TSTP Solution File: GRP050-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP050-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 11:16:56 EDT 2022
% Result : Unsatisfiable 1.86s 2.14s
% Output : Refutation 1.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP050-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n027.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 : Tue Jun 14 00:56:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.86/2.14 ============================== Prover9 ===============================
% 1.86/2.14 Prover9 (32) version 2009-11A, November 2009.
% 1.86/2.14 Process 25440 was started by sandbox on n027.cluster.edu,
% 1.86/2.14 Tue Jun 14 00:56:48 2022
% 1.86/2.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25286_n027.cluster.edu".
% 1.86/2.14 ============================== end of head ===========================
% 1.86/2.14
% 1.86/2.14 ============================== INPUT =================================
% 1.86/2.14
% 1.86/2.14 % Reading from file /tmp/Prover9_25286_n027.cluster.edu
% 1.86/2.14
% 1.86/2.14 set(prolog_style_variables).
% 1.86/2.14 set(auto2).
% 1.86/2.14 % set(auto2) -> set(auto).
% 1.86/2.14 % set(auto) -> set(auto_inference).
% 1.86/2.14 % set(auto) -> set(auto_setup).
% 1.86/2.14 % set(auto_setup) -> set(predicate_elim).
% 1.86/2.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.86/2.14 % set(auto) -> set(auto_limits).
% 1.86/2.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.86/2.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.86/2.14 % set(auto) -> set(auto_denials).
% 1.86/2.14 % set(auto) -> set(auto_process).
% 1.86/2.14 % set(auto2) -> assign(new_constants, 1).
% 1.86/2.14 % set(auto2) -> assign(fold_denial_max, 3).
% 1.86/2.14 % set(auto2) -> assign(max_weight, "200.000").
% 1.86/2.14 % set(auto2) -> assign(max_hours, 1).
% 1.86/2.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.86/2.14 % set(auto2) -> assign(max_seconds, 0).
% 1.86/2.14 % set(auto2) -> assign(max_minutes, 5).
% 1.86/2.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.86/2.14 % set(auto2) -> set(sort_initial_sos).
% 1.86/2.14 % set(auto2) -> assign(sos_limit, -1).
% 1.86/2.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.86/2.14 % set(auto2) -> assign(max_megs, 400).
% 1.86/2.14 % set(auto2) -> assign(stats, some).
% 1.86/2.14 % set(auto2) -> clear(echo_input).
% 1.86/2.14 % set(auto2) -> set(quiet).
% 1.86/2.14 % set(auto2) -> clear(print_initial_clauses).
% 1.86/2.14 % set(auto2) -> clear(print_given).
% 1.86/2.14 assign(lrs_ticks,-1).
% 1.86/2.14 assign(sos_limit,10000).
% 1.86/2.14 assign(order,kbo).
% 1.86/2.14 set(lex_order_vars).
% 1.86/2.14 clear(print_given).
% 1.86/2.14
% 1.86/2.14 % formulas(sos). % not echoed (2 formulas)
% 1.86/2.14
% 1.86/2.14 ============================== end of input ==========================
% 1.86/2.14
% 1.86/2.14 % From the command line: assign(max_seconds, 300).
% 1.86/2.14
% 1.86/2.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.86/2.14
% 1.86/2.14 % Formulas that are not ordinary clauses:
% 1.86/2.14
% 1.86/2.14 ============================== end of process non-clausal formulas ===
% 1.86/2.14
% 1.86/2.14 ============================== PROCESS INITIAL CLAUSES ===============
% 1.86/2.14
% 1.86/2.14 ============================== PREDICATE ELIMINATION =================
% 1.86/2.14
% 1.86/2.14 ============================== end predicate elimination =============
% 1.86/2.14
% 1.86/2.14 Auto_denials:
% 1.86/2.14 % copying label prove_these_axioms to answer in negative clause
% 1.86/2.14
% 1.86/2.14 Term ordering decisions:
% 1.86/2.14
% 1.86/2.14 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.86/2.14 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.86/2.14
% 1.86/2.14 ============================== end of process initial clauses ========
% 1.86/2.14
% 1.86/2.14 ============================== CLAUSES FOR SEARCH ====================
% 1.86/2.14
% 1.86/2.14 ============================== end of clauses for search =============
% 1.86/2.14
% 1.86/2.14 ============================== SEARCH ================================
% 1.86/2.14
% 1.86/2.14 % Starting search at 0.01 seconds.
% 1.86/2.14
% 1.86/2.14 ============================== PROOF =================================
% 1.86/2.14 % SZS status Unsatisfiable
% 1.86/2.14 % SZS output start Refutation
% 1.86/2.14
% 1.86/2.14 % Proof 1 at 1.15 (+ 0.02) seconds: prove_these_axioms.
% 1.86/2.14 % Length of proof is 149.
% 1.86/2.14 % Level of proof is 35.
% 1.86/2.14 % Maximum clause weight is 156.000.
% 1.86/2.14 % Given clauses 27.
% 1.86/2.14
% 1.86/2.14 1 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),multiply(inverse(B),B))))) = C # label(single_axiom) # label(axiom). [assumption].
% 1.86/2.14 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 1.86/2.14 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [copy(2),flip(a)].
% 1.86/2.14 4 multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),multiply(inverse(D),multiply(inverse(D),D))))))))) = C. [para(1(a,1),1(a,1,2,1,1,1,1,1))].
% 1.86/2.14 5 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(D),multiply(inverse(B),multiply(inverse(B),B))))). [para(1(a,1),1(a,1,2,1,1,1)),flip(a)].
% 1.86/2.14 7 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E)))))))) = multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),multiply(inverse(D),D))))). [para(4(a,1),1(a,1,2,1,1,1)),flip(a)].
% 1.86/2.14 8 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))))))). [para(1(a,1),4(a,1,2,1,1,1)),flip(a)].
% 1.86/2.14 18 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(inverse(B),multiply(inverse(B),B)))))) = C. [para(5(a,1),1(a,1,2))].
% 1.86/2.14 44 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C))),multiply(inverse(B),multiply(inverse(B),B)))) = C. [para(5(a,2),4(a,1)),rewrite([1(11)])].
% 1.86/2.14 45 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,inverse(multiply(inverse(A),multiply(inverse(D),multiply(inverse(D),D)))))),multiply(inverse(multiply(C,inverse(multiply(inverse(A),multiply(inverse(D),multiply(inverse(D),D)))))),multiply(C,inverse(multiply(inverse(A),multiply(inverse(D),multiply(inverse(D),D))))))))) = multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),multiply(inverse(D),D))))). [para(4(a,1),5(a,1,1,1,1,1,1)),rewrite([7(48),7(57),7(66)])].
% 1.86/2.14 54 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(multiply(D,E)),B)),F))),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,multiply(D,inverse(multiply(inverse(F),multiply(inverse(E),multiply(inverse(E),E)))))). [para(5(a,1),5(a,2,2))].
% 1.86/2.14 64 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(multiply(D,E)),inverse(multiply(inverse(C),multiply(inverse(multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),multiply(inverse(E),E)))))),multiply(inverse(multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),multiply(inverse(E),E)))))),multiply(D,inverse(multiply(inverse(A),multiply(inverse(E),multiply(inverse(E),E)))))))))). [para(18(a,1),5(a,1,1,1,1,1,1,1,1))].
% 1.86/2.14 101 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(44(a,1),18(a,1,2,2)),flip(a)].
% 1.86/2.14 102 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(B),multiply(inverse(B),B)))) = C. [para(44(a,1),44(a,1,1,1,1,1,1,1)),rewrite([44(15)])].
% 1.86/2.14 133 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),D))),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(A,inverse(multiply(inverse(multiply(E,D)),multiply(E,multiply(inverse(B),B))))). [para(101(a,1),5(a,2,2,1))].
% 1.86/2.14 147 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(C,D)),multiply(C,multiply(inverse(B),B)))))) = multiply(inverse(B),D). [para(101(a,1),18(a,1,2,2,1))].
% 1.86/2.14 153 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(101(a,1),101(a,1))].
% 1.86/2.14 181 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),multiply(inverse(C),multiply(inverse(C),C)))))),multiply(A,E)) = multiply(inverse(D),multiply(B,E)). [para(1(a,1),153(a,1,1,1)),flip(a)].
% 1.86/2.14 182 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),multiply(inverse(D),multiply(inverse(D),D)))))) = multiply(inverse(multiply(C,B)),E). [para(1(a,1),153(a,1,2)),flip(a)].
% 1.86/2.14 189 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(E),multiply(inverse(E),E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,E)),B)),multiply(inverse(E),multiply(inverse(E),E)))))))))),multiply(A,F)) = multiply(inverse(C),multiply(D,F)). [para(4(a,1),153(a,1,1,1)),flip(a)].
% 1.86/2.14 193 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(C,D))),E)),multiply(inverse(multiply(C,D)),multiply(inverse(multiply(F,D)),multiply(F,D))))) = multiply(A,inverse(multiply(inverse(E),multiply(inverse(B),multiply(inverse(B),B))))). [para(153(a,1),5(a,1,1,2,2))].
% 1.86/2.14 198 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(D),multiply(inverse(multiply(B,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D. [para(153(a,1),18(a,1,2,2,1,2,2))].
% 1.86/2.14 208 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)). [para(153(a,1),153(a,1,1,1))].
% 1.86/2.14 209 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))). [para(153(a,1),153(a,1,2))].
% 1.86/2.14 236 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)). [para(102(a,1),153(a,1,1)),flip(a)].
% 1.86/2.14 248 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),multiply(D,multiply(inverse(B),B)))))) = multiply(inverse(B),inverse(multiply(inverse(multiply(inverse(E),C)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),multiply(inverse(F),multiply(inverse(F),F))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),multiply(inverse(F),multiply(inverse(F),F))))),inverse(multiply(inverse(multiply(inverse(multiply(D,F)),E)),multiply(inverse(F),multiply(inverse(F),F))))))))). [para(4(a,1),147(a,1,2,2,1,1,1))].
% 1.86/2.14 251 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),multiply(inverse(A),A)))) = inverse(multiply(inverse(multiply(C,B)),multiply(C,multiply(inverse(A),A)))). [para(147(a,1),5(a,1,1,1,1)),rewrite([1(27)])].
% 1.86/2.14 265 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,E))),multiply(inverse(multiply(F,D)),multiply(inverse(B),B)))))) = multiply(inverse(B),multiply(F,E)). [para(153(a,1),147(a,1,2,2,1,1,1))].
% 1.86/2.14 281 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),D) = multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),D). [para(1(a,1),208(a,1,2)),rewrite([182(23)])].
% 1.86/2.14 488 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,C)),multiply(inverse(F),F))))) = multiply(A,inverse(multiply(inverse(multiply(inverse(F),multiply(E,D))),multiply(inverse(F),multiply(inverse(F),F))))). [para(208(a,2),7(a,2,2,1)),rewrite([7(48)]),flip(a)].
% 1.86/2.14 535 multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(A),multiply(inverse(multiply(E,C)),multiply(E,D))). [para(1(a,1),209(a,1,1,1)),rewrite([181(23)])].
% 1.86/2.14 616 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))). [para(209(a,1),208(a,1))].
% 1.86/2.14 705 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))). [para(102(a,1),535(a,1,1)),rewrite([102(16)])].
% 1.86/2.14 974 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D)))),multiply(inverse(multiply(E,C)),multiply(inverse(multiply(E,C)),multiply(E,C))))) = multiply(E,D). [para(616(a,1),5(a,1,1,1,1)),rewrite([1(28)])].
% 1.86/2.14 1004 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),E)),multiply(inverse(multiply(F,multiply(V6,D))),multiply(F,multiply(V6,C))))))) = multiply(inverse(multiply(B,C)),E). [para(616(a,1),147(a,1,2,2,1,2))].
% 1.86/2.14 1040 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),E)),multiply(inverse(multiply(F,D)),multiply(F,multiply(A,multiply(B,V6))))) = multiply(inverse(multiply(V7,E)),multiply(V7,multiply(inverse(multiply(V8,multiply(V9,C))),multiply(V8,multiply(V9,V6))))). [para(616(a,1),209(a,2,2,2))].
% 1.86/2.14 1074 inverse(multiply(inverse(multiply(A,B)),multiply(A,multiply(inverse(C),C)))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,multiply(inverse(C),C)))). [para(153(a,1),251(a,1,1))].
% 1.86/2.14 1087 inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),multiply(inverse(E),E)))) = inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(F,multiply(inverse(E),E)))). [para(208(a,2),251(a,1,1))].
% 1.86/2.14 1120 inverse(multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(B),B)))) = inverse(multiply(inverse(multiply(D,multiply(E,C))),multiply(D,multiply(E,B)))). [para(616(a,1),251(a,1,1)),flip(a)].
% 1.86/2.14 1139 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),multiply(inverse(multiply(E,C)),multiply(E,multiply(A,B))))) = inverse(multiply(inverse(multiply(F,D)),multiply(F,multiply(inverse(multiply(V6,B)),multiply(V6,B))))). [para(209(a,1),1074(a,1,1,2))].
% 1.86/2.14 1520 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(B),B))) = C. [para(236(a,2),18(a,1,2,2,1)),rewrite([147(30)])].
% 1.86/2.14 1611 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),B)),multiply(F,multiply(inverse(multiply(inverse(multiply(V6,E)),multiply(V6,F))),V7)))) = multiply(inverse(multiply(V8,C)),multiply(V8,multiply(A,multiply(D,V7)))). [para(236(a,1),209(a,1,2,2))].
% 1.86/2.14 1634 multiply(A,multiply(inverse(multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),D)),multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),V6)))) = multiply(A,multiply(inverse(multiply(V7,D)),multiply(V7,multiply(B,V6)))). [para(236(a,1),705(a,1,2,2))].
% 1.86/2.14 1713 multiply(inverse(multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,D)))),multiply(A,inverse(multiply(inverse(E),multiply(inverse(multiply(F,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D))),multiply(inverse(multiply(V7,multiply(B,D))),multiply(V7,multiply(B,D)))))))) = E. [para(236(a,1),198(a,1,2,2,1,2,1,1))].
% 1.86/2.14 1718 multiply(inverse(multiply(A,multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,D)))),multiply(A,inverse(multiply(inverse(E),multiply(inverse(multiply(F,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D))),multiply(inverse(multiply(V7,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D))),multiply(V7,multiply(inverse(multiply(inverse(multiply(V6,C)),multiply(V6,F))),D)))))))) = E. [para(236(a,2),198(a,1,1,1,2))].
% 1.86/2.14 1752 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),D)),C)),multiply(inverse(D),multiply(inverse(D),D)))) = multiply(inverse(B),multiply(inverse(B),B)). [para(1520(a,1),102(a,1,1,1,1,2))].
% 1.86/2.14 1785 multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,inverse(D)))),E))),multiply(A,D)) = multiply(inverse(multiply(F,multiply(V6,E))),multiply(F,multiply(V6,multiply(inverse(C),multiply(inverse(C),C))))). [para(1520(a,1),616(a,1,2,2))].
% 1.86/2.14 1786 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),D))),C) = multiply(inverse(multiply(E,multiply(F,D))),multiply(E,multiply(F,multiply(inverse(B),B)))). [para(1520(a,1),616(a,1,2))].
% 1.86/2.14 1800 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))) = multiply(inverse(C),C). [para(1520(a,1),236(a,2,2))].
% 1.86/2.14 1806 multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C))))),D)),multiply(inverse(A),multiply(inverse(A),A))))) = D. [para(1800(a,2),1(a,1,2,1,1,1,1,1))].
% 1.86/2.14 1808 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [para(1800(a,2),3(b,1,1))].
% 1.86/2.14 1831 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),C)),D)),multiply(inverse(C),multiply(inverse(C),C)))) = multiply(inverse(E),inverse(multiply(inverse(D),multiply(inverse(E),multiply(inverse(E),E))))). [para(1800(a,2),5(a,1,1,1,1,1,1,1,1))].
% 1.86/2.14 1833 inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),multiply(inverse(C),C)))) = C. [para(1800(a,2),5(a,1,1,1,1)),rewrite([1(30)])].
% 1.86/2.14 1842 multiply(inverse(multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D))))))),multiply(A,multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D)))),multiply(multiply(B,inverse(multiply(inverse(E),multiply(inverse(C),multiply(inverse(C),C))))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),E)),multiply(inverse(D),multiply(inverse(D),D))))))) = multiply(inverse(F),F). [para(5(a,1),1800(a,1,2,2,2,1))].
% 1.86/2.14 1847 multiply(inverse(multiply(inverse(inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(B),B))))),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))) = A. [para(1800(a,2),18(a,1,2))].
% 1.86/2.14 1860 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),D)) = multiply(inverse(multiply(E,C)),multiply(E,D)). [para(1800(a,2),153(a,1,1,1))].
% 1.86/2.14 1861 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))) = multiply(inverse(multiply(E,B)),multiply(E,A)). [para(1800(a,2),153(a,1,2))].
% 1.86/2.14 1885 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C))),multiply(inverse(D),D)) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,multiply(inverse(B),multiply(inverse(B),B))))). [para(1800(a,1),208(a,1,2))].
% 1.86/2.14 1890 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D)))))),multiply(inverse(multiply(E,B)),F)) = multiply(inverse(multiply(V6,multiply(E,A))),multiply(V6,F)). [para(1800(a,2),208(a,1,1,1,2))].
% 1.88/2.14 1894 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(multiply(C,D)),E)) = multiply(inverse(multiply(inverse(multiply(F,V6)),multiply(F,D))),multiply(inverse(multiply(C,V6)),E)). [para(1800(a,2),208(a,2,1,1)),flip(a)].
% 1.88/2.14 1895 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(inverse(E),multiply(D,C))),multiply(inverse(multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))),multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6))))). [para(1800(a,2),208(a,2,2))].
% 1.88/2.14 1918 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(C,D)),E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))),multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6))))))) = multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),multiply(inverse(D),D))))). [para(1800(a,2),7(a,1,1,2,2))].
% 1.88/2.14 1926 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),D))),E) = multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,D))),E). [para(1800(a,2),281(a,1,1,1,1,1))].
% 1.88/2.14 1927 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D)))))),E) = multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,A))),E). [para(1800(a,2),281(a,1,1,1,2))].
% 1.88/2.14 1941 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(D),B)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(E,multiply(inverse(F),multiply(inverse(F),F)))))) = multiply(inverse(multiply(V6,C)),multiply(V6,multiply(A,D))). [para(1800(a,2),209(a,1,2,2))].
% 1.88/2.14 1942 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(C),multiply(D,E))) = multiply(inverse(multiply(inverse(multiply(D,F)),C)),multiply(inverse(multiply(V6,F)),multiply(V6,E))). [para(1800(a,2),209(a,2,1,1)),flip(a)].
% 1.88/2.14 1944 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E))))) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),multiply(inverse(multiply(V6,F)),multiply(V6,B))). [para(1800(a,2),209(a,2,2)),flip(a)].
% 1.88/2.14 1954 multiply(A,multiply(inverse(multiply(inverse(multiply(B,multiply(inverse(C),multiply(inverse(C),C)))),multiply(B,multiply(inverse(C),multiply(inverse(C),C))))),multiply(inverse(D),E))) = multiply(A,multiply(inverse(multiply(F,D)),multiply(F,E))). [para(1800(a,2),705(a,1,2,1,1))].
% 1.88/2.14 1955 multiply(A,multiply(inverse(multiply(inverse(B),C)),multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E)))))) = multiply(A,multiply(inverse(multiply(F,C)),multiply(F,B))). [para(1800(a,2),705(a,1,2,2))].
% 1.88/2.14 1959 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(F),multiply(inverse(F),F))))),A)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(E,multiply(inverse(F),multiply(inverse(F),F)))))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(F),multiply(inverse(F),F))))),A)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(E,multiply(inverse(F),multiply(inverse(F),F)))))))),inverse(multiply(inverse(multiply(inverse(multiply(D,multiply(E,multiply(inverse(F),multiply(inverse(F),F))))),A)),multiply(inverse(multiply(E,multiply(inverse(F),multiply(inverse(F),F)))),multiply(inverse(V6),V6))))))))). [para(1800(a,1),8(a,2,2,1,2,2,2,1,2,2))].
% 1.88/2.14 1960 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),C)),multiply(inverse(D),multiply(inverse(D),D)))) = multiply(E,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(E,F)),D)),multiply(inverse(F),multiply(inverse(F),F))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(E,F)),D)),multiply(inverse(F),multiply(inverse(F),F))))),inverse(multiply(inverse(multiply(inverse(multiply(E,F)),D)),multiply(inverse(F),multiply(inverse(F),F))))))))). [para(1800(a,2),8(a,1,1,1,1,1,1))].
% 1.88/2.14 1968 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),multiply(inverse(B),B)))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))),multiply(F,multiply(inverse(V6),multiply(inverse(V6),V6)))))))). [para(1800(a,2),8(a,2,2,1,2,2))].
% 1.88/2.14 1972 multiply(inverse(A),A) = multiply(multiply(B,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(B,D)),E)),multiply(inverse(D),multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(B,D)),E)),multiply(inverse(D),multiply(inverse(D),D))))),inverse(multiply(inverse(multiply(inverse(multiply(B,D)),E)),multiply(inverse(D),multiply(inverse(D),D))))))))),multiply(inverse(multiply(inverse(multiply(inverse(E),F)),C)),multiply(inverse(F),multiply(inverse(F),F)))). [para(8(a,1),1800(a,1,1)),flip(a)].
% 1.88/2.14 1979 multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E)))))) = multiply(inverse(multiply(F,multiply(V6,C))),multiply(F,multiply(V6,B))). [para(1800(a,2),616(a,1,2,2))].
% 1.88/2.14 2023 multiply(inverse(multiply(A,multiply(inverse(B),B))),multiply(A,inverse(multiply(inverse(C),multiply(inverse(multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E))))),multiply(inverse(multiply(F,B)),multiply(F,B))))))) = C. [para(1800(a,2),198(a,1,2,2,1,2,1,1))].
% 1.88/2.14 2034 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))))),multiply(A,E)) = multiply(F,multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,F))),E)). [para(1800(a,2),236(a,1,1,1,2,2))].
% 1.88/2.14 2035 multiply(inverse(multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,multiply(inverse(B),multiply(inverse(B),B))))),multiply(inverse(multiply(inverse(C),multiply(inverse(C),C))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)). [para(1800(a,2),236(a,1,1,1))].
% 1.88/2.14 2036 multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(inverse(B),B)))),multiply(inverse(multiply(C,multiply(inverse(D),multiply(inverse(D),D)))),multiply(C,multiply(inverse(D),multiply(inverse(D),D))))) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,E))),A)). [para(1800(a,2),236(a,1,2))].
% 1.88/2.14 2039 multiply(inverse(multiply(A,multiply(inverse(B),multiply(inverse(B),B)))),multiply(A,C)) = multiply(B,multiply(inverse(multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E))))),C)). [para(1800(a,2),236(a,2,2,1,1))].
% 1.88/2.14 2052 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),multiply(inverse(multiply(D,multiply(inverse(E),multiply(inverse(E),E)))),multiply(D,multiply(inverse(E),multiply(inverse(E),E)))))) = C. [para(1800(a,2),1520(a,1,2,2))].
% 1.88/2.14 2053 multiply(inverse(A),A) = multiply(inverse(B),B). [para(1520(a,1),1800(a,1,1,1)),rewrite([1520(12)])].
% 1.88/2.14 2060 multiply(inverse(A),A) = c_0. [new_symbol(2053)].
% 1.88/2.14 2061 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_unit_del(1808),rewrite([2060(4),2060(5),2060(6),2060(11),2060(13)]),xx(a)].
% 1.88/2.14 2062 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),multiply(inverse(B),c_0)) = C. [back_rewrite(2052),rewrite([2060(10),2060(15),2060(17)])].
% 1.88/2.14 2071 multiply(inverse(multiply(A,multiply(inverse(B),c_0))),multiply(A,C)) = multiply(B,multiply(inverse(c_0),C)). [back_rewrite(2039),rewrite([2060(3),2060(10),2060(15),2060(17)])].
% 1.88/2.14 2074 multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(inverse(D),multiply(inverse(C),c_0))),c_0). [back_rewrite(2036),rewrite([2060(4),2060(9),2060(14),2060(16)]),flip(a)].
% 1.88/2.14 2075 multiply(inverse(multiply(inverse(A),multiply(inverse(B),c_0))),c_0) = multiply(inverse(c_0),multiply(inverse(multiply(inverse(B),c_0)),A)). [back_rewrite(2035),rewrite([2060(3),2060(8),2060(10),2060(5),2074(15)]),flip(a)].
% 1.88/2.14 2076 multiply(inverse(c_0),multiply(inverse(multiply(inverse(A),c_0)),B)) = multiply(A,multiply(inverse(c_0),B)). [back_rewrite(2034),rewrite([2060(4),2060(9),2060(11),2071(7),2074(11),2075(12)]),flip(a)].
% 1.88/2.14 2081 multiply(inverse(multiply(A,c_0)),multiply(A,inverse(multiply(inverse(B),c_0)))) = B. [back_rewrite(2023),rewrite([2060(2),2060(7),2060(12),2060(14),2060(10),2060(8)])].
% 1.88/2.14 2096 multiply(inverse(multiply(A,multiply(inverse(B),C))),multiply(A,c_0)) = multiply(inverse(multiply(D,multiply(E,C))),multiply(D,multiply(E,B))). [back_rewrite(1979),rewrite([2060(7),2060(12),2060(14)])].
% 1.88/2.14 2100 multiply(multiply(A,inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),multiply(inverse(C),c_0)))),c_0)))),multiply(inverse(multiply(inverse(multiply(inverse(D),E)),B)),multiply(inverse(E),c_0))) = c_0. [back_rewrite(1972),rewrite([2060(2),2060(9),2060(19),2060(29),2060(32),2060(25)]),flip(a)].
% 1.88/2.14 2103 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),c_0))) = multiply(D,inverse(multiply(inverse(C),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(D,E)),A)),multiply(inverse(E),c_0)))),c_0)))). [back_rewrite(1968),rewrite([2060(8),2060(18),2060(24),2060(29),2060(31)])].
% 1.88/2.14 2105 multiply(A,inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,C)),D)),multiply(inverse(C),c_0)))),c_0)))) = inverse(multiply(inverse(multiply(inverse(c_0),B)),multiply(inverse(D),c_0))). [back_rewrite(1960),rewrite([2060(3),2060(8),2060(10),2060(7),2060(17),2060(27),2060(37),2060(40)]),flip(a)].
% 1.88/2.14 2106 inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),multiply(inverse(B),c_0))) = inverse(multiply(inverse(multiply(inverse(c_0),C)),multiply(inverse(A),c_0))). [back_rewrite(1959),rewrite([2060(8),2060(14),2060(22),2060(27),2060(32),2060(34),2060(32),2060(40),2060(45),2060(50),2060(52),2060(50),2060(58),2060(62),2060(65),2105(34)])].
% 1.88/2.14 2107 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(inverse(D),C)),c_0)). [back_rewrite(1955),rewrite([2060(6),2060(11),2060(13)]),flip(a)].
% 1.88/2.14 2108 multiply(A,multiply(inverse(multiply(inverse(B),C)),c_0)) = multiply(A,multiply(inverse(c_0),multiply(inverse(C),B))). [back_rewrite(1954),rewrite([2060(3),2060(8),2060(10),2107(11)]),flip(a)].
% 1.88/2.14 2113 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(c_0),multiply(inverse(B),D))) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),c_0). [back_rewrite(1944),rewrite([2060(7),2060(12),2060(14),2107(15),2108(16)]),flip(a)].
% 1.88/2.14 2115 multiply(inverse(multiply(inverse(multiply(A,B)),C)),c_0) = multiply(inverse(c_0),multiply(inverse(C),multiply(A,B))). [back_rewrite(1942),rewrite([2060(3),2060(8),2060(10),2107(15),2108(16),2113(16)]),flip(a)].
% 1.88/2.14 2116 multiply(inverse(multiply(A,B)),multiply(A,multiply(C,D))) = multiply(inverse(c_0),multiply(inverse(B),multiply(C,D))). [back_rewrite(1941),rewrite([2060(10),2060(15),2060(17),2108(10),2113(10),2115(6)]),flip(a)].
% 1.88/2.14 2118 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),D) = multiply(inverse(multiply(inverse(multiply(inverse(C),B)),c_0)),D). [back_rewrite(1927),rewrite([2060(6),2060(11),2060(13)]),flip(a)].
% 1.88/2.14 2119 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),c_0)),C) = multiply(inverse(multiply(inverse(c_0),multiply(inverse(B),A))),C). [back_rewrite(1926),rewrite([2060(3),2060(8),2060(10),2118(13)]),flip(a)].
% 1.88/2.14 2121 inverse(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(c_0),A)),multiply(inverse(multiply(C,D)),c_0)))),c_0))) = multiply(C,inverse(multiply(inverse(B),multiply(inverse(D),c_0)))). [back_rewrite(1918),rewrite([2060(12),2106(14),2060(17),2060(22),2060(24),2060(22)])].
% 1.88/2.14 2125 multiply(inverse(multiply(inverse(c_0),multiply(inverse(A),B))),multiply(inverse(multiply(C,A)),D)) = multiply(inverse(multiply(inverse(D),multiply(C,B))),c_0). [back_rewrite(1895),rewrite([2118(9),2119(10),2060(17),2060(22),2060(24)])].
% 1.88/2.14 2126 multiply(inverse(multiply(inverse(A),multiply(B,C))),c_0) = multiply(inverse(c_0),multiply(inverse(multiply(B,C)),A)). [back_rewrite(1894),rewrite([2060(3),2060(8),2060(10),2118(15),2119(16),2125(16)]),flip(a)].
% 1.88/2.14 2128 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(inverse(c_0),multiply(inverse(multiply(B,C)),D)). [back_rewrite(1890),rewrite([2060(6),2060(11),2060(13),2119(10),2125(10),2126(6)]),flip(a)].
% 1.88/2.14 2129 multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(A),multiply(inverse(B),c_0)))) = multiply(inverse(multiply(B,multiply(inverse(c_0),A))),c_0). [back_rewrite(1885),rewrite([2060(3),2128(7),2076(8),2060(7),2060(13),2116(16),2116(16)]),flip(a)].
% 1.88/2.14 2137 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(1861),rewrite([2060(6),2060(11),2060(13)]),flip(a)].
% 1.88/2.14 2138 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(1860),rewrite([2060(3),2060(8),2060(10),2137(9)]),flip(a)].
% 1.88/2.14 2140 multiply(inverse(c_0),multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(A),c_0))))) = B. [back_rewrite(1847),rewrite([2060(4),2060(12),2060(17),2060(19),2138(11)])].
% 1.88/2.14 2142 multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(c_0),A)),multiply(inverse(multiply(B,C)),c_0))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),A)),multiply(inverse(D),c_0)))),multiply(multiply(B,inverse(multiply(inverse(A),multiply(inverse(C),c_0)))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(B,C)),D)),A)),multiply(inverse(D),c_0)))))) = c_0. [back_rewrite(1842),rewrite([2060(9),2106(11),2060(19),2106(21),2060(29),2060(43),2106(45),2060(48),2060(60),2137(65),2137(63),2138(44),2138(47),2138(46),2060(49)])].
% 1.88/2.14 2150 inverse(multiply(inverse(c_0),multiply(inverse(A),c_0))) = A. [back_rewrite(1833),rewrite([2060(3),2060(8),2060(10),2060(5)])].
% 1.88/2.14 2151 multiply(inverse(A),inverse(multiply(inverse(B),multiply(inverse(A),c_0)))) = B. [back_rewrite(1831),rewrite([2060(3),2060(8),2060(10),2060(9),2106(11),2060(8),2138(6),2150(7),2060(5)]),flip(a)].
% 1.88/2.14 2154 multiply(inverse(c_0),A) = A. [back_rewrite(1806),rewrite([2060(4),2060(9),2060(11),2060(8),2151(11)])].
% 1.88/2.14 2167 multiply(inverse(multiply(inverse(inverse(A)),B)),A) = multiply(inverse(B),c_0). [back_rewrite(1786),rewrite([2137(5),2138(6),2154(6),2137(7),2138(6),2154(6),2060(10),2137(12),2137(10),2138(11),2154(10),2154(8)])].
% 1.88/2.14 2168 multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(B))),C)),B) = multiply(inverse(C),multiply(inverse(A),c_0)). [back_rewrite(1785),rewrite([2137(5),2138(6),2154(6),2137(9),2138(10),2154(10),2060(13),2137(16),2137(14),2138(15),2154(15),2138(15),2154(15)])].
% 1.88/2.14 2191 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(1752),rewrite([2137(5),2138(6),2154(6),2168(7),2060(9),2137(10),2154(6),2138(6),2154(5),2154(3),2060(4)]),flip(a)].
% 1.88/2.14 2224 inverse(multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(B,multiply(inverse(inverse(multiply(inverse(B),C))),D)))))),inverse(multiply(inverse(D),inverse(C))))) = A. [back_rewrite(1718),rewrite([2060(3),2191(3),2137(5),2191(6),2137(11),2191(12),2137(18),2191(19),2137(25),2191(26),2060(28),2191(16),2137(18),2191(19)])].
% 1.88/2.14 2229 multiply(A,c_0) = A. [back_rewrite(1713),rewrite([2060(3),2191(3),2137(5),2191(6),2137(11),2191(12),2060(20),2191(16),2137(18),2224(17)])].
% 1.88/2.14 2304 multiply(A,multiply(inverse(multiply(inverse(multiply(B,inverse(C))),D)),multiply(E,multiply(inverse(inverse(multiply(inverse(E),C))),F)))) = multiply(A,inverse(multiply(inverse(multiply(B,F)),D))). [back_rewrite(1634),rewrite([2060(3),2229(3),2137(9),2229(10),2137(18),2229(19)])].
% 1.88/2.14 2322 multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(inverse(multiply(D,E)),B))) = inverse(multiply(inverse(multiply(A,multiply(D,E))),C)). [back_rewrite(1611),rewrite([2060(7),2229(7),2137(13),2229(14),2304(17),2137(15),2229(16)])].
% 1.88/2.14 2640 inverse(multiply(inverse(multiply(A,B)),A)) = inverse(inverse(B)). [back_rewrite(1139),rewrite([2137(11),2229(12),2322(11),2060(4),2154(3),2060(8),2229(6)]),flip(a)].
% 1.88/2.14 2650 inverse(inverse(inverse(multiply(inverse(A),B)))) = inverse(inverse(multiply(inverse(B),A))). [back_rewrite(1120),rewrite([2060(6),2229(6),2640(6),2137(10),2137(8),2229(9),2229(10)]),flip(a)].
% 1.88/2.14 2655 inverse(multiply(inverse(inverse(multiply(inverse(A),B))),inverse(multiply(C,B)))) = inverse(inverse(multiply(C,A))). [back_rewrite(1087),rewrite([2137(4),2229(5),2060(8),2229(8),2060(13),2229(13),2640(13)])].
% 1.88/2.14 2675 inverse(inverse(multiply(A,B))) = multiply(A,B). [back_rewrite(974),rewrite([2137(6),2137(4),2229(5),2229(6),2650(5),2060(10),2229(8),2655(8)])].
% 1.88/2.14 2908 multiply(A,inverse(multiply(multiply(inverse(B),C),inverse(multiply(D,C))))) = multiply(A,multiply(D,B)). [back_rewrite(488),rewrite([2137(4),2229(5),2675(4),2060(6),2229(6),2060(14),2229(14),2640(14),2675(10)])].
% 1.88/2.14 3033 inverse(multiply(inverse(multiply(A,B)),C)) = multiply(inverse(C),multiply(A,B)). [back_rewrite(265),rewrite([2137(6),2229(7),2675(6),2060(8),2229(8),2908(9),2137(5),2229(6)])].
% 1.88/2.14 3046 multiply(inverse(A),multiply(inverse(multiply(multiply(multiply(inverse(B),multiply(C,D)),inverse(D)),multiply(multiply(multiply(inverse(B),multiply(C,D)),inverse(D)),inverse(multiply(multiply(inverse(B),multiply(C,D)),inverse(D)))))),multiply(inverse(B),E))) = inverse(multiply(multiply(inverse(E),C),A)). [back_rewrite(248),rewrite([2060(5),2229(5),2137(7),2675(4),2229(6),3033(12),2060(14),2229(14),2675(15),3033(17),2060(19),2229(19),2675(20),3033(22),2060(24),2229(24),3033(28)]),flip(a)].
% 1.88/2.14 3053 multiply(A,multiply(multiply(inverse(A),B),C)) = inverse(multiply(inverse(C),inverse(B))). [back_rewrite(236),rewrite([2060(3),2229(3),2137(5),2229(6),2137(8),2229(9),2675(8)]),flip(a)].
% 1.88/2.14 3078 inverse(multiply(inverse(A),inverse(multiply(B,C)))) = multiply(B,inverse(multiply(inverse(A),inverse(C)))). [back_rewrite(193),rewrite([3033(5),2060(12),2229(10),3033(10),2675(3),3053(7),2060(9),2229(9)])].
% 1.88/2.14 3082 multiply(multiply(inverse(A),B),C) = multiply(inverse(A),multiply(B,C)). [back_rewrite(189),rewrite([3033(7),2060(9),2229(9),2675(10),3033(12),2060(14),2229(14),2675(15),3033(17),2060(19),2229(19),3033(23),2137(26),3046(24),2675(5),2229(5)])].
% 1.88/2.14 3097 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,inverse(inverse(C))). [back_rewrite(133),rewrite([3033(4),3082(6),2060(10),2229(10),2640(10),2675(6),2060(8),2229(8),2640(8)])].
% 1.88/2.14 3098 inverse(multiply(inverse(A),multiply(B,inverse(B)))) = A. [back_rewrite(102),rewrite([2137(4),2229(5),2675(4),2060(5),2229(5),3082(4)])].
% 1.88/2.14 3103 inverse(multiply(inverse(A),multiply(inverse(B),multiply(C,inverse(C))))) = inverse(multiply(inverse(A),inverse(B))). [back_rewrite(64),rewrite([3033(5),2060(7),2229(7),3082(6),3082(5),2060(14),2229(14),2060(20),2229(20),2060(26),2229(26),2060(28),2229(18),3078(18),2675(15),2137(17),2675(14),3082(13),3082(12),2060(11),2229(11),2229(13)])].
% 1.88/2.14 3112 multiply(A,multiply(multiply(B,C),D)) = multiply(A,multiply(B,inverse(multiply(inverse(D),inverse(C))))). [back_rewrite(54),rewrite([3033(4),3033(7),3082(7),3082(8),3097(7),2675(5),2060(9),2229(9),2640(9),2675(5),2060(7),2229(7)])].
% 1.88/2.14 3118 multiply(A,inverse(multiply(inverse(B),inverse(C)))) = multiply(A,multiply(inverse(inverse(C)),B)). [back_rewrite(45),rewrite([2060(7),2229(7),2060(13),2229(13),2060(19),2229(19),2060(21),2229(11),3078(11),2675(8),2137(7),2229(6),2675(5),2060(8),2229(8)]),flip(a)].
% 1.88/2.14 3131 inverse(inverse(A)) = A. [back_rewrite(18),rewrite([2060(6),2229(6),3118(7),2137(7),2167(5),2229(3),2229(4)])].
% 1.88/2.14 3150 inverse(multiply(inverse(A),inverse(B))) = multiply(B,A). [back_rewrite(2075),rewrite([2229(4),2229(6),2229(9),3131(8),2154(8)])].
% 1.88/2.14 3152 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(2081),rewrite([2229(2),2229(4),3131(3)])].
% 1.88/2.14 3154 multiply(A,inverse(multiply(inverse(B),multiply(inverse(C),multiply(A,inverse(multiply(D,inverse(D)))))))) = multiply(C,B). [back_rewrite(2103),rewrite([3033(5),2229(7),3082(6),3082(5),3103(7),3150(4),3033(6),2229(8),3082(7),3112(7),3131(5),3131(10),2229(10)]),flip(a)].
% 1.88/2.14 3156 multiply(A,inverse(A)) = c_0. [back_rewrite(2100),rewrite([3033(5),2229(7),3082(6),3112(6),3131(4),3131(9),2229(9),3154(10),3033(6),2229(8),3082(7),3082(6),3097(8),3098(5)])].
% 1.88/2.14 3169 inverse(multiply(inverse(A),multiply(B,C))) = multiply(inverse(C),multiply(inverse(B),A)). [back_rewrite(1040),rewrite([3033(5),3082(5),3112(5),3150(6),3112(4),3150(5),2137(12),3033(11),2229(12),2137(11),2137(7),2137(5),2229(6),3131(5),2229(5),2229(6),2137(12),2137(10),2229(11),3131(10),2229(10),2137(10),3033(9),2229(10)])].
% 1.88/2.14 3175 multiply(inverse(multiply(A,B)),C) = multiply(inverse(B),multiply(inverse(A),C)). [back_rewrite(1004),rewrite([2137(7),2229(8),3131(7),3082(6),3169(7),2137(13),2137(11),2229(12),3131(11),2229(11),3082(10),3097(9),3131(7),2060(6),2229(6),3131(5),2137(5),3169(4),2229(6)]),flip(a)].
% 1.88/2.14 3179 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(2096),rewrite([2229(6),3175(5),2060(5),2229(5),3175(9),3152(9),3175(7),3152(7)])].
% 1.88/2.14 3181 multiply(multiply(A,B),inverse(B)) = A. [back_rewrite(2062),rewrite([3175(5),3152(5),3179(4),3131(2),2229(4)])].
% 1.88/2.14 3184 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(2129),rewrite([2229(8),2154(8),2154(6),2154(6),2229(7)]),flip(a)].
% 1.88/2.14 3185 inverse(c_0) = c_0. [back_rewrite(2142),rewrite([2154(7),3184(7),2229(10),3184(10),3184(8),3131(6),3131(6),3131(7),3184(8),3082(10),3184(11),3184(9),3131(9),3131(10),3082(9),3082(10),3112(10),3184(11),3131(9),3131(9),3184(11),3184(9),3184(8),3082(11),3131(13),3082(12),3082(11),2229(15),3082(14),3082(13),3181(12),3097(12),3184(9),3131(7),3131(7),3184(7),3097(9),3131(6),3156(6),2229(10),3184(10),3131(8),3131(8),3184(10),3082(12),3184(13),3184(11),3131(11),3131(12),3082(11),3082(12),3112(12),3184(13),3131(11),3131(11),3184(13),3184(11),3184(10),3082(13),3131(15),3082(14),3082(13),2229(17),3082(16),3082(15),3181(14),3112(15),3184(12),3184(10),3131(8),3131(8),3131(9),3184(10),3097(12),3131(9),3181(9),3156(8),2229(8),2154(7),2154(5)])].
% 1.88/2.14 3186 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [back_rewrite(2121),rewrite([3184(3),3131(3),3185(4),3184(5),3185(5),2229(5),3184(5),2229(8),3184(8),3184(6),3131(4),3131(4),3131(5),3184(5),3184(5),2229(9),3097(8),3184(5),3131(3),3131(3),3184(3),3184(6),3184(4),3131(2),3131(2),3131(3),2229(6),3184(6),3131(4),3131(4)])].
% 1.88/2.14 3188 multiply(c_0,A) = A. [back_rewrite(2140),rewrite([3185(2),2229(6),3184(6),3131(4),3131(4),3152(4)])].
% 1.88/2.14 3189 $F # answer(prove_these_axioms). [back_rewrite(2061),rewrite([3188(3),3186(8)]),xx(a),xx(b)].
% 1.88/2.14
% 1.88/2.14 % SZS output end Refutation
% 1.88/2.14 ============================== end of proof ==========================
% 1.88/2.14
% 1.88/2.14 ============================== STATISTICS ============================
% 1.88/2.14
% 1.88/2.14 Given=27. Generated=8640. Kept=3187. proofs=1.
% 1.88/2.14 Usable=0. Sos=9. Demods=12. Limbo=3, Disabled=3177. Hints=0.
% 1.88/2.14 Megabytes=9.19.
% 1.88/2.14 User_CPU=1.15, System_CPU=0.02, Wall_clock=1.
% 1.88/2.14
% 1.88/2.14 ============================== end of statistics =====================
% 1.88/2.14
% 1.88/2.14 ============================== end of search =========================
% 1.88/2.14
% 1.88/2.14 THEOREM PROVED
% 1.88/2.14 % SZS status Unsatisfiable
% 1.88/2.14
% 1.88/2.14 Exiting with 1 proof.
% 1.88/2.14
% 1.88/2.14 Process 25440 exit (max_proofs) Tue Jun 14 00:56:49 2022
% 1.88/2.14 Prover9 interrupted
%------------------------------------------------------------------------------