TSTP Solution File: GRP654-11 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP654-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 113.66s 113.95s
% Output : Refutation 113.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP654-11 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 07:31:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 113.66/113.95 ============================== Prover9 ===============================
% 113.66/113.95 Prover9 (32) version 2009-11A, November 2009.
% 113.66/113.95 Process 18350 was started by sandbox on n006.cluster.edu,
% 113.66/113.95 Mon Jun 13 07:31:27 2022
% 113.66/113.95 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18197_n006.cluster.edu".
% 113.66/113.95 ============================== end of head ===========================
% 113.66/113.95
% 113.66/113.95 ============================== INPUT =================================
% 113.66/113.95
% 113.66/113.95 % Reading from file /tmp/Prover9_18197_n006.cluster.edu
% 113.66/113.95
% 113.66/113.95 set(prolog_style_variables).
% 113.66/113.95 set(auto2).
% 113.66/113.95 % set(auto2) -> set(auto).
% 113.66/113.95 % set(auto) -> set(auto_inference).
% 113.66/113.95 % set(auto) -> set(auto_setup).
% 113.66/113.95 % set(auto_setup) -> set(predicate_elim).
% 113.66/113.95 % set(auto_setup) -> assign(eq_defs, unfold).
% 113.66/113.95 % set(auto) -> set(auto_limits).
% 113.66/113.95 % set(auto_limits) -> assign(max_weight, "100.000").
% 113.66/113.95 % set(auto_limits) -> assign(sos_limit, 20000).
% 113.66/113.95 % set(auto) -> set(auto_denials).
% 113.66/113.95 % set(auto) -> set(auto_process).
% 113.66/113.95 % set(auto2) -> assign(new_constants, 1).
% 113.66/113.95 % set(auto2) -> assign(fold_denial_max, 3).
% 113.66/113.95 % set(auto2) -> assign(max_weight, "200.000").
% 113.66/113.95 % set(auto2) -> assign(max_hours, 1).
% 113.66/113.95 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 113.66/113.95 % set(auto2) -> assign(max_seconds, 0).
% 113.66/113.95 % set(auto2) -> assign(max_minutes, 5).
% 113.66/113.95 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 113.66/113.95 % set(auto2) -> set(sort_initial_sos).
% 113.66/113.95 % set(auto2) -> assign(sos_limit, -1).
% 113.66/113.95 % set(auto2) -> assign(lrs_ticks, 3000).
% 113.66/113.95 % set(auto2) -> assign(max_megs, 400).
% 113.66/113.95 % set(auto2) -> assign(stats, some).
% 113.66/113.95 % set(auto2) -> clear(echo_input).
% 113.66/113.95 % set(auto2) -> set(quiet).
% 113.66/113.95 % set(auto2) -> clear(print_initial_clauses).
% 113.66/113.95 % set(auto2) -> clear(print_given).
% 113.66/113.95 assign(lrs_ticks,-1).
% 113.66/113.95 assign(sos_limit,10000).
% 113.66/113.95 assign(order,kbo).
% 113.66/113.95 set(lex_order_vars).
% 113.66/113.95 clear(print_given).
% 113.66/113.95
% 113.66/113.95 % formulas(sos). % not echoed (6 formulas)
% 113.66/113.95
% 113.66/113.95 ============================== end of input ==========================
% 113.66/113.95
% 113.66/113.95 % From the command line: assign(max_seconds, 300).
% 113.66/113.95
% 113.66/113.95 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 113.66/113.95
% 113.66/113.95 % Formulas that are not ordinary clauses:
% 113.66/113.95
% 113.66/113.95 ============================== end of process non-clausal formulas ===
% 113.66/113.95
% 113.66/113.95 ============================== PROCESS INITIAL CLAUSES ===============
% 113.66/113.95
% 113.66/113.95 ============================== PREDICATE ELIMINATION =================
% 113.66/113.95
% 113.66/113.95 ============================== end predicate elimination =============
% 113.66/113.95
% 113.66/113.95 Auto_denials:
% 113.66/113.95 % copying label goal to answer in negative clause
% 113.66/113.95
% 113.66/113.95 Term ordering decisions:
% 113.66/113.95 Function symbol KB weights: x0=1. x1=1. mult=1. ld=1. rd=1.
% 113.66/113.95
% 113.66/113.95 ============================== end of process initial clauses ========
% 113.66/113.95
% 113.66/113.95 ============================== CLAUSES FOR SEARCH ====================
% 113.66/113.95
% 113.66/113.95 ============================== end of clauses for search =============
% 113.66/113.95
% 113.66/113.95 ============================== SEARCH ================================
% 113.66/113.95
% 113.66/113.95 % Starting search at 0.01 seconds.
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=95.000, iters=3551
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=71.000, iters=3416
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=67.000, iters=3366
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=59.000, iters=3343
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=55.000, iters=3346
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=51.000, iters=3357
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=47.000, iters=3384
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=43.000, iters=3335
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=39.000, iters=3358
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=35.000, iters=3372
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=31.000, iters=3333
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=27.000, iters=3373
% 113.66/113.95
% 113.66/113.95 Low Water (displace): id=6057, wt=135.000
% 113.66/113.95
% 113.66/113.95 Low Water (displace): id=7085, wt=119.000
% 113.66/113.95
% 113.66/113.95 Low Water (displace): id=12683, wt=23.000
% 113.66/113.95
% 113.66/113.95 Low Water (displace): id=12926, wt=19.000
% 113.66/113.95
% 113.66/113.95 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 10.08 sec).
% 113.66/113.95
% 113.66/113.95 Low Water (keep): wt=23.000, iters=3336
% 113.66/113.95
% 113.66/113.95 ============================== PROOF =================================
% 113.66/113.95 % SZS status Unsatisfiable
% 113.66/113.95 % SZS output start Refutation
% 113.66/113.95
% 113.66/113.95 % Proof 1 at 110.67 (+ 2.27) seconds: goal.
% 113.66/113.95 % Length of proof is 181.
% 113.66/113.95 % Level of proof is 35.
% 113.66/113.95 % Maximum clause weight is 39.000.
% 113.66/113.95 % Given clauses 1570.
% 113.66/113.95
% 113.66/113.95 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 113.66/113.95 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 113.66/113.95 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 113.66/113.95 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 113.66/113.95 5 mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C) # label(f05) # label(axiom). [assumption].
% 113.66/113.95 6 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))). [copy(5),flip(a)].
% 113.66/113.95 7 mult(x0,rd(x1,x1)) != x0 # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 113.66/113.95 9 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 113.66/113.95 10 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C. [para(6(a,1),1(a,1))].
% 113.66/113.95 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)].
% 113.66/113.95 12 ld(mult(mult(A,B),A),mult(A,mult(B,mult(A,C)))) = C. [para(6(a,1),2(a,1,2))].
% 113.66/113.95 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)].
% 113.66/113.95 14 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A). [para(6(a,1),4(a,1,1))].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 22 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)). [para(11(a,1),2(a,1,2))].
% 113.66/113.95 24 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B. [para(11(a,1),4(a,1,1))].
% 113.66/113.95 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)])].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 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))].
% 113.66/113.95 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)].
% 113.66/113.95 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))].
% 113.66/113.95 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)].
% 113.66/113.95 58 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C). [para(21(a,1),2(a,1,2))].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 125 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A). [para(3(a,1),41(a,1,1,2))].
% 113.66/113.95 142 ld(mult(A,rd(B,mult(A,C))),rd(mult(A,B),C)) = A. [para(43(a,1),2(a,1,2))].
% 113.66/113.95 144 rd(rd(mult(A,B),C),A) = mult(A,rd(B,mult(A,C))). [para(43(a,1),4(a,1,1))].
% 113.66/113.95 146 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)].
% 113.66/113.95 163 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)). [para(50(a,1),2(a,1,2))].
% 113.66/113.95 179 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))). [para(51(a,1),2(a,1,2)),flip(a)].
% 113.66/113.95 184 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))].
% 113.66/113.95 200 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)). [para(1(a,1),58(a,1,2,2))].
% 113.66/113.95 220 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C). [para(59(a,1),2(a,1,2))].
% 113.66/113.95 224 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)].
% 113.66/113.95 259 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)). [para(1(a,1),125(a,1,1)),flip(a)].
% 113.66/113.95 279 ld(mult(A,rd(B,mult(A,B))),A) = A. [para(4(a,1),142(a,1,2))].
% 113.66/113.95 329 ld(mult(A,rd(ld(A,B),B)),A) = A. [para(1(a,1),279(a,1,1,2,2))].
% 113.66/113.95 332 mult(A,rd(B,mult(A,B))) = rd(A,A). [para(279(a,1),9(a,1,2)),flip(a)].
% 113.66/113.95 345 mult(A,rd(ld(A,B),B)) = rd(A,A). [para(329(a,1),9(a,1,2)),flip(a)].
% 113.66/113.95 348 rd(A,mult(B,A)) = ld(B,rd(B,B)). [para(332(a,1),2(a,1,2)),flip(a)].
% 113.66/113.95 349 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)].
% 113.66/113.95 355 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)].
% 113.66/113.95 358 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)].
% 113.66/113.95 362 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)].
% 113.66/113.95 385 ld(ld(A,A),A) = A. [para(358(a,1),2(a,1,2))].
% 113.66/113.95 386 rd(A,A) = ld(A,A). [para(358(a,1),4(a,1,1))].
% 113.66/113.95 389 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)].
% 113.66/113.95 394 mult(ld(A,ld(A,A)),B) = ld(A,B). [para(358(a,1),50(a,1,2,2,1)),rewrite([1(4)])].
% 113.66/113.95 395 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)])].
% 113.66/113.95 421 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([386(9)])].
% 113.66/113.95 428 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)). [back_rewrite(349),rewrite([386(3)])].
% 113.66/113.95 429 rd(A,mult(B,A)) = ld(B,ld(B,B)). [back_rewrite(348),rewrite([386(3)])].
% 113.66/113.95 430 mult(A,rd(ld(A,B),B)) = ld(A,A). [back_rewrite(345),rewrite([386(4)])].
% 113.66/113.95 431 mult(A,rd(B,mult(A,B))) = ld(A,A). [back_rewrite(332),rewrite([386(4)])].
% 113.66/113.95 432 mult(x0,ld(x1,x1)) != x0 # answer(goal). [back_rewrite(7),rewrite([386(4)])].
% 113.66/113.95 460 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)). [para(385(a,1),21(a,2,2,1)),rewrite([1(2)]),flip(a)].
% 113.66/113.95 462 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A). [para(385(a,1),24(a,1,2,1)),rewrite([1(2)])].
% 113.66/113.95 463 mult(A,mult(ld(A,A),ld(A,B))) = ld(ld(A,A),B). [para(385(a,1),50(a,1,1)),rewrite([1(3)])].
% 113.66/113.95 469 rd(ld(A,B),B) = ld(A,ld(A,A)). [para(394(a,1),4(a,1,1))].
% 113.66/113.95 473 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)). [para(394(a,1),14(a,1,1,2,2)),rewrite([394(5),220(3),4(4),394(5)]),flip(a)].
% 113.66/113.95 475 mult(A,mult(ld(A,ld(B,ld(B,B))),C)) = mult(ld(B,A),ld(A,C)). [para(394(a,1),21(a,1,1)),flip(a)].
% 113.66/113.95 519 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),386(1),394(6),2(4)])].
% 113.66/113.95 522 ld(A,mult(ld(A,A),mult(mult(A,A),B))) = mult(A,B). [para(394(a,1),34(a,1,1,2)),rewrite([1(2)])].
% 113.66/113.95 548 mult(rd(A,mult(B,A)),C) = ld(B,C). [para(429(a,2),50(a,1,1)),rewrite([358(4),1(4)])].
% 113.66/113.95 562 rd(A,mult(B,A)) = rd(C,mult(B,C)). [para(429(a,2),429(a,2))].
% 113.66/113.95 578 mult(A,ld(B,rd(ld(ld(B,rd(A,B)),C),C))) = mult(B,mult(B,ld(A,rd(A,B)))). [para(430(a,1),59(a,1,2)),rewrite([163(5),3(2)]),flip(a)].
% 113.66/113.95 608 mult(rd(ld(A,B),B),C) = ld(A,C). [para(469(a,2),50(a,1,1)),rewrite([358(4),1(4)])].
% 113.66/113.95 611 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)].
% 113.66/113.95 614 rd(ld(A,B),B) = rd(C,mult(A,C)). [para(469(a,2),429(a,2)),flip(a)].
% 113.66/113.95 615 rd(ld(A,B),B) = rd(ld(A,C),C). [para(469(a,2),469(a,2))].
% 113.66/113.95 650 ld(rd(A,B),C) = mult(rd(B,A),C). [para(3(a,1),548(a,1,1,2)),flip(a)].
% 113.66/113.95 655 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)].
% 113.66/113.95 672 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)].
% 113.66/113.95 674 ld(ld(A,A),B) = mult(ld(A,A),B). [para(358(a,1),548(a,1,1,2)),rewrite([386(1)]),flip(a)].
% 113.66/113.95 685 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)). [back_rewrite(428),rewrite([650(3)])].
% 113.66/113.95 709 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)])].
% 113.66/113.95 739 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)])].
% 113.66/113.95 752 mult(A,mult(ld(A,A),ld(A,B))) = mult(ld(A,A),B). [back_rewrite(463),rewrite([674(6)])].
% 113.66/113.95 753 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)). [back_rewrite(460),rewrite([674(5)])].
% 113.66/113.95 761 rd(A,mult(rd(B,C),A)) = rd(C,B). [para(3(a,1),562(a,1,2)),flip(a)].
% 113.66/113.95 769 rd(A,mult(ld(B,B),A)) = ld(B,B). [para(358(a,1),562(a,1,2)),rewrite([386(1)]),flip(a)].
% 113.66/113.95 774 mult(rd(A,B),mult(rd(B,A),C)) = C. [para(1(a,1),37(a,2)),rewrite([709(12),1(11)])].
% 113.66/113.95 803 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),429(a,1,2)),rewrite([650(17),650(18)])].
% 113.66/113.95 813 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)])].
% 113.66/113.95 822 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)].
% 113.66/113.95 841 rd(mult(A,B),mult(C,mult(A,B))) = rd(ld(C,D),D). [para(614(a,2),43(a,2)),rewrite([43(6)])].
% 113.66/113.95 891 mult(ld(A,A),mult(ld(A,A),B)) = B. [para(674(a,1),1(a,1,2))].
% 113.66/113.95 894 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)].
% 113.66/113.95 895 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)])].
% 113.66/113.95 910 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)])].
% 113.66/113.95 960 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)). [para(50(a,1),891(a,1,2))].
% 113.66/113.95 967 mult(A,mult(A,ld(mult(A,A),B))) = mult(ld(A,A),B). [back_rewrite(752),rewrite([960(3)])].
% 113.66/113.95 986 mult(A,rd(rd(ld(A,B),B),mult(A,C))) = rd(rd(ld(A,A),C),A). [para(430(a,1),144(a,1,1,1)),flip(a)].
% 113.66/113.95 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)])].
% 113.66/113.95 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)])].
% 113.66/113.95 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)].
% 113.66/113.95 1125 mult(ld(mult(A,A),ld(A,A)),B) = ld(mult(A,A),B). [para(200(a,1),394(a,1,1,2)),rewrite([674(3),358(3)])].
% 113.66/113.95 1129 rd(A,mult(mult(B,B),A)) = ld(mult(B,B),ld(B,B)). [para(200(a,1),429(a,2,2)),rewrite([674(6),358(6)])].
% 113.66/113.95 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)])].
% 113.66/113.95 1164 mult(ld(A,rd(ld(B,ld(B,B)),A)),C) = ld(A,ld(B,ld(A,C))). [para(394(a,1),220(a,1,2)),flip(a)].
% 113.66/113.95 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)].
% 113.66/113.95 1326 mult(mult(A,ld(B,rd(B,A))),ld(A,rd(B,A))) = ld(A,rd(B,A)). [para(3(a,1),395(a,1,1,2,1))].
% 113.66/113.95 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)].
% 113.66/113.95 1394 mult(A,ld(mult(A,A),A)) = ld(A,A). [para(430(a,1),462(a,1,1)),rewrite([822(5),386(2),1(4),386(3),674(3),960(3)])].
% 113.66/113.95 1411 ld(mult(A,A),A) = ld(A,ld(A,A)). [para(1394(a,1),2(a,1,2)),flip(a)].
% 113.66/113.95 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),394(6),1164(5),1411(5)]),flip(a)].
% 113.66/113.95 1424 rd(A,ld(A,ld(A,A))) = mult(A,A). [para(1411(a,1),9(a,1,2))].
% 113.66/113.95 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([394(6),22(4),753(4)])].
% 113.66/113.95 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)])].
% 113.66/113.95 1442 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))). [back_rewrite(1415),rewrite([1434(3),1125(5)])].
% 113.66/113.95 1443 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))). [back_rewrite(1434),rewrite([1442(6)])].
% 113.66/113.95 1446 rd(ld(mult(A,A),B),B) = ld(A,ld(A,ld(A,A))). [back_rewrite(1135),rewrite([1442(6)])].
% 113.66/113.95 1447 rd(A,mult(mult(B,B),A)) = ld(B,ld(B,ld(B,B))). [back_rewrite(1129),rewrite([1442(6)])].
% 113.66/113.95 1500 rd(A,rd(B,mult(A,B))) = mult(A,A). [para(429(a,2),1424(a,1,2))].
% 113.66/113.95 1501 rd(A,rd(ld(A,B),B)) = mult(A,A). [para(469(a,2),1424(a,1,2))].
% 113.66/113.95 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)].
% 113.66/113.95 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)])].
% 113.66/113.95 1517 mult(mult(A,A),rd(B,mult(A,B))) = A. [para(1500(a,1),3(a,1,1))].
% 113.66/113.95 1533 mult(mult(A,A),rd(ld(A,B),B)) = A. [para(1501(a,1),3(a,1,1))].
% 113.66/113.95 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)])].
% 113.66/113.95 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),429(6)]),flip(a)].
% 113.66/113.95 1685 ld(mult(A,mult(A,A)),B) = ld(A,ld(A,ld(A,B))). [para(1546(a,1),179(a,1,1))].
% 113.66/113.95 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)])].
% 113.66/113.95 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)])].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 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),429(7)])].
% 113.66/113.95 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)].
% 113.66/113.95 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)])].
% 113.66/113.95 1868 ld(A,mult(ld(A,A),B)) = mult(A,ld(mult(A,A),B)). [para(1(a,1),522(a,1,2,2))].
% 113.66/113.95 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)])].
% 113.66/113.95 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))].
% 113.66/113.95 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)])].
% 113.66/113.95 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)].
% 113.66/113.95 2983 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)). [para(1042(a,1),220(a,1,2)),rewrite([429(6),1761(7),1835(10),1868(6),2(7)])].
% 113.66/113.95 3341 rd(A,rd(ld(B,C),C)) = rd(A,rd(ld(B,D),D)). [para(469(a,2),1239(a,2,2))].
% 113.66/113.95 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)])].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 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)])].
% 113.66/113.95 5188 ld(A,rd(rd(A,B),B)) = ld(B,ld(B,ld(B,B))). [para(1715(a,1),2(a,1,2))].
% 113.66/113.95 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)].
% 113.66/113.95 5752 ld(A,rd(ld(B,C),C)) = ld(A,rd(ld(B,D),D)). [para(615(a,1),1735(a,2,2))].
% 113.66/113.95 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)].
% 113.66/113.95 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))].
% 113.66/113.95 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))].
% 113.66/113.95 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([386(1),386(2),960(3),1411(2),1(3),674(2),4(3),386(3),386(5)]),flip(a)].
% 113.66/113.95 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)].
% 113.66/113.95 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)])].
% 113.66/113.95 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))].
% 113.66/113.95 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))].
% 113.66/113.95 11901 rd(ld(A,ld(A,A)),ld(B,B)) = mult(ld(A,ld(B,B)),ld(B,B)). [para(394(a,1),8990(a,1,1)),flip(a)].
% 113.66/113.95 14334 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A). [para(774(a,1),389(a,2,1)),rewrite([386(1),386(2),386(4),1025(6),891(7),386(4),386(6)])].
% 113.66/113.95 14341 rd(ld(mult(A,ld(B,B)),A),ld(B,B)) = mult(ld(A,A),ld(B,B)). [para(389(a,1),8990(a,1,1)),rewrite([891(4),386(1),1025(9),891(10)]),flip(a)].
% 113.66/113.95 14344 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A). [para(14334(a,1),4(a,1,1))].
% 113.66/113.95 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)].
% 113.66/113.95 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),431(3),14344(3)]),flip(a)].
% 113.66/113.95 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))].
% 113.66/113.95 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)])].
% 113.66/113.95 20954 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(mult(B,ld(A,A)),B)). [para(891(a,1),421(a,1,2,2,2,1)),rewrite([910(10),14365(5),891(10),891(10)]),flip(a)].
% 113.66/113.95 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)])].
% 113.66/113.95 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))].
% 113.66/113.95 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)].
% 113.66/113.95 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)].
% 113.66/113.95 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)])].
% 113.66/113.95 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),430(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)].
% 113.66/113.95 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)])].
% 113.66/113.95 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)])].
% 113.66/113.95 41621 ld(A,A) = ld(B,B). [para(10660(a,1),14341(a,1,1,1,2)),rewrite([650(7),4(4),430(3),41613(3),41618(3),650(10),4(5),431(6),14344(3),41613(3),41618(3),650(11),4(6),431(7),41618(4)])].
% 113.66/113.95 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),386(3),674(3),960(3),1411(2),1(3),163(6)]),flip(a)].
% 113.66/113.95 41632 ld(mult(ld(A,A),B),ld(B,B)) = ld(B,ld(B,B)). [back_rewrite(20954),rewrite([41613(7),41618(7)])].
% 113.66/113.95 41667 ld(A,A) = c_0. [new_symbol(41621)].
% 113.66/113.95 41710 ld(mult(c_0,A),c_0) = ld(A,c_0). [back_rewrite(41632),rewrite([41667(1),41667(3),41667(5)])].
% 113.66/113.95 41713 mult(c_0,c_0) = c_0. [back_rewrite(41628),rewrite([41667(1),41667(3),41710(4),1(3),41667(2),41667(4)])].
% 113.66/113.95 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)])].
% 113.66/113.95 41976 mult(A,c_0) = A. [back_rewrite(28088),rewrite([41667(2),41667(3),41968(9),21(4),41667(1),41713(3)])].
% 113.66/113.95 42977 $F # answer(goal). [back_rewrite(432),rewrite([41667(4),41976(3)]),xx(a)].
% 113.66/113.95
% 113.66/113.95 % SZS output end Refutation
% 113.66/113.95 ============================== end of proof ==========================
% 113.66/113.95
% 113.66/113.95 ============================== STATISTICS ============================
% 113.66/113.95
% 113.66/113.95 Given=1570. Generated=4051317. Kept=42975. proofs=1.
% 113.66/113.95 Usable=1015. Sos=6462. Demods=6437. Limbo=1310, Disabled=34194. Hints=0.
% 113.66/113.95 Megabytes=38.88.
% 113.66/113.95 User_CPU=110.68, System_CPU=2.27, Wall_clock=113.
% 113.66/113.95
% 113.66/113.95 ============================== end of statistics =====================
% 113.66/113.95
% 113.66/113.95 ============================== end of search =========================
% 113.66/113.95
% 113.66/113.95 THEOREM PROVED
% 113.66/113.95 % SZS status Unsatisfiable
% 113.66/113.95
% 113.66/113.95 Exiting with 1 proof.
% 113.66/113.95
% 113.66/113.95 Process 18350 exit (max_proofs) Mon Jun 13 07:33:20 2022
% 113.66/113.95 Prover9 interrupted
%------------------------------------------------------------------------------