TSTP Solution File: GRP120-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP120-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:17:14 EDT 2022
% Result : Unsatisfiable 0.97s 1.29s
% Output : Refutation 0.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP120-1 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.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 04:10:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.97/1.29 ============================== Prover9 ===============================
% 0.97/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.97/1.29 Process 18422 was started by sandbox on n018.cluster.edu,
% 0.97/1.29 Mon Jun 13 04:10:27 2022
% 0.97/1.29 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18269_n018.cluster.edu".
% 0.97/1.29 ============================== end of head ===========================
% 0.97/1.29
% 0.97/1.29 ============================== INPUT =================================
% 0.97/1.29
% 0.97/1.29 % Reading from file /tmp/Prover9_18269_n018.cluster.edu
% 0.97/1.29
% 0.97/1.29 set(prolog_style_variables).
% 0.97/1.29 set(auto2).
% 0.97/1.29 % set(auto2) -> set(auto).
% 0.97/1.29 % set(auto) -> set(auto_inference).
% 0.97/1.29 % set(auto) -> set(auto_setup).
% 0.97/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.97/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.97/1.29 % set(auto) -> set(auto_limits).
% 0.97/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.97/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.97/1.29 % set(auto) -> set(auto_denials).
% 0.97/1.29 % set(auto) -> set(auto_process).
% 0.97/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.97/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.97/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.97/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.97/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.97/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.97/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.97/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.97/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.97/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.97/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.97/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.97/1.29 % set(auto2) -> assign(stats, some).
% 0.97/1.29 % set(auto2) -> clear(echo_input).
% 0.97/1.29 % set(auto2) -> set(quiet).
% 0.97/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.97/1.29 % set(auto2) -> clear(print_given).
% 0.97/1.29 assign(lrs_ticks,-1).
% 0.97/1.29 assign(sos_limit,10000).
% 0.97/1.29 assign(order,kbo).
% 0.97/1.29 set(lex_order_vars).
% 0.97/1.29 clear(print_given).
% 0.97/1.29
% 0.97/1.29 % formulas(sos). % not echoed (3 formulas)
% 0.97/1.29
% 0.97/1.29 ============================== end of input ==========================
% 0.97/1.29
% 0.97/1.29 % From the command line: assign(max_seconds, 300).
% 0.97/1.29
% 0.97/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.97/1.29
% 0.97/1.29 % Formulas that are not ordinary clauses:
% 0.97/1.29
% 0.97/1.29 ============================== end of process non-clausal formulas ===
% 0.97/1.29
% 0.97/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.97/1.29
% 0.97/1.29 ============================== PREDICATE ELIMINATION =================
% 0.97/1.29
% 0.97/1.29 ============================== end predicate elimination =============
% 0.97/1.29
% 0.97/1.29 Auto_denials:
% 0.97/1.29 % copying label prove_order3 to answer in negative clause
% 0.97/1.29
% 0.97/1.29 Term ordering decisions:
% 0.97/1.29 Function symbol KB weights: identity=1. a=1. multiply=1.
% 0.97/1.29
% 0.97/1.29 ============================== end of process initial clauses ========
% 0.97/1.29
% 0.97/1.29 ============================== CLAUSES FOR SEARCH ====================
% 0.97/1.29
% 0.97/1.29 ============================== end of clauses for search =============
% 0.97/1.29
% 0.97/1.29 ============================== SEARCH ================================
% 0.97/1.29
% 0.97/1.29 % Starting search at 0.01 seconds.
% 0.97/1.29
% 0.97/1.29 ============================== PROOF =================================
% 0.97/1.29 % SZS status Unsatisfiable
% 0.97/1.29 % SZS output start Refutation
% 0.97/1.29
% 0.97/1.29 % Proof 1 at 0.32 (+ 0.01) seconds: prove_order3.
% 0.97/1.29 % Length of proof is 162.
% 0.97/1.29 % Level of proof is 40.
% 0.97/1.29 % Maximum clause weight is 117.000.
% 0.97/1.29 % Given clauses 70.
% 0.97/1.29
% 0.97/1.29 1 multiply(identity,identity) = identity # label(single_axiom2) # label(axiom). [assumption].
% 0.97/1.29 2 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(C,C)))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.97/1.29 3 multiply(identity,a) != a # label(prove_order3) # label(negated_conjecture) # answer(prove_order3). [assumption].
% 0.97/1.29 4 multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B)))) = A. [para(1(a,1),2(a,1,2,1,2,1))].
% 0.97/1.29 5 multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),identity)) = identity. [para(1(a,1),2(a,1,2,1,2,2)),rewrite([1(8),1(7)])].
% 0.97/1.29 6 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,identity))),identity)) = B. [para(1(a,1),2(a,1,2,2,2)),rewrite([1(8)])].
% 0.97/1.29 7 multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))),multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))))))) = C. [para(2(a,1),2(a,1,2,1,2,2))].
% 0.97/1.29 8 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,C))) = multiply(A,multiply(multiply(A,B),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C)))))). [para(2(a,1),2(a,1,2,1,2)),flip(a)].
% 0.97/1.29 9 multiply(identity,multiply(multiply(identity,multiply(identity,multiply(A,identity))),identity)) = A. [para(1(a,1),4(a,1,2,2,2)),rewrite([1(10)])].
% 0.97/1.29 14 multiply(A,multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(multiply(multiply(B,multiply(multiply(B,B),identity)),identity),multiply(multiply(multiply(B,multiply(multiply(B,B),identity)),identity),multiply(multiply(B,multiply(multiply(B,B),identity)),identity))))) = B. [para(5(a,1),2(a,1,2,1,2,2))].
% 0.97/1.29 15 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),identity)) = multiply(A,multiply(multiply(A,identity),identity)). [para(5(a,1),2(a,1,2,1,2)),rewrite([1(6),1(5)]),flip(a)].
% 0.97/1.29 19 multiply(identity,multiply(multiply(identity,A),identity)) = multiply(identity,multiply(identity,multiply(A,identity))). [para(9(a,1),4(a,1,2,1,2)),rewrite([1(7),1(6)])].
% 0.97/1.29 20 multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = A. [back_rewrite(9),rewrite([19(10),19(9)])].
% 0.97/1.29 21 multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))))))) = identity. [para(20(a,1),2(a,1,2,1,2,2))].
% 0.97/1.29 24 multiply(identity,multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity))))) = identity. [para(20(a,1),4(a,1,2,1))].
% 0.97/1.29 26 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))) = multiply(A,multiply(multiply(A,B),identity)). [para(6(a,1),2(a,1,2,1,2)),rewrite([1(5),1(4)]),flip(a)].
% 0.97/1.29 52 multiply(identity,multiply(identity,multiply(multiply(multiply(identity,A),identity),identity))) = A. [para(19(a,1),19(a,1,2,1)),rewrite([19(10),19(9),20(10)]),flip(a)].
% 0.97/1.29 54 multiply(multiply(identity,multiply(identity,multiply(A,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))). [para(2(a,1),52(a,1,2,2,1,1)),rewrite([1(12)]),flip(a)].
% 0.97/1.29 55 multiply(multiply(identity,A),identity) = multiply(identity,multiply(A,identity)). [para(52(a,1),4(a,1,2,1)),rewrite([1(5),1(4)]),flip(a)].
% 0.97/1.29 57 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(identity,multiply(B,identity)))),identity)) = multiply(identity,B). [para(55(a,1),2(a,1,2,1,2,2)),rewrite([1(11),1(10)])].
% 0.97/1.29 60 multiply(A,multiply(multiply(A,multiply(multiply(A,A),B)),identity)) = multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))). [para(6(a,1),57(a,1,2,1,2,2)),rewrite([1(11)])].
% 0.97/1.29 67 multiply(A,multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(A,B))),multiply(multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))),multiply(multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B))))))) = multiply(B,multiply(B,B)). [para(8(a,2),2(a,1,2,1))].
% 0.97/1.29 68 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(B,multiply(C,multiply(C,C)))),C))) = B. [para(8(a,2),2(a,1))].
% 0.97/1.29 88 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))),multiply(multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D))),multiply(multiply(C,multiply(multiply(C,C),multiply(B,D))),multiply(D,multiply(D,D)))))),E))) = multiply(A,multiply(C,multiply(multiply(E,multiply(E,E)),multiply(multiply(E,multiply(E,E)),multiply(E,multiply(E,E)))))). [para(7(a,1),8(a,2,2,1))].
% 0.97/1.29 90 multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(multiply(identity,A),multiply(identity,A))),multiply(identity,B))) = multiply(multiply(identity,A),multiply(multiply(identity,multiply(A,identity)),multiply(multiply(B,multiply(B,B)),multiply(multiply(B,multiply(B,B)),multiply(B,multiply(B,B)))))). [para(55(a,1),8(a,2,2,1))].
% 0.97/1.29 97 multiply(A,multiply(multiply(A,multiply(A,multiply(multiply(A,identity),identity))),identity)) = multiply(multiply(A,A),multiply(A,A)). [para(15(a,1),2(a,1,2,1,2)),rewrite([1(10),1(9)])].
% 0.97/1.29 103 multiply(A,multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A)))),identity)) = multiply(multiply(A,A),multiply(multiply(A,A),multiply(multiply(multiply(A,A),identity),identity))). [para(15(a,1),8(a,1,2)),rewrite([1(21),1(20),1(22),1(21),1(23),1(22),1(21),1(20)]),flip(a)].
% 0.97/1.29 106 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),B)) = multiply(A,multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(B,identity))))),identity)). [para(60(a,1),2(a,1,2,1,2)),rewrite([1(13),1(12)]),flip(a)].
% 0.97/1.29 110 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(multiply(B,B),multiply(multiply(multiply(B,B),multiply(B,B)),C)))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity))))) = B. [para(60(a,1),7(a,1,2,2,1,1,2)),rewrite([1(22),1(21),60(30),1(33),1(32),60(41),1(44),1(43)])].
% 0.97/1.29 112 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))))) = multiply(A,multiply(multiply(A,C),multiply(multiply(multiply(multiply(C,multiply(multiply(C,C),B)),identity),multiply(multiply(multiply(C,multiply(multiply(C,C),B)),identity),multiply(multiply(C,multiply(multiply(C,C),B)),identity))),multiply(multiply(multiply(multiply(C,multiply(multiply(C,C),B)),identity),multiply(multiply(multiply(C,multiply(multiply(C,C),B)),identity),multiply(multiply(C,multiply(multiply(C,C),B)),identity))),multiply(multiply(multiply(C,multiply(multiply(C,C),B)),identity),multiply(multiply(multiply(C,multiply(multiply(C,C),B)),identity),multiply(multiply(C,multiply(multiply(C,C),B)),identity))))))). [para(60(a,1),8(a,1,2,2))].
% 0.97/1.29 114 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,multiply(multiply(A,A),B)),identity),C))) = multiply(A,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C)))))). [para(60(a,1),8(a,2,2,1))].
% 0.97/1.29 119 multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(A,identity),identity)),identity)) = identity. [para(15(a,1),60(a,1,2,1)),rewrite([1(15),1(14),1(13),1(12)])].
% 0.97/1.29 122 multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(multiply(multiply(identity,A),multiply(identity,multiply(multiply(A,identity),identity))),identity)) = identity. [para(55(a,1),119(a,1,2,1,2,1)),rewrite([55(13)])].
% 0.97/1.29 130 multiply(multiply(A,A),multiply(multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))))) = multiply(A,multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(multiply(A,A),multiply(A,A)),identity),identity)))),identity)). [para(97(a,1),8(a,1,2)),rewrite([1(37),1(36),1(38),1(37),1(39),1(38),1(37),1(36)])].
% 0.97/1.29 134 multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,multiply(multiply(A,A),identity)),identity),multiply(multiply(multiply(A,multiply(multiply(A,A),identity)),identity),multiply(multiply(A,multiply(multiply(A,A),identity)),identity))),identity))) = multiply(A,identity). [para(14(a,1),55(a,1,1)),rewrite([1(7),1(7),1(6),55(27)]),flip(a)].
% 0.97/1.29 144 multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(A,B),identity)),identity)) = B. [para(26(a,1),2(a,1,2,1)),rewrite([1(9),1(8)])].
% 0.97/1.29 154 multiply(multiply(A,multiply(multiply(A,A),multiply(B,C))),multiply(C,multiply(C,C))) = multiply(multiply(A,A),multiply(multiply(A,multiply(B,identity)),identity)). [para(2(a,1),144(a,1,2,1,2,1)),flip(a)].
% 0.97/1.29 158 multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(multiply(C,C),multiply(multiply(C,multiply(B,identity)),identity)),multiply(multiply(multiply(C,C),multiply(multiply(C,multiply(B,identity)),identity)),multiply(multiply(C,C),multiply(multiply(C,multiply(B,identity)),identity))))) = multiply(multiply(A,A),multiply(multiply(A,multiply(C,identity)),identity)). [para(7(a,1),144(a,1,2,1,2,1)),rewrite([154(17),154(24),154(31)]),flip(a)].
% 0.97/1.29 161 multiply(multiply(A,B),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C))))) = multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,C))),identity)),identity)). [para(8(a,2),144(a,1,2,1,2,1)),flip(a)].
% 0.97/1.29 162 multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,multiply(multiply(A,identity),identity)),identity)) = multiply(A,A). [para(15(a,1),144(a,1,2,1))].
% 0.97/1.29 163 multiply(multiply(A,multiply(multiply(A,A),B)),identity) = multiply(multiply(A,A),multiply(multiply(A,B),identity)). [para(60(a,1),144(a,1,2,1,2,1)),rewrite([55(11),55(10),55(9),20(11)]),flip(a)].
% 0.97/1.29 166 multiply(A,multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity)))) = identity. [para(24(a,1),144(a,1,2,1,2,1)),rewrite([1(3),1(5),1(4),1(4),1(3)]),flip(a)].
% 0.97/1.29 175 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(multiply(A,multiply(B,identity)),identity)),C))) = multiply(A,multiply(B,multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C)))))). [back_rewrite(88),rewrite([154(14),154(21),154(28),158(31)])].
% 0.97/1.29 195 multiply(multiply(A,B),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C))))) = multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(B,C)),identity))),identity)). [back_rewrite(161),rewrite([163(20)])].
% 0.97/1.29 198 multiply(identity,multiply(identity,multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),identity))) = multiply(A,identity). [back_rewrite(134),rewrite([163(8),163(14),163(20)])].
% 0.97/1.29 201 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(multiply(A,B),identity)),C))) = multiply(A,multiply(multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C)))))). [back_rewrite(114),rewrite([163(9)])].
% 0.97/1.29 202 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))))) = multiply(A,multiply(multiply(A,C),multiply(multiply(multiply(multiply(C,C),multiply(multiply(C,B),identity)),multiply(multiply(multiply(C,C),multiply(multiply(C,B),identity)),multiply(multiply(C,C),multiply(multiply(C,B),identity)))),multiply(multiply(multiply(multiply(C,C),multiply(multiply(C,B),identity)),multiply(multiply(multiply(C,C),multiply(multiply(C,B),identity)),multiply(multiply(C,C),multiply(multiply(C,B),identity)))),multiply(multiply(multiply(C,C),multiply(multiply(C,B),identity)),multiply(multiply(multiply(C,C),multiply(multiply(C,B),identity)),multiply(multiply(C,C),multiply(multiply(C,B),identity)))))))). [back_rewrite(112),rewrite([163(20),163(25),163(30),163(37),163(42),163(47),163(54),163(59),163(64)])].
% 0.97/1.29 206 multiply(A,multiply(multiply(A,A),multiply(multiply(A,B),identity))) = multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))). [back_rewrite(60),rewrite([163(5)])].
% 0.97/1.29 208 multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,A),multiply(multiply(A,B),identity)),identity)))) = multiply(A,multiply(multiply(A,A),B)). [para(163(a,1),20(a,1,2,2,2,1))].
% 0.97/1.29 211 multiply(multiply(A,multiply(A,multiply(multiply(A,B),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C))))))),identity) = multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,C))),identity)). [para(8(a,1),163(a,1,1,2))].
% 0.97/1.29 219 multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,identity))),identity)) = multiply(multiply(A,multiply(A,multiply(multiply(A,B),identity))),identity). [para(26(a,1),163(a,1,1,2)),flip(a)].
% 0.97/1.29 223 multiply(multiply(A,B),multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C))))) = multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(B,C),identity))))),identity). [back_rewrite(195),rewrite([219(24),163(16),206(17)])].
% 0.97/1.29 227 multiply(multiply(A,multiply(A,multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(B,C),identity))))),identity))),identity) = multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,C))),identity)). [back_rewrite(211),rewrite([223(10)])].
% 0.97/1.29 229 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))))) = multiply(A,multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,B)))),identity)). [back_rewrite(202),rewrite([223(69),206(23),55(27),55(26),55(25),20(27)])].
% 0.97/1.29 230 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(multiply(A,B),identity)),C))) = multiply(A,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(B,identity))),C))). [back_rewrite(201),rewrite([223(29),55(31),55(30),55(29),55(28),20(30)])].
% 0.97/1.29 253 multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(multiply(identity,A),multiply(identity,A))),multiply(identity,B))) = multiply(multiply(identity,A),multiply(identity,multiply(multiply(A,identity),B))). [back_rewrite(90),rewrite([223(35),55(37),55(36),55(35),55(34),20(36)])].
% 0.97/1.29 258 multiply(A,multiply(B,multiply(multiply(C,multiply(C,C)),multiply(multiply(C,multiply(C,C)),multiply(C,multiply(C,C)))))) = multiply(A,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))),C))). [back_rewrite(175),rewrite([230(14)]),flip(a)].
% 0.97/1.29 265 multiply(multiply(A,multiply(multiply(A,A),B)),multiply(multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))),multiply(multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))),multiply(identity,multiply(identity,multiply(multiply(B,identity),identity)))))) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)). [para(21(a,1),144(a,1,2,1,2,1)),rewrite([1(4)]),flip(a)].
% 0.97/1.29 271 multiply(multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))),multiply(multiply(A,A),identity)) = multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))),identity)),identity). [para(162(a,1),163(a,2,2,1)),rewrite([26(19)]),flip(a)].
% 0.97/1.29 273 multiply(multiply(identity,A),multiply(multiply(identity,multiply(multiply(A,identity),identity)),multiply(multiply(identity,multiply(multiply(A,identity),identity)),multiply(identity,multiply(multiply(A,identity),identity))))) = identity. [para(55(a,1),166(a,1,2,1,1)),rewrite([55(8),55(12),55(14),55(18),55(20)])].
% 0.97/1.29 274 multiply(multiply(multiply(A,identity),identity),multiply(multiply(multiply(A,identity),identity),multiply(multiply(A,identity),identity))) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)). [para(166(a,1),144(a,1,2,1,2,1)),rewrite([1(4)]),flip(a)].
% 0.97/1.29 297 multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),multiply(identity,multiply(identity,multiply(identity,multiply(A,identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),multiply(A,identity)),identity)) = identity. [para(206(a,1),122(a,1,1,1)),rewrite([1(12),55(14),1(21),55(23),1(29),55(31),55(34),55(33),55(36),55(35),20(37)])].
% 0.97/1.29 314 multiply(identity,multiply(identity,multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B))) = A. [para(1(a,1),68(a,1,1)),rewrite([1(4),1(5),1(4),1(5)])].
% 0.97/1.29 320 multiply(identity,multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B)) = multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))). [para(314(a,1),144(a,1,2,1,2,1)),rewrite([1(3),55(7)]),flip(a)].
% 0.97/1.29 329 multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))))) = multiply(identity,multiply(identity,A)). [para(67(a,1),54(a,1,1,2)),rewrite([223(58),55(20),55(19),55(18),55(17),20(19),1(15),1(16),1(17),1(16),55(20),55(19),55(18),55(22),55(21),55(20),20(22)])].
% 0.97/1.29 333 multiply(multiply(identity,multiply(A,multiply(B,multiply(B,B)))),B) = multiply(identity,multiply(multiply(A,identity),identity)). [para(320(a,1),144(a,1,2,1,2,1)),rewrite([1(3),55(12),55(11),20(13)]),flip(a)].
% 0.97/1.29 338 multiply(multiply(A,multiply(A,A)),multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))) = multiply(identity,A). [para(329(a,1),144(a,1,2,1,2,1)),rewrite([1(3),55(8),55(7),55(11),55(10),55(9),20(11)]),flip(a)].
% 0.97/1.29 343 multiply(A,multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(B,identity),identity))),C))) = multiply(A,multiply(B,multiply(identity,C))). [back_rewrite(258),rewrite([338(8)]),flip(a)].
% 0.97/1.29 345 multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(multiply(B,C),identity))))),identity) = multiply(multiply(A,B),multiply(identity,C)). [back_rewrite(223),rewrite([338(9)]),flip(a)].
% 0.97/1.29 375 multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(B,C))),identity)) = multiply(multiply(A,multiply(A,multiply(multiply(A,B),multiply(identity,C)))),identity). [back_rewrite(227),rewrite([345(12)]),flip(a)].
% 0.97/1.29 388 multiply(multiply(identity,multiply(A,multiply(identity,B))),multiply(B,multiply(B,B))) = multiply(identity,multiply(multiply(A,identity),identity)). [para(338(a,1),333(a,1,1,2,2))].
% 0.97/1.29 389 multiply(multiply(identity,A),multiply(multiply(identity,A),multiply(identity,A))) = multiply(identity,multiply(A,multiply(A,A))). [para(338(a,1),338(a,1,1)),rewrite([338(10),338(12)])].
% 0.97/1.29 394 multiply(multiply(identity,A),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))) = identity. [back_rewrite(273),rewrite([389(22),274(17)])].
% 0.97/1.29 397 multiply(multiply(A,multiply(multiply(A,A),B)),multiply(identity,multiply(identity,multiply(multiply(B,B),multiply(multiply(B,identity),identity))))) = multiply(multiply(A,A),multiply(multiply(A,identity),identity)). [back_rewrite(265),rewrite([389(29),389(24),274(19)])].
% 0.97/1.29 418 multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity))))) = multiply(A,multiply(A,A)). [para(20(a,1),389(a,1,1)),rewrite([20(10),20(10),389(29),389(24),274(19)]),flip(a)].
% 0.97/1.29 459 multiply(identity,multiply(identity,multiply(multiply(multiply(A,multiply(identity,B)),identity),identity))) = multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),B). [para(388(a,1),333(a,1,1,2)),rewrite([55(17),55(19)]),flip(a)].
% 0.97/1.29 460 multiply(identity,multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(A,A),multiply(multiply(A,identity),identity))))) = multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))). [para(394(a,1),388(a,1,1,2)),rewrite([1(3),55(27),55(29)])].
% 0.97/1.29 464 multiply(multiply(A,multiply(A,A)),identity) = multiply(A,multiply(multiply(A,A),identity)). [para(418(a,1),55(a,1,1)),rewrite([55(17),55(16),208(18)])].
% 0.97/1.29 466 multiply(multiply(identity,multiply(A,multiply(A,A))),multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = identity. [para(418(a,1),54(a,1,1,2)),rewrite([389(30),460(26),1(18),1(18),1(17),1(16)])].
% 0.97/1.29 480 multiply(identity,multiply(identity,multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(A,A),multiply(multiply(A,identity),identity))),identity)))) = multiply(A,identity). [back_rewrite(198),rewrite([464(24)])].
% 0.97/1.29 482 multiply(multiply(A,A),multiply(multiply(A,multiply(A,multiply(multiply(A,A),identity))),identity)) = multiply(A,A). [para(464(a,1),144(a,1,2,1,2))].
% 0.97/1.29 498 multiply(multiply(A,multiply(multiply(A,multiply(A,multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(A,A))))),identity)),identity) = multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))). [para(103(a,1),163(a,2,2,1)),rewrite([375(12),97(26)])].
% 0.97/1.29 504 multiply(A,multiply(multiply(identity,B),multiply(identity,C))) = multiply(A,multiply(identity,multiply(B,C))). [para(55(a,1),343(a,1,2,2,1,2,2,1)),rewrite([55(9),20(11)]),flip(a)].
% 0.97/1.29 510 multiply(identity,multiply(multiply(identity,multiply(identity,multiply(multiply(A,identity),identity))),B)) = multiply(A,multiply(identity,B)). [para(343(a,1),144(a,1,2,1,2,1)),rewrite([144(11)]),flip(a)].
% 0.97/1.29 539 multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(multiply(multiply(multiply(identity,A),multiply(identity,A)),multiply(identity,multiply(A,A))),multiply(identity,B))) = multiply(multiply(identity,A),multiply(identity,multiply(multiply(A,identity),B))). [back_rewrite(253),rewrite([504(16)])].
% 0.97/1.29 550 multiply(multiply(identity,A),multiply(identity,B)) = multiply(identity,multiply(A,B)). [para(504(a,1),144(a,1,2,1,2,1)),rewrite([144(11)]),flip(a)].
% 0.97/1.29 560 multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity)))) = identity. [para(466(a,1),504(a,2)),rewrite([1(7),550(13)])].
% 0.97/1.29 564 multiply(identity,multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),B))) = multiply(identity,multiply(A,multiply(multiply(A,identity),B))). [back_rewrite(539),rewrite([550(5),550(8),550(10),550(11),550(10),550(16)])].
% 0.97/1.29 588 multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),multiply(A,identity))))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),multiply(A,identity)),identity)) = identity. [back_rewrite(297),rewrite([550(17),550(14),550(11)])].
% 0.97/1.29 610 multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),identity),multiply(B,identity))))) = multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(B,identity))))). [para(106(a,2),206(a,1,2,2,1)),rewrite([163(9),206(10),459(27),550(25),550(22)]),flip(a)].
% 0.97/1.29 635 multiply(multiply(A,multiply(A,A)),multiply(identity,multiply(multiply(A,identity),identity))) = identity. [para(560(a,1),144(a,1,2,1,2,1)),rewrite([1(3),1(5),1(4),1(4),1(3)]),flip(a)].
% 0.97/1.29 636 multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),multiply(multiply(A,A),multiply(multiply(A,identity),identity))) = multiply(identity,multiply(multiply(A,identity),identity)). [para(635(a,1),144(a,1,2,1,2,1)),rewrite([1(10),464(9),163(11)])].
% 0.97/1.29 643 multiply(multiply(A,multiply(identity,multiply(B,multiply(B,B)))),B) = multiply(multiply(A,identity),identity). [para(510(a,1),333(a,1,1)),rewrite([55(17),55(16),55(19),55(18),20(20)])].
% 0.97/1.29 652 multiply(multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),multiply(multiply(multiply(identity,multiply(A,multiply(A,A))),A),identity)) = multiply(identity,multiply(multiply(multiply(A,multiply(A,A)),multiply(multiply(A,A),multiply(multiply(A,identity),identity))),identity)). [para(643(a,1),163(a,1,1,2)),rewrite([55(10),464(9),55(12),163(11),550(13),55(13),550(22)]),flip(a)].
% 0.97/1.29 663 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(multiply(B,B),multiply(multiply(multiply(B,B),multiply(B,B)),multiply(identity,C))))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity))))) = B. [para(55(a,1),110(a,1,2,2,1,1,2,2,2,2)),rewrite([55(31),55(44)])].
% 0.97/1.29 665 multiply(multiply(A,multiply(multiply(A,A),multiply(multiply(B,B),multiply(multiply(multiply(B,B),multiply(B,B)),C)))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity)))) = multiply(multiply(A,A),multiply(multiply(A,multiply(B,identity)),identity)). [para(110(a,1),144(a,1,2,1,2,1)),flip(a)].
% 0.97/1.29 667 multiply(A,multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(B,identity))))),identity)) = multiply(A,multiply(multiply(A,identity),B)). [para(110(a,1),333(a,1,1)),rewrite([1(17),564(22),55(23),55(22),55(25),55(24),20(26)])].
% 0.97/1.29 692 multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,A)),B)) = multiply(A,multiply(multiply(A,identity),B)). [back_rewrite(106),rewrite([667(18)])].
% 0.97/1.29 705 multiply(multiply(A,multiply(multiply(A,A),multiply(B,multiply(multiply(B,identity),C)))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),identity)))) = multiply(multiply(A,A),multiply(multiply(A,multiply(B,identity)),identity)). [back_rewrite(665),rewrite([692(7)])].
% 0.97/1.29 706 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,multiply(multiply(B,identity),multiply(identity,C))))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity))))) = B. [back_rewrite(663),rewrite([692(9)])].
% 0.97/1.29 729 multiply(A,multiply(multiply(A,identity),multiply(identity,multiply(identity,multiply(identity,multiply(B,identity)))))) = multiply(A,multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,B)))),identity)). [back_rewrite(229),rewrite([692(14)])].
% 0.97/1.29 732 multiply(A,multiply(multiply(A,identity),multiply(B,identity))) = multiply(A,multiply(multiply(A,B),identity)). [back_rewrite(26),rewrite([692(8)])].
% 0.97/1.29 738 multiply(multiply(A,identity),multiply(B,identity)) = multiply(multiply(A,B),identity). [para(732(a,1),144(a,1,2,1,2,1)),rewrite([144(11)]),flip(a)].
% 0.97/1.29 751 multiply(A,multiply(multiply(A,multiply(multiply(A,A),multiply(B,multiply(multiply(B,identity),multiply(identity,C))))),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))))),identity)))) = B. [back_rewrite(706),rewrite([738(49),738(48),464(46)])].
% 0.97/1.29 752 multiply(multiply(A,multiply(multiply(A,A),multiply(B,multiply(multiply(B,identity),C)))),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),multiply(multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity))))),multiply(B,multiply(identity,multiply(identity,multiply(identity,multiply(C,identity)))))),identity))) = multiply(multiply(A,A),multiply(multiply(A,multiply(B,identity)),identity)). [back_rewrite(705),rewrite([738(41),738(40),464(38)])].
% 0.97/1.29 772 multiply(identity,multiply(identity,multiply(identity,multiply(multiply(multiply(A,identity),B),identity)))) = multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(B,identity))))). [back_rewrite(610),rewrite([738(10)])].
% 0.97/1.29 773 multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))),multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),multiply(A,identity)),identity)) = identity. [back_rewrite(588),rewrite([738(8)])].
% 0.97/1.29 805 multiply(multiply(identity,multiply(A,identity)),multiply(B,identity)) = multiply(multiply(multiply(identity,A),B),identity). [para(55(a,1),738(a,1,1))].
% 0.97/1.29 806 multiply(multiply(A,identity),multiply(identity,multiply(B,identity))) = multiply(multiply(A,multiply(identity,B)),identity). [para(55(a,1),738(a,1,2))].
% 0.97/1.29 809 multiply(multiply(multiply(A,A),multiply(multiply(A,B),identity)),multiply(C,identity)) = multiply(multiply(multiply(A,multiply(multiply(A,A),B)),C),identity). [para(163(a,1),738(a,1,1))].
% 0.97/1.29 810 multiply(multiply(A,identity),multiply(multiply(B,B),multiply(multiply(B,C),identity))) = multiply(multiply(A,multiply(B,multiply(multiply(B,B),C))),identity). [para(163(a,1),738(a,1,2))].
% 0.97/1.29 816 multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(A,multiply(multiply(A,A),identity)))) = multiply(identity,multiply(A,identity)). [para(738(a,1),338(a,1,1,2)),rewrite([738(6),464(4),738(11),738(10),464(8),738(15),738(14),464(12)])].
% 0.97/1.29 828 multiply(identity,multiply(identity,multiply(multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(multiply(multiply(A,A),multiply(multiply(A,identity),identity)),multiply(multiply(A,A),multiply(multiply(A,identity),identity)))),identity))) = multiply(A,identity). [back_rewrite(480),rewrite([809(24)])].
% 0.97/1.29 834 multiply(multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))),B),identity) = multiply(A,multiply(B,identity)). [para(206(a,1),805(a,2,1,1)),rewrite([1(4),55(6),55(9),55(8),20(10)]),flip(a)].
% 0.97/1.29 835 multiply(multiply(identity,multiply(A,multiply(multiply(A,A),identity))),multiply(B,identity)) = multiply(multiply(multiply(identity,multiply(A,multiply(A,A))),B),identity). [para(464(a,1),805(a,1,1,2))].
% 0.97/1.29 838 multiply(multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,A),identity)))),multiply(A,multiply(multiply(A,identity),identity))) = identity. [back_rewrite(773),rewrite([834(22)])].
% 0.97/1.29 842 multiply(multiply(A,multiply(identity,multiply(identity,multiply(identity,multiply(B,identity))))),identity) = multiply(multiply(A,identity),B). [para(206(a,1),806(a,2,1,2)),rewrite([1(6),55(8),55(11),55(10),20(12)]),flip(a)].
% 0.97/1.29 845 multiply(multiply(A,identity),multiply(B,C)) = multiply(multiply(A,B),multiply(identity,C)). [back_rewrite(345),rewrite([842(12)])].
% 0.97/1.29 846 multiply(multiply(A,A),multiply(multiply(A,multiply(multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))))),identity)) = multiply(multiply(A,multiply(A,multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(multiply(A,A),multiply(A,A)),identity),identity)))),identity))),identity). [para(130(a,1),163(a,1,1,2)),flip(a)].
% 0.97/1.29 878 multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(identity,B)) = multiply(multiply(A,A),multiply(multiply(A,identity),B)). [para(845(a,1),208(a,2)),rewrite([738(8),738(12),20(15),738(10)]),flip(a)].
% 0.97/1.29 890 multiply(multiply(A,multiply(multiply(A,A),identity)),multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),B)) = multiply(identity,multiply(A,B)). [para(338(a,1),845(a,2,1)),rewrite([464(4),550(16)])].
% 0.97/1.29 895 multiply(multiply(A,multiply(A,identity)),multiply(identity,multiply(A,identity))) = multiply(A,multiply(multiply(A,A),identity)). [para(845(a,1),418(a,2)),rewrite([738(8),738(13),208(14)]),flip(a)].
% 0.97/1.29 902 multiply(multiply(A,multiply(B,B)),multiply(identity,multiply(multiply(B,multiply(B,multiply(multiply(B,B),identity))),identity))) = multiply(multiply(A,identity),multiply(B,B)). [para(482(a,1),845(a,1,2)),flip(a)].
% 0.97/1.29 907 multiply(multiply(A,multiply(A,multiply(multiply(A,A),identity))),identity) = identity. [para(845(a,2),635(a,1)),rewrite([810(9)])].
% 0.97/1.29 913 multiply(multiply(multiply(A,identity),multiply(B,C)),identity) = multiply(multiply(multiply(A,B),multiply(identity,C)),identity). [para(845(a,1),738(a,2,1)),rewrite([738(8)])].
% 0.97/1.29 922 multiply(multiply(A,multiply(B,identity)),multiply(identity,multiply(C,D))) = multiply(multiply(A,identity),multiply(multiply(B,C),multiply(identity,D))). [para(845(a,1),845(a,1,2)),flip(a)].
% 0.97/1.29 924 multiply(multiply(A,multiply(B,C)),multiply(identity,multiply(identity,D))) = multiply(multiply(A,identity),multiply(multiply(B,identity),multiply(C,D))). [para(845(a,2),845(a,1,2)),flip(a)].
% 0.97/1.29 925 multiply(multiply(multiply(A,identity),multiply(B,C)),multiply(identity,D)) = multiply(multiply(multiply(A,B),identity),multiply(multiply(identity,C),D)). [para(845(a,2),845(a,2,1)),flip(a)].
% 0.97/1.29 930 multiply(multiply(A,multiply(B,B)),identity) = multiply(multiply(A,identity),multiply(B,B)). [back_rewrite(902),rewrite([907(10),1(5)])].
% 0.97/1.29 931 multiply(multiply(A,A),identity) = multiply(A,A). [back_rewrite(482),rewrite([907(8)])].
% 0.97/1.29 934 multiply(multiply(A,identity),multiply(A,A)) = multiply(A,multiply(A,A)). [back_rewrite(895),rewrite([922(8),1(6),931(5),931(7)])].
% 0.97/1.29 943 multiply(multiply(A,A),multiply(multiply(A,identity),identity)) = multiply(A,multiply(A,A)). [back_rewrite(397),rewrite([924(14),931(5),206(10),1(9),1(8),1(7),1(6),931(5),934(4)]),flip(a)].
% 0.97/1.29 952 multiply(multiply(A,A),multiply(multiply(A,identity),multiply(multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A)))))) = multiply(multiply(A,multiply(A,multiply(multiply(A,multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))))),identity))),identity). [back_rewrite(846),rewrite([930(19),931(31),931(31)])].
% 0.97/1.29 954 multiply(identity,multiply(identity,multiply(identity,multiply(A,identity)))) = multiply(A,identity). [back_rewrite(828),rewrite([931(5),943(10),943(12),338(10),55(6)])].
% 0.97/1.29 968 multiply(multiply(A,multiply(A,multiply(A,A))),identity) = identity. [back_rewrite(907),rewrite([931(3)])].
% 0.97/1.29 970 multiply(multiply(A,multiply(A,A)),multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),B)) = multiply(identity,multiply(A,B)). [back_rewrite(890),rewrite([931(3)])].
% 0.97/1.29 971 multiply(multiply(A,multiply(A,A)),multiply(identity,B)) = multiply(multiply(A,A),multiply(multiply(A,identity),B)). [back_rewrite(878),rewrite([931(3)])].
% 0.97/1.29 975 multiply(multiply(identity,multiply(identity,multiply(identity,multiply(A,A)))),multiply(A,multiply(multiply(A,identity),identity))) = identity. [back_rewrite(838),rewrite([931(6)])].
% 0.97/1.29 977 multiply(multiply(multiply(identity,multiply(A,multiply(A,A))),B),identity) = multiply(multiply(identity,multiply(A,multiply(A,A))),multiply(B,identity)). [back_rewrite(835),rewrite([931(4)]),flip(a)].
% 0.97/1.29 982 multiply(identity,multiply(A,identity)) = multiply(identity,A). [back_rewrite(816),rewrite([931(3),931(5),931(7),338(8)]),flip(a)].
% 0.97/1.29 1013 multiply(multiply(A,multiply(multiply(A,A),multiply(B,multiply(multiply(B,identity),C)))),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,C)))),multiply(multiply(B,multiply(identity,multiply(identity,multiply(identity,C)))),multiply(B,multiply(identity,multiply(identity,multiply(identity,C))))))) = multiply(multiply(A,A),multiply(multiply(A,multiply(B,identity)),identity)). [back_rewrite(752),rewrite([982(13),982(20),982(27),931(31)])].
% 0.97/1.29 1014 multiply(identity,multiply(identity,multiply(identity,A))) = A. [back_rewrite(751),rewrite([982(16),982(25),982(34),931(39),1013(39),206(8),982(8),982(6)])].
% 0.97/1.29 1039 multiply(multiply(multiply(multiply(A,A),multiply(A,A)),multiply(multiply(A,A),multiply(A,A))),multiply(A,A)) = multiply(multiply(multiply(A,A),multiply(multiply(multiply(A,A),multiply(A,multiply(multiply(A,identity),identity))),identity)),identity). [back_rewrite(271),rewrite([931(10)])].
% 0.97/1.29 1046 multiply(multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))),multiply(multiply(identity,multiply(A,multiply(A,A))),multiply(A,identity))) = multiply(identity,multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A)))). [back_rewrite(652),rewrite([977(14),943(24),931(23)])].
% 0.97/1.29 1047 multiply(multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))),multiply(A,multiply(A,A))) = multiply(identity,A). [back_rewrite(636),rewrite([943(11),982(14),982(12)])].
% 0.97/1.29 1062 multiply(multiply(A,identity),B) = multiply(multiply(A,B),identity). [back_rewrite(842),rewrite([982(6),1014(6)]),flip(a)].
% 0.97/1.29 1063 multiply(multiply(A,B),identity) = multiply(A,multiply(B,identity)). [back_rewrite(834),rewrite([982(6),1014(6)])].
% 0.97/1.29 1065 multiply(A,multiply(B,identity)) = multiply(A,B). [back_rewrite(772),rewrite([1063(8),738(8),1063(6),1014(9),982(9),1014(9)])].
% 0.97/1.29 1066 multiply(A,multiply(multiply(A,identity),B)) = multiply(A,multiply(A,B)). [back_rewrite(729),rewrite([1065(8),1014(8),1014(10),1063(7),1065(7)])].
% 0.97/1.29 1083 multiply(multiply(A,A),multiply(A,B)) = multiply(A,multiply(multiply(A,A),B)). [back_rewrite(208),rewrite([1063(7),1065(7),1062(8,R),931(6),1014(9)])].
% 0.97/1.29 1084 multiply(A,multiply(A,multiply(multiply(A,A),B))) = B. [back_rewrite(206),rewrite([1063(4),1065(4),1083(3),1065(10),1014(10)])].
% 0.97/1.29 1094 multiply(multiply(A,multiply(multiply(A,A),A)),multiply(A,multiply(multiply(A,A),A))) = multiply(multiply(A,identity),multiply(A,multiply(A,A))). [back_rewrite(498),rewrite([971(6),934(5),1083(4),1083(3),1084(4),1062(4,R),934(4),1062(5,R),1083(8),1083(11)]),flip(a)].
% 0.97/1.29 1096 multiply(multiply(A,identity),multiply(A,multiply(A,A))) = identity. [back_rewrite(968),rewrite([1062(5,R)])].
% 0.97/1.29 1097 multiply(multiply(A,A),A) = multiply(A,multiply(A,A)). [back_rewrite(952),rewrite([1083(6),1083(9),1094(10),1096(8),1083(7),1083(10),1094(11),1096(9),1(6),1063(5),1(4),1065(4),1083(5),1083(8),1083(11),1094(12),1096(10),1062(7,R),1066(8),1084(6),1065(5),1062(6,R),934(6)])].
% 0.97/1.29 1105 multiply(A,identity) = A. [back_rewrite(954),rewrite([1065(6),1014(6)]),flip(a)].
% 0.97/1.29 1143 multiply(A,multiply(A,multiply(A,A))) = identity. [back_rewrite(975),rewrite([1014(7),1105(3),1105(3),1083(3),1097(2)])].
% 0.97/1.29 1157 multiply(identity,multiply(A,A)) = multiply(A,A). [back_rewrite(1039),rewrite([1083(3),1097(2),1143(3),1083(4),1097(3),1143(4),1105(3),1105(7),1105(7),1083(7),1097(6),1143(7),1105(7),1105(6),1105(6)])].
% 0.97/1.29 1168 multiply(multiply(A,B),multiply(identity,C)) = multiply(A,multiply(B,C)). [back_rewrite(913),rewrite([1105(2),1105(4),1105(8)]),flip(a)].
% 0.97/1.29 1182 multiply(multiply(A,B),multiply(multiply(identity,C),D)) = multiply(A,multiply(multiply(B,C),D)). [back_rewrite(925),rewrite([1105(2),1168(5),1105(6)]),flip(a)].
% 0.97/1.29 1188 multiply(multiply(A,multiply(A,A)),multiply(A,multiply(A,A))) = multiply(A,A). [back_rewrite(1046),rewrite([1157(7),1105(11),1182(11),970(9),1157(3),1157(8)]),flip(a)].
% 0.97/1.29 1197 multiply(identity,A) = A. [back_rewrite(1047),rewrite([1188(5),1083(4),1083(3),1097(2),1143(3),1105(2)]),flip(a)].
% 0.97/1.29 1198 $F # answer(prove_order3). [resolve(1197,a,3,a)].
% 0.97/1.29
% 0.97/1.29 % SZS output end Refutation
% 0.97/1.29 ============================== end of proof ==========================
% 0.97/1.29
% 0.97/1.29 ============================== STATISTICS ============================
% 0.97/1.29
% 0.97/1.29 Given=70. Generated=3911. Kept=1197. proofs=1.
% 0.97/1.29 Usable=5. Sos=39. Demods=140. Limbo=100, Disabled=1055. Hints=0.
% 0.97/1.29 Megabytes=2.01.
% 0.97/1.29 User_CPU=0.32, System_CPU=0.01, Wall_clock=1.
% 0.97/1.29
% 0.97/1.29 ============================== end of statistics =====================
% 0.97/1.29
% 0.97/1.29 ============================== end of search =========================
% 0.97/1.29
% 0.97/1.29 THEOREM PROVED
% 0.97/1.29 % SZS status Unsatisfiable
% 0.97/1.29
% 0.97/1.29 Exiting with 1 proof.
% 0.97/1.29
% 0.97/1.29 Process 18422 exit (max_proofs) Mon Jun 13 04:10:28 2022
% 0.97/1.29 Prover9 interrupted
%------------------------------------------------------------------------------