TSTP Solution File: GRP121-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP121-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 1.01s 1.33s
% Output : Refutation 1.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP121-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 09:41:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.01/1.33 ============================== Prover9 ===============================
% 1.01/1.33 Prover9 (32) version 2009-11A, November 2009.
% 1.01/1.33 Process 15211 was started by sandbox on n015.cluster.edu,
% 1.01/1.33 Tue Jun 14 09:41:24 2022
% 1.01/1.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15057_n015.cluster.edu".
% 1.01/1.33 ============================== end of head ===========================
% 1.01/1.33
% 1.01/1.33 ============================== INPUT =================================
% 1.01/1.33
% 1.01/1.33 % Reading from file /tmp/Prover9_15057_n015.cluster.edu
% 1.01/1.33
% 1.01/1.33 set(prolog_style_variables).
% 1.01/1.33 set(auto2).
% 1.01/1.33 % set(auto2) -> set(auto).
% 1.01/1.33 % set(auto) -> set(auto_inference).
% 1.01/1.33 % set(auto) -> set(auto_setup).
% 1.01/1.33 % set(auto_setup) -> set(predicate_elim).
% 1.01/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.01/1.33 % set(auto) -> set(auto_limits).
% 1.01/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.01/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.01/1.33 % set(auto) -> set(auto_denials).
% 1.01/1.33 % set(auto) -> set(auto_process).
% 1.01/1.33 % set(auto2) -> assign(new_constants, 1).
% 1.01/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 1.01/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 1.01/1.33 % set(auto2) -> assign(max_hours, 1).
% 1.01/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.01/1.33 % set(auto2) -> assign(max_seconds, 0).
% 1.01/1.33 % set(auto2) -> assign(max_minutes, 5).
% 1.01/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.01/1.33 % set(auto2) -> set(sort_initial_sos).
% 1.01/1.33 % set(auto2) -> assign(sos_limit, -1).
% 1.01/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.01/1.33 % set(auto2) -> assign(max_megs, 400).
% 1.01/1.33 % set(auto2) -> assign(stats, some).
% 1.01/1.33 % set(auto2) -> clear(echo_input).
% 1.01/1.33 % set(auto2) -> set(quiet).
% 1.01/1.33 % set(auto2) -> clear(print_initial_clauses).
% 1.01/1.33 % set(auto2) -> clear(print_given).
% 1.01/1.33 assign(lrs_ticks,-1).
% 1.01/1.33 assign(sos_limit,10000).
% 1.01/1.33 assign(order,kbo).
% 1.01/1.33 set(lex_order_vars).
% 1.01/1.33 clear(print_given).
% 1.01/1.33
% 1.01/1.33 % formulas(sos). % not echoed (3 formulas)
% 1.01/1.33
% 1.01/1.33 ============================== end of input ==========================
% 1.01/1.33
% 1.01/1.33 % From the command line: assign(max_seconds, 300).
% 1.01/1.33
% 1.01/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.01/1.33
% 1.01/1.33 % Formulas that are not ordinary clauses:
% 1.01/1.33
% 1.01/1.33 ============================== end of process non-clausal formulas ===
% 1.01/1.33
% 1.01/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 1.01/1.33
% 1.01/1.33 ============================== PREDICATE ELIMINATION =================
% 1.01/1.33
% 1.01/1.33 ============================== end predicate elimination =============
% 1.01/1.33
% 1.01/1.33 Auto_denials:
% 1.01/1.33 % copying label prove_order3 to answer in negative clause
% 1.01/1.33
% 1.01/1.33 Term ordering decisions:
% 1.01/1.33 Function symbol KB weights: identity=1. a=1. multiply=1.
% 1.01/1.33
% 1.01/1.33 ============================== end of process initial clauses ========
% 1.01/1.33
% 1.01/1.33 ============================== CLAUSES FOR SEARCH ====================
% 1.01/1.33
% 1.01/1.33 ============================== end of clauses for search =============
% 1.01/1.33
% 1.01/1.33 ============================== SEARCH ================================
% 1.01/1.33
% 1.01/1.33 % Starting search at 0.01 seconds.
% 1.01/1.33
% 1.01/1.33 ============================== PROOF =================================
% 1.01/1.33 % SZS status Unsatisfiable
% 1.01/1.33 % SZS output start Refutation
% 1.01/1.33
% 1.01/1.33 % Proof 1 at 0.31 (+ 0.01) seconds: prove_order3.
% 1.01/1.33 % Length of proof is 108.
% 1.01/1.33 % Level of proof is 33.
% 1.01/1.33 % Maximum clause weight is 91.000.
% 1.01/1.33 % Given clauses 70.
% 1.01/1.33
% 1.01/1.33 1 multiply(identity,identity) = identity # label(single_axiom2) # label(axiom). [assumption].
% 1.01/1.33 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].
% 1.01/1.33 3 multiply(a,identity) != a # label(prove_order3) # label(negated_conjecture) # answer(prove_order3). [assumption].
% 1.01/1.33 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))].
% 1.01/1.33 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)])].
% 1.01/1.33 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)])].
% 1.01/1.33 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))].
% 1.01/1.33 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)].
% 1.01/1.33 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)])].
% 1.01/1.33 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))].
% 1.01/1.33 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)])].
% 1.01/1.33 20 multiply(identity,multiply(identity,multiply(identity,multiply(multiply(A,identity),identity)))) = A. [back_rewrite(9),rewrite([19(10),19(9)])].
% 1.01/1.33 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))].
% 1.01/1.33 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))].
% 1.01/1.33 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)].
% 1.01/1.33 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)].
% 1.01/1.33 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)].
% 1.01/1.33 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)].
% 1.01/1.33 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)])].
% 1.01/1.33 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)])].
% 1.01/1.33 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))].
% 1.01/1.33 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))].
% 1.01/1.33 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))].
% 1.01/1.33 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))].
% 1.01/1.33 106 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)].
% 1.01/1.33 110 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)])].
% 1.01/1.33 114 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))].
% 1.01/1.33 134 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)].
% 1.01/1.33 144 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)])].
% 1.01/1.33 154 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)].
% 1.01/1.33 158 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)].
% 1.01/1.33 161 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)].
% 1.01/1.33 163 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)].
% 1.01/1.33 166 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)].
% 1.01/1.33 175 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)])].
% 1.01/1.33 195 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)])].
% 1.01/1.33 198 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)])].
% 1.01/1.33 201 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)])].
% 1.01/1.33 206 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)])].
% 1.01/1.33 208 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))].
% 1.01/1.33 219 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)].
% 1.01/1.33 223 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)])].
% 1.01/1.33 230 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)])].
% 1.01/1.33 253 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)])].
% 1.01/1.33 258 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)].
% 1.01/1.33 265 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)].
% 1.01/1.33 273 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)])].
% 1.01/1.33 274 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)].
% 1.01/1.33 314 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)])].
% 1.01/1.33 320 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)].
% 1.01/1.33 329 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)])].
% 1.01/1.33 333 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)].
% 1.01/1.33 338 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)].
% 1.01/1.33 343 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)].
% 1.01/1.33 345 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)].
% 1.01/1.33 388 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))].
% 1.01/1.33 389 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)])].
% 1.01/1.33 394 multiply(multiply(identity,A),multiply(identity,multiply(multiply(A,A),multiply(multiply(A,identity),identity)))) = identity. [back_rewrite(273),rewrite([389(22),274(17)])].
% 1.01/1.33 397 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)])].
% 1.01/1.33 418 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)].
% 1.01/1.33 459 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)].
% 1.01/1.33 460 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)])].
% 1.01/1.33 464 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)])].
% 1.01/1.33 466 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)])].
% 1.01/1.33 480 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)])].
% 1.01/1.33 482 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))].
% 1.01/1.33 504 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)].
% 1.01/1.33 539 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)])].
% 1.01/1.33 550 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)].
% 1.01/1.33 560 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)])].
% 1.01/1.33 564 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)])].
% 1.01/1.33 610 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)].
% 1.01/1.33 635 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)].
% 1.01/1.33 663 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)])].
% 1.01/1.33 665 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)].
% 1.01/1.33 667 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)])].
% 1.01/1.33 692 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)])].
% 1.01/1.33 705 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)])].
% 1.01/1.33 706 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)])].
% 1.01/1.33 732 multiply(A,multiply(multiply(A,identity),multiply(B,identity))) = multiply(A,multiply(multiply(A,B),identity)). [back_rewrite(26),rewrite([692(8)])].
% 1.01/1.33 738 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)].
% 1.01/1.33 751 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)])].
% 1.01/1.33 752 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)])].
% 1.01/1.33 772 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)])].
% 1.01/1.33 805 multiply(multiply(identity,multiply(A,identity)),multiply(B,identity)) = multiply(multiply(multiply(identity,A),B),identity). [para(55(a,1),738(a,1,1))].
% 1.01/1.33 806 multiply(multiply(A,identity),multiply(identity,multiply(B,identity))) = multiply(multiply(A,multiply(identity,B)),identity). [para(55(a,1),738(a,1,2))].
% 1.01/1.33 809 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))].
% 1.01/1.33 810 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))].
% 1.01/1.33 816 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)])].
% 1.01/1.33 828 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)])].
% 1.01/1.33 834 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)].
% 1.01/1.33 842 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)].
% 1.01/1.33 845 multiply(multiply(A,identity),multiply(B,C)) = multiply(multiply(A,B),multiply(identity,C)). [back_rewrite(345),rewrite([842(12)])].
% 1.01/1.33 895 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)].
% 1.01/1.33 907 multiply(multiply(A,multiply(A,multiply(multiply(A,A),identity))),identity) = identity. [para(845(a,2),635(a,1)),rewrite([810(9)])].
% 1.01/1.33 922 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)].
% 1.01/1.33 924 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)].
% 1.01/1.33 931 multiply(multiply(A,A),identity) = multiply(A,A). [back_rewrite(482),rewrite([907(8)])].
% 1.01/1.33 934 multiply(multiply(A,identity),multiply(A,A)) = multiply(A,multiply(A,A)). [back_rewrite(895),rewrite([922(8),1(6),931(5),931(7)])].
% 1.01/1.33 943 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)].
% 1.01/1.33 954 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)])].
% 1.01/1.33 982 multiply(identity,multiply(A,identity)) = multiply(identity,A). [back_rewrite(816),rewrite([931(3),931(5),931(7),338(8)]),flip(a)].
% 1.01/1.33 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)])].
% 1.01/1.33 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)])].
% 1.01/1.33 1063 multiply(multiply(A,B),identity) = multiply(A,multiply(B,identity)). [back_rewrite(834),rewrite([982(6),1014(6)])].
% 1.01/1.33 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)])].
% 1.01/1.33 1105 multiply(A,identity) = A. [back_rewrite(954),rewrite([1065(6),1014(6)]),flip(a)].
% 1.01/1.33 1106 $F # answer(prove_order3). [resolve(1105,a,3,a)].
% 1.01/1.33
% 1.01/1.33 % SZS output end Refutation
% 1.01/1.33 ============================== end of proof ==========================
% 1.01/1.33
% 1.01/1.33 ============================== STATISTICS ============================
% 1.01/1.33
% 1.01/1.33 Given=70. Generated=3670. Kept=1105. proofs=1.
% 1.01/1.33 Usable=18. Sos=157. Demods=281. Limbo=123, Disabled=809. Hints=0.
% 1.01/1.33 Megabytes=1.96.
% 1.01/1.33 User_CPU=0.31, System_CPU=0.01, Wall_clock=1.
% 1.01/1.33
% 1.01/1.33 ============================== end of statistics =====================
% 1.01/1.33
% 1.01/1.33 ============================== end of search =========================
% 1.01/1.33
% 1.01/1.33 THEOREM PROVED
% 1.01/1.33 % SZS status Unsatisfiable
% 1.01/1.33
% 1.01/1.33 Exiting with 1 proof.
% 1.01/1.33
% 1.01/1.33 Process 15211 exit (max_proofs) Tue Jun 14 09:41:25 2022
% 1.01/1.33 Prover9 interrupted
%------------------------------------------------------------------------------