TSTP Solution File: GRP060-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP060-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:16:59 EDT 2022
% Result : Unsatisfiable 1.29s 1.64s
% Output : Refutation 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP060-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 13:20:12 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.29/1.63 ============================== Prover9 ===============================
% 1.29/1.63 Prover9 (32) version 2009-11A, November 2009.
% 1.29/1.63 Process 20025 was started by sandbox2 on n006.cluster.edu,
% 1.29/1.63 Mon Jun 13 13:20:12 2022
% 1.29/1.63 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19872_n006.cluster.edu".
% 1.29/1.63 ============================== end of head ===========================
% 1.29/1.63
% 1.29/1.63 ============================== INPUT =================================
% 1.29/1.63
% 1.29/1.63 % Reading from file /tmp/Prover9_19872_n006.cluster.edu
% 1.29/1.63
% 1.29/1.63 set(prolog_style_variables).
% 1.29/1.63 set(auto2).
% 1.29/1.63 % set(auto2) -> set(auto).
% 1.29/1.63 % set(auto) -> set(auto_inference).
% 1.29/1.63 % set(auto) -> set(auto_setup).
% 1.29/1.63 % set(auto_setup) -> set(predicate_elim).
% 1.29/1.63 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.29/1.63 % set(auto) -> set(auto_limits).
% 1.29/1.63 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.29/1.63 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.29/1.63 % set(auto) -> set(auto_denials).
% 1.29/1.63 % set(auto) -> set(auto_process).
% 1.29/1.63 % set(auto2) -> assign(new_constants, 1).
% 1.29/1.63 % set(auto2) -> assign(fold_denial_max, 3).
% 1.29/1.63 % set(auto2) -> assign(max_weight, "200.000").
% 1.29/1.63 % set(auto2) -> assign(max_hours, 1).
% 1.29/1.63 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.29/1.63 % set(auto2) -> assign(max_seconds, 0).
% 1.29/1.63 % set(auto2) -> assign(max_minutes, 5).
% 1.29/1.63 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.29/1.63 % set(auto2) -> set(sort_initial_sos).
% 1.29/1.63 % set(auto2) -> assign(sos_limit, -1).
% 1.29/1.63 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.29/1.63 % set(auto2) -> assign(max_megs, 400).
% 1.29/1.63 % set(auto2) -> assign(stats, some).
% 1.29/1.63 % set(auto2) -> clear(echo_input).
% 1.29/1.63 % set(auto2) -> set(quiet).
% 1.29/1.63 % set(auto2) -> clear(print_initial_clauses).
% 1.29/1.63 % set(auto2) -> clear(print_given).
% 1.29/1.63 assign(lrs_ticks,-1).
% 1.29/1.63 assign(sos_limit,10000).
% 1.29/1.63 assign(order,kbo).
% 1.29/1.63 set(lex_order_vars).
% 1.29/1.63 clear(print_given).
% 1.29/1.63
% 1.29/1.63 % formulas(sos). % not echoed (2 formulas)
% 1.29/1.63
% 1.29/1.63 ============================== end of input ==========================
% 1.29/1.63
% 1.29/1.63 % From the command line: assign(max_seconds, 300).
% 1.29/1.63
% 1.29/1.63 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.29/1.63
% 1.29/1.63 % Formulas that are not ordinary clauses:
% 1.29/1.63
% 1.29/1.63 ============================== end of process non-clausal formulas ===
% 1.29/1.63
% 1.29/1.63 ============================== PROCESS INITIAL CLAUSES ===============
% 1.29/1.63
% 1.29/1.63 ============================== PREDICATE ELIMINATION =================
% 1.29/1.63
% 1.29/1.63 ============================== end predicate elimination =============
% 1.29/1.63
% 1.29/1.63 Auto_denials:
% 1.29/1.63 % copying label prove_these_axioms to answer in negative clause
% 1.29/1.63
% 1.29/1.63 Term ordering decisions:
% 1.29/1.63
% 1.29/1.63 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.29/1.63 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.29/1.63
% 1.29/1.63 ============================== end of process initial clauses ========
% 1.29/1.63
% 1.29/1.63 ============================== CLAUSES FOR SEARCH ====================
% 1.29/1.63
% 1.29/1.63 ============================== end of clauses for search =============
% 1.29/1.63
% 1.29/1.63 ============================== SEARCH ================================
% 1.29/1.63
% 1.29/1.63 % Starting search at 0.01 seconds.
% 1.29/1.63
% 1.29/1.63 ============================== PROOF =================================
% 1.29/1.64 % SZS status Unsatisfiable
% 1.29/1.64 % SZS output start Refutation
% 1.29/1.64
% 1.29/1.64 % Proof 1 at 0.60 (+ 0.01) seconds: prove_these_axioms.
% 1.29/1.64 % Length of proof is 251.
% 1.29/1.64 % Level of proof is 53.
% 1.29/1.64 % Maximum clause weight is 62.000.
% 1.29/1.64 % Given clauses 47.
% 1.29/1.64
% 1.29/1.64 1 multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D # label(single_axiom) # label(axiom). [assumption].
% 1.29/1.64 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].
% 1.29/1.64 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)].
% 1.29/1.64 4 multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E)))),multiply(F,multiply(multiply(inverse(F),inverse(D)),A))))) = E. [para(1(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.29/1.64 5 multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,D))),inverse(E))),multiply(E,multiply(C,A))))) = D. [para(1(a,1),1(a,1,2,1,2,2,1))].
% 1.29/1.64 6 multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(E,F))))))),inverse(multiply(F,multiply(D,C)))) = E. [para(1(a,1),1(a,1,2,1,2,2))].
% 1.29/1.64 7 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E)))),multiply(F,multiply(multiply(inverse(F),inverse(D)),V6)))),multiply(V7,multiply(multiply(inverse(V7),inverse(E)),A))))) = V6. [para(4(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.29/1.64 11 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(E,F))))))) = multiply(V6,inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(V7,multiply(multiply(inverse(V7),inverse(E)),V6))))). [para(1(a,1),4(a,1,2,1,1,1,2,2)),flip(a)].
% 1.29/1.64 19 multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(D))),multiply(D,multiply(E,A))))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(C,E))),inverse(B))). [para(5(a,1),1(a,1,2,1,2,2,1))].
% 1.29/1.64 59 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(F,inverse(multiply(multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(B,D))),inverse(A))))),inverse(V8))),multiply(V8,multiply(E,F))))). [para(19(a,1),5(a,1,2,1,1,2,1,2,1)),flip(a)].
% 1.29/1.64 63 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B))) = D. [para(19(a,1),5(a,1))].
% 1.29/1.64 85 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(C)),D))),inverse(F))). [para(1(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.29/1.64 90 inverse(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(C)),F)))) = multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(multiply(inverse(V7),inverse(D)),F))),inverse(V7))). [para(4(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.29/1.64 91 multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(B)),inverse(C))). [para(4(a,1),63(a,1,2,1,2,1,1)),rewrite([1(10)])].
% 1.29/1.64 94 multiply(inverse(A),inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(multiply(inverse(A),inverse(multiply(D,E))),D))),F))),inverse(C))),E))) = F. [para(63(a,1),5(a,1,2,1,2))].
% 1.29/1.64 97 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(C),inverse(multiply(V6,B))),V6))),D))),inverse(F))). [para(63(a,1),19(a,1,2,1,1))].
% 1.29/1.64 104 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B)) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(D)),A))),inverse(F))). [para(63(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.29/1.64 113 multiply(A,inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(E))))),inverse(F))),multiply(F,multiply(V6,A))))) = multiply(multiply(inverse(V6),inverse(D)),inverse(E)). [para(91(a,1),5(a,1,2,1,1,2,1,2,1))].
% 1.29/1.64 123 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(E))))),F))),inverse(B))) = multiply(multiply(inverse(F),inverse(D)),inverse(E)). [para(91(a,1),63(a,1,2,1,2,1,1,2,1))].
% 1.29/1.64 125 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,multiply(D,E)))) = multiply(multiply(inverse(E),inverse(multiply(B,D))),inverse(A)). [back_rewrite(59),rewrite([113(25)])].
% 1.29/1.64 137 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(E,multiply(multiply(inverse(E),inverse(F)),V6)))),multiply(V7,multiply(multiply(inverse(V7),inverse(inverse(multiply(V8,multiply(V9,multiply(multiply(inverse(V9),inverse(multiply(D,V8))),multiply(inverse(C),inverse(multiply(F,B))))))))),A))))) = V6. [para(6(a,1),4(a,1,2,1,1,1,2,2,1,2,1))].
% 1.29/1.64 175 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(D,E))),D))),F))),inverse(B)) = inverse(multiply(E,multiply(C,multiply(F,A)))). [para(63(a,1),125(a,1,1,1)),flip(a)].
% 1.29/1.64 177 multiply(multiply(inverse(inverse(A)),inverse(multiply(B,multiply(inverse(C),inverse(multiply(multiply(inverse(A),inverse(multiply(D,E))),D)))))),inverse(F)) = inverse(multiply(multiply(F,multiply(B,inverse(C))),E)). [para(63(a,1),125(a,1,1,2)),flip(a)].
% 1.29/1.64 194 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))). [back_rewrite(97),rewrite([175(19)])].
% 1.29/1.64 195 multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(C,multiply(A,multiply(D,B))))),C))) = D. [back_rewrite(94),rewrite([175(15)])].
% 1.29/1.64 202 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))),B)) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(D)),inverse(C)))),inverse(F))). [para(195(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.29/1.64 203 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))),inverse(E))) = D. [para(195(a,1),63(a,1,2,1,2,1,1))].
% 1.29/1.64 205 multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))) = multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(E,D))),E))). [para(63(a,1),195(a,1,2,1,1,2,1,2))].
% 1.29/1.64 229 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(D,inverse(E)))))),inverse(F))) = multiply(E,multiply(multiply(V6,inverse(multiply(B,multiply(C,multiply(D,V6))))),inverse(F))). [para(194(a,1),91(a,1,2,1)),flip(a)].
% 1.29/1.64 244 multiply(inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))),B)),inverse(multiply(E,multiply(F,D)))) = multiply(V6,inverse(multiply(E,multiply(F,multiply(inverse(C),V6))))). [para(195(a,1),194(a,1,2,1,2,2))].
% 1.29/1.64 345 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(multiply(inverse(A),inverse(multiply(D,C))),D)). [para(205(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([63(19)])].
% 1.29/1.64 385 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(A)))))),B)) = inverse(D). [para(4(a,1),345(a,1,1,1)),rewrite([1(9)]),flip(a)].
% 1.29/1.64 404 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(D,multiply(E,inverse(multiply(C,multiply(A,multiply(D,E))))))). [para(195(a,1),345(a,1,1,1)),flip(a)].
% 1.29/1.64 409 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(multiply(inverse(D),inverse(multiply(E,F))),E)))))),inverse(V6))) = multiply(inverse(D),inverse(multiply(multiply(V6,multiply(B,C)),F))). [para(345(a,1),203(a,1,2,1,2,1,2,2))].
% 1.29/1.64 445 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C))))) = inverse(D). [para(195(a,1),385(a,1,1,1)),rewrite([125(10)])].
% 1.29/1.64 449 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B)) = inverse(D). [para(194(a,1),385(a,1,1,1))].
% 1.29/1.64 469 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))),B)) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),inverse(multiply(D,E))),inverse(C))))). [para(1(a,1),449(a,1,1,1,2,1,2,2,1))].
% 1.29/1.64 489 multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))),inverse(B)) = inverse(D). [para(125(a,1),449(a,1,1,1,2)),rewrite([125(15)])].
% 1.29/1.64 709 inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(multiply(C,multiply(D,multiply(E,B))))))),F)) = inverse(multiply(V6,multiply(V7,inverse(multiply(inverse(multiply(C,multiply(D,multiply(E,F)))),multiply(A,multiply(V6,V7))))))). [para(194(a,1),404(a,1,1,1,2,1))].
% 1.29/1.64 718 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))),multiply(inverse(E),inverse(multiply(F,D))))) = inverse(multiply(multiply(inverse(A),inverse(multiply(V6,F))),V6)). [para(203(a,1),404(a,2,1,2,2,1,2)),flip(a)].
% 1.29/1.64 776 multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))) = multiply(E,inverse(multiply(inverse(B),multiply(F,multiply(multiply(inverse(F),inverse(inverse(D))),E))))). [para(489(a,1),1(a,1,2,1,2,2,1,2,1)),flip(a)].
% 1.29/1.64 780 multiply(inverse(A),inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C))))) = inverse(A). [para(489(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([409(23)])].
% 1.29/1.64 791 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))),B)) = multiply(multiply(inverse(inverse(C)),inverse(multiply(multiply(inverse(E),inverse(multiply(F,D))),F))),inverse(E)). [para(195(a,1),489(a,1,1,2,1,1,2,1,2)),flip(a)].
% 1.29/1.64 806 inverse(multiply(inverse(A),multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))))) = inverse(multiply(multiply(inverse(A),inverse(multiply(E,multiply(inverse(D),inverse(C))))),E)). [para(489(a,1),445(a,1,1,2,2,1,2,1))].
% 1.29/1.64 807 inverse(multiply(multiply(inverse(A),inverse(inverse(B))),multiply(inverse(inverse(C)),inverse(multiply(multiply(inverse(D),inverse(multiply(E,multiply(inverse(C),inverse(B))))),E))))) = inverse(multiply(F,multiply(V6,inverse(multiply(inverse(D),multiply(A,multiply(F,V6))))))). [para(489(a,1),404(a,1,1,1,2,1))].
% 1.29/1.64 808 inverse(multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))),multiply(inverse(B),inverse(multiply(E,multiply(F,inverse(D))))))) = inverse(multiply(multiply(inverse(F),inverse(multiply(V6,E))),V6)). [para(489(a,1),404(a,2,1,2,2,1,2,2)),flip(a)].
% 1.29/1.64 814 multiply(A,inverse(multiply(multiply(inverse(B),inverse(C)),multiply(D,multiply(inverse(D),A))))) = multiply(E,multiply(multiply(inverse(E),inverse(inverse(C))),inverse(inverse(B)))). [para(780(a,1),1(a,1,2,1,2,2,1))].
% 1.29/1.64 817 multiply(A,inverse(multiply(inverse(multiply(multiply(inverse(B),inverse(C)),multiply(D,multiply(inverse(D),E)))),multiply(F,multiply(multiply(inverse(F),inverse(multiply(V6,multiply(multiply(inverse(V6),inverse(inverse(C))),inverse(inverse(B)))))),A))))) = E. [para(780(a,1),4(a,1,2,1,1,1,2,2,1))].
% 1.29/1.64 820 inverse(multiply(multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),inverse(inverse(C)))),multiply(inverse(C),inverse(B)))) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(inverse(F))),inverse(F)))),inverse(E))). [para(780(a,1),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.29/1.64 822 multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(inverse(C),inverse(B))). [para(780(a,1),91(a,1,2,1)),rewrite([780(19)])].
% 1.29/1.64 838 multiply(inverse(multiply(multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),inverse(inverse(C)))),multiply(inverse(C),inverse(B)))),inverse(multiply(D,multiply(E,inverse(F))))) = multiply(V6,inverse(multiply(D,multiply(E,multiply(inverse(F),V6))))). [para(780(a,1),194(a,1,2,1,2,2))].
% 1.29/1.64 841 multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))),multiply(inverse(D),inverse(C)))),multiply(E,multiply(multiply(inverse(E),inverse(inverse(F))),V6)))),multiply(V7,multiply(multiply(inverse(V7),inverse(inverse(F))),V8)))),multiply(V9,multiply(multiply(inverse(V9),inverse(V6)),A))))) = V8. [para(780(a,1),7(a,1,2,1,1,1,1,1,2,2,1,2,1))].
% 1.29/1.64 853 multiply(inverse(A),inverse(multiply(multiply(multiply(multiply(B,inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(E)),B))))),C),multiply(multiply(inverse(E),inverse(inverse(F))),inverse(inverse(V6)))),multiply(inverse(V6),inverse(F))))) = inverse(A). [para(449(a,1),780(a,1,2,1,1,2,1,1))].
% 1.29/1.64 865 inverse(multiply(inverse(A),multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),inverse(inverse(D)))))) = inverse(multiply(E,multiply(F,inverse(multiply(multiply(inverse(D),inverse(C)),multiply(A,multiply(E,F))))))). [para(780(a,1),404(a,1,1,1))].
% 1.29/1.64 874 multiply(multiply(inverse(inverse(A)),inverse(multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(inverse(D))),inverse(inverse(A))))))),inverse(B)) = inverse(D). [para(780(a,1),489(a,1,1,2,1,1))].
% 1.29/1.64 881 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),F)))),A))),multiply(inverse(F),inverse(multiply(V6,V7))))))) = multiply(V8,inverse(multiply(inverse(multiply(V7,E)),multiply(V9,multiply(multiply(inverse(V9),inverse(V6)),V8))))). [para(1(a,1),11(a,2,2,1,1,1,2))].
% 1.29/1.64 929 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(E)))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(V6,multiply(V7,V8))),multiply(D,C))),multiply(V9,multiply(multiply(inverse(V9),inverse(inverse(multiply(V10,multiply(V11,multiply(multiply(inverse(V11),inverse(multiply(V8,V10))),multiply(inverse(V7),inverse(multiply(E,V6))))))))),F))))). [para(6(a,1),11(a,1,1,2,2,2,2,1))].
% 1.29/1.64 957 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(E,inverse(multiply(F,multiply(V6,multiply(V7,E))))))))))) = multiply(V8,inverse(multiply(inverse(multiply(inverse(multiply(F,multiply(V6,multiply(V7,V9)))),multiply(D,C))),multiply(V10,multiply(multiply(inverse(V10),inverse(V9)),V8))))). [para(194(a,1),11(a,1,1,2,2,2,2,1))].
% 1.29/1.64 1088 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(F,inverse(multiply(inverse(multiply(inverse(multiply(multiply(V6,multiply(multiply(inverse(V6),inverse(inverse(V7))),inverse(inverse(V8)))),multiply(inverse(V8),inverse(V7)))),multiply(D,C))),multiply(V9,multiply(multiply(inverse(V9),inverse(inverse(E))),F))))). [para(780(a,1),11(a,1,1,2,2,2,2,1))].
% 1.29/1.64 1089 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(D))))) = multiply(E,inverse(multiply(inverse(multiply(multiply(inverse(F),inverse(V6)),multiply(D,C))),multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(V8,multiply(multiply(inverse(V8),inverse(inverse(V6))),inverse(inverse(F)))))),E))))). [para(780(a,1),11(a,1,1,2,2,2))].
% 1.29/1.64 1154 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),inverse(C))))),D)) = inverse(multiply(E,multiply(F,inverse(multiply(multiply(inverse(D),inverse(C)),multiply(A,multiply(E,F))))))). [para(822(a,1),404(a,1,1,1,2,1))].
% 1.29/1.64 1161 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(780(a,1),822(a,1,2)),rewrite([780(17)])].
% 1.29/1.64 1171 multiply(A,inverse(A)) = c_0. [new_symbol(1161)].
% 1.29/1.64 1174 multiply(A,inverse(multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(c_0)),A))))) = B. [para(1171(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.29/1.64 1175 multiply(inverse(multiply(inverse(A),inverse(multiply(B,C)))),inverse(multiply(C,multiply(A,c_0)))) = B. [para(1171(a,1),1(a,1,2,1,2,2))].
% 1.29/1.64 1180 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(c_0)),C))),inverse(B))) = inverse(C). [para(1171(a,1),63(a,1,2,1,2,1,1,2,1))].
% 1.29/1.64 1181 multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),inverse(C))) = multiply(B,multiply(c_0,inverse(C))). [para(1171(a,1),91(a,1,2,1)),flip(a)].
% 1.29/1.64 1186 inverse(multiply(multiply(A,c_0),multiply(B,multiply(C,D)))) = multiply(multiply(inverse(D),inverse(multiply(B,C))),inverse(A)). [para(1171(a,1),125(a,1,1,1,2))].
% 1.29/1.64 1190 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(inverse(D),inverse(multiply(B,multiply(C,c_0)))). [para(1171(a,1),194(a,1,2,1,2,2)),flip(a)].
% 1.29/1.64 1198 inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B)) = inverse(multiply(multiply(inverse(A),inverse(c_0)),C)). [para(1171(a,1),345(a,1,1,1,2,1)),flip(a)].
% 1.29/1.64 1200 inverse(multiply(multiply(inverse(c_0),inverse(multiply(A,multiply(B,c_0)))),A)) = inverse(inverse(B)). [para(1171(a,1),449(a,1,1,1,2,1,2,2,1)),rewrite([1190(6)])].
% 1.29/1.64 1211 inverse(multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))))) = inverse(multiply(multiply(inverse(C),inverse(c_0)),B)). [para(1171(a,1),404(a,1,1,1,2,1)),rewrite([1190(12)]),flip(a)].
% 1.29/1.64 1220 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(multiply(inverse(E),F))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(F,multiply(D,C))),multiply(E,c_0)))). [para(1171(a,1),11(a,2,2,1,2,2,1)),rewrite([1190(22)])].
% 1.29/1.64 1223 multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,c_0). [para(1171(a,1),822(a,1,2)),flip(a)].
% 1.29/1.64 1226 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(D))))) = multiply(inverse(multiply(inverse(E),inverse(multiply(F,multiply(c_0,inverse(inverse(V6))))))),inverse(multiply(inverse(multiply(multiply(inverse(V6),inverse(F)),multiply(D,C))),multiply(E,c_0)))). [back_rewrite(1089),rewrite([1181(24),1190(28)])].
% 1.29/1.64 1227 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(multiply(inverse(F),inverse(inverse(E)))),inverse(multiply(inverse(multiply(inverse(multiply(multiply(V6,multiply(c_0,inverse(inverse(V7)))),multiply(inverse(V7),inverse(V6)))),multiply(D,C))),multiply(F,c_0)))). [back_rewrite(1088),rewrite([1181(20),1190(34)])].
% 1.29/1.64 1235 multiply(multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))),inverse(A)) = inverse(B). [back_rewrite(874),rewrite([1181(11),1190(11)])].
% 1.29/1.64 1242 inverse(multiply(A,multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(C)),multiply(D,c_0)))))) = inverse(multiply(inverse(D),multiply(C,multiply(c_0,inverse(inverse(B)))))). [back_rewrite(865),rewrite([1181(9),1190(16)]),flip(a)].
% 1.29/1.64 1262 multiply(inverse(multiply(inverse(A),inverse(B))),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(C,multiply(c_0,inverse(inverse(D)))),multiply(inverse(D),inverse(C)))),multiply(E,multiply(multiply(inverse(E),inverse(inverse(F))),B)))),multiply(V6,multiply(multiply(inverse(V6),inverse(inverse(F))),V7)))),multiply(A,c_0)))) = V7. [back_rewrite(841),rewrite([1181(8),1190(34)])].
% 1.29/1.64 1265 multiply(inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))),inverse(multiply(C,multiply(D,inverse(E))))) = multiply(inverse(inverse(E)),inverse(multiply(C,multiply(D,c_0)))). [back_rewrite(838),rewrite([1181(8),1190(21)])].
% 1.29/1.64 1278 inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))) = multiply(C,multiply(multiply(inverse(C),inverse(multiply(multiply(inverse(D),inverse(inverse(E))),inverse(E)))),inverse(D))). [back_rewrite(820),rewrite([1181(8)])].
% 1.29/1.64 1281 multiply(inverse(multiply(inverse(A),inverse(multiply(B,multiply(c_0,inverse(inverse(C))))))),inverse(multiply(inverse(multiply(multiply(inverse(C),inverse(B)),multiply(D,multiply(inverse(D),E)))),multiply(A,c_0)))) = E. [back_rewrite(817),rewrite([1181(17),1190(21)])].
% 1.29/1.64 1284 multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(C)),multiply(A,c_0)))) = multiply(C,multiply(c_0,inverse(inverse(B)))). [back_rewrite(814),rewrite([1190(9),1181(18)])].
% 1.29/1.64 1286 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(C),inverse(D))))),B)) = inverse(multiply(inverse(A),multiply(D,multiply(c_0,inverse(inverse(C)))))). [back_rewrite(806),rewrite([1181(9)]),flip(a)].
% 1.29/1.64 1290 multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(multiply(inverse(B),multiply(A,c_0)))) = B. [back_rewrite(1174),rewrite([1190(10)])].
% 1.29/1.64 1302 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),inverse(C))))),D)) = inverse(multiply(inverse(A),multiply(C,multiply(c_0,inverse(inverse(D)))))). [back_rewrite(1154),rewrite([1190(17),1242(20)])].
% 1.29/1.64 1429 multiply(inverse(multiply(inverse(A),inverse(B))),inverse(multiply(inverse(multiply(inverse(multiply(C,multiply(D,multiply(E,B)))),multiply(F,V6))),multiply(A,c_0)))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(C,multiply(D,c_0))),multiply(F,V6))),multiply(E,c_0)))). [back_rewrite(957),rewrite([1190(10),1220(17),1190(29)]),flip(a)].
% 1.29/1.64 1453 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(E)))))) = multiply(inverse(multiply(inverse(F),inverse(inverse(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(V8,V6))),multiply(inverse(V9),inverse(multiply(E,V10)))))))))),inverse(multiply(inverse(multiply(inverse(multiply(V10,multiply(V9,V8))),multiply(D,C))),multiply(F,c_0)))). [back_rewrite(929),rewrite([1190(37)])].
% 1.29/1.64 1486 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),F)))),A))),multiply(inverse(F),inverse(multiply(V6,V7))))))) = multiply(inverse(multiply(inverse(V8),inverse(V6))),inverse(multiply(inverse(multiply(V7,E)),multiply(V8,c_0)))). [back_rewrite(881),rewrite([1190(30)])].
% 1.29/1.64 1493 multiply(inverse(A),inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(B),inverse(C))),inverse(multiply(D,multiply(B,c_0)))),D),multiply(multiply(inverse(C),inverse(inverse(E))),inverse(inverse(F)))),multiply(inverse(F),inverse(E))))) = inverse(A). [back_rewrite(853),rewrite([1190(9)])].
% 1.29/1.64 1498 inverse(multiply(multiply(inverse(A),inverse(inverse(B))),multiply(inverse(c_0),inverse(multiply(inverse(C),multiply(B,c_0)))))) = inverse(multiply(multiply(inverse(A),inverse(c_0)),C)). [back_rewrite(807),rewrite([1286(15),1190(15),1190(20),1211(23)])].
% 1.29/1.64 1504 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)) = multiply(multiply(inverse(inverse(C)),inverse(multiply(multiply(inverse(D),inverse(multiply(E,A))),E))),inverse(D)). [back_rewrite(791),rewrite([1190(5)])].
% 1.29/1.64 1506 multiply(inverse(multiply(inverse(A),inverse(inverse(B)))),inverse(multiply(inverse(C),multiply(A,c_0)))) = multiply(inverse(c_0),inverse(multiply(inverse(C),multiply(B,c_0)))). [back_rewrite(776),rewrite([1286(11),1190(11),1190(18)]),flip(a)].
% 1.29/1.64 1557 inverse(multiply(inverse(A),multiply(multiply(B,multiply(C,c_0)),multiply(c_0,inverse(inverse(multiply(inverse(C),inverse(multiply(D,B))))))))) = inverse(multiply(multiply(inverse(A),inverse(multiply(E,D))),E)). [back_rewrite(718),rewrite([1190(6),1302(16)])].
% 1.29/1.64 1566 inverse(multiply(multiply(inverse(A),inverse(multiply(inverse(B),inverse(multiply(C,multiply(D,c_0)))))),E)) = inverse(multiply(multiply(inverse(A),inverse(c_0)),multiply(C,multiply(D,multiply(B,E))))). [back_rewrite(709),rewrite([1190(6),1190(20),1211(23)])].
% 1.29/1.64 1696 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)) = inverse(multiply(D,multiply(E,multiply(multiply(inverse(E),inverse(multiply(A,D))),inverse(C))))). [back_rewrite(469),rewrite([1190(5)])].
% 1.29/1.64 1785 multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)),inverse(multiply(D,multiply(E,A)))) = multiply(inverse(inverse(C)),inverse(multiply(D,multiply(E,c_0)))). [back_rewrite(244),rewrite([1190(5),1190(18)])].
% 1.29/1.64 1794 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(D,inverse(E)))))),inverse(F))) = multiply(E,multiply(multiply(inverse(D),inverse(multiply(B,multiply(C,c_0)))),inverse(F))). [back_rewrite(229),rewrite([1190(15)])].
% 1.29/1.64 1810 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(A)),inverse(C)))),inverse(E))). [back_rewrite(202),rewrite([1190(5)])].
% 1.29/1.64 1821 multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(D,multiply(multiply(inverse(D),inverse(E)),F)))),multiply(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(C,V6))),multiply(inverse(B),inverse(multiply(E,A)))))),c_0)))) = F. [back_rewrite(137),rewrite([1190(30),1506(31)])].
% 1.29/1.64 1845 inverse(multiply(multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))),multiply(inverse(A),inverse(multiply(C,multiply(D,inverse(B))))))) = inverse(multiply(multiply(inverse(D),inverse(multiply(E,C))),E)). [back_rewrite(808),rewrite([1286(11),1190(11)])].
% 1.29/1.64 1868 multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))),multiply(C,c_0))),multiply(D,multiply(multiply(inverse(D),inverse(inverse(E))),F)))),multiply(multiply(inverse(C),inverse(inverse(E))),c_0)))) = F. [back_rewrite(1262),rewrite([1429(35)])].
% 1.29/1.64 1874 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(E)))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(F,multiply(V6,V7))),multiply(D,C))),multiply(multiply(V8,multiply(V9,multiply(multiply(inverse(V9),inverse(multiply(V7,V8))),multiply(inverse(V6),inverse(multiply(E,F)))))),c_0)))). [back_rewrite(1453),rewrite([1506(38)])].
% 1.29/1.64 1883 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(multiply(F,multiply(c_0,inverse(inverse(V6)))),multiply(inverse(V6),inverse(F)))),multiply(D,C))),multiply(E,c_0)))). [back_rewrite(1227),rewrite([1506(35)])].
% 1.29/1.64 1912 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(D,c_0))) = multiply(multiply(inverse(inverse(inverse(D))),inverse(multiply(B,inverse(C)))),inverse(A)). [para(1223(a,1),125(a,1,1,2))].
% 1.29/1.64 1916 inverse(multiply(multiply(inverse(A),inverse(multiply(B,c_0))),C)) = inverse(multiply(inverse(A),multiply(inverse(B),multiply(c_0,inverse(inverse(C)))))). [para(1223(a,1),345(a,1,1,1,2,1)),rewrite([1286(17)])].
% 1.29/1.64 1950 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(C)),D))),inverse(B)) = multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(inverse(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(C,V6))),D)))))),A))),inverse(F))). [para(85(a,2),63(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.29/1.64 1980 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(multiply(inverse(C),inverse(multiply(D,E))),D),A))),F)))) = multiply(inverse(F),inverse(multiply(E,multiply(C,c_0)))). [para(205(a,1),85(a,2,2,1,2,1,1)),rewrite([175(27),1190(18)])].
% 1.29/1.64 2014 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),D)))) = inverse(multiply(A,multiply(C,multiply(c_0,D)))). [para(1200(a,1),85(a,1,1,2,2,1,2)),rewrite([1566(21),1180(23)])].
% 1.29/1.64 2016 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(inverse(C))),D))),inverse(B))) = multiply(inverse(D),inverse(multiply(multiply(C,c_0),multiply(c_0,c_0)))). [para(1200(a,1),85(a,2,2,1,2,1,1,2)),rewrite([1980(16)]),flip(a)].
% 1.29/1.64 2035 multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))),multiply(C,c_0))),multiply(D,multiply(c_0,E)))),multiply(multiply(inverse(C),inverse(inverse(D))),c_0)))) = E. [back_rewrite(1868),rewrite([2014(24)])].
% 1.29/1.64 2046 multiply(inverse(A),inverse(multiply(multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E))),c_0),multiply(c_0,c_0)))) = multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(F),inverse(D)),E))),inverse(F)). [back_rewrite(1950),rewrite([2016(27)]),flip(a)].
% 1.29/1.64 2047 inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))) = multiply(inverse(inverse(C)),inverse(multiply(multiply(C,c_0),multiply(c_0,c_0)))). [back_rewrite(1278),rewrite([2016(22)])].
% 1.29/1.64 2051 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))),inverse(B))) = multiply(c_0,inverse(C)). [para(1235(a,1),91(a,1,2)),flip(a)].
% 1.29/1.64 2054 inverse(multiply(multiply(A,c_0),multiply(c_0,inverse(A)))) = multiply(inverse(inverse(B)),inverse(multiply(multiply(B,c_0),multiply(c_0,c_0)))). [para(1235(a,1),85(a,1,1,2,2)),rewrite([2016(19)])].
% 1.29/1.64 2056 multiply(multiply(inverse(c_0),inverse(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,c_0)))),multiply(F,multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(V6),inverse(C)),D))),inverse(V6)))) = inverse(E). [para(85(a,1),1235(a,1,2))].
% 1.29/1.64 2058 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))),inverse(D))) = multiply(multiply(inverse(C),inverse(c_0)),multiply(B,inverse(D))). [para(1290(a,1),91(a,1,2,1)),flip(a)].
% 1.29/1.64 2064 inverse(multiply(multiply(inverse(A),inverse(c_0)),multiply(inverse(B),multiply(C,c_0)))) = inverse(multiply(multiply(inverse(A),inverse(B)),inverse(multiply(inverse(C),inverse(c_0))))). [para(1290(a,1),345(a,1,1,1,2,1)),rewrite([1198(21)]),flip(a)].
% 1.29/1.64 2067 multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0))))) = multiply(multiply(inverse(C),inverse(c_0)),B). [para(1290(a,1),822(a,1,2)),flip(a)].
% 1.29/1.64 2068 multiply(multiply(inverse(c_0),inverse(multiply(A,multiply(B,c_0)))),A) = inverse(B). [para(1200(a,1),1290(a,1,2,1,1)),rewrite([1290(12)]),flip(a)].
% 1.29/1.64 2074 multiply(multiply(inverse(A),inverse(c_0)),c_0) = multiply(c_0,inverse(A)). [back_rewrite(2051),rewrite([2058(10),1171(6)])].
% 1.29/1.64 2086 multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(c_0))),inverse(multiply(inverse(B),multiply(c_0,inverse(A))))) = B. [para(2074(a,1),1290(a,1,2,1,2))].
% 1.29/1.64 2156 inverse(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,c_0))) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(V6),inverse(D)),inverse(multiply(inverse(E),inverse(C)))))),inverse(V6))). [para(1171(a,1),90(a,1,1,2,2))].
% 1.29/1.64 2161 inverse(multiply(inverse(multiply(multiply(inverse(A),inverse(inverse(B))),multiply(C,multiply(multiply(inverse(C),inverse(multiply(B,c_0))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(A)),F)))) = multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(multiply(inverse(V7),inverse(D)),F))),inverse(V7))). [para(1223(a,1),90(a,1,1,1,1,2,2,1,2,1))].
% 1.29/1.64 2166 inverse(multiply(multiply(A,multiply(multiply(inverse(A),inverse(B)),C)),multiply(D,multiply(multiply(inverse(D),multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(V6)),C))),inverse(F)))),V7)))) = multiply(inverse(V7),inverse(multiply(multiply(multiply(V8,multiply(V9,multiply(multiply(inverse(V9),inverse(multiply(B,V8))),V6))),c_0),multiply(c_0,c_0)))). [para(90(a,1),85(a,1,1,2,2,1,2)),rewrite([2016(39)])].
% 1.29/1.64 2246 multiply(inverse(A),inverse(multiply(multiply(B,c_0),multiply(c_0,inverse(B))))) = inverse(A). [para(1290(a,1),1175(a,1,1,1)),rewrite([2074(9)])].
% 1.29/1.64 2249 multiply(inverse(multiply(inverse(A),inverse(inverse(B)))),inverse(multiply(C,multiply(A,c_0)))) = multiply(inverse(c_0),inverse(multiply(C,multiply(B,c_0)))). [para(2068(a,1),1175(a,1,1,1,2,1))].
% 1.29/1.64 2271 multiply(inverse(A),inverse(multiply(multiply(c_0,c_0),c_0))) = inverse(A). [para(1171(a,1),2246(a,1,2,1,2))].
% 1.29/1.64 2285 multiply(inverse(inverse(A)),inverse(multiply(multiply(A,c_0),multiply(c_0,c_0)))) = inverse(multiply(multiply(c_0,c_0),c_0)). [para(2271(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([2016(12)])].
% 1.29/1.64 2288 multiply(multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D)),inverse(multiply(multiply(c_0,c_0),c_0))) = multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D)). [para(125(a,1),2271(a,1,1)),rewrite([125(20)])].
% 1.29/1.64 2292 inverse(multiply(inverse(A),multiply(inverse(B),multiply(c_0,inverse(inverse(B)))))) = inverse(multiply(inverse(A),multiply(c_0,c_0))). [para(2271(a,1),345(a,1,1,1)),rewrite([1916(13)]),flip(a)].
% 1.29/1.64 2294 inverse(multiply(c_0,multiply(A,multiply(inverse(A),B)))) = multiply(inverse(B),inverse(inverse(c_0))). [para(2271(a,1),85(a,1,1,2,2,1)),rewrite([1916(15),1794(21),2068(19)])].
% 1.29/1.64 2296 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(C)),D))),inverse(F))),inverse(multiply(multiply(c_0,c_0),c_0))). [para(85(a,1),2271(a,1,1)),flip(a)].
% 1.29/1.64 2301 multiply(inverse(inverse(A)),inverse(multiply(c_0,multiply(A,c_0)))) = multiply(c_0,c_0). [para(2271(a,1),1175(a,1,1,1))].
% 1.29/1.64 2302 inverse(multiply(multiply(A,c_0),multiply(c_0,inverse(A)))) = inverse(multiply(multiply(c_0,c_0),c_0)). [back_rewrite(2054),rewrite([2285(17)])].
% 1.29/1.64 2303 inverse(multiply(multiply(A,multiply(c_0,inverse(inverse(B)))),multiply(inverse(B),inverse(A)))) = inverse(multiply(multiply(c_0,c_0),c_0)). [back_rewrite(2047),rewrite([2285(20)])].
% 1.29/1.64 2309 multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,c_0),c_0)),multiply(A,c_0))),multiply(B,multiply(c_0,C)))),multiply(multiply(inverse(A),inverse(inverse(B))),c_0)))) = C. [back_rewrite(2035),rewrite([2303(12)])].
% 1.29/1.64 2310 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,c_0),c_0)),multiply(D,C))),multiply(E,c_0)))). [back_rewrite(1883),rewrite([2303(24)])].
% 1.29/1.64 2312 multiply(inverse(multiply(multiply(c_0,c_0),c_0)),inverse(multiply(A,multiply(B,inverse(C))))) = multiply(inverse(inverse(C)),inverse(multiply(A,multiply(B,c_0)))). [back_rewrite(1265),rewrite([2303(10)])].
% 1.29/1.64 2318 inverse(multiply(c_0,multiply(A,c_0))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0))). [para(2301(a,1),63(a,1,2,1,2,1,1,2,1)),rewrite([1916(11),1794(17),2068(15)]),flip(a)].
% 1.29/1.64 2323 multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(c_0,c_0)))),inverse(B)) = inverse(A). [para(2301(a,1),85(a,1,1,2,2,1)),rewrite([1186(10),1180(21)])].
% 1.29/1.64 2345 multiply(multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(C)),D))),inverse(B))),inverse(multiply(E,A))),inverse(F)) = inverse(multiply(multiply(F,multiply(E,inverse(D))),C)). [para(104(a,1),125(a,1,1,2,2)),rewrite([125(16),177(30)])].
% 1.29/1.64 2390 multiply(A,multiply(multiply(inverse(A),inverse(multiply(c_0,inverse(B)))),inverse(B))) = inverse(c_0). [para(2074(a,1),104(a,2,2,1,2,1)),rewrite([1916(9),2292(11),2323(11)]),flip(a)].
% 1.29/1.64 2410 multiply(inverse(multiply(inverse(A),inverse(multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),E))),inverse(C)))))),inverse(multiply(inverse(F),multiply(A,c_0)))) = multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(multiply(V6,D))),V6))). [para(104(a,1),1175(a,1,1,1,2,1))].
% 1.29/1.64 2418 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(c_0,c_0),c_0)))),C))),inverse(B)) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(inverse(E),A))),inverse(E))). [para(2271(a,1),104(a,2,2,1,2,1,1))].
% 1.29/1.64 2441 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,c_0)))),B)) = inverse(multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(C))),inverse(inverse(c_0)))),c_0)). [para(2318(a,1),345(a,1,1,1,2)),flip(a)].
% 1.29/1.64 2453 multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(multiply(multiply(inverse(inverse(inverse(B))),inverse(inverse(c_0))),multiply(A,c_0)))) = multiply(c_0,multiply(B,c_0)). [para(2318(a,1),1290(a,1,2,1,1))].
% 1.29/1.64 2471 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),multiply(inverse(inverse(inverse(C))),inverse(inverse(c_0)))),c_0))),inverse(B)) = multiply(inverse(A),inverse(inverse(C))). [para(2318(a,1),104(a,1,1,2,1,1,2)),rewrite([1916(24),1794(30),2068(28)])].
% 1.29/1.64 2475 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = multiply(inverse(C),inverse(inverse(multiply(c_0,c_0)))). [back_rewrite(2418),rewrite([2441(12),2471(19)]),flip(a)].
% 1.29/1.64 2487 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(C)),inverse(D)))),inverse(B))) = inverse(multiply(multiply(inverse(C),multiply(inverse(inverse(inverse(D))),inverse(inverse(c_0)))),c_0)). [back_rewrite(1810),rewrite([2441(8)]),flip(a)].
% 1.29/1.64 2493 multiply(inverse(multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(B))),inverse(inverse(c_0)))),c_0)),inverse(multiply(C,multiply(D,A)))) = multiply(inverse(inverse(B)),inverse(multiply(C,multiply(D,c_0)))). [back_rewrite(1785),rewrite([2441(8)])].
% 1.29/1.64 2494 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),inverse(D))))) = inverse(multiply(multiply(inverse(C),multiply(inverse(inverse(inverse(D))),inverse(inverse(c_0)))),c_0)). [back_rewrite(1696),rewrite([2441(8)]),flip(a)].
% 1.29/1.64 2506 multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B)) = inverse(multiply(multiply(inverse(D),multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0)))),c_0)). [back_rewrite(1504),rewrite([2441(8)]),flip(a)].
% 1.29/1.64 2521 inverse(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,c_0))) = inverse(multiply(multiply(inverse(D),multiply(inverse(inverse(inverse(multiply(inverse(E),inverse(C))))),inverse(inverse(c_0)))),c_0)). [back_rewrite(2156),rewrite([2487(26)])].
% 1.29/1.64 2529 multiply(inverse(multiply(inverse(A),inverse(multiply(B,multiply(c_0,inverse(inverse(C))))))),inverse(multiply(inverse(multiply(multiply(inverse(C),inverse(B)),multiply(D,E))),multiply(A,c_0)))) = inverse(multiply(multiply(inverse(E),multiply(inverse(inverse(inverse(D))),inverse(inverse(c_0)))),c_0)). [back_rewrite(1226),rewrite([2494(9)]),flip(a)].
% 1.29/1.64 2532 multiply(multiply(inverse(c_0),inverse(multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(multiply(inverse(B),inverse(C))))),inverse(inverse(c_0)))),c_0))),multiply(D,multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(C)),A))),inverse(E)))) = inverse(B). [back_rewrite(2056),rewrite([2521(14)])].
% 1.29/1.64 2540 inverse(multiply(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0)))),c_0)) = B. [back_rewrite(1281),rewrite([2529(22)])].
% 1.29/1.64 2548 inverse(multiply(c_0,multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(C)),inverse(D)))))) = multiply(inverse(multiply(multiply(inverse(inverse(A)),inverse(C)),inverse(D))),inverse(inverse(c_0))). [para(91(a,1),2294(a,1,1,2,2))].
% 1.29/1.64 2586 inverse(multiply(c_0,multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E)))),multiply(F,multiply(multiply(inverse(F),inverse(D)),V6))))))) = multiply(inverse(multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(V7),inverse(E)),V6))),inverse(V7))),inverse(inverse(c_0))). [para(90(a,2),2294(a,1,1,2,2))].
% 1.29/1.64 2597 multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(c_0,multiply(D,multiply(inverse(D),E)))))),C))),inverse(B)) = multiply(F,multiply(multiply(inverse(F),inverse(multiply(multiply(inverse(V6),multiply(inverse(E),inverse(inverse(c_0)))),A))),inverse(V6))). [para(2294(a,1),104(a,2,2,1,2,1,1,2))].
% 1.29/1.64 2598 inverse(multiply(c_0,multiply(A,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(multiply(D,E))),D))),inverse(C))))) = multiply(inverse(multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(F),inverse(E)),B))),inverse(F))),inverse(inverse(c_0))). [para(104(a,2),2294(a,1,1,2,2))].
% 1.29/1.64 2602 multiply(inverse(multiply(A,c_0)),inverse(inverse(multiply(c_0,c_0)))) = multiply(c_0,inverse(A)). [para(2302(a,1),63(a,1,2,1,2,1,1,2)),rewrite([2271(9),2475(10)])].
% 1.29/1.64 2614 multiply(multiply(A,c_0),multiply(c_0,inverse(A))) = multiply(multiply(c_0,c_0),c_0). [para(2302(a,1),1290(a,1,2,1,1)),rewrite([1290(16)]),flip(a)].
% 1.29/1.64 2617 inverse(multiply(multiply(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(C)),F))),multiply(c_0,inverse(F))),D)) = inverse(multiply(multiply(c_0,c_0),c_0)). [para(90(a,1),2302(a,1,1,2,2)),rewrite([1186(30),2345(30)])].
% 1.29/1.64 2623 multiply(multiply(inverse(inverse(inverse(multiply(c_0,c_0)))),inverse(multiply(A,inverse(multiply(B,c_0))))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(multiply(A,c_0))),inverse(C)). [para(2614(a,1),125(a,1,1,2)),rewrite([1912(12)])].
% 1.29/1.64 2702 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(multiply(inverse(C),inverse(D)),multiply(inverse(E),inverse(inverse(c_0))))))),F))),inverse(B))) = multiply(multiply(inverse(F),inverse(D)),multiply(inverse(E),inverse(inverse(c_0)))). [para(2294(a,1),123(a,1,2,1,2,1,1,2,1,2,2)),rewrite([2294(29)])].
% 1.29/1.64 2709 multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)),inverse(inverse(multiply(c_0,c_0)))) = multiply(c_0,inverse(multiply(inverse(A),inverse(multiply(c_0,C))))). [para(345(a,1),2602(a,1,1))].
% 1.29/1.64 2716 multiply(inverse(multiply(inverse(A),inverse(multiply(c_0,inverse(B))))),inverse(multiply(inverse(inverse(multiply(c_0,c_0))),multiply(A,c_0)))) = inverse(multiply(B,c_0)). [para(2602(a,1),1175(a,1,1,1,2,1))].
% 1.29/1.64 2734 inverse(multiply(inverse(c_0),inverse(c_0))) = c_0. [para(1290(a,1),2323(a,1,1)),rewrite([1171(2)]),flip(a)].
% 1.29/1.64 2740 multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))) = multiply(inverse(B),inverse(multiply(inverse(A),multiply(c_0,c_0)))). [para(2323(a,1),1175(a,1,1,1,2,1)),rewrite([2249(11)])].
% 1.29/1.64 2742 multiply(multiply(inverse(A),inverse(inverse(B))),inverse(B)) = multiply(inverse(A),inverse(inverse(c_0))). [para(2323(a,1),104(a,1,1,2,1)),rewrite([1916(15),1794(21),2068(19)])].
% 1.29/1.64 2752 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(multiply(c_0,inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B))),inverse(A))) = C. [para(2734(a,1),63(a,1,2,1,1))].
% 1.29/1.64 2755 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(multiply(c_0,inverse(A)),inverse(B))) = multiply(C,multiply(multiply(inverse(C),inverse(A)),inverse(B))). [para(2734(a,1),91(a,1,2,1,1))].
% 1.29/1.64 2762 inverse(multiply(multiply(inverse(A),c_0),inverse(c_0))) = inverse(multiply(c_0,inverse(A))). [para(2734(a,1),345(a,1,1,1,2)),rewrite([1198(15),2074(13)])].
% 1.29/1.64 2763 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(c_0,inverse(A))) = multiply(B,multiply(inverse(B),inverse(A))). [para(2734(a,1),822(a,1,2,1))].
% 1.29/1.64 2765 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(c_0,inverse(inverse(A)))) = multiply(A,c_0). [para(2734(a,1),1223(a,1,2,1))].
% 1.29/1.64 2786 multiply(multiply(c_0,inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B))),inverse(A)) = multiply(D,multiply(multiply(inverse(D),inverse(multiply(multiply(inverse(E),inverse(C)),multiply(inverse(c_0),inverse(c_0))))),inverse(E))). [para(2734(a,1),104(a,1,1,1))].
% 1.29/1.64 2792 inverse(multiply(c_0,c_0)) = multiply(inverse(inverse(c_0)),inverse(inverse(c_0))). [para(2734(a,1),2318(a,2,1,1,1)),rewrite([2074(8),1171(5)])].
% 1.29/1.64 2794 multiply(multiply(c_0,c_0),c_0) = multiply(c_0,multiply(c_0,c_0)). [para(2734(a,1),2614(a,1,2,2)),rewrite([2074(7),1171(4)]),flip(a)].
% 1.29/1.64 2801 multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))),c_0) = inverse(A). [para(2734(a,1),2323(a,1,1,2,1,1)),rewrite([2318(7),2734(16)])].
% 1.29/1.64 2803 multiply(inverse(multiply(inverse(A),inverse(multiply(c_0,inverse(B))))),inverse(multiply(inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0)))),multiply(A,c_0)))) = inverse(multiply(B,c_0)). [back_rewrite(2716),rewrite([2792(11)])].
% 1.29/1.64 2807 multiply(inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))) = multiply(c_0,inverse(multiply(inverse(A),inverse(multiply(c_0,C))))). [back_rewrite(2709),rewrite([2792(10)])].
% 1.29/1.64 2811 multiply(multiply(inverse(inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))),inverse(multiply(A,inverse(multiply(B,c_0))))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(multiply(A,c_0))),inverse(C)). [back_rewrite(2623),rewrite([2792(4)])].
% 1.29/1.64 2813 multiply(inverse(multiply(A,c_0)),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))) = multiply(c_0,inverse(A)). [back_rewrite(2602),rewrite([2792(7)])].
% 1.29/1.64 2819 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = multiply(inverse(C),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))). [back_rewrite(2475),rewrite([2792(13)])].
% 1.29/1.64 2835 inverse(multiply(multiply(multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),multiply(E,multiply(multiply(inverse(E),inverse(C)),F))),multiply(c_0,inverse(F))),D)) = multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0))). [back_rewrite(2617),rewrite([2794(25),2318(26)])].
% 1.29/1.64 2843 multiply(multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0))),inverse(multiply(A,multiply(B,inverse(C))))) = multiply(inverse(inverse(C)),inverse(multiply(A,multiply(B,c_0)))). [back_rewrite(2312),rewrite([2794(5),2318(6)])].
% 1.29/1.64 2845 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),inverse(inverse(E))))))) = multiply(inverse(c_0),inverse(multiply(inverse(multiply(multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0))),multiply(D,C))),multiply(E,c_0)))). [back_rewrite(2310),rewrite([2794(19),2318(20)])].
% 1.29/1.64 2846 multiply(inverse(c_0),inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0))),multiply(A,c_0))),multiply(B,multiply(c_0,C)))),multiply(multiply(inverse(A),inverse(inverse(B))),c_0)))) = C. [back_rewrite(2309),rewrite([2794(7),2318(8)])].
% 1.29/1.64 2852 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(C)),D))),inverse(F))),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))). [back_rewrite(2296),rewrite([2794(23),2318(24)])].
% 1.29/1.64 2854 multiply(multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D)),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))) = multiply(multiply(inverse(A),inverse(multiply(B,C))),inverse(D)). [back_rewrite(2288),rewrite([2794(11),2318(12)])].
% 1.29/1.64 2857 multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))) = inverse(A). [back_rewrite(2271),rewrite([2794(6),2318(7)])].
% 1.29/1.64 2859 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(2801),rewrite([2857(10)])].
% 1.29/1.64 2871 inverse(multiply(inverse(A),inverse(c_0))) = inverse(multiply(c_0,inverse(A))). [back_rewrite(2762),rewrite([2859(3)])].
% 1.29/1.64 2876 inverse(multiply(multiply(A,multiply(B,inverse(C))),multiply(C,inverse(D)))) = multiply(multiply(inverse(c_0),inverse(multiply(B,inverse(D)))),inverse(A)). [para(2859(a,1),125(a,1,1,2,2))].
% 1.29/1.64 2888 multiply(multiply(inverse(A),inverse(multiply(inverse(B),inverse(inverse(c_0))))),inverse(B)) = inverse(A). [para(2859(a,1),104(a,1,1,2,1,1,2,1)),rewrite([2742(7),1180(21)])].
% 1.29/1.64 2889 inverse(multiply(c_0,inverse(A))) = multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(c_0))). [para(2859(a,1),2318(a,1,1,2))].
% 1.29/1.64 2893 multiply(c_0,c_0) = c_0. [para(2734(a,1),2859(a,1,1)),rewrite([2734(9)])].
% 1.29/1.64 2901 multiply(inverse(A),inverse(c_0)) = inverse(A). [back_rewrite(1493),rewrite([2876(24),2742(9),2441(21),2540(25),2888(12)])].
% 1.29/1.64 2913 multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))) = multiply(inverse(B),inverse(inverse(A))). [back_rewrite(2740),rewrite([2893(13),2859(12)])].
% 1.29/1.64 2920 multiply(inverse(A),inverse(inverse(c_0))) = inverse(A). [back_rewrite(2323),rewrite([2893(5),2859(4),2742(6)])].
% 1.29/1.64 2953 inverse(multiply(multiply(A,multiply(multiply(inverse(A),inverse(B)),C)),multiply(D,multiply(multiply(inverse(D),multiply(E,multiply(multiply(inverse(E),inverse(multiply(multiply(inverse(F),inverse(V6)),C))),inverse(F)))),V7)))) = multiply(inverse(V7),inverse(multiply(multiply(multiply(V8,multiply(V9,multiply(multiply(inverse(V9),inverse(multiply(B,V8))),V6))),c_0),c_0))). [back_rewrite(2166),rewrite([2893(34)])].
% 1.29/1.64 2962 multiply(inverse(A),inverse(multiply(multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E))),c_0),c_0))) = multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(F),inverse(D)),E))),inverse(F)). [back_rewrite(2046),rewrite([2893(13)])].
% 1.29/1.64 2964 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(inverse(C))),D))),inverse(B))) = multiply(inverse(D),inverse(multiply(multiply(C,c_0),c_0))). [back_rewrite(2016),rewrite([2893(17)])].
% 1.29/1.64 2968 inverse(inverse(inverse(inverse(A)))) = inverse(inverse(A)). [back_rewrite(2871),rewrite([2901(4),2889(6),2920(10)]),flip(a)].
% 1.29/1.64 2971 inverse(multiply(A,c_0)) = inverse(A). [back_rewrite(2803),rewrite([2889(5),2968(5),2920(7),2920(12),2249(14),2913(11),2968(6),2920(5)]),flip(a)].
% 1.29/1.64 2975 inverse(c_0) = c_0. [back_rewrite(2390),rewrite([2889(5),2968(5),2920(7),2742(6),2920(5),1171(2)]),flip(a)].
% 1.29/1.64 2982 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = inverse(C). [back_rewrite(2819),rewrite([2975(11),2975(11),2975(12),2975(12),2893(12),2975(11),2859(11)])].
% 1.29/1.64 2985 multiply(c_0,inverse(A)) = inverse(A). [back_rewrite(2813),rewrite([2971(3),2975(3),2975(3),2975(4),2975(4),2893(4),2975(3),2859(3)]),flip(a)].
% 1.29/1.64 2987 multiply(inverse(multiply(A,inverse(B))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(A)),inverse(C)). [back_rewrite(2811),rewrite([2975(2),2975(2),2975(3),2975(3),2893(3),2975(2),2975(2),2971(4),2985(5),2971(10)])].
% 1.29/1.64 2988 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(inverse(A),inverse(multiply(c_0,C)))). [back_rewrite(2807),rewrite([2975(8),2975(8),2975(9),2975(9),2893(9),2975(8),2859(8),2985(14)])].
% 1.29/1.64 3010 inverse(inverse(multiply(c_0,A))) = inverse(inverse(A)). [back_rewrite(2786),rewrite([2988(7),2985(8),2987(8),2742(9),2975(6),2975(6),2859(6),2975(10),2975(11),2893(11),2971(11),2982(13)])].
% 1.29/1.64 3016 multiply(A,c_0) = inverse(inverse(A)). [back_rewrite(2765),rewrite([2975(2),2975(3),2893(3),2985(5),2985(4)]),flip(a)].
% 1.29/1.64 3017 multiply(A,multiply(inverse(A),inverse(B))) = inverse(B). [back_rewrite(2763),rewrite([2975(2),2975(3),3016(3),2975(2),2975(2),2985(4),2985(3)]),flip(a)].
% 1.29/1.64 3019 multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(c_0,multiply(inverse(B),inverse(C))). [back_rewrite(2755),rewrite([2975(2),2975(3),3016(3),2975(2),2975(2),2985(4)]),flip(a)].
% 1.29/1.64 3020 inverse(inverse(A)) = A. [back_rewrite(2752),rewrite([2975(2),2975(3),3016(3),2975(2),2975(2),2988(8),2985(9),2987(9),3010(5),2742(8),2975(5),2975(5),3016(5),2968(5),2985(4)])].
% 1.29/1.64 3028 multiply(A,inverse(multiply(inverse(B),A))) = multiply(c_0,B). [back_rewrite(2453),rewrite([2975(3),3016(3),3020(2),3020(2),3020(2),2975(3),2975(3),3016(3),3020(2),3016(3),3020(3),3016(7),3020(7)])].
% 1.29/1.64 3041 multiply(c_0,A) = A. [back_rewrite(2086),rewrite([2975(3),3016(3),3020(2),3020(2),2975(2),3016(2),3020(2),2985(5),3028(6)])].
% 1.29/1.64 3044 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(2067),rewrite([3016(4),3020(4),3017(6),2975(6),3016(6),3020(5)])].
% 1.29/1.64 3046 inverse(multiply(multiply(inverse(A),inverse(B)),C)) = multiply(multiply(inverse(C),B),A). [back_rewrite(2064),rewrite([2975(3),3016(3),3020(2),3016(4),3020(4),3044(5),3044(3),2975(9),3016(9),3020(8),3020(8)]),flip(a)].
% 1.29/1.64 3063 inverse(multiply(multiply(inverse(A),B),multiply(inverse(B),C))) = multiply(inverse(C),A). [back_rewrite(1498),rewrite([3020(3),2975(4),3016(6),3020(6),3044(6),3041(6),2975(9),3016(9),3020(8),3044(9)])].
% 1.29/1.64 3065 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(1290),rewrite([2975(3),3016(3),3020(2),3020(2),3016(3),3020(3),3044(3)])].
% 1.29/1.64 3072 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(2846),rewrite([2975(2),2975(3),2975(3),2975(3),2975(4),2975(4),3016(4),2975(3),2975(3),3016(4),3020(4),3041(3),3041(4),3044(5),3020(7),3016(8),3044(7),3044(7),3063(8),3041(5)])].
% 1.29/1.64 3073 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),multiply(inverse(D),E))))) = multiply(inverse(E),multiply(D,C)). [back_rewrite(2845),rewrite([3020(7),2975(12),2975(13),2975(13),2975(13),2975(14),2975(14),3016(14),2975(13),2975(13),3041(14),3016(15),3020(15),3044(15),3041(15)])].
% 1.29/1.64 3084 inverse(multiply(multiply(inverse(multiply(A,B)),multiply(C,multiply(D,E))),inverse(multiply(multiply(F,C),multiply(D,E))))) = multiply(F,multiply(A,B)). [back_rewrite(1874),rewrite([3073(11),3020(2),2975(4),3044(9),3016(21),3073(20),3020(11),3041(15)]),flip(a)].
% 1.29/1.64 3099 multiply(multiply(A,multiply(B,inverse(C))),C) = multiply(A,B). [back_rewrite(1845),rewrite([2975(2),3016(4),3020(4),3044(4),3041(4),3063(10),3020(5),3046(10),3072(7)])].
% 1.29/1.64 3102 multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C))) = C. [back_rewrite(1821),rewrite([2975(2),3044(11),3016(23),3073(22),3020(13),3084(16),3041(8)])].
% 1.29/1.64 3136 multiply(multiply(inverse(A),B),multiply(C,D)) = multiply(inverse(A),multiply(B,multiply(C,D))). [back_rewrite(1220),rewrite([3044(8),3073(12),3044(3),2975(6),3016(10),3020(10),3044(10),3041(10)])].
% 1.29/1.64 3150 multiply(A,multiply(multiply(inverse(A),multiply(multiply(inverse(B),C),D)),inverse(D))) = multiply(inverse(B),C). [back_rewrite(2161),rewrite([3020(3),3016(5),3020(5),3136(8),3102(7),3044(3),3136(8),3102(7),3044(3),3046(8)]),flip(a)].
% 1.29/1.64 3174 multiply(multiply(inverse(A),B),inverse(B)) = inverse(A). [back_rewrite(2888),rewrite([2975(4),2975(4),3016(4),3020(3),3020(3)])].
% 1.29/1.64 3175 inverse(multiply(multiply(A,multiply(B,C)),D)) = multiply(multiply(inverse(D),inverse(multiply(B,C))),inverse(A)). [back_rewrite(2854),rewrite([2975(8),2975(8),2975(8),2975(9),2975(9),3016(9),2975(8),2975(8),3016(8),3046(7),3020(2)])].
% 1.29/1.64 3176 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(inverse(D),C). [back_rewrite(2852),rewrite([3046(14),3150(16),2975(12),2975(12),2975(12),2975(13),2975(13),3016(13),2975(12),2975(12),3016(12),3044(11),3044(11)])].
% 1.29/1.64 3177 inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))). [back_rewrite(2843),rewrite([2975(2),2975(2),2975(2),2975(3),2975(3),3016(3),2975(2),2975(2),3041(6),3020(6),3016(6),3020(6)])].
% 1.29/1.64 3182 multiply(inverse(A),A) = c_0. [back_rewrite(2835),rewrite([3176(8),3136(8),3102(7),3041(5),3174(4),3044(3),2975(4),2975(4),2975(4),2975(5),2975(5),3016(5),2975(4),2975(4)])].
% 1.29/1.64 3183 multiply(multiply(inverse(A),inverse(B)),inverse(C)) = multiply(inverse(A),inverse(multiply(C,B))). [back_rewrite(2702),rewrite([2975(8),2975(8),3016(8),3020(7),3019(8),3041(7),3044(6),3020(4),3175(6),3020(7),3150(10),2975(10),2975(10),3016(10),3020(9)]),flip(a)].
% 1.29/1.64 3185 multiply(multiply(A,inverse(multiply(multiply(inverse(B),C),A))),inverse(D)) = multiply(inverse(C),inverse(multiply(D,inverse(B)))). [back_rewrite(2598),rewrite([3046(8),3072(5),3041(8),3177(7),1190(6),3016(4),3020(3),3020(7),3046(10),3175(12),3020(7),2975(14),2975(14),3016(14),3020(14)]),flip(a)].
% 1.29/1.64 3186 multiply(multiply(inverse(A),multiply(B,C)),inverse(C)) = multiply(inverse(A),B). [back_rewrite(2597),rewrite([3065(6),3041(4),3046(7),3072(4),2975(10),2975(10),3016(10),3020(9),3046(11),3150(13)])].
% 1.29/1.64 3188 inverse(multiply(multiply(A,inverse(B)),C)) = inverse(multiply(A,multiply(inverse(B),C))). [back_rewrite(2586),rewrite([3176(9),3136(9),3102(8),3044(4),3041(5),3020(6),3046(9),3175(11),3020(6),3185(11),2975(11),2975(11),3016(11),3044(10),3020(8)]),flip(a)].
% 1.29/1.64 3193 inverse(multiply(A,inverse(multiply(B,C)))) = multiply(B,inverse(multiply(A,inverse(C)))). [back_rewrite(2548),rewrite([3183(6),3065(6),3041(5),3020(6),3188(9),3177(9),2975(10),2975(10),3016(10),3020(10)])].
% 1.29/1.64 3197 multiply(inverse(multiply(A,B)),A) = inverse(B). [back_rewrite(2532),rewrite([2975(2),3044(6),3020(4),3020(5),2975(5),2975(5),3016(5),3020(5),3016(6),3044(5),3044(5),3044(5),3041(5),3188(9),3044(9),3044(7),3186(10),3065(8),3136(6),3065(5)])].
% 1.29/1.64 3200 inverse(multiply(multiply(inverse(A),B),C)) = multiply(inverse(multiply(B,C)),A). [back_rewrite(2521),rewrite([3176(8),3016(4),3020(4),3044(9),3020(7),3020(8),2975(8),2975(8),3016(8),3020(8),3016(9),3044(8),3044(8),3044(8)])].
% 1.29/1.64 3203 multiply(multiply(A,multiply(B,C)),inverse(C)) = multiply(A,B). [back_rewrite(2506),rewrite([3020(2),3188(6),3197(4),3044(4),3020(2),3020(7),2975(8),2975(8),3016(8),3020(7),3016(9),3044(8),3020(6),3020(7)])].
% 1.29/1.64 3206 multiply(multiply(A,B),inverse(multiply(C,multiply(D,B)))) = multiply(A,inverse(multiply(C,D))). [back_rewrite(2493),rewrite([3020(3),2975(4),2975(4),3016(4),3020(3),3016(5),3044(4),3020(2),3020(3),3020(7),3016(7),3020(7)])].
% 1.29/1.64 3218 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,C). [back_rewrite(1557),rewrite([3016(3),3020(3),3193(8),3044(7),3020(5),3041(7),3206(6),3177(6),3044(4),3188(10),3197(8),3044(8),3020(6)])].
% 1.29/1.64 3223 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(1284),rewrite([3020(2),3016(5),3020(5),3188(5),3044(5),3044(3),3020(7),3041(6)])].
% 1.29/1.64 3242 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(2964),rewrite([3020(4),3200(5),3203(7),3065(5),3016(5),3020(5),3016(5),3020(5)])].
% 1.29/1.64 3243 multiply(multiply(inverse(A),multiply(inverse(B),multiply(C,D))),inverse(D)) = multiply(inverse(A),multiply(inverse(B),C)). [back_rewrite(2962),rewrite([3242(4),3223(8),3223(6),3016(5),3242(4),3020(4),3242(4),3020(4),3016(5),3242(4),3020(4),3242(4),3020(4),3242(4),3020(4),3242(10),3242(10),3020(8),3020(8)]),flip(a)].
% 1.29/1.64 3248 multiply(multiply(inverse(A),inverse(B)),C) = multiply(inverse(A),multiply(inverse(B),C)). [back_rewrite(2953),rewrite([3223(5),3242(9),3242(9),3020(7),3020(7),3243(10),3065(8),3223(8),3136(6),3223(5),3242(4),3242(2),3020(5),3242(8),3223(12),3223(10),3016(9),3242(8),3020(8),3242(8),3020(8),3016(9),3242(8),3020(8),3242(8),3020(8),3242(8),3020(8)])].
% 1.29/1.64 3267 multiply(multiply(inverse(A),B),C) = multiply(inverse(A),multiply(B,C)). [back_rewrite(2410),rewrite([3248(6),3242(7),3242(5),3020(5),3020(6),3203(8),3065(6),3242(4),3020(4),3242(5),3242(3),3020(3),3020(4),3016(6),3020(6),3242(6),3020(6),3218(6),3242(7),3099(10),3242(8),3020(6),3020(6)])].
% 1.29/1.64 3288 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [back_rewrite(1486),rewrite([3242(4),3267(7),3267(6),3065(8),3065(6),3242(4),3020(4),3267(4),3242(5),3242(3),3020(6),3267(5),3242(9),3267(12),3267(11),3218(10),3065(10),3065(8),3242(6),3242(4),3020(2),3020(2),3020(3),3242(6),3020(4),3020(4),3242(5),3016(8),3020(8),3267(7),3242(8),3242(6),3020(6),3020(7),3267(6),3218(7)])].
% 1.29/1.64 3290 $F # answer(prove_these_axioms). [back_rewrite(3),rewrite([3182(4),3182(5),3182(7),3041(6),3288(11)]),xx(a),xx(b),xx(c)].
% 1.29/1.64
% 1.29/1.64 % SZS output end Refutation
% 1.29/1.64 ============================== end of proof ==========================
% 1.29/1.64
% 1.29/1.64 ============================== STATISTICS ============================
% 1.29/1.64
% 1.29/1.64 Given=47. Generated=6368. Kept=3288. proofs=1.
% 1.29/1.64 Usable=2. Sos=64. Demods=189. Limbo=136, Disabled=3088. Hints=0.
% 1.29/1.64 Megabytes=5.72.
% 1.29/1.64 User_CPU=0.61, System_CPU=0.01, Wall_clock=1.
% 1.29/1.64
% 1.29/1.64 ============================== end of statistics =====================
% 1.29/1.64
% 1.29/1.64 ============================== end of search =========================
% 1.29/1.64
% 1.29/1.64 THEOREM PROVED
% 1.29/1.64 % SZS status Unsatisfiable
% 1.29/1.64
% 1.29/1.64 Exiting with 1 proof.
% 1.29/1.64
% 1.29/1.64 Process 20025 exit (max_proofs) Mon Jun 13 13:20:13 2022
% 1.29/1.64 Prover9 interrupted
%------------------------------------------------------------------------------