(A,ld(B,ld(B,B))),mult(B,B)) = mult(mult(B,B),rd(ld(mult(B,B),A),B)). [para(1411(a,1),1209(a,1,1,2))].
% 115.06/115.38 3226 rd(A,rd(ld(B,C),C)) = rd(A,rd(D,mult(B,D))). [para(469(a,2),1237(a,2,2)),flip(a)].
% 115.06/115.38 3341 rd(A,rd(ld(B,C),C)) = rd(A,rd(ld(B,D),D)). [para(469(a,2),1239(a,2,2))].
% 115.06/115.38 3559 rd(ld(A,ld(A,B)),ld(mult(A,A),B)) = ld(A,A). [para(395(a,1),1377(a,1,1,2)),rewrite([395(4),473(7),469(4),1448(6),163(10),358(7),1(8)])].
% 115.06/115.38 3634 rd(mult(ld(A,A),B),ld(A,ld(A,B))) = mult(A,A). [para(967(a,1),1382(a,1,1)),rewrite([2665(6)])].
% 115.06/115.38 3794 rd(A,rd(ld(mult(B,B),C),C)) = mult(mult(A,B),B). [para(1446(a,2),259(a,2,2)),rewrite([1728(5),1(2)]),flip(a)].
% 115.06/115.38 4737 mult(mult(A,B),ld(mult(C,B),rd(C,B))) = rd(A,B). [para(1703(a,1),11(a,1,2,2)),rewrite([473(4),1(3)]),flip(a)].
% 115.06/115.38 4739 mult(rd(A,B),mult(B,rd(B,A))) = rd(A,rd(A,B)). [para(1703(a,1),13(a,1,2,2)),rewrite([650(5),650(6),813(6),4737(12)])].
% 115.06/115.38 5188 ld(A,rd(rd(A,B),B)) = ld(B,ld(B,ld(B,B))). [para(1715(a,1),2(a,1,2))].
% 115.06/115.38 5255 mult(ld(A,A),rd(rd(A,B),B)) = mult(A,rd(rd(ld(A,A),B),B)). [para(1715(a,1),753(a,1,2)),rewrite([1715(9)])].
% 115.06/115.38 5311 rd(A,ld(B,ld(B,B))) = ld(B,mult(mult(B,A),B)). [para(1728(a,1),2(a,1,2)),flip(a)].
% 115.06/115.38 5560 mult(mult(A,A),rd(ld(mult(A,A),B),A)) = mult(B,ld(A,ld(A,A))). [back_rewrite(3198),rewrite([5311(3),526(5),4(3),1704(3)]),flip(a)].
% 115.06/115.38 5752 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,D),D)). [para(615(a,1),1735(a,2,2))].
% 115.06/115.38 5934 mult(A,rd(rd(B,mult(C,B)),D)) = mult(A,rd(ld(C,ld(C,C)),D)). [para(1940(a,1),554(a,1,2,2)),rewrite([650(14),650(15),813(15)]),flip(a)].
% 115.06/115.38 6563 rd(A,mult(mult(B,B),A)) = mult(ld(C,C),rd(rd(ld(C,C),B),B)). [para(2002(a,1),891(a,1,2)),flip(a)].
% 115.06/115.38 7306 rd(ld(mult(A,A),B),B) = mult(ld(C,C),rd(rd(ld(C,C),A),A)). [para(2184(a,1),891(a,1,2)),flip(a)].
% 115.06/115.38 8011 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(2665(a,1),2265(a,1,2,2,2)),rewrite([674(12)])].
% 115.06/115.38 8405 mult(rd(ld(A,rd(B,mult(C,B))),rd(ld(C,D),D)),E) = ld(A,E). [para(3226(a,2),608(a,1,1))].
% 115.06/115.38 8407 rd(ld(A,rd(B,mult(C,B))),rd(ld(C,D),D)) = rd(E,mult(A,E)). [para(3226(a,2),614(a,1))].
% 115.06/115.38 8678 mult(mult(A,A),rd(ld(A,rd(ld(B,C),C)),rd(ld(B,D),D))) = A. [para(3341(a,1),1533(a,1,2))].
% 115.06/115.39 8860 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(3559(a,1),221(a,1,2,1,2))].
% 115.06/115.39 8971 mult(mult(ld(A,rd(ld(mult(B,B),C),C)),B),B) = ld(A,ld(A,A)). [para(3794(a,1),469(a,1))].
% 115.06/115.39 8990 mult(mult(A,ld(B,B)),ld(B,B)) = rd(A,ld(B,B)). [para(685(a,1),3794(a,1,2,1,1)),rewrite([387(1),387(2),960(3),1411(2),1(3),674(2),4(3),387(3),387(5)]),flip(a)].
% 115.06/115.39 9653 rd(mult(mult(A,A),B),mult(A,A)) = mult(mult(A,A),rd(rd(B,A),A)). [para(1447(a,1),4739(a,1,2,2)),rewrite([4(3),1715(5),4(9)]),flip(a)].
% 115.06/115.39 9984 rd(ld(A,ld(A,A)),ld(A,ld(B,rd(rd(B,A),A)))) = mult(A,A). [para(5188(a,2),3634(a,1,2,2)),rewrite([960(4),2983(3),1411(2),1(4)])].
% 115.06/115.39 10075 ld(A,mult(mult(A,mult(A,B)),A)) = mult(mult(A,rd(B,ld(A,A))),A). [para(5311(a,1),125(a,1))].
% 115.06/115.39 10660 ld(A,rd(ld(B,C),mult(D,ld(B,C)))) = ld(A,rd(ld(D,E),E)). [para(2618(a,2),5752(a,1,2))].
% 115.06/115.39 11901 rd(ld(A,ld(A,A)),ld(B,B)) = mult(ld(A,ld(B,B)),ld(B,B)). [para(395(a,1),8990(a,1,1)),flip(a)].
% 115.06/115.39 14334 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A). [para(774(a,1),390(a,2,1)),rewrite([387(1),387(2),387(4),1025(6),891(7),387(4),387(6)])].
% 115.06/115.39 14341 rd(ld(mult(A,ld(B,B)),A),ld(B,B)) = mult(ld(A,A),ld(B,B)). [para(390(a,1),8990(a,1,1)),rewrite([891(4),387(1),1025(9),891(10)]),flip(a)].
% 115.06/115.39 14344 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A). [para(14334(a,1),4(a,1,1))].
% 115.06/115.39 14347 ld(ld(mult(A,ld(B,B)),A),C) = mult(ld(mult(B,ld(A,A)),B),C). [para(14334(a,1),548(a,1,1,2)),rewrite([14344(3)]),flip(a)].
% 115.06/115.39 14365 ld(ld(A,ld(B,B)),rd(C,mult(A,C))) = ld(mult(A,ld(B,B)),A). [para(548(a,1),14344(a,2,1)),rewrite([650(5),4(2),432(3),14344(3)]),flip(a)].
% 115.06/115.39 14371 rd(mult(A,ld(mult(B,A),B)),ld(C,C)) = ld(mult(ld(A,B),ld(C,C)),ld(A,B)). [para(163(a,1),14344(a,1,1))].
% 115.06/115.39 14972 mult(mult(ld(A,A),rd(B,mult(C,B))),A) = mult(ld(A,A),mult(ld(C,ld(A,A)),A)). [para(358(a,1),660(a,1,2)),rewrite([674(4),674(10)])].
% 115.06/115.39 14983 ld(mult(A,ld(mult(A,B),mult(A,B))),C) = mult(rd(A,rd(mult(A,mult(A,B)),B)),C). [para(387(a,1),666(a,1,1,2))].
% 115.06/115.39 15487 mult(ld(mult(A,ld(B,B)),A),mult(ld(B,B),ld(A,A))) = ld(A,A). [para(14334(a,1),986(a,1,2,2)),rewrite([14347(7),4(8),14341(8),163(14),14371(16),14334(12),674(12),4(16)])].
% 115.06/115.39 16623 rd(mult(ld(A,A),rd(B,ld(A,A))),mult(ld(B,ld(A,A)),mult(B,ld(A,A)))) = B. [para(1738(a,1),24(a,1,1))].
% 115.06/115.39 20865 rd(rd(rd(A,B),B),mult(A,rd(rd(ld(A,A),B),B))) = ld(A,A). [para(5255(a,1),430(a,1,2)),rewrite([674(11),960(11),1411(10),1(11),674(10),960(10),1411(9),1(10)])].
% 115.06/115.39 20875 rd(ld(A,A),mult(ld(A,A),ld(B,ld(A,A)))) = mult(ld(A,A),rd(B,ld(A,A))). [para(5255(a,1),2768(a,1,2,2,2,2)),rewrite([674(3),960(3),1411(2),1(3),20865(9),674(5),1738(10)])].
% 115.06/115.39 20954 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(mult(B,ld(A,A)),B)). [para(891(a,1),422(a,1,2,2,2,1)),rewrite([910(10),14365(5),891(10),891(10)]),flip(a)].
% 115.06/115.39 22222 mult(mult(A,A),rd(rd(B,mult(mult(A,A),B)),A)) = ld(A,ld(A,A)). [para(5934(a,2),5560(a,1)),rewrite([200(9),674(8),358(8),960(10),2983(9),1411(8),1(10)])].
% 115.06/115.39 26693 mult(mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C),D) = ld(A,D). [para(6563(a,1),8405(a,1,1,1,2)),rewrite([3794(10)])].
% 115.06/115.39 26782 rd(A,mult(B,A)) = mult(mult(ld(B,mult(ld(C,C),rd(rd(ld(C,C),D),D))),D),D). [para(6563(a,1),8407(a,1,1,2)),rewrite([3794(10)]),flip(a)].
% 115.06/115.39 28088 mult(mult(A,A),mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C)) = A. [para(7306(a,1),8678(a,1,2,1,2)),rewrite([3794(11)])].
% 115.06/115.39 28323 mult(mult(ld(A,mult(ld(B,B),rd(rd(ld(B,B),C),C))),C),C) = ld(A,ld(A,A)). [para(7306(a,1),8971(a,1,1,1,2))].
% 115.06/115.39 41610 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = mult(ld(B,B),ld(A,A)). [para(14341(a,1),1326(a,1,1,2,2)),rewrite([14347(8),15487(8),960(3),1411(2),1(3),14341(7),674(6),891(7),14341(9),674(8)]),flip(a)].
% 115.06/115.39 41611 mult(ld(A,A),ld(mult(B,ld(A,A)),B)) = ld(B,B). [para(14341(a,1),2228(a,1,2,2)),rewrite([769(3),674(6),41610(6),769(5),674(6),1026(8)]),flip(a)].
% 115.06/115.39 41613 ld(mult(A,ld(B,B)),A) = mult(ld(B,B),ld(A,A)). [para(14341(a,1),9653(a,2,2,1)),rewrite([960(3),1411(2),1(3),41611(5),960(4),1411(3),1(4),14344(3),960(6),1411(5),1(6),4(9)])].
% 115.06/115.39 41614 mult(ld(A,A),ld(mult(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(14341(a,1),739(a,2,2,2,2)),rewrite([41613(3),41613(8),1025(11),891(12),674(10),894(11),431(10),1025(8),41613(7),674(6),960(6),1411(5),1(6),891(6),960(3),1411(2),1(3),41613(6),200(10),674(7),674(10),891(12)]),flip(a)].
% 115.06/115.39 41618 mult(ld(A,A),ld(B,B)) = ld(B,B). [para(14341(a,1),9984(a,1,2,2,2,1)),rewrite([674(4),960(4),1411(3),1(4),674(3),960(3),1411(2),1(3),41613(5),4(10),674(8),41614(8),14344(3),41613(3),960(6),1411(5),1(6)])].
% 115.06/115.39 41619 mult(mult(A,ld(B,B)),A) = mult(A,A). [para(14341(a,1),10075(a,2,1,2)),rewrite([41613(3),41618(3),10075(5),14344(3),41613(3),41618(3),41618(6),1(5)])].
% 115.06/115.39 41621 ld(A,A) = ld(B,B). [para(10660(a,1),14341(a,1,1,1,2)),rewrite([650(7),4(4),431(3),41613(3),41618(3),650(10),4(5),432(6),14344(3),41613(3),41618(3),650(11),4(6),432(7),41618(4)])].
% 115.06/115.39 41628 mult(mult(A,ld(mult(ld(B,B),A),ld(B,B))),ld(B,B)) = ld(B,B). [para(11901(a,2),14341(a,1,1,1)),rewrite([650(7),5311(4),41619(3),2(2),1(3),387(3),674(3),960(3),1411(2),1(3),163(6)]),flip(a)].
% 115.06/115.39 41632 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(B,B)). [back_rewrite(20954),rewrite([41613(7),41618(7)])].
% 115.06/115.39 41655 ld(mult(A,ld(B,B)),A) = ld(A,A). [back_rewrite(41613),rewrite([41618(6)])].
% 115.06/115.39 41666 rd(mult(A,mult(A,B)),B) = mult(A,A). [back_rewrite(390),rewrite([41619(5)]),flip(a)].
% 115.06/115.39 41667 ld(A,A) = c_0. [new_symbol(41621)].
% 115.06/115.39 41680 ld(mult(A,c_0),B) = mult(ld(A,c_0),B). [back_rewrite(14983),rewrite([41667(3),41666(6),430(5),41667(4)])].
% 115.06/115.39 41693 mult(ld(A,c_0),A) = c_0. [back_rewrite(41655),rewrite([41667(1),41680(3),41667(4)])].
% 115.06/115.39 41710 ld(mult(c_0,A),c_0) = ld(A,c_0). [back_rewrite(41632),rewrite([41667(1),41667(3),41667(5)])].
% 115.06/115.39 41713 mult(c_0,c_0) = c_0. [back_rewrite(41628),rewrite([41667(1),41667(3),41710(4),1(3),41667(2),41667(4)])].
% 115.06/115.39 41968 mult(mult(ld(A,mult(c_0,rd(rd(c_0,B),B))),B),B) = ld(A,c_0). [back_rewrite(28323),rewrite([41667(1),41667(2),41667(9)])].
% 115.06/115.39 41976 mult(A,c_0) = A. [back_rewrite(28088),rewrite([41667(2),41667(3),41968(9),21(4),41667(1),41713(3)])].
% 115.06/115.39 41985 rd(A,mult(B,A)) = ld(B,c_0). [back_rewrite(26782),rewrite([41667(3),41667(4),41968(10)])].
% 115.06/115.39 41986 mult(ld(A,c_0),B) = ld(A,B). [back_rewrite(26693),rewrite([41667(1),41667(2),41968(8)])].
% 115.06/115.39 42063 mult(c_0,ld(A,c_0)) = ld(A,c_0). [back_rewrite(22222),rewrite([41985(4),5560(6),41667(2),41667(5)])].
% 115.06/115.39 42091 mult(c_0,rd(A,c_0)) = A. [back_rewrite(20875),rewrite([41667(1),41667(2),41667(3),42063(5),9(4),41667(1),41667(2)]),flip(a)].
% 115.06/115.39 42247 rd(A,c_0) = A. [back_rewrite(16623),rewrite([41667(1),41667(2),42091(4),41667(1),41667(3),41976(4),41693(3)])].
% 115.06/115.39 42308 mult(c_0,ld(A,B)) = ld(A,B). [back_rewrite(14972),rewrite([41667(1),41985(3),42063(4),41986(3),41667(2),41667(3),41986(5)]),flip(a)].
% 115.06/115.39 42685 ld(mult(A,A),B) = ld(A,ld(A,B)). [back_rewrite(8860),rewrite([41667(9),41986(11),4(10)]),flip(a)].
% 115.06/115.39 42718 mult(c_0,A) = A. [back_rewrite(8011),rewrite([42685(2),41667(3),42308(7),9(6),41667(1),41667(2),42247(3)]),flip(a)].
% 115.06/115.39 42979 $F # answer(goal). [back_rewrite(385),rewrite([41667(3),42718(3)]),xx(a)].
% 115.06/115.39
% 115.06/115.39 % SZS output end Refutation
% 115.06/115.39 ============================== end of proof ==========================
% 115.06/115.39
% 115.06/115.39 ============================== STATISTICS ============================
% 115.06/115.39
% 115.06/115.39 Given=1570. Generated=4051334. Kept=42977. proofs=1.
% 115.06/115.39 Usable=998. Sos=6462. Demods=6427. Limbo=1312, Disabled=34211. Hints=0.
% 115.06/115.39 Megabytes=38.88.
% 115.06/115.39 User_CPU=112.09, System_CPU=2.32, Wall_clock=115.
% 115.06/115.39
% 115.06/115.39 ============================== end of statistics =====================
% 115.06/115.39
% 115.06/115.39 ============================== end of search =========================
% 115.06/115.39
% 115.06/115.39 THEOREM PROVED
% 115.06/115.39 % SZS status Unsatisfiable
% 115.06/115.39
% 115.06/115.39 Exiting with 1 proof.
% 115.06/115.39
% 115.06/115.39 Process 32229 exit (max_proofs) Tue Jun 14 13:00:54 2022
% 115.06/115.39 Prover9 interrupted
%------------------------------------------------------------------------------