TSTP Solution File: GRP655-13 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP655-13 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:20:19 EDT 2022
% Result : Unsatisfiable 18.47s 18.77s
% Output : Refutation 18.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP655-13 : TPTP v8.1.0. Released v8.1.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 13 13:53:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 18.47/18.77 ============================== Prover9 ===============================
% 18.47/18.77 Prover9 (32) version 2009-11A, November 2009.
% 18.47/18.77 Process 22366 was started by sandbox on n021.cluster.edu,
% 18.47/18.77 Mon Jun 13 13:53:12 2022
% 18.47/18.77 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_22213_n021.cluster.edu".
% 18.47/18.77 ============================== end of head ===========================
% 18.47/18.77
% 18.47/18.77 ============================== INPUT =================================
% 18.47/18.77
% 18.47/18.77 % Reading from file /tmp/Prover9_22213_n021.cluster.edu
% 18.47/18.77
% 18.47/18.77 set(prolog_style_variables).
% 18.47/18.77 set(auto2).
% 18.47/18.77 % set(auto2) -> set(auto).
% 18.47/18.77 % set(auto) -> set(auto_inference).
% 18.47/18.77 % set(auto) -> set(auto_setup).
% 18.47/18.77 % set(auto_setup) -> set(predicate_elim).
% 18.47/18.77 % set(auto_setup) -> assign(eq_defs, unfold).
% 18.47/18.77 % set(auto) -> set(auto_limits).
% 18.47/18.77 % set(auto_limits) -> assign(max_weight, "100.000").
% 18.47/18.77 % set(auto_limits) -> assign(sos_limit, 20000).
% 18.47/18.77 % set(auto) -> set(auto_denials).
% 18.47/18.77 % set(auto) -> set(auto_process).
% 18.47/18.77 % set(auto2) -> assign(new_constants, 1).
% 18.47/18.77 % set(auto2) -> assign(fold_denial_max, 3).
% 18.47/18.77 % set(auto2) -> assign(max_weight, "200.000").
% 18.47/18.77 % set(auto2) -> assign(max_hours, 1).
% 18.47/18.77 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 18.47/18.77 % set(auto2) -> assign(max_seconds, 0).
% 18.47/18.77 % set(auto2) -> assign(max_minutes, 5).
% 18.47/18.77 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 18.47/18.77 % set(auto2) -> set(sort_initial_sos).
% 18.47/18.77 % set(auto2) -> assign(sos_limit, -1).
% 18.47/18.77 % set(auto2) -> assign(lrs_ticks, 3000).
% 18.47/18.77 % set(auto2) -> assign(max_megs, 400).
% 18.47/18.77 % set(auto2) -> assign(stats, some).
% 18.47/18.77 % set(auto2) -> clear(echo_input).
% 18.47/18.77 % set(auto2) -> set(quiet).
% 18.47/18.77 % set(auto2) -> clear(print_initial_clauses).
% 18.47/18.77 % set(auto2) -> clear(print_given).
% 18.47/18.77 assign(lrs_ticks,-1).
% 18.47/18.77 assign(sos_limit,10000).
% 18.47/18.77 assign(order,kbo).
% 18.47/18.77 set(lex_order_vars).
% 18.47/18.77 clear(print_given).
% 18.47/18.77
% 18.47/18.77 % formulas(sos). % not echoed (6 formulas)
% 18.47/18.77
% 18.47/18.77 ============================== end of input ==========================
% 18.47/18.77
% 18.47/18.77 % From the command line: assign(max_seconds, 300).
% 18.47/18.77
% 18.47/18.77 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 18.47/18.77
% 18.47/18.77 % Formulas that are not ordinary clauses:
% 18.47/18.77
% 18.47/18.77 ============================== end of process non-clausal formulas ===
% 18.47/18.77
% 18.47/18.77 ============================== PROCESS INITIAL CLAUSES ===============
% 18.47/18.77
% 18.47/18.77 ============================== PREDICATE ELIMINATION =================
% 18.47/18.77
% 18.47/18.77 ============================== end predicate elimination =============
% 18.47/18.77
% 18.47/18.77 Auto_denials:
% 18.47/18.77 % copying label goal to answer in negative clause
% 18.47/18.77
% 18.47/18.77 Term ordering decisions:
% 18.47/18.77 Function symbol KB weights: x0=1. x1=1. mult=1. ld=1. rd=1.
% 18.47/18.77
% 18.47/18.77 ============================== end of process initial clauses ========
% 18.47/18.77
% 18.47/18.77 ============================== CLAUSES FOR SEARCH ====================
% 18.47/18.77
% 18.47/18.77 ============================== end of clauses for search =============
% 18.47/18.77
% 18.47/18.77 ============================== SEARCH ================================
% 18.47/18.77
% 18.47/18.77 % Starting search at 0.01 seconds.
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=95.000, iters=3360
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=83.000, iters=3339
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=79.000, iters=3347
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=71.000, iters=3385
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=67.000, iters=3345
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=59.000, iters=3377
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=55.000, iters=3404
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=51.000, iters=3348
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=47.000, iters=3343
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=43.000, iters=3343
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=39.000, iters=3334
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=35.000, iters=3347
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=31.000, iters=3395
% 18.47/18.77
% 18.47/18.77 Low Water (displace): id=4346, wt=183.000
% 18.47/18.77
% 18.47/18.77 Low Water (displace): id=4364, wt=151.000
% 18.47/18.77
% 18.47/18.77 Low Water (displace): id=6129, wt=147.000
% 18.47/18.77
% 18.47/18.77 Low Water (displace): id=12609, wt=23.000
% 18.47/18.77
% 18.47/18.77 Low Water (displace): id=13168, wt=19.000
% 18.47/18.77
% 18.47/18.77 Low Water (keep): wt=27.000, iters=3371
% 18.47/18.77
% 18.47/18.77 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 7.15 sec).
% 18.47/18.77
% 18.47/18.77 ============================== PROOF =================================
% 18.47/18.77 % SZS status Unsatisfiable
% 18.47/18.77 % SZS output start Refutation
% 18.47/18.77
% 18.47/18.77 % Proof 1 at 17.42 (+ 0.43) seconds: goal.
% 18.47/18.77 % Length of proof is 120.
% 18.47/18.77 % Level of proof is 27.
% 18.47/18.77 % Maximum clause weight is 31.000.
% 18.47/18.77 % Given clauses 734.
% 18.47/18.77
% 18.47/18.77 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 18.47/18.77 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 18.47/18.77 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 18.47/18.77 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 18.47/18.77 5 mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) # label(f05) # label(axiom). [assumption].
% 18.47/18.77 6 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [copy(5),flip(a)].
% 18.47/18.77 7 mult(x0,ld(x1,x1)) != x0 # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 18.47/18.77 8 ld(rd(A,B),A) = B. [para(3(a,1),2(a,1,2))].
% 18.47/18.77 9 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 18.47/18.77 10 mult(A,mult(ld(A,B),mult(C,ld(A,B)))) = mult(mult(B,C),ld(A,B)). [para(1(a,1),6(a,1,1,1)),flip(a)].
% 18.47/18.77 11 mult(A,mult(B,mult(ld(mult(A,B),C),B))) = mult(C,B). [para(1(a,1),6(a,1,1)),flip(a)].
% 18.47/18.77 12 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,B)))) = B. [para(6(a,1),2(a,1,2))].
% 18.47/18.77 13 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B). [para(3(a,1),6(a,1,1,1)),flip(a)].
% 18.47/18.77 14 rd(mult(A,mult(B,mult(C,B))),B) = mult(mult(A,B),C). [para(6(a,1),4(a,1,1))].
% 18.47/18.77 15 mult(mult(mult(A,mult(B,mult(C,B))),D),B) = mult(mult(mult(A,B),C),mult(B,mult(D,B))). [para(6(a,1),6(a,1,1,1))].
% 18.47/18.77 16 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [para(6(a,1),6(a,1,1))].
% 18.47/18.77 17 mult(A,mult(mult(B,mult(C,B)),mult(D,mult(B,mult(C,B))))) = mult(A,mult(B,mult(mult(C,mult(mult(B,mult(D,B)),C)),B))). [para(6(a,1),6(a,2)),rewrite([15(5),6(6),6(7)]),flip(a)].
% 18.47/18.77 18 mult(A,mult(ld(mult(B,A),C),A)) = ld(B,mult(C,A)). [para(11(a,1),2(a,1,2)),flip(a)].
% 18.47/18.77 28 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)). [para(3(a,1),13(a,1,2,2)),flip(a)].
% 18.47/18.77 29 rd(mult(mult(A,B),C),mult(C,mult(B,C))) = rd(A,C). [para(13(a,1),4(a,1,1))].
% 18.47/18.77 34 mult(mult(A,B),ld(B,A)) = mult(B,mult(ld(B,A),A)). [para(1(a,1),10(a,1,2,2)),flip(a)].
% 18.47/18.77 35 ld(A,mult(mult(B,C),ld(A,B))) = mult(ld(A,B),mult(C,ld(A,B))). [para(10(a,1),2(a,1,2))].
% 18.47/18.77 41 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(3(a,1),14(a,1,1,2,2))].
% 18.47/18.77 42 mult(mult(rd(A,mult(B,mult(C,B))),B),C) = rd(A,B). [para(3(a,1),14(a,1,1)),flip(a)].
% 18.47/18.77 44 ld(A,ld(B,mult(C,A))) = mult(ld(mult(B,A),C),A). [para(18(a,1),2(a,1,2))].
% 18.47/18.77 45 ld(rd(A,B),mult(C,B)) = mult(B,mult(ld(A,C),B)). [para(3(a,1),18(a,1,2,1,1)),flip(a)].
% 18.47/18.77 74 mult(rd(rd(A,rd(B,C)),C),mult(C,B)) = mult(A,C). [para(3(a,1),28(a,1,1)),flip(a)].
% 18.47/18.77 112 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B). [para(3(a,1),29(a,1,1,1))].
% 18.47/18.77 144 mult(mult(A,B),rd(ld(B,C),B)) = rd(mult(A,C),B). [para(1(a,1),41(a,1,1,2)),flip(a)].
% 18.47/18.77 146 mult(mult(rd(A,mult(B,C)),B),rd(C,B)) = rd(A,B). [para(3(a,1),41(a,1,1)),flip(a)].
% 18.47/18.77 161 mult(rd(A,mult(B,mult(C,B))),B) = rd(rd(A,B),C). [para(42(a,1),4(a,1,1)),flip(a)].
% 18.47/18.77 178 ld(mult(mult(mult(A,B),mult(C,mult(B,C))),D),mult(mult(A,mult(B,mult(C,B))),mult(C,mult(D,C)))) = C. [para(16(a,1),12(a,1,1,1))].
% 18.47/18.77 179 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(mult(C,mult(mult(B,mult(C,B)),C)),B)))) = mult(B,mult(C,B)). [para(16(a,1),12(a,1,1)),rewrite([17(11)])].
% 18.47/18.77 198 mult(ld(mult(A,B),A),B) = ld(B,B). [para(2(a,1),44(a,1,2)),flip(a)].
% 18.47/18.77 201 mult(ld(mult(rd(mult(A,B),C),B),A),B) = ld(B,C). [para(8(a,1),44(a,1,2)),flip(a)].
% 18.47/18.77 211 ld(ld(A,B),ld(A,B)) = mult(ld(B,A),ld(A,B)). [para(1(a,1),198(a,1,1,1)),flip(a)].
% 18.47/18.77 212 ld(ld(mult(A,B),A),ld(B,B)) = B. [para(198(a,1),2(a,1,2))].
% 18.47/18.77 213 mult(ld(A,rd(A,B)),B) = ld(B,B). [para(3(a,1),198(a,1,1,1))].
% 18.47/18.77 214 rd(ld(A,A),A) = ld(mult(B,A),B). [para(198(a,1),4(a,1,1))].
% 18.47/18.77 221 mult(A,mult(ld(ld(A,A),B),A)) = ld(ld(mult(C,A),C),mult(B,A)). [para(198(a,1),18(a,1,2,1,1))].
% 18.47/18.77 236 mult(ld(mult(A,B),ld(mult(C,B),C)),B) = ld(B,ld(A,ld(B,B))). [para(198(a,1),44(a,1,2,2)),flip(a)].
% 18.47/18.77 246 rd(ld(A,A),A) = ld(B,rd(B,A)). [para(213(a,1),4(a,1,1))].
% 18.47/18.77 250 mult(mult(A,ld(B,rd(B,C))),C) = A. [para(213(a,1),13(a,1,2,2)),rewrite([1(3),3(2)]),flip(a)].
% 18.47/18.77 251 mult(A,mult(ld(ld(A,A),B),A)) = ld(ld(C,rd(C,A)),mult(B,A)). [para(213(a,1),18(a,1,2,1,1))].
% 18.47/18.77 259 mult(mult(A,ld(B,rd(B,C))),rd(C,ld(B,rd(B,C)))) = rd(mult(A,ld(C,C)),ld(B,rd(B,C))). [para(213(a,1),41(a,1,1,2)),flip(a)].
% 18.47/18.77 320 ld(mult(A,mult(ld(A,B),B)),mult(B,A)) = ld(B,A). [para(34(a,1),214(a,2,1)),rewrite([211(3),4(5)]),flip(a)].
% 18.47/18.77 321 mult(mult(A,B),ld(mult(C,B),C)) = A. [para(214(a,1),41(a,2,2)),rewrite([1(2),4(2)]),flip(a)].
% 18.47/18.77 322 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = rd(ld(C,C),C). [para(16(a,1),214(a,2,1)),flip(a)].
% 18.47/18.77 326 ld(mult(A,B),A) = ld(mult(C,B),C). [para(214(a,1),214(a,1))].
% 18.47/18.77 328 mult(A,rd(ld(B,B),B)) = rd(A,B). [para(246(a,2),1(a,1,2))].
% 18.47/18.77 349 rd(A,ld(B,rd(B,C))) = mult(A,C). [para(3(a,1),250(a,1,1)),flip(a)].
% 18.47/18.77 350 mult(A,ld(B,rd(B,C))) = rd(A,C). [para(250(a,1),4(a,1,1)),flip(a)].
% 18.47/18.77 353 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(9(a,1),250(a,1,1,2,2))].
% 18.47/18.77 357 mult(mult(A,ld(B,B)),B) = mult(rd(A,B),mult(B,B)). [back_rewrite(259),rewrite([350(3),349(4),349(8)]),flip(a)].
% 18.47/18.77 392 mult(A,ld(mult(B,C),B)) = rd(A,C). [para(3(a,1),321(a,1,1))].
% 18.47/18.77 416 ld(mult(A,ld(B,C)),A) = ld(C,B). [para(1(a,1),326(a,1,1)),flip(a)].
% 18.47/18.77 417 ld(mult(mult(A,B),C),rd(A,C)) = ld(mult(D,mult(C,mult(B,C))),D). [para(13(a,1),326(a,1,1))].
% 18.47/18.77 469 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(9(a,1),349(a,1,2,2))].
% 18.47/18.77 518 mult(mult(A,mult(B,ld(C,D))),ld(D,C)) = mult(mult(A,ld(C,D)),mult(ld(D,C),B)). [para(353(a,1),13(a,1,2,2)),rewrite([469(2)]),flip(a)].
% 18.47/18.77 519 ld(mult(A,ld(B,C)),mult(D,ld(C,B))) = mult(ld(C,B),mult(ld(A,D),ld(C,B))). [para(353(a,1),18(a,1,2,1,1)),flip(a)].
% 18.47/18.77 536 rd(A,mult(ld(B,C),mult(D,ld(B,C)))) = mult(A,ld(mult(mult(C,D),ld(B,C)),B)). [para(10(a,1),392(a,1,2,1)),flip(a)].
% 18.47/18.77 558 mult(mult(A,mult(ld(B,C),D)),ld(C,B)) = mult(mult(A,ld(B,C)),mult(D,ld(C,B))). [para(469(a,1),41(a,1)),rewrite([469(9)])].
% 18.47/18.77 602 mult(ld(A,B),mult(ld(C,A),ld(A,B))) = ld(mult(C,ld(B,A)),B). [para(1(a,1),45(a,1,2)),rewrite([469(2)]),flip(a)].
% 18.47/18.77 603 mult(A,mult(ld(B,rd(C,A)),A)) = ld(rd(B,A),C). [para(3(a,1),45(a,1,2)),flip(a)].
% 18.47/18.77 654 rd(rd(A,rd(B,C)),C) = rd(mult(A,C),mult(C,B)). [para(74(a,1),4(a,1,1)),flip(a)].
% 18.47/18.77 665 rd(rd(rd(A,B),C),B) = rd(A,mult(B,mult(C,B))). [para(3(a,1),112(a,1,1)),flip(a)].
% 18.47/18.77 691 mult(rd(mult(A,ld(B,C)),D),ld(B,C)) = mult(A,ld(mult(mult(B,D),ld(C,B)),C)). [para(353(a,1),112(a,1,1)),rewrite([536(5),469(10)]),flip(a)].
% 18.47/18.77 775 ld(mult(A,B),rd(mult(A,C),B)) = rd(ld(B,C),B). [para(144(a,1),2(a,1,2))].
% 18.47/18.77 1065 rd(mult(A,mult(B,A)),A) = ld(rd(ld(A,A),A),B). [para(201(a,1),328(a,1)),rewrite([328(6),328(8),665(6),8(7)]),flip(a)].
% 18.47/18.77 1067 mult(ld(ld(A,B),C),ld(B,A)) = mult(ld(B,A),mult(C,ld(B,A))). [para(201(a,1),353(a,1,1)),rewrite([691(9),416(10),35(8)])].
% 18.47/18.77 1068 mult(mult(ld(A,B),ld(A,B)),mult(ld(B,A),C)) = ld(ld(B,A),C). [para(353(a,1),201(a,1,1,1,1,1)),rewrite([519(6),8(3),518(6)])].
% 18.47/18.77 1074 mult(ld(A,B),mult(mult(ld(B,A),ld(A,B)),ld(A,B))) = ld(ld(B,A),ld(A,B)). [para(211(a,1),34(a,1,2)),rewrite([1068(7),211(7)]),flip(a)].
% 18.47/18.77 1100 ld(mult(A,mult(ld(A,A),A)),mult(A,mult(A,A))) = A. [para(198(a,1),320(a,1,1,2)),rewrite([34(3),2(8)])].
% 18.47/18.77 1144 mult(ld(mult(A,B),A),rd(C,B)) = rd(ld(B,C),B). [para(214(a,2),35(a,1,2,2)),rewrite([328(5),775(4),392(7)]),flip(a)].
% 18.47/18.77 1180 mult(rd(A,A),mult(A,A)) = mult(A,A). [para(1(a,1),357(a,1,1)),flip(a)].
% 18.47/18.77 1182 mult(A,rd(B,B)) = mult(A,ld(B,B)). [para(357(a,1),4(a,1,1)),rewrite([41(4),3(2)])].
% 18.47/18.77 1230 ld(ld(A,B),ld(B,A)) = mult(ld(B,A),ld(B,A)). [para(357(a,1),35(a,1,2)),rewrite([469(2),1(2),2(5),211(7),1074(10)]),flip(a)].
% 18.47/18.77 1234 mult(A,mult(ld(A,A),A)) = mult(A,A). [para(1180(a,1),2(a,1,2)),rewrite([45(3)])].
% 18.47/18.77 1235 rd(mult(A,A),mult(A,A)) = rd(A,A). [para(1180(a,1),4(a,1,1))].
% 18.47/18.77 1275 ld(mult(A,A),mult(A,mult(A,A))) = A. [back_rewrite(1100),rewrite([1234(3)])].
% 18.47/18.77 1335 rd(A,A) = ld(A,A). [para(1182(a,1),2(a,1,2)),rewrite([2(3)]),flip(a)].
% 18.47/18.77 1361 ld(mult(A,A),mult(A,A)) = ld(A,A). [back_rewrite(1235),rewrite([1335(3),1335(4)])].
% 18.47/18.77 1374 mult(ld(A,A),A) = A. [para(1335(a,1),3(a,1,1))].
% 18.47/18.77 1377 mult(ld(A,ld(A,A)),A) = ld(A,A). [para(1335(a,1),213(a,1,1,2))].
% 18.47/18.77 1379 rd(ld(A,A),A) = ld(A,ld(A,A)). [para(1335(a,1),246(a,2,2))].
% 18.47/18.77 1386 mult(mult(ld(mult(A,B),mult(A,B)),A),rd(B,A)) = rd(mult(A,B),A). [para(1335(a,1),146(a,1,1,1))].
% 18.47/18.77 1388 ld(rd(A,B),rd(A,B)) = mult(rd(A,mult(B,A)),B). [para(1335(a,1),161(a,2)),rewrite([3(2)]),flip(a)].
% 18.47/18.77 1434 rd(mult(A,mult(B,A)),A) = ld(ld(A,ld(A,A)),B). [back_rewrite(1065),rewrite([1379(5)])].
% 18.47/18.77 1470 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = ld(C,ld(C,C)). [back_rewrite(322),rewrite([1379(10)])].
% 18.47/18.77 1489 mult(rd(A,B),mult(B,B)) = mult(mult(A,B),ld(B,B)). [para(1374(a,1),28(a,2,2)),rewrite([469(2),1(2),469(5),357(6)]),flip(a)].
% 18.47/18.77 1498 ld(ld(A,B),mult(ld(B,A),ld(A,B))) = ld(B,A). [para(1374(a,1),416(a,1,1)),rewrite([211(4)])].
% 18.47/18.77 1547 mult(mult(A,ld(B,B)),B) = mult(mult(A,B),ld(B,B)). [back_rewrite(357),rewrite([1489(6)])].
% 18.47/18.77 1611 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1275(a,1),1(a,1,2))].
% 18.47/18.77 1630 mult(ld(A,A),ld(A,A)) = ld(A,A). [para(350(a,1),1361(a,1,1)),rewrite([350(8),1388(7),350(5),1335(3),469(4),1547(5),213(3),211(8),8(5),350(6),1335(4)])].
% 18.47/18.77 1642 mult(ld(A,ld(A,A)),mult(A,mult(B,A))) = mult(mult(ld(A,A),B),A). [para(1377(a,1),6(a,1,1,1)),flip(a)].
% 18.47/18.77 1849 ld(ld(A,ld(A,A)),A) = mult(A,A). [para(1611(a,1),4(a,1,1)),rewrite([1434(3)])].
% 18.47/18.77 1934 mult(ld(A,ld(B,B)),mult(ld(B,B),ld(A,ld(B,B)))) = ld(A,mult(ld(B,B),ld(A,ld(B,B)))). [para(1630(a,1),35(a,1,2,1)),flip(a)].
% 18.47/18.77 1943 rd(ld(mult(A,B),A),B) = ld(B,ld(mult(A,B),A)). [para(392(a,1),1849(a,2)),rewrite([211(7),2(4),392(5),1335(3),212(4)]),flip(a)].
% 18.47/18.77 2510 mult(rd(A,mult(B,ld(C,A))),ld(C,A)) = rd(C,mult(ld(A,C),B)). [para(1(a,1),654(a,2,1)),rewrite([469(2),469(5)])].
% 18.47/18.77 3714 mult(ld(A,ld(mult(B,A),B)),mult(A,C)) = ld(A,C). [para(1144(a,1),28(a,1,1)),rewrite([3(3),1943(4)]),flip(a)].
% 18.47/18.77 4421 ld(mult(A,ld(B,C)),mult(A,ld(B,C))) = mult(rd(A,mult(ld(C,B),A)),ld(C,B)). [para(469(a,1),1388(a,1,1)),rewrite([469(4)])].
% 18.47/18.77 4432 mult(A,mult(mult(rd(B,mult(A,B)),A),A)) = ld(rd(rd(B,A),A),B). [para(1388(a,1),603(a,1,2,1))].
% 18.47/18.77 5295 ld(ld(A,B),mult(C,ld(A,B))) = mult(mult(ld(B,A),C),ld(A,B)). [para(353(a,1),1434(a,1,1,2)),rewrite([469(4),211(8),1498(9)]),flip(a)].
% 18.47/18.77 5334 mult(ld(A,A),mult(ld(A,A),B)) = ld(ld(A,A),B). [para(1230(a,1),1434(a,2,1,2)),rewrite([469(6),518(6),1630(3),1630(8),211(7),1630(7)])].
% 18.47/18.77 10538 mult(ld(A,ld(mult(B,A),B)),C) = ld(A,ld(A,C)). [para(1(a,1),3714(a,1,2))].
% 18.47/18.77 13074 ld(ld(A,B),ld(ld(A,B),C)) = mult(mult(ld(B,A),ld(B,A)),C). [para(1(a,1),10538(a,1,1,2,1)),rewrite([1230(3)]),flip(a)].
% 18.47/18.77 23939 mult(ld(A,A),rd(B,mult(ld(A,A),B))) = ld(B,B). [para(353(a,1),4432(a,1,2)),rewrite([469(7),469(9),353(9)])].
% 18.47/18.77 23971 mult(ld(A,ld(B,B)),ld(ld(B,B),A)) = mult(ld(B,B),rd(ld(ld(B,B),A),A)). [para(1(a,1),23939(a,1,2,2)),rewrite([211(10)]),flip(a)].
% 18.47/18.77 23972 rd(A,mult(ld(B,B),A)) = ld(ld(B,B),ld(A,A)). [para(23939(a,1),2(a,1,2)),flip(a)].
% 18.47/18.77 23985 ld(ld(ld(A,A),ld(B,B)),ld(A,A)) = ld(B,B). [para(23939(a,1),221(a,2,2)),rewrite([23972(3),23972(6),23972(9),211(10),23971(10),469(9),23972(15),602(17),558(11),1(5),1(6),416(5),23972(4),416(6)]),flip(a)].
% 18.47/18.77 23986 mult(ld(A,A),mult(ld(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(23939(a,1),236(a,1,1,1)),rewrite([23972(4),416(6),13074(5),1630(3),23972(6),34(7),23972(10),23972(14),23972(17),211(18),23971(18),469(17),2(19),2(16)])].
% 18.47/18.77 23988 mult(ld(ld(A,A),ld(B,B)),ld(B,B)) = ld(A,A). [para(23939(a,1),251(a,2,2)),rewrite([23972(3),23972(6),23972(9),211(10),23971(10),469(9),23986(10),23972(9),23971(10),469(9),23986(10),23972(8),469(9),2(10),23985(10)])].
% 18.47/18.77 23990 ld(ld(A,A),mult(ld(B,B),ld(ld(A,A),ld(B,B)))) = ld(B,B). [para(23939(a,1),417(a,2,1,2,2)),rewrite([23972(5),23972(9),469(10),519(11),416(6),1934(9),23972(10),23988(12),416(10)])].
% 18.47/18.77 23993 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = ld(ld(A,A),ld(B,B)). [para(23939(a,1),178(a,1,2,2,2)),rewrite([23972(4),23972(7),23972(15),23972(21),23988(23),519(21),1470(18),211(11),23971(11),469(10),23988(10),1630(7),23985(6),23972(8)])].
% 18.47/18.77 23994 ld(ld(A,A),ld(B,B)) = ld(B,B). [para(23939(a,1),179(a,1,1,2,2)),rewrite([23972(5),23988(7),353(4),23972(4),23972(8),1067(10),23993(10),1(9),23972(8),1934(10),23990(8),23993(5),2(5),23972(7),1067(9),23993(9),1(8)])].
% 18.47/18.77 24000 mult(mult(ld(A,A),ld(B,B)),ld(A,A)) = ld(A,A). [para(23939(a,1),1386(a,1,1,1,1)),rewrite([23972(5),23994(5),5295(5),6(7),23993(6),23994(4),1630(3),23972(4),23994(4),469(4),5334(5),23994(3),23972(5),23994(5),469(6)]),flip(a)].
% 18.47/18.77 24001 mult(ld(A,A),ld(B,B)) = ld(A,A). [para(23939(a,1),1386(a,2,1)),rewrite([23972(4),23994(4),23972(7),23994(7),4421(7),23972(5),23994(4),23994(3),24000(5),23972(4),23994(4),469(4),23993(5),23994(3),469(4)]),flip(a)].
% 18.47/18.77 24009 mult(ld(A,A),B) = B. [para(23939(a,1),1642(a,2,1)),rewrite([23972(5),23994(5),1642(6),24001(3),1374(2)]),flip(a)].
% 18.47/18.77 24023 mult(A,ld(B,B)) = A. [para(23939(a,1),2510(a,2,2)),rewrite([24009(2),1335(1),24009(3),469(2),1(2),1(2),469(2)]),flip(a)].
% 18.47/18.77 24024 $F # answer(goal). [resolve(24023,a,7,a)].
% 18.47/18.77
% 18.47/18.77 % SZS output end Refutation
% 18.47/18.77 ============================== end of proof ==========================
% 18.47/18.77
% 18.47/18.77 ============================== STATISTICS ============================
% 18.47/18.77
% 18.47/18.77 Given=734. Generated=744793. Kept=24022. proofs=1.
% 18.47/18.77 Usable=698. Sos=9999. Demods=8634. Limbo=52, Disabled=13278. Hints=0.
% 18.47/18.77 Megabytes=27.55.
% 18.47/18.77 User_CPU=17.42, System_CPU=0.43, Wall_clock=18.
% 18.47/18.77
% 18.47/18.77 ============================== end of statistics =====================
% 18.47/18.77
% 18.47/18.77 ============================== end of search =========================
% 18.47/18.77
% 18.47/18.77 THEOREM PROVED
% 18.47/18.77 % SZS status Unsatisfiable
% 18.47/18.77
% 18.47/18.77 Exiting with 1 proof.
% 18.47/18.77
% 18.47/18.77 Process 22366 exit (max_proofs) Mon Jun 13 13:53:30 2022
% 18.47/18.77 Prover9 interrupted
%------------------------------------------------------------------------------