TSTP Solution File: GRP655-11 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP655-11 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 19.94s 20.22s
% Output : Refutation 19.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP655-11 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.32 % Computer : n011.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 09:48:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 19.94/20.22 ============================== Prover9 ===============================
% 19.94/20.22 Prover9 (32) version 2009-11A, November 2009.
% 19.94/20.22 Process 13262 was started by sandbox2 on n011.cluster.edu,
% 19.94/20.22 Tue Jun 14 09:48:20 2022
% 19.94/20.22 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13109_n011.cluster.edu".
% 19.94/20.22 ============================== end of head ===========================
% 19.94/20.22
% 19.94/20.22 ============================== INPUT =================================
% 19.94/20.22
% 19.94/20.22 % Reading from file /tmp/Prover9_13109_n011.cluster.edu
% 19.94/20.22
% 19.94/20.22 set(prolog_style_variables).
% 19.94/20.22 set(auto2).
% 19.94/20.22 % set(auto2) -> set(auto).
% 19.94/20.22 % set(auto) -> set(auto_inference).
% 19.94/20.22 % set(auto) -> set(auto_setup).
% 19.94/20.22 % set(auto_setup) -> set(predicate_elim).
% 19.94/20.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 19.94/20.22 % set(auto) -> set(auto_limits).
% 19.94/20.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 19.94/20.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 19.94/20.22 % set(auto) -> set(auto_denials).
% 19.94/20.22 % set(auto) -> set(auto_process).
% 19.94/20.22 % set(auto2) -> assign(new_constants, 1).
% 19.94/20.22 % set(auto2) -> assign(fold_denial_max, 3).
% 19.94/20.22 % set(auto2) -> assign(max_weight, "200.000").
% 19.94/20.22 % set(auto2) -> assign(max_hours, 1).
% 19.94/20.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 19.94/20.22 % set(auto2) -> assign(max_seconds, 0).
% 19.94/20.22 % set(auto2) -> assign(max_minutes, 5).
% 19.94/20.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 19.94/20.22 % set(auto2) -> set(sort_initial_sos).
% 19.94/20.22 % set(auto2) -> assign(sos_limit, -1).
% 19.94/20.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 19.94/20.22 % set(auto2) -> assign(max_megs, 400).
% 19.94/20.22 % set(auto2) -> assign(stats, some).
% 19.94/20.22 % set(auto2) -> clear(echo_input).
% 19.94/20.22 % set(auto2) -> set(quiet).
% 19.94/20.22 % set(auto2) -> clear(print_initial_clauses).
% 19.94/20.22 % set(auto2) -> clear(print_given).
% 19.94/20.22 assign(lrs_ticks,-1).
% 19.94/20.22 assign(sos_limit,10000).
% 19.94/20.22 assign(order,kbo).
% 19.94/20.22 set(lex_order_vars).
% 19.94/20.22 clear(print_given).
% 19.94/20.22
% 19.94/20.22 % formulas(sos). % not echoed (6 formulas)
% 19.94/20.22
% 19.94/20.22 ============================== end of input ==========================
% 19.94/20.22
% 19.94/20.22 % From the command line: assign(max_seconds, 300).
% 19.94/20.22
% 19.94/20.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 19.94/20.22
% 19.94/20.22 % Formulas that are not ordinary clauses:
% 19.94/20.22
% 19.94/20.22 ============================== end of process non-clausal formulas ===
% 19.94/20.22
% 19.94/20.22 ============================== PROCESS INITIAL CLAUSES ===============
% 19.94/20.22
% 19.94/20.22 ============================== PREDICATE ELIMINATION =================
% 19.94/20.22
% 19.94/20.22 ============================== end predicate elimination =============
% 19.94/20.22
% 19.94/20.22 Auto_denials:
% 19.94/20.22 % copying label goal to answer in negative clause
% 19.94/20.22
% 19.94/20.22 Term ordering decisions:
% 19.94/20.22 Function symbol KB weights: x0=1. x1=1. mult=1. ld=1. rd=1.
% 19.94/20.22
% 19.94/20.22 ============================== end of process initial clauses ========
% 19.94/20.22
% 19.94/20.22 ============================== CLAUSES FOR SEARCH ====================
% 19.94/20.22
% 19.94/20.22 ============================== end of clauses for search =============
% 19.94/20.22
% 19.94/20.22 ============================== SEARCH ================================
% 19.94/20.22
% 19.94/20.22 % Starting search at 0.01 seconds.
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=95.000, iters=3360
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=83.000, iters=3339
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=79.000, iters=3347
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=71.000, iters=3385
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=67.000, iters=3345
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=59.000, iters=3377
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=55.000, iters=3404
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=51.000, iters=3348
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=47.000, iters=3343
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=43.000, iters=3343
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=39.000, iters=3334
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=35.000, iters=3347
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=31.000, iters=3395
% 19.94/20.22
% 19.94/20.22 Low Water (displace): id=4347, wt=183.000
% 19.94/20.22
% 19.94/20.22 Low Water (displace): id=4365, wt=151.000
% 19.94/20.22
% 19.94/20.22 Low Water (displace): id=6130, wt=147.000
% 19.94/20.22
% 19.94/20.22 Low Water (displace): id=12610, wt=23.000
% 19.94/20.22
% 19.94/20.22 Low Water (displace): id=13169, wt=19.000
% 19.94/20.22
% 19.94/20.22 Low Water (keep): wt=27.000, iters=3371
% 19.94/20.22
% 19.94/20.22 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 42 (0.00 of 7.76 sec).
% 19.94/20.22
% 19.94/20.22 ============================== PROOF =================================
% 19.94/20.22 % SZS status Unsatisfiable
% 19.94/20.22 % SZS output start Refutation
% 19.94/20.22
% 19.94/20.22 % Proof 1 at 18.78 (+ 0.47) seconds: goal.
% 19.94/20.22 % Length of proof is 121.
% 19.94/20.22 % Level of proof is 27.
% 19.94/20.22 % Maximum clause weight is 31.000.
% 19.94/20.22 % Given clauses 735.
% 19.94/20.22
% 19.94/20.22 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 19.94/20.22 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 19.94/20.22 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 19.94/20.22 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 19.94/20.22 5 mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B) # label(f05) # label(axiom). [assumption].
% 19.94/20.22 6 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [copy(5),flip(a)].
% 19.94/20.22 7 mult(x0,rd(x1,x1)) != x0 # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 19.94/20.22 8 ld(rd(A,B),A) = B. [para(3(a,1),2(a,1,2))].
% 19.94/20.22 9 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 19.94/20.22 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)].
% 19.94/20.22 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)].
% 19.94/20.22 12 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,B)))) = B. [para(6(a,1),2(a,1,2))].
% 19.94/20.22 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)].
% 19.94/20.22 14 rd(mult(A,mult(B,mult(C,B))),B) = mult(mult(A,B),C). [para(6(a,1),4(a,1,1))].
% 19.94/20.22 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))].
% 19.94/20.22 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))].
% 19.94/20.22 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)].
% 19.94/20.22 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)].
% 19.94/20.22 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)].
% 19.94/20.22 29 rd(mult(mult(A,B),C),mult(C,mult(B,C))) = rd(A,C). [para(13(a,1),4(a,1,1))].
% 19.94/20.22 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)].
% 19.94/20.22 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))].
% 19.94/20.22 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))].
% 19.94/20.22 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)].
% 19.94/20.22 44 ld(A,ld(B,mult(C,A))) = mult(ld(mult(B,A),C),A). [para(18(a,1),2(a,1,2))].
% 19.94/20.22 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)].
% 19.94/20.22 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)].
% 19.94/20.22 112 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B). [para(3(a,1),29(a,1,1,1))].
% 19.94/20.22 144 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)].
% 19.94/20.22 146 mult(mult(rd(A,mult(B,C)),B),rd(C,B)) = rd(A,B). [para(3(a,1),41(a,1,1)),flip(a)].
% 19.94/20.22 161 mult(rd(A,mult(B,mult(C,B))),B) = rd(rd(A,B),C). [para(42(a,1),4(a,1,1)),flip(a)].
% 19.94/20.22 178 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))].
% 19.94/20.22 179 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)])].
% 19.94/20.22 198 mult(ld(mult(A,B),A),B) = ld(B,B). [para(2(a,1),44(a,1,2)),flip(a)].
% 19.94/20.22 201 mult(ld(mult(rd(mult(A,B),C),B),A),B) = ld(B,C). [para(8(a,1),44(a,1,2)),flip(a)].
% 19.94/20.22 211 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)].
% 19.94/20.22 212 ld(ld(mult(A,B),A),ld(B,B)) = B. [para(198(a,1),2(a,1,2))].
% 19.94/20.22 213 mult(ld(A,rd(A,B)),B) = ld(B,B). [para(3(a,1),198(a,1,1,1))].
% 19.94/20.22 214 rd(ld(A,A),A) = ld(mult(B,A),B). [para(198(a,1),4(a,1,1))].
% 19.94/20.22 221 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))].
% 19.94/20.22 236 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)].
% 19.94/20.22 246 rd(ld(A,A),A) = ld(B,rd(B,A)). [para(213(a,1),4(a,1,1))].
% 19.94/20.22 250 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)].
% 19.94/20.22 251 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))].
% 19.94/20.22 259 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)].
% 19.94/20.22 320 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)].
% 19.94/20.22 321 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)].
% 19.94/20.22 322 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)].
% 19.94/20.22 326 ld(mult(A,B),A) = ld(mult(C,B),C). [para(214(a,1),214(a,1))].
% 19.94/20.22 328 mult(A,rd(ld(B,B),B)) = rd(A,B). [para(246(a,2),1(a,1,2))].
% 19.94/20.22 349 rd(A,ld(B,rd(B,C))) = mult(A,C). [para(3(a,1),250(a,1,1)),flip(a)].
% 19.94/20.22 350 mult(A,ld(B,rd(B,C))) = rd(A,C). [para(250(a,1),4(a,1,1)),flip(a)].
% 19.94/20.22 353 mult(mult(A,ld(B,C)),ld(C,B)) = A. [para(9(a,1),250(a,1,1,2,2))].
% 19.94/20.22 357 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)].
% 19.94/20.22 392 mult(A,ld(mult(B,C),B)) = rd(A,C). [para(3(a,1),321(a,1,1))].
% 19.94/20.22 416 ld(mult(A,ld(B,C)),A) = ld(C,B). [para(1(a,1),326(a,1,1)),flip(a)].
% 19.94/20.22 417 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))].
% 19.94/20.22 469 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(9(a,1),349(a,1,2,2))].
% 19.94/20.22 518 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)].
% 19.94/20.22 519 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)].
% 19.94/20.22 536 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)].
% 19.94/20.22 558 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)])].
% 19.94/20.22 602 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)].
% 19.94/20.22 603 mult(A,mult(ld(B,rd(C,A)),A)) = ld(rd(B,A),C). [para(3(a,1),45(a,1,2)),flip(a)].
% 19.94/20.22 654 rd(rd(A,rd(B,C)),C) = rd(mult(A,C),mult(C,B)). [para(74(a,1),4(a,1,1)),flip(a)].
% 19.94/20.22 665 rd(rd(rd(A,B),C),B) = rd(A,mult(B,mult(C,B))). [para(3(a,1),112(a,1,1)),flip(a)].
% 19.94/20.22 691 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)].
% 19.94/20.22 775 ld(mult(A,B),rd(mult(A,C),B)) = rd(ld(B,C),B). [para(144(a,1),2(a,1,2))].
% 19.94/20.22 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)].
% 19.94/20.22 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)])].
% 19.94/20.22 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)])].
% 19.94/20.22 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)].
% 19.94/20.22 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)])].
% 19.94/20.22 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)].
% 19.94/20.22 1180 mult(rd(A,A),mult(A,A)) = mult(A,A). [para(1(a,1),357(a,1,1)),flip(a)].
% 19.94/20.22 1182 mult(A,rd(B,B)) = mult(A,ld(B,B)). [para(357(a,1),4(a,1,1)),rewrite([41(4),3(2)])].
% 19.94/20.22 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)].
% 19.94/20.22 1231 mult(x0,ld(x1,x1)) != x0 # answer(goal). [back_rewrite(7),rewrite([1182(5)])].
% 19.94/20.22 1235 mult(A,mult(ld(A,A),A)) = mult(A,A). [para(1180(a,1),2(a,1,2)),rewrite([45(3)])].
% 19.94/20.22 1236 rd(mult(A,A),mult(A,A)) = rd(A,A). [para(1180(a,1),4(a,1,1))].
% 19.94/20.22 1276 ld(mult(A,A),mult(A,mult(A,A))) = A. [back_rewrite(1100),rewrite([1235(3)])].
% 19.94/20.22 1336 rd(A,A) = ld(A,A). [para(1182(a,1),2(a,1,2)),rewrite([2(3)]),flip(a)].
% 19.94/20.22 1362 ld(mult(A,A),mult(A,A)) = ld(A,A). [back_rewrite(1236),rewrite([1336(3),1336(4)])].
% 19.94/20.22 1375 mult(ld(A,A),A) = A. [para(1336(a,1),3(a,1,1))].
% 19.94/20.22 1378 mult(ld(A,ld(A,A)),A) = ld(A,A). [para(1336(a,1),213(a,1,1,2))].
% 19.94/20.22 1380 rd(ld(A,A),A) = ld(A,ld(A,A)). [para(1336(a,1),246(a,2,2))].
% 19.94/20.22 1387 mult(mult(ld(mult(A,B),mult(A,B)),A),rd(B,A)) = rd(mult(A,B),A). [para(1336(a,1),146(a,1,1,1))].
% 19.94/20.22 1389 ld(rd(A,B),rd(A,B)) = mult(rd(A,mult(B,A)),B). [para(1336(a,1),161(a,2)),rewrite([3(2)]),flip(a)].
% 19.94/20.22 1435 rd(mult(A,mult(B,A)),A) = ld(ld(A,ld(A,A)),B). [back_rewrite(1065),rewrite([1380(5)])].
% 19.94/20.22 1471 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([1380(10)])].
% 19.94/20.22 1490 mult(rd(A,B),mult(B,B)) = mult(mult(A,B),ld(B,B)). [para(1375(a,1),28(a,2,2)),rewrite([469(2),1(2),469(5),357(6)]),flip(a)].
% 19.94/20.22 1499 ld(ld(A,B),mult(ld(B,A),ld(A,B))) = ld(B,A). [para(1375(a,1),416(a,1,1)),rewrite([211(4)])].
% 19.94/20.22 1548 mult(mult(A,ld(B,B)),B) = mult(mult(A,B),ld(B,B)). [back_rewrite(357),rewrite([1490(6)])].
% 19.94/20.22 1612 mult(mult(A,A),A) = mult(A,mult(A,A)). [para(1276(a,1),1(a,1,2))].
% 19.94/20.22 1631 mult(ld(A,A),ld(A,A)) = ld(A,A). [para(350(a,1),1362(a,1,1)),rewrite([350(8),1389(7),350(5),1336(3),469(4),1548(5),213(3),211(8),8(5),350(6),1336(4)])].
% 19.94/20.22 1643 mult(ld(A,ld(A,A)),mult(A,mult(B,A))) = mult(mult(ld(A,A),B),A). [para(1378(a,1),6(a,1,1,1)),flip(a)].
% 19.94/20.22 1850 ld(ld(A,ld(A,A)),A) = mult(A,A). [para(1612(a,1),4(a,1,1)),rewrite([1435(3)])].
% 19.94/20.22 1935 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(1631(a,1),35(a,1,2,1)),flip(a)].
% 19.94/20.22 1944 rd(ld(mult(A,B),A),B) = ld(B,ld(mult(A,B),A)). [para(392(a,1),1850(a,2)),rewrite([211(7),2(4),392(5),1336(3),212(4)]),flip(a)].
% 19.94/20.22 2511 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)])].
% 19.94/20.22 3715 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),1944(4)]),flip(a)].
% 19.94/20.22 4422 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),1389(a,1,1)),rewrite([469(4)])].
% 19.94/20.22 4433 mult(A,mult(mult(rd(B,mult(A,B)),A),A)) = ld(rd(rd(B,A),A),B). [para(1389(a,1),603(a,1,2,1))].
% 19.94/20.22 5296 ld(ld(A,B),mult(C,ld(A,B))) = mult(mult(ld(B,A),C),ld(A,B)). [para(353(a,1),1435(a,1,1,2)),rewrite([469(4),211(8),1499(9)]),flip(a)].
% 19.94/20.22 5335 mult(ld(A,A),mult(ld(A,A),B)) = ld(ld(A,A),B). [para(1230(a,1),1435(a,2,1,2)),rewrite([469(6),518(6),1631(3),1631(8),211(7),1631(7)])].
% 19.94/20.22 10539 mult(ld(A,ld(mult(B,A),B)),C) = ld(A,ld(A,C)). [para(1(a,1),3715(a,1,2))].
% 19.94/20.22 13075 ld(ld(A,B),ld(ld(A,B),C)) = mult(mult(ld(B,A),ld(B,A)),C). [para(1(a,1),10539(a,1,1,2,1)),rewrite([1230(3)]),flip(a)].
% 19.94/20.22 23940 mult(ld(A,A),rd(B,mult(ld(A,A),B))) = ld(B,B). [para(353(a,1),4433(a,1,2)),rewrite([469(7),469(9),353(9)])].
% 19.94/20.22 23972 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),23940(a,1,2,2)),rewrite([211(10)]),flip(a)].
% 19.94/20.22 23973 rd(A,mult(ld(B,B),A)) = ld(ld(B,B),ld(A,A)). [para(23940(a,1),2(a,1,2)),flip(a)].
% 19.94/20.22 23986 ld(ld(ld(A,A),ld(B,B)),ld(A,A)) = ld(B,B). [para(23940(a,1),221(a,2,2)),rewrite([23973(3),23973(6),23973(9),211(10),23972(10),469(9),23973(15),602(17),558(11),1(5),1(6),416(5),23973(4),416(6)]),flip(a)].
% 19.94/20.22 23987 mult(ld(A,A),mult(ld(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B). [para(23940(a,1),236(a,1,1,1)),rewrite([23973(4),416(6),13075(5),1631(3),23973(6),34(7),23973(10),23973(14),23973(17),211(18),23972(18),469(17),2(19),2(16)])].
% 19.94/20.22 23989 mult(ld(ld(A,A),ld(B,B)),ld(B,B)) = ld(A,A). [para(23940(a,1),251(a,2,2)),rewrite([23973(3),23973(6),23973(9),211(10),23972(10),469(9),23987(10),23973(9),23972(10),469(9),23987(10),23973(8),469(9),2(10),23986(10)])].
% 19.94/20.22 23991 ld(ld(A,A),mult(ld(B,B),ld(ld(A,A),ld(B,B)))) = ld(B,B). [para(23940(a,1),417(a,2,1,2,2)),rewrite([23973(5),23973(9),469(10),519(11),416(6),1935(9),23973(10),23989(12),416(10)])].
% 19.94/20.22 23994 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = ld(ld(A,A),ld(B,B)). [para(23940(a,1),178(a,1,2,2,2)),rewrite([23973(4),23973(7),23973(15),23973(21),23989(23),519(21),1471(18),211(11),23972(11),469(10),23989(10),1631(7),23986(6),23973(8)])].
% 19.94/20.22 23995 ld(ld(A,A),ld(B,B)) = ld(B,B). [para(23940(a,1),179(a,1,1,2,2)),rewrite([23973(5),23989(7),353(4),23973(4),23973(8),1067(10),23994(10),1(9),23973(8),1935(10),23991(8),23994(5),2(5),23973(7),1067(9),23994(9),1(8)])].
% 19.94/20.22 24001 mult(mult(ld(A,A),ld(B,B)),ld(A,A)) = ld(A,A). [para(23940(a,1),1387(a,1,1,1,1)),rewrite([23973(5),23995(5),5296(5),6(7),23994(6),23995(4),1631(3),23973(4),23995(4),469(4),5335(5),23995(3),23973(5),23995(5),469(6)]),flip(a)].
% 19.94/20.22 24002 mult(ld(A,A),ld(B,B)) = ld(A,A). [para(23940(a,1),1387(a,2,1)),rewrite([23973(4),23995(4),23973(7),23995(7),4422(7),23973(5),23995(4),23995(3),24001(5),23973(4),23995(4),469(4),23994(5),23995(3),469(4)]),flip(a)].
% 19.94/20.23 24010 mult(ld(A,A),B) = B. [para(23940(a,1),1643(a,2,1)),rewrite([23973(5),23995(5),1643(6),24002(3),1375(2)]),flip(a)].
% 19.94/20.23 24024 mult(A,ld(B,B)) = A. [para(23940(a,1),2511(a,2,2)),rewrite([24010(2),1336(1),24010(3),469(2),1(2),1(2),469(2)]),flip(a)].
% 19.94/20.23 24025 $F # answer(goal). [resolve(24024,a,1231,a)].
% 19.94/20.23
% 19.94/20.23 % SZS output end Refutation
% 19.94/20.23 ============================== end of proof ==========================
% 19.94/20.23
% 19.94/20.23 ============================== STATISTICS ============================
% 19.94/20.23
% 19.94/20.23 Given=735. Generated=744794. Kept=24023. proofs=1.
% 19.94/20.23 Usable=698. Sos=9999. Demods=8634. Limbo=52, Disabled=13279. Hints=0.
% 19.94/20.23 Megabytes=27.55.
% 19.94/20.23 User_CPU=18.78, System_CPU=0.47, Wall_clock=19.
% 19.94/20.23
% 19.94/20.23 ============================== end of statistics =====================
% 19.94/20.23
% 19.94/20.23 ============================== end of search =========================
% 19.94/20.23
% 19.94/20.23 THEOREM PROVED
% 19.94/20.23 % SZS status Unsatisfiable
% 19.94/20.23
% 19.94/20.23 Exiting with 1 proof.
% 19.94/20.23
% 19.94/20.23 Process 13262 exit (max_proofs) Tue Jun 14 09:48:39 2022
% 19.94/20.23 Prover9 interrupted
%------------------------------------------------------------------------------