TSTP Solution File: GRP751-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP751-1 : TPTP v8.1.0. Released v4.0.0.
% 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 11:20:54 EDT 2022
% Result : Unsatisfiable 10.03s 10.30s
% Output : Refutation 10.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP751-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 13 11:39:14 EDT 2022
% 0.14/0.34 % CPUTime :
% 10.03/10.30 ============================== Prover9 ===============================
% 10.03/10.30 Prover9 (32) version 2009-11A, November 2009.
% 10.03/10.30 Process 15625 was started by sandbox2 on n013.cluster.edu,
% 10.03/10.30 Mon Jun 13 11:39:14 2022
% 10.03/10.30 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_15363_n013.cluster.edu".
% 10.03/10.30 ============================== end of head ===========================
% 10.03/10.30
% 10.03/10.30 ============================== INPUT =================================
% 10.03/10.30
% 10.03/10.30 % Reading from file /tmp/Prover9_15363_n013.cluster.edu
% 10.03/10.30
% 10.03/10.30 set(prolog_style_variables).
% 10.03/10.30 set(auto2).
% 10.03/10.30 % set(auto2) -> set(auto).
% 10.03/10.30 % set(auto) -> set(auto_inference).
% 10.03/10.30 % set(auto) -> set(auto_setup).
% 10.03/10.30 % set(auto_setup) -> set(predicate_elim).
% 10.03/10.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 10.03/10.30 % set(auto) -> set(auto_limits).
% 10.03/10.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 10.03/10.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 10.03/10.30 % set(auto) -> set(auto_denials).
% 10.03/10.30 % set(auto) -> set(auto_process).
% 10.03/10.30 % set(auto2) -> assign(new_constants, 1).
% 10.03/10.30 % set(auto2) -> assign(fold_denial_max, 3).
% 10.03/10.30 % set(auto2) -> assign(max_weight, "200.000").
% 10.03/10.30 % set(auto2) -> assign(max_hours, 1).
% 10.03/10.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 10.03/10.30 % set(auto2) -> assign(max_seconds, 0).
% 10.03/10.30 % set(auto2) -> assign(max_minutes, 5).
% 10.03/10.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 10.03/10.30 % set(auto2) -> set(sort_initial_sos).
% 10.03/10.30 % set(auto2) -> assign(sos_limit, -1).
% 10.03/10.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 10.03/10.30 % set(auto2) -> assign(max_megs, 400).
% 10.03/10.30 % set(auto2) -> assign(stats, some).
% 10.03/10.30 % set(auto2) -> clear(echo_input).
% 10.03/10.30 % set(auto2) -> set(quiet).
% 10.03/10.30 % set(auto2) -> clear(print_initial_clauses).
% 10.03/10.30 % set(auto2) -> clear(print_given).
% 10.03/10.30 assign(lrs_ticks,-1).
% 10.03/10.30 assign(sos_limit,10000).
% 10.03/10.30 assign(order,kbo).
% 10.03/10.30 set(lex_order_vars).
% 10.03/10.30 clear(print_given).
% 10.03/10.30
% 10.03/10.30 % formulas(sos). % not echoed (8 formulas)
% 10.03/10.30
% 10.03/10.30 ============================== end of input ==========================
% 10.03/10.30
% 10.03/10.30 % From the command line: assign(max_seconds, 300).
% 10.03/10.30
% 10.03/10.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 10.03/10.30
% 10.03/10.30 % Formulas that are not ordinary clauses:
% 10.03/10.30
% 10.03/10.30 ============================== end of process non-clausal formulas ===
% 10.03/10.30
% 10.03/10.30 ============================== PROCESS INITIAL CLAUSES ===============
% 10.03/10.30
% 10.03/10.30 ============================== PREDICATE ELIMINATION =================
% 10.03/10.30
% 10.03/10.30 ============================== end predicate elimination =============
% 10.03/10.30
% 10.03/10.30 Auto_denials:
% 10.03/10.30 % copying label goals to answer in negative clause
% 10.03/10.30
% 10.03/10.30 Term ordering decisions:
% 10.03/10.30 Function symbol KB weights: a=1. b=1. c=1. mult=1. ld=1. rd=1.
% 10.03/10.30
% 10.03/10.30 ============================== end of process initial clauses ========
% 10.03/10.30
% 10.03/10.30 ============================== CLAUSES FOR SEARCH ====================
% 10.03/10.30
% 10.03/10.30 ============================== end of clauses for search =============
% 10.03/10.30
% 10.03/10.30 ============================== SEARCH ================================
% 10.03/10.30
% 10.03/10.30 % Starting search at 0.01 seconds.
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=79.000, iters=3358
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=71.000, iters=3559
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=67.000, iters=3555
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=59.000, iters=3338
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=55.000, iters=3503
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=51.000, iters=3399
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=47.000, iters=3448
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=43.000, iters=3374
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=39.000, iters=3335
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=35.000, iters=3336
% 10.03/10.30
% 10.03/10.30 Low Water (displace): id=6156, wt=83.000
% 10.03/10.30
% 10.03/10.30 Low Water (displace): id=13950, wt=31.000
% 10.03/10.30
% 10.03/10.30 Low Water (displace): id=14051, wt=27.000
% 10.03/10.30
% 10.03/10.30 Low Water (displace): id=14054, wt=23.000
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=31.000, iters=3350
% 10.03/10.30
% 10.03/10.30 Low Water (displace): id=18487, wt=19.000
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=27.000, iters=3342
% 10.03/10.30
% 10.03/10.30 Low Water (keep): wt=23.000, iters=3371
% 10.03/10.30
% 10.03/10.30 ============================== PROOF =================================
% 10.03/10.30 % SZS status Unsatisfiable
% 10.03/10.30 % SZS output start Refutation
% 10.03/10.30
% 10.03/10.30 % Proof 1 at 9.18 (+ 0.15) seconds: goals.
% 10.03/10.30 % Length of proof is 151.
% 10.03/10.30 % Level of proof is 19.
% 10.03/10.30 % Maximum clause weight is 23.000.
% 10.03/10.30 % Given clauses 376.
% 10.03/10.30
% 10.03/10.30 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 10.03/10.30 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 10.03/10.30 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 10.03/10.30 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 10.03/10.30 5 mult(mult(A,A),mult(B,C)) = mult(mult(A,B),mult(A,C)) # label(f06) # label(axiom). [assumption].
% 10.03/10.30 6 mult(mult(A,B),mult(A,C)) = mult(mult(A,A),mult(B,C)). [copy(5),flip(a)].
% 10.03/10.30 7 mult(mult(A,B),mult(C,C)) = mult(mult(A,C),mult(B,C)) # label(f07) # label(axiom). [assumption].
% 10.03/10.30 8 mult(mult(A,mult(A,A)),mult(B,C)) = mult(mult(A,B),mult(mult(A,A),C)) # label(f05) # label(axiom). [assumption].
% 10.03/10.30 9 mult(a,mult(b,c)) != mult(mult(rd(a,a),b),mult(a,c)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 10.03/10.30 10 mult(mult(rd(a,a),b),mult(a,c)) != mult(a,mult(b,c)) # answer(goals). [copy(9),flip(a)].
% 10.03/10.30 11 ld(rd(A,B),A) = B. [para(3(a,1),2(a,1,2))].
% 10.03/10.30 12 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 10.03/10.30 13 mult(mult(A,A),mult(ld(A,B),C)) = mult(B,mult(A,C)). [para(1(a,1),6(a,1,1)),flip(a)].
% 10.03/10.30 14 mult(mult(A,A),mult(B,ld(A,C))) = mult(mult(A,B),C). [para(1(a,1),6(a,1,2)),flip(a)].
% 10.03/10.30 15 mult(mult(A,B),mult(A,ld(B,C))) = mult(mult(A,A),C). [para(1(a,1),6(a,2,2))].
% 10.03/10.30 19 mult(mult(rd(A,B),rd(A,B)),mult(C,B)) = mult(mult(rd(A,B),C),A). [para(3(a,1),6(a,1,2)),flip(a)].
% 10.03/10.30 31 mult(mult(A,B),mult(ld(A,C),B)) = mult(C,mult(B,B)). [para(1(a,1),7(a,1,1)),flip(a)].
% 10.03/10.30 34 ld(mult(A,B),mult(mult(A,C),mult(B,C))) = mult(C,C). [para(7(a,1),2(a,1,2))].
% 10.03/10.30 36 mult(mult(rd(A,B),C),mult(B,C)) = mult(A,mult(C,C)). [para(3(a,1),7(a,1,1)),flip(a)].
% 10.03/10.30 37 mult(mult(rd(A,B),C),mult(B,B)) = mult(A,mult(C,B)). [para(3(a,1),7(a,2,1))].
% 10.03/10.30 63 ld(mult(A,mult(A,A)),mult(mult(A,B),mult(mult(A,A),C))) = mult(B,C). [para(8(a,1),2(a,1,2))].
% 10.03/10.30 68 rd(mult(mult(A,mult(A,A)),mult(B,C)),mult(mult(A,A),C)) = mult(A,B). [para(8(a,2),4(a,1,1))].
% 10.03/10.30 98 mult(A,mult(B,ld(ld(B,A),C))) = mult(mult(B,B),C). [para(1(a,1),13(a,1,2)),flip(a)].
% 10.03/10.30 99 ld(mult(A,A),mult(B,mult(A,C))) = mult(ld(A,B),C). [para(13(a,1),2(a,1,2))].
% 10.03/10.30 100 rd(mult(A,mult(B,C)),mult(ld(B,A),C)) = mult(B,B). [para(13(a,1),4(a,1,1))].
% 10.03/10.30 115 mult(mult(A,rd(B,ld(A,C))),C) = mult(mult(A,A),B). [para(3(a,1),14(a,1,2)),flip(a)].
% 10.03/10.30 116 rd(mult(mult(A,B),C),mult(B,ld(A,C))) = mult(A,A). [para(14(a,1),4(a,1,1))].
% 10.03/10.30 131 mult(mult(rd(A,B),rd(A,B)),C) = mult(A,mult(rd(A,B),ld(B,C))). [para(3(a,1),15(a,1,1)),flip(a)].
% 10.03/10.30 152 mult(A,mult(rd(A,B),ld(B,mult(C,B)))) = mult(mult(rd(A,B),C),A). [back_rewrite(19),rewrite([131(5)])].
% 10.03/10.30 205 ld(mult(A,B),mult(C,mult(B,B))) = mult(ld(A,C),B). [para(31(a,1),2(a,1,2))].
% 10.03/10.30 206 mult(A,mult(ld(rd(A,B),C),B)) = mult(C,mult(B,B)). [para(3(a,1),31(a,1,1))].
% 10.03/10.30 233 ld(mult(rd(A,B),C),mult(A,mult(C,B))) = mult(B,B). [para(3(a,1),34(a,1,2,1))].
% 10.03/10.30 234 ld(mult(A,rd(B,C)),mult(mult(A,C),B)) = mult(C,C). [para(3(a,1),34(a,1,2,2))].
% 10.03/10.30 263 mult(A,mult(ld(rd(A,B),C),ld(rd(A,B),C))) = mult(C,mult(B,ld(rd(A,B),C))). [para(1(a,1),36(a,1,1)),flip(a)].
% 10.03/10.30 265 mult(mult(rd(A,rd(B,C)),C),B) = mult(A,mult(C,C)). [para(3(a,1),36(a,1,2))].
% 10.03/10.30 266 rd(mult(A,mult(B,B)),mult(C,B)) = mult(rd(A,C),B). [para(36(a,1),4(a,1,1))].
% 10.03/10.30 423 rd(mult(A,mult(B,C)),mult(C,C)) = mult(rd(A,C),B). [para(37(a,1),4(a,1,1))].
% 10.03/10.30 466 ld(A,mult(mult(B,B),C)) = mult(B,ld(ld(B,A),C)). [para(98(a,1),2(a,1,2))].
% 10.03/10.30 498 ld(mult(A,A),mult(B,C)) = mult(ld(A,B),ld(A,C)). [para(1(a,1),99(a,1,2,2))].
% 10.03/10.30 499 mult(ld(A,rd(B,mult(A,C))),C) = ld(mult(A,A),B). [para(3(a,1),99(a,1,2)),flip(a)].
% 10.03/10.30 688 mult(rd(mult(A,B),ld(B,mult(A,C))),C) = mult(B,B). [para(7(a,2),100(a,1,1)),rewrite([266(7)])].
% 10.03/10.30 712 rd(mult(mult(A,A),B),C) = mult(A,rd(B,ld(A,C))). [para(115(a,1),4(a,1,1))].
% 10.03/10.30 748 rd(A,mult(B,ld(C,ld(mult(C,B),A)))) = mult(C,C). [para(1(a,1),116(a,1,1))].
% 10.03/10.30 781 ld(A,mult(B,mult(C,C))) = mult(ld(rd(A,C),B),C). [para(3(a,1),205(a,1,1))].
% 10.03/10.30 782 mult(ld(A,rd(B,mult(C,C))),C) = ld(mult(A,C),B). [para(3(a,1),205(a,1,2)),flip(a)].
% 10.03/10.30 1030 mult(rd(A,ld(ld(rd(B,C),A),B)),C) = mult(ld(rd(B,C),A),ld(rd(B,C),A)). [para(206(a,1),100(a,1,1)),rewrite([266(7)])].
% 10.03/10.30 1037 ld(mult(rd(A,B),rd(C,B)),mult(A,C)) = mult(B,B). [para(3(a,1),233(a,1,2,2))].
% 10.03/10.30 1081 mult(A,ld(rd(mult(A,B),C),mult(C,B))) = mult(C,C). [para(6(a,1),234(a,1,2)),rewrite([466(7),2(4)])].
% 10.03/10.30 1096 mult(A,ld(rd(mult(A,ld(B,C)),B),C)) = mult(B,B). [para(15(a,1),234(a,1,2)),rewrite([466(7),2(5)])].
% 10.03/10.30 1125 rd(mult(A,mult(B,B)),C) = mult(rd(A,rd(C,B)),B). [para(265(a,1),4(a,1,1))].
% 10.03/10.30 1391 rd(mult(A,B),mult(C,C)) = mult(rd(A,C),rd(B,C)). [para(3(a,1),423(a,1,1,2))].
% 10.03/10.30 1393 mult(rd(mult(A,B),C),A) = mult(rd(mult(A,A),C),B). [para(6(a,1),423(a,1,1)),rewrite([1391(5),4(4)]),flip(a)].
% 10.03/10.30 1396 mult(rd(mult(A,A),B),ld(A,C)) = mult(rd(C,B),A). [para(13(a,1),423(a,1,1)),rewrite([1391(4),4(3)]),flip(a)].
% 10.03/10.30 1416 ld(A,mult(mult(B,C),mult(B,D))) = mult(B,ld(ld(B,A),mult(C,D))). [para(6(a,2),466(a,1,2))].
% 10.03/10.30 1424 mult(rd(A,B),ld(ld(rd(A,B),C),mult(B,B))) = ld(C,mult(A,A)). [para(37(a,1),466(a,1,2)),rewrite([3(2)]),flip(a)].
% 10.03/10.30 1443 mult(ld(A,B),ld(A,ld(B,C))) = ld(mult(A,A),C). [para(1(a,1),498(a,1,2)),flip(a)].
% 10.03/10.30 1477 ld(mult(rd(A,B),rd(A,B)),C) = mult(ld(rd(A,B),rd(C,A)),B). [para(3(a,1),499(a,1,1,2,2)),flip(a)].
% 10.03/10.30 1478 rd(ld(mult(A,A),B),C) = ld(A,rd(B,mult(A,C))). [para(499(a,1),4(a,1,1))].
% 10.03/10.30 1814 mult(rd(mult(A,B),ld(B,C)),ld(A,C)) = mult(B,B). [para(1(a,1),688(a,1,1,2,2))].
% 10.03/10.30 1816 mult(rd(A,ld(B,mult(rd(A,B),C))),C) = mult(B,B). [para(3(a,1),688(a,1,1,1))].
% 10.03/10.30 1818 rd(mult(A,B),ld(B,mult(A,C))) = rd(mult(B,B),C). [para(688(a,1),4(a,1,1)),flip(a)].
% 10.03/10.30 1883 rd(mult(mult(A,B),mult(A,C)),D) = mult(A,rd(mult(B,C),ld(A,D))). [para(6(a,2),712(a,1,1))].
% 10.03/10.30 1892 mult(rd(A,B),rd(mult(B,B),ld(rd(A,B),C))) = rd(mult(A,A),C). [para(37(a,1),712(a,1,1)),rewrite([3(2)]),flip(a)].
% 10.03/10.30 1925 rd(A,mult(B,ld(rd(C,B),ld(C,A)))) = mult(rd(C,B),rd(C,B)). [para(3(a,1),748(a,1,2,2,2,1))].
% 10.03/10.30 1932 mult(A,ld(B,ld(mult(B,A),C))) = ld(mult(B,B),C). [para(748(a,1),11(a,1,1)),flip(a)].
% 10.03/10.30 2207 mult(ld(rd(A,B),mult(C,C)),B) = mult(C,ld(ld(C,A),mult(B,B))). [para(6(a,2),781(a,1,2)),rewrite([1416(4)]),flip(a)].
% 10.03/10.30 2235 rd(ld(mult(A,B),C),B) = ld(A,rd(C,mult(B,B))). [para(782(a,1),4(a,1,1))].
% 10.03/10.30 2340 ld(rd(mult(A,B),C),mult(C,B)) = ld(A,mult(C,C)). [para(1081(a,1),2(a,1,2)),flip(a)].
% 10.03/10.30 2737 ld(rd(mult(A,ld(B,C)),B),C) = ld(A,mult(B,B)). [para(1096(a,1),2(a,1,2)),flip(a)].
% 10.03/10.30 2738 mult(rd(A,ld(B,C)),ld(rd(A,B),C)) = mult(B,B). [para(3(a,1),1096(a,1,2,1,1))].
% 10.03/10.30 2758 mult(rd(A,rd(B,ld(C,A))),C) = rd(mult(A,A),B). [para(13(a,1),1125(a,1,1)),rewrite([1(2),1396(8)]),flip(a)].
% 10.03/10.30 3024 mult(rd(mult(rd(A,B),rd(A,B)),C),B) = mult(rd(A,C),rd(A,B)). [para(3(a,1),1393(a,1,1,1)),flip(a)].
% 10.03/10.30 3025 rd(mult(rd(mult(A,A),B),C),A) = rd(mult(A,C),B). [para(1393(a,1),4(a,1,1))].
% 10.03/10.30 3026 rd(mult(rd(mult(A,B),C),A),B) = rd(mult(A,A),C). [para(1393(a,2),4(a,1,1))].
% 10.03/10.30 3279 rd(mult(rd(A,B),C),ld(C,A)) = rd(mult(C,C),B). [para(1396(a,1),4(a,1,1))].
% 10.03/10.30 3288 mult(rd(A,ld(B,mult(C,C))),C) = mult(B,ld(C,A)). [para(12(a,1),1396(a,1,1)),flip(a)].
% 10.03/10.30 3359 mult(ld(rd(A,B),rd(C,A)),B) = mult(B,ld(rd(A,B),ld(A,C))). [para(11(a,1),1443(a,1,1)),rewrite([1477(8)]),flip(a)].
% 10.03/10.30 3398 ld(mult(rd(A,B),rd(A,B)),C) = mult(B,ld(rd(A,B),ld(A,C))). [back_rewrite(1477),rewrite([3359(8)])].
% 10.03/10.30 3557 rd(mult(ld(A,B),ld(A,C)),D) = ld(A,rd(mult(B,C),mult(A,D))). [para(498(a,1),1478(a,1,1))].
% 10.03/10.30 3593 rd(mult(A,B),ld(B,C)) = rd(mult(B,B),ld(A,C)). [para(1814(a,1),4(a,1,1)),flip(a)].
% 10.03/10.30 3681 rd(A,ld(B,mult(rd(A,B),C))) = rd(mult(B,B),C). [para(1816(a,1),4(a,1,1)),flip(a)].
% 10.03/10.30 3688 mult(mult(rd(A,B),rd(A,C)),mult(B,C)) = mult(A,A). [para(1816(a,1),36(a,2)),rewrite([781(4),3359(4),1925(5),3024(5)])].
% 10.03/10.30 4096 ld(rd(mult(A,A),B),mult(C,A)) = ld(A,mult(C,B)). [para(1818(a,1),11(a,1,1))].
% 10.03/10.30 4180 ld(A,ld(mult(B,B),C)) = ld(B,ld(mult(B,A),C)). [para(1932(a,1),2(a,1,2))].
% 10.03/10.30 4231 mult(rd(A,B),ld(C,mult(B,B))) = mult(B,ld(C,A)). [para(234(a,1),1932(a,1,2,2)),rewrite([498(8),2(6)])].
% 10.03/10.30 4285 mult(A,ld(ld(rd(B,A),C),B)) = ld(C,mult(B,B)). [back_rewrite(1424),rewrite([4231(6)])].
% 10.03/10.30 4361 ld(rd(A,B),rd(C,mult(B,B))) = rd(ld(A,C),B). [para(3(a,1),2235(a,1,1,1)),flip(a)].
% 10.03/10.30 4894 ld(rd(A,B),mult(C,C)) = ld(rd(A,C),mult(C,B)). [para(3(a,1),2340(a,1,1,1)),flip(a)].
% 10.03/10.30 4907 rd(mult(A,B),ld(C,mult(A,A))) = rd(mult(C,B),A). [para(2340(a,1),12(a,1,2))].
% 10.03/10.30 5591 rd(mult(A,ld(B,C)),B) = rd(C,ld(A,mult(B,B))). [para(2737(a,1),12(a,1,2)),flip(a)].
% 10.03/10.30 5631 rd(mult(A,A),ld(rd(B,A),C)) = rd(B,ld(A,C)). [para(2738(a,1),4(a,1,1))].
% 10.03/10.30 5693 mult(rd(A,B),rd(A,ld(B,C))) = rd(mult(A,A),C). [back_rewrite(1892),rewrite([5631(5)])].
% 10.03/10.30 5706 mult(rd(A,rd(B,C)),rd(A,C)) = rd(mult(A,A),B). [para(11(a,1),2758(a,1,1,2,2))].
% 10.03/10.30 7072 rd(mult(A,ld(B,C)),ld(B,D)) = ld(B,rd(mult(mult(B,A),C),D)). [para(3025(a,1),1478(a,2,2)),rewrite([1883(5),498(7),2(5),3025(6)])].
% 10.03/10.30 7103 rd(mult(A,A),ld(B,mult(A,C))) = rd(mult(B,A),C). [para(12(a,1),3026(a,1,1,1)),flip(a)].
% 10.03/10.30 7134 ld(rd(mult(A,B),C),mult(B,B)) = ld(A,mult(B,C)). [para(3026(a,1),2340(a,1,1)),rewrite([4096(4)]),flip(a)].
% 10.03/10.30 7165 rd(A,ld(ld(rd(B,C),A),B)) = ld(rd(B,C),rd(mult(A,A),B)). [para(1(a,1),3279(a,1,1)),rewrite([3557(10),3(8)])].
% 10.03/10.30 7195 mult(ld(rd(A,B),C),ld(rd(A,B),C)) = mult(B,ld(rd(A,B),ld(A,mult(C,C)))). [back_rewrite(1030),rewrite([7165(4),3359(5)]),flip(a)].
% 10.03/10.30 7218 mult(A,mult(B,ld(rd(A,B),ld(A,mult(C,C))))) = mult(C,mult(B,ld(rd(A,B),C))). [back_rewrite(263),rewrite([7195(5)])].
% 10.03/10.30 8526 mult(A,ld(B,mult(C,C))) = mult(C,ld(B,mult(A,C))). [para(3593(a,1),3288(a,1,1)),rewrite([3288(5)])].
% 10.03/10.30 8764 ld(rd(mult(A,A),B),C) = ld(A,mult(rd(C,A),B)). [para(3681(a,1),11(a,1,1))].
% 10.03/10.30 8937 rd(mult(A,A),mult(B,C)) = mult(rd(A,B),rd(A,C)). [para(3688(a,1),4(a,1,1))].
% 10.03/10.30 9645 mult(A,mult(B,ld(rd(A,B),ld(A,C)))) = mult(rd(C,A),mult(B,B)). [para(1037(a,1),4231(a,1,2)),rewrite([3398(7)]),flip(a)].
% 10.03/10.30 9706 mult(rd(mult(A,A),B),mult(C,C)) = mult(A,mult(C,ld(rd(B,C),A))). [back_rewrite(7218),rewrite([9645(6)])].
% 10.03/10.30 9726 ld(ld(rd(A,B),C),A) = ld(B,ld(C,mult(A,A))). [para(4285(a,1),2(a,1,2)),flip(a)].
% 10.03/10.30 9795 ld(rd(A,B),mult(rd(C,B),rd(D,B))) = rd(ld(A,mult(C,D)),B). [para(1391(a,1),4361(a,1,2))].
% 10.03/10.30 10056 rd(ld(A,mult(B,B)),C) = ld(rd(A,rd(B,C)),B). [para(3(a,1),4894(a,2,2)),rewrite([9795(5)])].
% 10.03/10.30 10880 ld(rd(A,B),rd(mult(A,A),C)) = rd(A,ld(B,C)). [para(5693(a,1),2(a,1,2))].
% 10.03/10.30 11346 mult(rd(mult(A,B),ld(rd(C,B),mult(A,D))),A) = rd(mult(C,mult(A,B)),mult(D,B)). [para(7(a,2),7103(a,1,2,2)),rewrite([781(7),8937(8),4(7)])].
% 10.03/10.30 11376 mult(rd(A,ld(B,mult(C,D))),C) = mult(rd(mult(B,C),D),ld(C,A)). [para(7103(a,1),1396(a,1,1)),flip(a)].
% 10.03/10.30 11427 rd(mult(A,mult(B,C)),mult(D,C)) = mult(rd(mult(rd(A,C),B),D),C). [back_rewrite(11346),rewrite([11376(6),2(5)]),flip(a)].
% 10.03/10.30 11456 mult(mult(rd(A,rd(B,A)),rd(C,A)),B) = mult(A,C). [back_rewrite(68),rewrite([11427(7),1125(3),1391(6),4(4)])].
% 10.03/10.30 11458 ld(mult(A,B),mult(mult(A,C),D)) = mult(A,ld(B,mult(C,ld(A,D)))). [para(6(a,1),7134(a,1,1,1)),rewrite([712(4),1416(8),2(5),7134(5)]),flip(a)].
% 10.03/10.30 11510 ld(A,mult(B,ld(C,mult(A,A)))) = ld(C,mult(B,A)). [para(4907(a,1),7134(a,1,1)),rewrite([7134(4)]),flip(a)].
% 10.03/10.30 11547 mult(A,mult(ld(A,B),ld(ld(A,A),C))) = mult(B,C). [back_rewrite(63),rewrite([11458(7),466(4),498(6),2(5)])].
% 10.03/10.30 12604 ld(mult(rd(A,B),rd(A,C)),D) = ld(A,mult(rd(D,A),mult(B,C))). [para(8937(a,1),8764(a,1,1))].
% 10.03/10.30 12640 ld(ld(A,B),ld(C,mult(B,B))) = ld(ld(A,C),B). [para(12(a,1),9726(a,1,1,1)),flip(a)].
% 10.03/10.30 12834 rd(mult(A,ld(ld(A,B),mult(C,C))),D) = ld(rd(B,rd(mult(A,C),D)),mult(A,C)). [para(6(a,1),10056(a,1,1,2)),rewrite([781(4),2207(4)])].
% 10.03/10.30 12910 mult(rd(A,ld(B,C)),B) = mult(B,ld(rd(C,B),A)). [para(10880(a,1),781(a,2,1)),rewrite([9706(4),2(5)]),flip(a)].
% 10.03/10.30 13043 mult(rd(A,rd(B,A)),rd(C,A)) = rd(mult(A,C),B). [para(11456(a,1),4(a,1,1)),flip(a)].
% 10.03/10.30 13137 ld(A,mult(rd(B,C),ld(rd(D,A),mult(A,C)))) = rd(ld(D,mult(B,mult(A,C))),C). [para(11510(a,1),2235(a,1,1)),rewrite([1416(8),1391(11),12834(10),4(7)]),flip(a)].
% 10.03/10.30 13139 ld(ld(A,B),mult(ld(A,C),D)) = ld(A,ld(B,mult(C,mult(A,D)))). [para(11510(a,1),4180(a,2,2)),rewrite([1416(5),498(7),2(6),11510(6)])].
% 10.03/10.30 13142 ld(A,mult(B,ld(rd(C,A),mult(A,D)))) = ld(rd(C,D),mult(B,A)). [para(4894(a,1),11510(a,1,2,2))].
% 10.03/10.30 13165 rd(ld(A,mult(B,mult(C,D))),D) = ld(rd(A,D),mult(rd(B,D),C)). [back_rewrite(13137),rewrite([13142(6)]),flip(a)].
% 10.03/10.30 13209 mult(ld(A,B),ld(ld(A,A),C)) = ld(A,mult(B,C)). [para(11547(a,1),2(a,1,2)),flip(a)].
% 10.03/10.30 13211 mult(A,mult(ld(B,B),C)) = mult(B,mult(ld(B,A),C)). [para(2(a,1),11547(a,1,2,2)),flip(a)].
% 10.03/10.30 13594 rd(mult(A,ld(rd(B,A),C)),A) = rd(C,ld(A,B)). [para(12910(a,1),4(a,1,1))].
% 10.03/10.30 13595 mult(A,ld(rd(B,A),mult(C,ld(A,B)))) = mult(C,A). [para(4(a,1),12910(a,1,1)),flip(a)].
% 10.03/10.30 13741 rd(rd(mult(A,B),C),rd(B,A)) = rd(A,rd(C,A)). [para(13043(a,1),4(a,1,1))].
% 10.03/10.31 13743 rd(mult(A,mult(B,A)),C) = mult(rd(A,rd(C,A)),B). [para(4(a,1),13043(a,1,2)),flip(a)].
% 10.03/10.31 14235 mult(ld(A,B),ld(ld(A,C),A)) = ld(C,mult(B,A)). [para(11510(a,1),13209(a,2)),rewrite([12640(5)])].
% 10.03/10.31 14364 mult(A,mult(ld(B,B),ld(ld(B,A),C))) = mult(B,C). [para(1(a,1),13211(a,2,2))].
% 10.03/10.31 14367 mult(ld(A,rd(mult(mult(A,rd(A,B)),C),A)),B) = C. [para(13211(a,1),4(a,1,1)),rewrite([11427(6),7072(5)])].
% 10.03/10.31 14856 rd(mult(A,ld(B,C)),A) = rd(C,ld(A,mult(B,A))). [para(4(a,1),13594(a,1,1,2,1))].
% 10.03/10.31 14957 mult(mult(rd(A,B),C),A) = mult(A,mult(C,ld(B,A))). [para(13595(a,1),14(a,1,2)),rewrite([131(5),152(5),3(5)])].
% 10.03/10.31 15278 rd(A,rd(ld(B,mult(A,C)),A)) = rd(B,rd(C,A)). [para(12(a,1),13741(a,1,1)),flip(a)].
% 10.03/10.31 15470 mult(rd(A,ld(rd(B,A),mult(rd(A,A),C))),C) = B. [para(13743(a,1),12(a,1)),rewrite([13165(4)])].
% 10.03/10.31 15501 rd(mult(A,mult(B,C)),C) = mult(rd(A,rd(C,C)),B). [para(13743(a,1),4907(a,1)),rewrite([10056(3),12(4)]),flip(a)].
% 10.03/10.31 16175 rd(ld(A,mult(B,C)),ld(C,A)) = rd(C,ld(C,ld(B,mult(A,A)))). [para(14235(a,1),5591(a,1,1)),rewrite([13139(9),1(6)])].
% 10.03/10.31 16368 mult(ld(A,A),ld(ld(A,B),C)) = ld(B,mult(A,C)). [para(14364(a,1),2(a,1,2)),flip(a)].
% 10.03/10.31 16474 ld(A,rd(mult(mult(A,rd(A,B)),C),A)) = rd(C,B). [para(14367(a,1),4(a,1,1)),flip(a)].
% 10.03/10.31 16496 rd(ld(A,B),ld(C,A)) = ld(rd(A,C),rd(B,A)). [para(14367(a,1),1478(a,2,2,2)),rewrite([16474(5),16474(6),12604(4),781(4),3359(4),14856(5),3(3),16474(8)])].
% 10.03/10.31 16531 rd(A,ld(A,ld(B,mult(C,C)))) = ld(rd(C,A),rd(mult(B,A),C)). [back_rewrite(16175),rewrite([16496(4)]),flip(a)].
% 10.03/10.31 17853 mult(rd(A,rd(B,C)),rd(C,C)) = rd(mult(A,C),B). [para(15278(a,1),5706(a,1,1)),rewrite([7103(8)])].
% 10.03/10.31 18698 mult(rd(A,ld(B,mult(rd(A,A),C))),C) = mult(B,A). [para(4(a,1),15470(a,1,1,2,1))].
% 10.03/10.31 18743 mult(mult(rd(A,rd(B,B)),C),B) = mult(A,mult(C,B)). [para(15501(a,1),3(a,1,1))].
% 10.03/10.31 20733 ld(A,mult(B,mult(C,ld(B,B)))) = mult(C,ld(B,ld(A,mult(B,B)))). [para(16368(a,1),8526(a,2)),rewrite([13139(5),1(2)]),flip(a)].
% 10.03/10.31 23027 rd(mult(A,B),mult(C,B)) = mult(rd(A,C),rd(B,B)). [para(4(a,1),17853(a,1,1,2)),flip(a)].
% 10.03/10.31 23836 mult(A,mult(ld(rd(A,A),B),C)) = mult(B,mult(A,C)). [para(18698(a,1),1393(a,1)),rewrite([23027(6),14957(7),20733(8),8937(9),16531(8),4(7),18743(8)]),flip(a)].
% 10.03/10.31 30650 mult(mult(rd(A,A),B),mult(A,C)) = mult(A,mult(B,C)). [para(2(a,1),23836(a,1,2,1)),flip(a)].
% 10.03/10.31 30651 $F # answer(goals). [resolve(30650,a,10,a)].
% 10.03/10.31
% 10.03/10.31 % SZS output end Refutation
% 10.03/10.31 ============================== end of proof ==========================
% 10.03/10.31
% 10.03/10.31 ============================== STATISTICS ============================
% 10.03/10.31
% 10.03/10.31 Given=376. Generated=240813. Kept=30648. proofs=1.
% 10.03/10.31 Usable=291. Sos=9999. Demods=8429. Limbo=1, Disabled=20364. Hints=0.
% 10.03/10.31 Megabytes=29.86.
% 10.03/10.31 User_CPU=9.18, System_CPU=0.15, Wall_clock=10.
% 10.03/10.31
% 10.03/10.31 ============================== end of statistics =====================
% 10.03/10.31
% 10.03/10.31 ============================== end of search =========================
% 10.03/10.31
% 10.03/10.31 THEOREM PROVED
% 10.03/10.31 % SZS status Unsatisfiable
% 10.03/10.31
% 10.03/10.31 Exiting with 1 proof.
% 10.03/10.31
% 10.03/10.31 Process 15625 exit (max_proofs) Mon Jun 13 11:39:24 2022
% 10.03/10.31 Prover9 interrupted
%------------------------------------------------------------------------------