TSTP Solution File: GRP683+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP683+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 11:20:35 EDT 2022
% Result : Theorem 0.81s 1.08s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP683+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 : Mon Jun 13 07:55:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.81/1.08 ============================== Prover9 ===============================
% 0.81/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.08 Process 5241 was started by sandbox on n016.cluster.edu,
% 0.81/1.08 Mon Jun 13 07:55:14 2022
% 0.81/1.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5088_n016.cluster.edu".
% 0.81/1.08 ============================== end of head ===========================
% 0.81/1.08
% 0.81/1.08 ============================== INPUT =================================
% 0.81/1.08
% 0.81/1.08 % Reading from file /tmp/Prover9_5088_n016.cluster.edu
% 0.81/1.08
% 0.81/1.08 set(prolog_style_variables).
% 0.81/1.08 set(auto2).
% 0.81/1.08 % set(auto2) -> set(auto).
% 0.81/1.08 % set(auto) -> set(auto_inference).
% 0.81/1.08 % set(auto) -> set(auto_setup).
% 0.81/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.08 % set(auto) -> set(auto_limits).
% 0.81/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.08 % set(auto) -> set(auto_denials).
% 0.81/1.08 % set(auto) -> set(auto_process).
% 0.81/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.08 % set(auto2) -> assign(stats, some).
% 0.81/1.08 % set(auto2) -> clear(echo_input).
% 0.81/1.08 % set(auto2) -> set(quiet).
% 0.81/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.08 % set(auto2) -> clear(print_given).
% 0.81/1.08 assign(lrs_ticks,-1).
% 0.81/1.08 assign(sos_limit,10000).
% 0.81/1.08 assign(order,kbo).
% 0.81/1.08 set(lex_order_vars).
% 0.81/1.08 clear(print_given).
% 0.81/1.08
% 0.81/1.08 % formulas(sos). % not echoed (8 formulas)
% 0.81/1.08
% 0.81/1.08 ============================== end of input ==========================
% 0.81/1.08
% 0.81/1.08 % From the command line: assign(max_seconds, 300).
% 0.81/1.08
% 0.81/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.08
% 0.81/1.08 % Formulas that are not ordinary clauses:
% 0.81/1.08 1 (all A ld(A,mult(A,A)) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 2 (all A rd(mult(A,A),A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 3 (all B all A mult(A,ld(A,B)) = ld(A,mult(A,B))) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 4 (all B all A mult(rd(A,B),B) = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 5 (all D all C all B all A ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 6 (all D all C all B all A rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 7 (all B all A ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 8 -(all X3 all X4 all X5 (mult(X3,ld(X4,mult(X4,X5))) = mult(X3,X5) & mult(rd(mult(X3,X4),X4),X5) = mult(X3,X5))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.08
% 0.81/1.08 ============================== end of process non-clausal formulas ===
% 0.81/1.08
% 0.81/1.08 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.08
% 0.81/1.08 ============================== PREDICATE ELIMINATION =================
% 0.81/1.08
% 0.81/1.08 ============================== end predicate elimination =============
% 0.81/1.08
% 0.81/1.08 Auto_denials:
% 0.81/1.08 % copying label goals to answer in negative clause
% 0.81/1.08
% 0.81/1.08 Term ordering decisions:
% 0.81/1.08 Function symbol KB weights: c1=1. c2=1. c3=1. mult=1. ld=1. rd=1.
% 0.81/1.08
% 0.81/1.08 ============================== end of process initial clauses ========
% 0.81/1.08
% 0.81/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.08
% 0.81/1.08 ============================== end of clauses for search =============
% 0.81/1.08
% 0.81/1.08 ============================== SEARCH ================================
% 0.81/1.08
% 0.81/1.08 % Starting search at 0.01 seconds.
% 0.81/1.08
% 0.81/1.08 ============================== PROOF =================================
% 0.81/1.08 % SZS status Theorem
% 0.81/1.08 % SZS output start Refutation
% 0.81/1.08
% 0.81/1.08 % Proof 1 at 0.11 (+ 0.01) seconds: goals.
% 0.81/1.08 % Length of proof is 88.
% 0.81/1.08 % Level of proof is 19.
% 0.81/1.08 % Maximum clause weight is 35.000.
% 0.81/1.08 % Given clauses 75.
% 0.81/1.08
% 0.81/1.08 1 (all A ld(A,mult(A,A)) = A) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 2 (all A rd(mult(A,A),A) = A) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 3 (all B all A mult(A,ld(A,B)) = ld(A,mult(A,B))) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 4 (all B all A mult(rd(A,B),B) = rd(mult(A,B),B)) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 5 (all D all C all B all A ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D)) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 6 (all D all C all B all A rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D))) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 7 (all B all A ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.08 8 -(all X3 all X4 all X5 (mult(X3,ld(X4,mult(X4,X5))) = mult(X3,X5) & mult(rd(mult(X3,X4),X4),X5) = mult(X3,X5))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.08 9 ld(A,mult(A,A)) = A # label(f01) # label(axiom). [clausify(1)].
% 0.81/1.08 10 rd(mult(A,A),A) = A # label(f02) # label(axiom). [clausify(2)].
% 0.81/1.08 11 ld(A,mult(A,B)) = mult(A,ld(A,B)) # label(f03) # label(axiom). [clausify(3)].
% 0.81/1.08 12 rd(mult(A,B),B) = mult(rd(A,B),B) # label(f04) # label(axiom). [clausify(4)].
% 0.81/1.08 13 rd(mult(rd(A,A),B),B) = ld(A,mult(A,ld(B,B))) # label(f07) # label(axiom). [clausify(7)].
% 0.81/1.08 14 mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))). [copy(13),rewrite([12(3),11(6)])].
% 0.81/1.08 15 ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) # label(f05) # label(axiom). [clausify(5)].
% 0.81/1.08 16 mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D). [copy(15),rewrite([11(5),11(7)])].
% 0.81/1.08 17 rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) # label(f06) # label(axiom). [clausify(6)].
% 0.81/1.08 18 mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)). [copy(17),rewrite([12(5),12(7)])].
% 0.81/1.08 19 mult(c1,ld(c2,mult(c2,c3))) != mult(c1,c3) | mult(rd(mult(c1,c2),c2),c3) != mult(c1,c3) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(8)].
% 0.81/1.08 20 mult(c1,mult(c2,ld(c2,c3))) != mult(c1,c3) | mult(mult(rd(c1,c2),c2),c3) != mult(c1,c3) # answer(goals). [copy(19),rewrite([11(6),12(16)])].
% 0.81/1.08 21 mult(A,ld(A,A)) = A. [back_rewrite(9),rewrite([11(2)])].
% 0.81/1.08 22 mult(rd(A,A),A) = A. [back_rewrite(10),rewrite([12(2)])].
% 0.81/1.08 25 mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),mult(C,D)))) = ld(ld(A,B),mult(mult(A,ld(A,C)),D)). [para(16(a,1),11(a,1,2)),flip(a)].
% 0.81/1.08 26 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D). [para(11(a,1),16(a,1,1)),rewrite([11(4)])].
% 0.81/1.08 31 mult(rd(mult(A,B),rd(C,D)),ld(rd(mult(A,B),rd(C,D)),rd(C,D))) = ld(rd(mult(A,B),rd(C,D)),mult(A,mult(rd(B,D),D))). [para(18(a,1),11(a,1,2)),flip(a)].
% 0.81/1.08 33 mult(rd(mult(A,B),mult(rd(C,D),D)),mult(rd(C,D),D)) = mult(A,mult(rd(B,D),D)). [para(12(a,1),18(a,1,1,2)),rewrite([12(6)])].
% 0.81/1.08 39 mult(A,ld(A,ld(A,A))) = ld(A,A). [para(21(a,1),11(a,1,2)),flip(a)].
% 0.81/1.08 40 mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)). [para(21(a,1),12(a,1,1)),flip(a)].
% 0.81/1.08 42 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(rd(ld(A,A),C),C)). [para(21(a,1),18(a,1,1,1))].
% 0.81/1.08 44 rd(A,A) = ld(A,A). [para(22(a,1),12(a,1,1)),rewrite([14(4),39(4)])].
% 0.81/1.08 45 mult(ld(A,A),A) = A. [para(22(a,1),12(a,2)),rewrite([12(2),44(1)])].
% 0.81/1.08 46 mult(A,ld(A,ld(ld(A,A),ld(A,A)))) = ld(A,A). [para(22(a,1),14(a,1)),rewrite([44(1),44(2),44(3)]),flip(a)].
% 0.81/1.08 47 mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,ld(C,C))),C). [para(22(a,1),16(a,1,2,2)),rewrite([44(5)])].
% 0.81/1.08 54 mult(rd(ld(A,A),B),B) = mult(A,ld(A,ld(B,B))). [back_rewrite(14),rewrite([44(1)])].
% 0.81/1.08 55 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(A,ld(A,ld(C,C)))). [back_rewrite(42),rewrite([54(7)])].
% 0.81/1.08 57 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D)))) = ld(mult(A,ld(A,B)),mult(mult(A,ld(A,C)),D)). [para(11(a,1),25(a,1,1)),rewrite([11(4),11(6),11(12)])].
% 0.81/1.08 65 ld(ld(A,B),mult(mult(A,ld(A,ld(C,C))),C)) = mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),C))). [para(45(a,1),25(a,1,2,2,2)),flip(a)].
% 0.81/1.08 82 mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))). [para(21(a,1),26(a,1,1)),rewrite([21(2)]),flip(a)].
% 0.81/1.08 83 mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,C)). [para(21(a,1),26(a,1,2,2)),rewrite([82(6),82(10),21(8)])].
% 0.81/1.08 84 mult(A,mult(A,ld(A,B))) = mult(A,B). [para(21(a,1),26(a,2,1)),rewrite([82(7),83(7),11(2)])].
% 0.81/1.08 86 mult(A,ld(A,mult(ld(A,A),B))) = mult(ld(A,A),B). [para(39(a,1),26(a,2,1)),rewrite([82(8),83(8)])].
% 0.81/1.08 96 mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),C))) = ld(ld(A,B),mult(A,ld(A,C))). [back_rewrite(65),rewrite([82(5),45(3)]),flip(a)].
% 0.81/1.08 101 ld(mult(A,ld(A,B)),mult(A,ld(A,mult(C,D)))) = mult(A,ld(A,ld(mult(A,ld(A,B)),mult(C,D)))). [back_rewrite(57),rewrite([82(10),83(10),82(11)]),flip(a)].
% 0.81/1.08 103 mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,C)). [back_rewrite(47),rewrite([82(8),45(6)])].
% 0.81/1.08 108 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,ld(C,C)). [back_rewrite(55),rewrite([84(8)])].
% 0.81/1.08 109 ld(ld(A,B),mult(A,ld(A,C))) = mult(A,ld(A,ld(ld(A,B),C))). [back_rewrite(96),rewrite([103(6)]),flip(a)].
% 0.81/1.08 117 mult(mult(A,B),ld(C,C)) = mult(A,mult(rd(B,C),C)). [back_rewrite(18),rewrite([108(5)])].
% 0.81/1.08 127 mult(rd(A,rd(B,C)),ld(rd(A,rd(B,C)),rd(B,C))) = ld(rd(A,rd(B,C)),mult(A,ld(C,C))). [para(21(a,1),31(a,1,1,1)),rewrite([21(4),21(9),54(12),84(13)])].
% 0.81/1.08 138 mult(A,ld(A,ld(mult(A,ld(A,B)),mult(B,C)))) = mult(A,ld(A,C)). [para(82(a,1),11(a,1,2)),rewrite([101(6),82(12),83(12)])].
% 0.81/1.08 139 mult(A,ld(A,mult(mult(A,B),C))) = mult(mult(A,B),C). [para(11(a,1),82(a,1,1,2)),rewrite([84(3)]),flip(a)].
% 0.81/1.08 151 ld(ld(A,A),ld(A,A)) = ld(A,A). [para(39(a,1),86(a,1,2,2)),rewrite([46(5),39(8)]),flip(a)].
% 0.81/1.08 158 mult(rd(A,mult(rd(B,C),C)),mult(rd(B,C),C)) = mult(A,ld(C,C)). [para(21(a,1),33(a,1,1,1)),rewrite([54(9),84(10)])].
% 0.81/1.08 161 mult(A,mult(rd(B,ld(C,C)),ld(C,C))) = mult(A,mult(rd(B,C),C)). [para(40(a,1),33(a,1,1,2)),rewrite([40(8),108(7),151(4),117(3)]),flip(a)].
% 0.81/1.08 186 mult(A,ld(A,ld(A,B))) = ld(A,B). [para(103(a,1),21(a,1))].
% 0.81/1.08 194 mult(A,ld(A,ld(mult(A,ld(A,B)),C))) = ld(mult(A,ld(A,B)),C). [para(186(a,1),82(a,1)),rewrite([83(12)]),flip(a)].
% 0.81/1.08 195 mult(A,ld(A,ld(ld(A,B),C))) = ld(ld(A,B),C). [para(186(a,1),103(a,1)),flip(a)].
% 0.81/1.08 196 ld(mult(A,ld(A,B)),mult(B,C)) = mult(A,ld(A,C)). [back_rewrite(138),rewrite([194(6)])].
% 0.81/1.08 198 ld(ld(A,B),mult(A,ld(A,C))) = ld(ld(A,B),C). [back_rewrite(109),rewrite([195(8)])].
% 0.81/1.08 207 mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,ld(B,B)). [para(44(a,1),108(a,1,1,2)),rewrite([44(3)])].
% 0.81/1.08 208 mult(rd(A,B),ld(B,B)) = rd(A,B). [para(44(a,1),108(a,1,1)),rewrite([45(5)]),flip(a)].
% 0.81/1.08 210 mult(ld(A,A),ld(B,B)) = mult(A,ld(A,ld(B,B))). [para(54(a,1),108(a,2)),rewrite([108(7),207(5),151(6)])].
% 0.81/1.08 214 mult(A,mult(rd(B,C),C)) = mult(A,mult(B,ld(C,C))). [back_rewrite(161),rewrite([207(4)]),flip(a)].
% 0.81/1.08 216 rd(A,ld(A,A)) = A. [back_rewrite(40),rewrite([207(4),21(2)]),flip(a)].
% 0.81/1.08 248 mult(rd(A,mult(rd(B,C),C)),mult(B,ld(C,C))) = mult(A,ld(C,C)). [back_rewrite(158),rewrite([214(6)])].
% 0.81/1.08 255 mult(mult(A,B),ld(C,C)) = mult(A,mult(B,ld(C,C))). [back_rewrite(117),rewrite([214(6)])].
% 0.81/1.08 259 mult(rd(A,B),B) = mult(A,ld(B,B)). [para(216(a,1),108(a,1,1,2)),rewrite([216(3),151(5)])].
% 0.81/1.08 262 mult(A,ld(mult(B,ld(C,C)),mult(B,ld(C,C)))) = mult(A,ld(C,C)). [back_rewrite(248),rewrite([259(2),259(6)])].
% 0.81/1.08 278 mult(c1,mult(c2,ld(c2,c3))) != mult(c1,c3) | mult(mult(c1,ld(c2,c2)),c3) != mult(c1,c3) # answer(goals). [back_rewrite(20),rewrite([259(16)])].
% 0.81/1.08 279 rd(mult(A,B),B) = mult(A,ld(B,B)). [back_rewrite(12),rewrite([259(4)])].
% 0.81/1.08 282 rd(A,ld(B,B)) = mult(A,ld(B,B)). [para(151(a,1),208(a,1,2)),rewrite([259(4),151(3)]),flip(a)].
% 0.81/1.08 294 mult(mult(A,ld(B,B)),B) = mult(A,B). [para(279(a,1),259(a,1,1)),rewrite([255(6),21(5)])].
% 0.81/1.08 303 ld(A,mult(B,ld(mult(A,ld(A,B)),C))) = ld(A,C). [para(83(a,1),11(a,1,2)),rewrite([11(3),186(3),186(8)]),flip(a)].
% 0.81/1.08 304 mult(mult(A,B),ld(mult(A,B),C)) = mult(A,ld(A,C)). [para(11(a,1),83(a,1,2,2,2,1,2)),rewrite([84(4),139(6)])].
% 0.81/1.08 344 ld(mult(A,ld(A,B)),B) = mult(A,ld(A,ld(B,B))). [para(21(a,1),196(a,1,2))].
% 0.81/1.08 346 mult(A,ld(A,mult(B,ld(B,C)))) = mult(A,ld(A,C)). [para(84(a,1),196(a,1,2)),rewrite([196(4)]),flip(a)].
% 0.81/1.08 367 ld(mult(A,ld(A,B)),mult(A,ld(A,C))) = ld(mult(A,ld(A,B)),C). [para(11(a,1),198(a,1,1)),rewrite([11(7)])].
% 0.81/1.08 375 mult(ld(A,A),B) = mult(A,ld(A,B)). [para(210(a,1),294(a,1,1)),rewrite([82(4),45(2)]),flip(a)].
% 0.81/1.08 376 ld(ld(A,A),B) = mult(A,ld(A,B)). [para(210(a,1),139(a,1,2,2,1)),rewrite([82(6),375(4),346(6),198(5),375(4),195(4),375(5),82(6),375(4),346(6)])].
% 0.81/1.08 378 ld(mult(A,ld(B,B)),mult(A,ld(B,B))) = mult(A,ld(A,ld(B,B))). [para(44(a,1),127(a,1,1,2)),rewrite([282(2),44(3),282(4),44(5),304(7),44(4),282(5)]),flip(a)].
% 0.81/1.08 389 mult(A,mult(B,ld(B,ld(C,C)))) = mult(A,ld(C,C)). [back_rewrite(262),rewrite([378(5)])].
% 0.81/1.08 391 ld(mult(A,ld(A,ld(B,B))),C) = mult(A,ld(A,C)). [para(82(a,1),376(a,2)),rewrite([367(5),344(3),303(9)])].
% 0.81/1.08 401 mult(rd(A,B),mult(B,ld(C,C))) = mult(A,ld(C,C)). [para(259(a,1),255(a,1,1)),rewrite([255(4),375(3),389(4)]),flip(a)].
% 0.81/1.08 403 mult(mult(A,mult(B,ld(C,C))),C) = mult(mult(A,B),C). [para(255(a,1),294(a,1,1))].
% 0.81/1.08 450 ld(A,mult(B,ld(B,C))) = ld(A,C). [para(375(a,1),303(a,1,2)),rewrite([391(4),346(4)])].
% 0.81/1.08 456 mult(A,mult(B,ld(B,C))) = mult(A,C). [para(450(a,1),84(a,1,2,2)),rewrite([84(3)]),flip(a)].
% 0.81/1.08 466 mult(mult(c1,ld(c2,c2)),c3) != mult(c1,c3) # answer(goals). [back_rewrite(278),rewrite([456(7)]),xx(a)].
% 0.81/1.08 562 mult(mult(A,ld(B,B)),C) = mult(A,C). [para(259(a,1),403(a,2,1)),rewrite([401(4),294(3)]),flip(a)].
% 0.81/1.08 563 $F # answer(goals). [resolve(562,a,466,a)].
% 0.81/1.08
% 0.81/1.08 % SZS output end Refutation
% 0.81/1.08 ============================== end of proof ==========================
% 0.81/1.08
% 0.81/1.08 ============================== STATISTICS ============================
% 0.81/1.08
% 0.81/1.08 Given=75. Generated=2739. Kept=550. proofs=1.
% 0.81/1.08 Usable=31. Sos=103. Demods=133. Limbo=1, Disabled=422. Hints=0.
% 0.81/1.08 Megabytes=0.65.
% 0.81/1.08 User_CPU=0.11, System_CPU=0.01, Wall_clock=1.
% 0.81/1.08
% 0.81/1.08 ============================== end of statistics =====================
% 0.81/1.08
% 0.81/1.08 ============================== end of search =========================
% 0.81/1.08
% 0.81/1.08 THEOREM PROVED
% 0.81/1.08 % SZS status Theorem
% 0.81/1.08
% 0.81/1.08 Exiting with 1 proof.
% 0.81/1.08
% 0.81/1.08 Process 5241 exit (max_proofs) Mon Jun 13 07:55:15 2022
% 0.81/1.08 Prover9 interrupted
%------------------------------------------------------------------------------