TSTP Solution File: GRP438-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP438-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:19:05 EDT 2022
% Result : Unsatisfiable 1.25s 1.55s
% Output : Refutation 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP438-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 21:08:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.25/1.55 ============================== Prover9 ===============================
% 1.25/1.55 Prover9 (32) version 2009-11A, November 2009.
% 1.25/1.55 Process 23629 was started by sandbox2 on n009.cluster.edu,
% 1.25/1.55 Mon Jun 13 21:08:23 2022
% 1.25/1.55 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23358_n009.cluster.edu".
% 1.25/1.55 ============================== end of head ===========================
% 1.25/1.55
% 1.25/1.55 ============================== INPUT =================================
% 1.25/1.55
% 1.25/1.55 % Reading from file /tmp/Prover9_23358_n009.cluster.edu
% 1.25/1.55
% 1.25/1.55 set(prolog_style_variables).
% 1.25/1.55 set(auto2).
% 1.25/1.55 % set(auto2) -> set(auto).
% 1.25/1.55 % set(auto) -> set(auto_inference).
% 1.25/1.55 % set(auto) -> set(auto_setup).
% 1.25/1.55 % set(auto_setup) -> set(predicate_elim).
% 1.25/1.55 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.25/1.55 % set(auto) -> set(auto_limits).
% 1.25/1.55 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.25/1.55 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.25/1.55 % set(auto) -> set(auto_denials).
% 1.25/1.55 % set(auto) -> set(auto_process).
% 1.25/1.55 % set(auto2) -> assign(new_constants, 1).
% 1.25/1.55 % set(auto2) -> assign(fold_denial_max, 3).
% 1.25/1.55 % set(auto2) -> assign(max_weight, "200.000").
% 1.25/1.55 % set(auto2) -> assign(max_hours, 1).
% 1.25/1.55 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.25/1.55 % set(auto2) -> assign(max_seconds, 0).
% 1.25/1.55 % set(auto2) -> assign(max_minutes, 5).
% 1.25/1.55 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.25/1.55 % set(auto2) -> set(sort_initial_sos).
% 1.25/1.55 % set(auto2) -> assign(sos_limit, -1).
% 1.25/1.55 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.25/1.55 % set(auto2) -> assign(max_megs, 400).
% 1.25/1.55 % set(auto2) -> assign(stats, some).
% 1.25/1.55 % set(auto2) -> clear(echo_input).
% 1.25/1.55 % set(auto2) -> set(quiet).
% 1.25/1.55 % set(auto2) -> clear(print_initial_clauses).
% 1.25/1.55 % set(auto2) -> clear(print_given).
% 1.25/1.55 assign(lrs_ticks,-1).
% 1.25/1.55 assign(sos_limit,10000).
% 1.25/1.55 assign(order,kbo).
% 1.25/1.55 set(lex_order_vars).
% 1.25/1.55 clear(print_given).
% 1.25/1.55
% 1.25/1.55 % formulas(sos). % not echoed (2 formulas)
% 1.25/1.55
% 1.25/1.55 ============================== end of input ==========================
% 1.25/1.55
% 1.25/1.55 % From the command line: assign(max_seconds, 300).
% 1.25/1.55
% 1.25/1.55 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.25/1.55
% 1.25/1.55 % Formulas that are not ordinary clauses:
% 1.25/1.55
% 1.25/1.55 ============================== end of process non-clausal formulas ===
% 1.25/1.55
% 1.25/1.55 ============================== PROCESS INITIAL CLAUSES ===============
% 1.25/1.55
% 1.25/1.55 ============================== PREDICATE ELIMINATION =================
% 1.25/1.55
% 1.25/1.55 ============================== end predicate elimination =============
% 1.25/1.55
% 1.25/1.55 Auto_denials:
% 1.25/1.55 % copying label prove_these_axioms_3 to answer in negative clause
% 1.25/1.55
% 1.25/1.55 Term ordering decisions:
% 1.25/1.55
% 1.25/1.55 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.25/1.55 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.25/1.55
% 1.25/1.55 ============================== end of process initial clauses ========
% 1.25/1.55
% 1.25/1.55 ============================== CLAUSES FOR SEARCH ====================
% 1.25/1.55
% 1.25/1.55 ============================== end of clauses for search =============
% 1.25/1.55
% 1.25/1.55 ============================== SEARCH ================================
% 1.25/1.55
% 1.25/1.55 % Starting search at 0.01 seconds.
% 1.25/1.55
% 1.25/1.55 ============================== PROOF =================================
% 1.25/1.55 % SZS status Unsatisfiable
% 1.25/1.55 % SZS output start Refutation
% 1.25/1.55
% 1.25/1.55 % Proof 1 at 0.55 (+ 0.01) seconds: prove_these_axioms_3.
% 1.25/1.55 % Length of proof is 244.
% 1.25/1.55 % Level of proof is 53.
% 1.25/1.55 % Maximum clause weight is 62.000.
% 1.25/1.55 % Given clauses 47.
% 1.25/1.55
% 1.25/1.55 1 multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D # label(single_axiom) # label(axiom). [assumption].
% 1.25/1.55 2 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 1.25/1.55 3 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))].
% 1.25/1.55 4 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))].
% 1.25/1.55 5 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))].
% 1.25/1.55 6 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(3(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.25/1.55 10 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),3(a,1,2,1,1,1,2,2)),flip(a)].
% 1.25/1.55 18 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(4(a,1),1(a,1,2,1,2,2,1))].
% 1.25/1.55 58 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(18(a,1),4(a,1,2,1,1,2,1,2,1)),flip(a)].
% 1.25/1.55 62 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(multiply(C,D))),C))),inverse(B))) = D. [para(18(a,1),4(a,1))].
% 1.25/1.55 84 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),62(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.25/1.55 89 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(3(a,1),62(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.25/1.55 90 multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(D,multiply(multiply(inverse(D),inverse(B)),inverse(C))). [para(3(a,1),62(a,1,2,1,2,1,1)),rewrite([1(10)])].
% 1.25/1.55 93 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(62(a,1),4(a,1,2,1,2))].
% 1.25/1.55 96 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(62(a,1),18(a,1,2,1,1))].
% 1.25/1.55 103 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(62(a,1),62(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.25/1.55 112 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(90(a,1),4(a,1,2,1,1,2,1,2,1))].
% 1.25/1.55 122 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(90(a,1),62(a,1,2,1,2,1,1,2,1))].
% 1.25/1.55 124 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(58),rewrite([112(25)])].
% 1.25/1.55 136 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(5(a,1),3(a,1,2,1,1,1,2,2,1,2,1))].
% 1.25/1.55 174 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(62(a,1),124(a,1,1,1)),flip(a)].
% 1.25/1.55 193 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(E,inverse(multiply(B,multiply(C,multiply(D,E))))). [back_rewrite(96),rewrite([174(19)])].
% 1.25/1.55 194 multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(C,multiply(A,multiply(D,B))))),C))) = D. [back_rewrite(93),rewrite([174(15)])].
% 1.25/1.55 201 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(194(a,1),62(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.25/1.55 202 multiply(A,multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,inverse(multiply(D,multiply(E,multiply(B,C)))))))),inverse(E))) = D. [para(194(a,1),62(a,1,2,1,2,1,1))].
% 1.25/1.55 204 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(62(a,1),194(a,1,2,1,1,2,1,2))].
% 1.25/1.55 228 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(193(a,1),90(a,1,2,1)),flip(a)].
% 1.25/1.55 243 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(194(a,1),193(a,1,2,1,2,2))].
% 1.25/1.55 344 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(multiply(inverse(A),inverse(multiply(D,C))),D)). [para(204(a,1),62(a,1,2,1,2,1,1,2,1)),rewrite([62(19)])].
% 1.25/1.55 384 inverse(multiply(multiply(inverse(A),inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),inverse(A)))))),B)) = inverse(D). [para(3(a,1),344(a,1,1,1)),rewrite([1(9)]),flip(a)].
% 1.25/1.55 403 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(D,multiply(E,inverse(multiply(C,multiply(A,multiply(D,E))))))). [para(194(a,1),344(a,1,1,1)),flip(a)].
% 1.25/1.55 408 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(344(a,1),202(a,1,2,1,2,1,2,2))].
% 1.25/1.55 444 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),A))),inverse(C))))) = inverse(D). [para(194(a,1),384(a,1,1,1)),rewrite([124(10)])].
% 1.25/1.55 448 inverse(multiply(multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(D)),A))))),B)) = inverse(D). [para(193(a,1),384(a,1,1,1))].
% 1.25/1.55 468 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),448(a,1,1,1,2,1,2,2,1))].
% 1.25/1.55 488 multiply(multiply(inverse(inverse(A)),inverse(multiply(multiply(inverse(B),inverse(multiply(C,multiply(inverse(A),inverse(D))))),C))),inverse(B)) = inverse(D). [para(124(a,1),448(a,1,1,1,2)),rewrite([124(15)])].
% 1.25/1.55 708 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(193(a,1),403(a,1,1,1,2,1))].
% 1.25/1.55 717 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(202(a,1),403(a,2,1,2,2,1,2)),flip(a)].
% 1.25/1.55 775 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(488(a,1),1(a,1,2,1,2,2,1,2,1)),flip(a)].
% 1.25/1.55 779 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(488(a,1),62(a,1,2,1,2,1,1,2,1)),rewrite([408(23)])].
% 1.25/1.55 790 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(194(a,1),488(a,1,1,2,1,1,2,1,2)),flip(a)].
% 1.25/1.55 805 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(488(a,1),444(a,1,1,2,2,1,2,1))].
% 1.25/1.55 806 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(488(a,1),403(a,1,1,1,2,1))].
% 1.25/1.55 807 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(488(a,1),403(a,2,1,2,2,1,2,2)),flip(a)].
% 1.25/1.55 813 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(779(a,1),1(a,1,2,1,2,2,1))].
% 1.25/1.55 816 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(779(a,1),3(a,1,2,1,1,1,2,2,1))].
% 1.25/1.55 819 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(779(a,1),62(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.25/1.55 821 multiply(A,multiply(inverse(A),inverse(B))) = multiply(C,multiply(inverse(C),inverse(B))). [para(779(a,1),90(a,1,2,1)),rewrite([779(19)])].
% 1.25/1.55 837 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(779(a,1),193(a,1,2,1,2,2))].
% 1.25/1.55 840 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(779(a,1),6(a,1,2,1,1,1,1,1,2,2,1,2,1))].
% 1.25/1.55 852 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(448(a,1),779(a,1,2,1,1,2,1,1))].
% 1.25/1.55 864 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(779(a,1),403(a,1,1,1))].
% 1.25/1.55 873 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(779(a,1),488(a,1,1,2,1,1))].
% 1.25/1.55 880 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),10(a,2,2,1,1,1,2))].
% 1.25/1.55 928 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(5(a,1),10(a,1,1,2,2,2,2,1))].
% 1.25/1.55 956 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(193(a,1),10(a,1,1,2,2,2,2,1))].
% 1.25/1.55 1087 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(779(a,1),10(a,1,1,2,2,2,2,1))].
% 1.25/1.55 1088 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(779(a,1),10(a,1,1,2,2,2))].
% 1.25/1.55 1153 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(821(a,1),403(a,1,1,1,2,1))].
% 1.25/1.55 1160 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(779(a,1),821(a,1,2)),rewrite([779(17)])].
% 1.25/1.55 1170 multiply(A,inverse(A)) = c_0. [new_symbol(1160)].
% 1.25/1.55 1173 multiply(A,inverse(multiply(inverse(B),multiply(C,multiply(multiply(inverse(C),inverse(c_0)),A))))) = B. [para(1170(a,1),1(a,1,2,1,2,2,1,2,1))].
% 1.25/1.55 1174 multiply(inverse(multiply(inverse(A),inverse(multiply(B,C)))),inverse(multiply(C,multiply(A,c_0)))) = B. [para(1170(a,1),1(a,1,2,1,2,2))].
% 1.25/1.55 1179 multiply(A,multiply(multiply(inverse(A),inverse(multiply(multiply(inverse(B),inverse(c_0)),C))),inverse(B))) = inverse(C). [para(1170(a,1),62(a,1,2,1,2,1,1,2,1))].
% 1.25/1.55 1180 multiply(A,multiply(multiply(inverse(A),inverse(inverse(B))),inverse(C))) = multiply(B,multiply(c_0,inverse(C))). [para(1170(a,1),90(a,1,2,1)),flip(a)].
% 1.25/1.55 1185 inverse(multiply(multiply(A,c_0),multiply(B,multiply(C,D)))) = multiply(multiply(inverse(D),inverse(multiply(B,C))),inverse(A)). [para(1170(a,1),124(a,1,1,1,2))].
% 1.25/1.55 1189 multiply(A,inverse(multiply(B,multiply(C,multiply(D,A))))) = multiply(inverse(D),inverse(multiply(B,multiply(C,c_0)))). [para(1170(a,1),193(a,1,2,1,2,2)),flip(a)].
% 1.25/1.55 1197 inverse(multiply(multiply(inverse(A),inverse(multiply(B,inverse(C)))),B)) = inverse(multiply(multiply(inverse(A),inverse(c_0)),C)). [para(1170(a,1),344(a,1,1,1,2,1)),flip(a)].
% 1.25/1.55 1199 inverse(multiply(multiply(inverse(c_0),inverse(multiply(A,multiply(B,c_0)))),A)) = inverse(inverse(B)). [para(1170(a,1),448(a,1,1,1,2,1,2,2,1)),rewrite([1189(6)])].
% 1.25/1.55 1210 inverse(multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))))) = inverse(multiply(multiply(inverse(C),inverse(c_0)),B)). [para(1170(a,1),403(a,1,1,1,2,1)),rewrite([1189(12)]),flip(a)].
% 1.25/1.55 1219 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(1170(a,1),10(a,2,2,1,2,2,1)),rewrite([1189(22)])].
% 1.25/1.55 1222 multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,c_0). [para(1170(a,1),821(a,1,2)),flip(a)].
% 1.25/1.55 1225 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(1088),rewrite([1180(24),1189(28)])].
% 1.25/1.55 1226 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(1087),rewrite([1180(20),1189(34)])].
% 1.25/1.55 1234 multiply(multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))),inverse(A)) = inverse(B). [back_rewrite(873),rewrite([1180(11),1189(11)])].
% 1.25/1.55 1241 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(864),rewrite([1180(9),1189(16)]),flip(a)].
% 1.25/1.55 1261 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(840),rewrite([1180(8),1189(34)])].
% 1.25/1.55 1264 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(837),rewrite([1180(8),1189(21)])].
% 1.25/1.55 1277 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(819),rewrite([1180(8)])].
% 1.25/1.55 1280 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(816),rewrite([1180(17),1189(21)])].
% 1.25/1.55 1283 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(813),rewrite([1189(9),1180(18)])].
% 1.25/1.55 1285 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(805),rewrite([1180(9)]),flip(a)].
% 1.25/1.55 1289 multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(multiply(inverse(B),multiply(A,c_0)))) = B. [back_rewrite(1173),rewrite([1189(10)])].
% 1.25/1.55 1301 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(1153),rewrite([1189(17),1241(20)])].
% 1.25/1.55 1428 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(956),rewrite([1189(10),1219(17),1189(29)]),flip(a)].
% 1.25/1.55 1452 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(928),rewrite([1189(37)])].
% 1.25/1.55 1485 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(880),rewrite([1189(30)])].
% 1.25/1.55 1492 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(852),rewrite([1189(9)])].
% 1.25/1.55 1497 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(806),rewrite([1285(15),1189(15),1189(20),1210(23)])].
% 1.25/1.55 1503 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(790),rewrite([1189(5)])].
% 1.25/1.55 1505 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(775),rewrite([1285(11),1189(11),1189(18)]),flip(a)].
% 1.25/1.55 1556 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(717),rewrite([1189(6),1301(16)])].
% 1.25/1.55 1565 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(708),rewrite([1189(6),1189(20),1210(23)])].
% 1.25/1.55 1695 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(468),rewrite([1189(5)])].
% 1.25/1.55 1784 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(243),rewrite([1189(5),1189(18)])].
% 1.25/1.55 1793 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(228),rewrite([1189(15)])].
% 1.25/1.55 1809 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(201),rewrite([1189(5)])].
% 1.25/1.55 1820 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(136),rewrite([1189(30),1505(31)])].
% 1.25/1.55 1844 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(807),rewrite([1285(11),1189(11)])].
% 1.25/1.55 1867 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(1261),rewrite([1428(35)])].
% 1.25/1.55 1873 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(1452),rewrite([1505(38)])].
% 1.25/1.55 1882 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(1226),rewrite([1505(35)])].
% 1.25/1.55 1911 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(1222(a,1),124(a,1,1,2))].
% 1.25/1.55 1915 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(1222(a,1),344(a,1,1,1,2,1)),rewrite([1285(17)])].
% 1.25/1.55 1949 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(84(a,2),62(a,1,2,1,2,1,1,2,1)),flip(a)].
% 1.25/1.55 1979 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(204(a,1),84(a,2,2,1,2,1,1)),rewrite([174(27),1189(18)])].
% 1.25/1.55 2013 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(inverse(C))),D)))) = inverse(multiply(A,multiply(C,multiply(c_0,D)))). [para(1199(a,1),84(a,1,1,2,2,1,2)),rewrite([1565(21),1179(23)])].
% 1.25/1.55 2015 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(1199(a,1),84(a,2,2,1,2,1,1,2)),rewrite([1979(16)]),flip(a)].
% 1.25/1.55 2034 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(1867),rewrite([2013(24)])].
% 1.25/1.55 2045 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(1949),rewrite([2015(27)]),flip(a)].
% 1.25/1.55 2046 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(1277),rewrite([2015(22)])].
% 1.25/1.55 2050 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0)))),inverse(B))) = multiply(c_0,inverse(C)). [para(1234(a,1),90(a,1,2)),flip(a)].
% 1.25/1.55 2053 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(1234(a,1),84(a,1,1,2,2)),rewrite([2015(19)])].
% 1.25/1.55 2055 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(84(a,1),1234(a,1,2))].
% 1.25/1.55 2057 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(1289(a,1),90(a,1,2,1)),flip(a)].
% 1.25/1.55 2063 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(1289(a,1),344(a,1,1,1,2,1)),rewrite([1197(21)]),flip(a)].
% 1.25/1.55 2066 multiply(A,multiply(inverse(A),inverse(multiply(inverse(B),multiply(C,c_0))))) = multiply(multiply(inverse(C),inverse(c_0)),B). [para(1289(a,1),821(a,1,2)),flip(a)].
% 1.25/1.55 2067 multiply(multiply(inverse(c_0),inverse(multiply(A,multiply(B,c_0)))),A) = inverse(B). [para(1199(a,1),1289(a,1,2,1,1)),rewrite([1289(12)]),flip(a)].
% 1.25/1.55 2073 multiply(multiply(inverse(A),inverse(c_0)),c_0) = multiply(c_0,inverse(A)). [back_rewrite(2050),rewrite([2057(10),1170(6)])].
% 1.25/1.55 2085 multiply(inverse(multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(c_0))),inverse(multiply(inverse(B),multiply(c_0,inverse(A))))) = B. [para(2073(a,1),1289(a,1,2,1,2))].
% 1.25/1.55 2155 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(1170(a,1),89(a,1,1,2,2))].
% 1.25/1.55 2160 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(1222(a,1),89(a,1,1,1,1,2,2,1,2,1))].
% 1.25/1.55 2165 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(89(a,1),84(a,1,1,2,2,1,2)),rewrite([2015(39)])].
% 1.25/1.55 2245 multiply(inverse(A),inverse(multiply(multiply(B,c_0),multiply(c_0,inverse(B))))) = inverse(A). [para(1289(a,1),1174(a,1,1,1)),rewrite([2073(9)])].
% 1.25/1.55 2248 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(2067(a,1),1174(a,1,1,1,2,1))].
% 1.25/1.55 2270 multiply(inverse(A),inverse(multiply(multiply(c_0,c_0),c_0))) = inverse(A). [para(1170(a,1),2245(a,1,2,1,2))].
% 1.25/1.55 2284 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(2270(a,1),62(a,1,2,1,2,1,1,2,1)),rewrite([2015(12)])].
% 1.25/1.55 2287 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(124(a,1),2270(a,1,1)),rewrite([124(20)])].
% 1.25/1.55 2291 inverse(multiply(inverse(A),multiply(inverse(B),multiply(c_0,inverse(inverse(B)))))) = inverse(multiply(inverse(A),multiply(c_0,c_0))). [para(2270(a,1),344(a,1,1,1)),rewrite([1915(13)]),flip(a)].
% 1.25/1.55 2293 inverse(multiply(c_0,multiply(A,multiply(inverse(A),B)))) = multiply(inverse(B),inverse(inverse(c_0))). [para(2270(a,1),84(a,1,1,2,2,1)),rewrite([1915(15),1793(21),2067(19)])].
% 1.25/1.55 2295 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(84(a,1),2270(a,1,1)),flip(a)].
% 1.25/1.55 2300 multiply(inverse(inverse(A)),inverse(multiply(c_0,multiply(A,c_0)))) = multiply(c_0,c_0). [para(2270(a,1),1174(a,1,1,1))].
% 1.25/1.55 2301 inverse(multiply(multiply(A,c_0),multiply(c_0,inverse(A)))) = inverse(multiply(multiply(c_0,c_0),c_0)). [back_rewrite(2053),rewrite([2284(17)])].
% 1.25/1.55 2302 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(2046),rewrite([2284(20)])].
% 1.25/1.55 2308 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(2034),rewrite([2302(12)])].
% 1.25/1.55 2309 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(1882),rewrite([2302(24)])].
% 1.25/1.55 2311 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(1264),rewrite([2302(10)])].
% 1.25/1.55 2317 inverse(multiply(c_0,multiply(A,c_0))) = multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0))). [para(2300(a,1),62(a,1,2,1,2,1,1,2,1)),rewrite([1915(11),1793(17),2067(15)]),flip(a)].
% 1.25/1.55 2322 multiply(multiply(inverse(A),inverse(multiply(inverse(B),multiply(c_0,c_0)))),inverse(B)) = inverse(A). [para(2300(a,1),84(a,1,1,2,2,1)),rewrite([1185(10),1179(21)])].
% 1.25/1.55 2389 multiply(A,multiply(multiply(inverse(A),inverse(multiply(c_0,inverse(B)))),inverse(B))) = inverse(c_0). [para(2073(a,1),103(a,2,2,1,2,1)),rewrite([1915(9),2291(11),2322(11)]),flip(a)].
% 1.25/1.55 2409 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(103(a,1),1174(a,1,1,1,2,1))].
% 1.25/1.55 2417 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(2270(a,1),103(a,2,2,1,2,1,1))].
% 1.25/1.55 2440 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(2317(a,1),344(a,1,1,1,2)),flip(a)].
% 1.25/1.55 2452 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(2317(a,1),1289(a,1,2,1,1))].
% 1.25/1.55 2470 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(2317(a,1),103(a,1,1,2,1,1,2)),rewrite([1915(24),1793(30),2067(28)])].
% 1.25/1.55 2474 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(2417),rewrite([2440(12),2470(19)]),flip(a)].
% 1.25/1.55 2486 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(1809),rewrite([2440(8)]),flip(a)].
% 1.25/1.55 2492 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(1784),rewrite([2440(8)])].
% 1.25/1.55 2493 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(1695),rewrite([2440(8)]),flip(a)].
% 1.25/1.55 2505 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(1503),rewrite([2440(8)]),flip(a)].
% 1.25/1.55 2520 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(2155),rewrite([2486(26)])].
% 1.25/1.55 2528 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(1225),rewrite([2493(9)]),flip(a)].
% 1.25/1.55 2531 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(2055),rewrite([2520(14)])].
% 1.25/1.55 2539 inverse(multiply(multiply(inverse(multiply(inverse(A),B)),multiply(inverse(inverse(inverse(A))),inverse(inverse(c_0)))),c_0)) = B. [back_rewrite(1280),rewrite([2528(22)])].
% 1.25/1.55 2547 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(90(a,1),2293(a,1,1,2,2))].
% 1.25/1.55 2585 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(89(a,2),2293(a,1,1,2,2))].
% 1.25/1.55 2596 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(2293(a,1),103(a,2,2,1,2,1,1,2))].
% 1.25/1.55 2597 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(103(a,2),2293(a,1,1,2,2))].
% 1.25/1.55 2601 multiply(inverse(multiply(A,c_0)),inverse(inverse(multiply(c_0,c_0)))) = multiply(c_0,inverse(A)). [para(2301(a,1),62(a,1,2,1,2,1,1,2)),rewrite([2270(9),2474(10)])].
% 1.25/1.55 2613 multiply(multiply(A,c_0),multiply(c_0,inverse(A))) = multiply(multiply(c_0,c_0),c_0). [para(2301(a,1),1289(a,1,2,1,1)),rewrite([1289(16)]),flip(a)].
% 1.25/1.55 2622 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(2613(a,1),124(a,1,1,2)),rewrite([1911(12)])].
% 1.25/1.55 2701 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(2293(a,1),122(a,1,2,1,2,1,1,2,1,2,2)),rewrite([2293(29)])].
% 1.25/1.55 2708 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(344(a,1),2601(a,1,1))].
% 1.25/1.55 2715 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(2601(a,1),1174(a,1,1,1,2,1))].
% 1.25/1.55 2733 inverse(multiply(inverse(c_0),inverse(c_0))) = c_0. [para(1289(a,1),2322(a,1,1)),rewrite([1170(2)]),flip(a)].
% 1.25/1.55 2739 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(2322(a,1),1174(a,1,1,1,2,1)),rewrite([2248(11)])].
% 1.25/1.55 2741 multiply(multiply(inverse(A),inverse(inverse(B))),inverse(B)) = multiply(inverse(A),inverse(inverse(c_0))). [para(2322(a,1),103(a,1,1,2,1)),rewrite([1915(15),1793(21),2067(19)])].
% 1.25/1.55 2751 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(2733(a,1),62(a,1,2,1,1))].
% 1.25/1.55 2754 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(2733(a,1),90(a,1,2,1,1))].
% 1.25/1.55 2761 inverse(multiply(multiply(inverse(A),c_0),inverse(c_0))) = inverse(multiply(c_0,inverse(A))). [para(2733(a,1),344(a,1,1,1,2)),rewrite([1197(15),2073(13)])].
% 1.25/1.55 2762 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(c_0,inverse(A))) = multiply(B,multiply(inverse(B),inverse(A))). [para(2733(a,1),821(a,1,2,1))].
% 1.25/1.55 2764 multiply(multiply(inverse(c_0),inverse(c_0)),multiply(c_0,inverse(inverse(A)))) = multiply(A,c_0). [para(2733(a,1),1222(a,1,2,1))].
% 1.25/1.55 2785 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(2733(a,1),103(a,1,1,1))].
% 1.25/1.55 2791 inverse(multiply(c_0,c_0)) = multiply(inverse(inverse(c_0)),inverse(inverse(c_0))). [para(2733(a,1),2317(a,2,1,1,1)),rewrite([2073(8),1170(5)])].
% 1.25/1.55 2793 multiply(multiply(c_0,c_0),c_0) = multiply(c_0,multiply(c_0,c_0)). [para(2733(a,1),2613(a,1,2,2)),rewrite([2073(7),1170(4)]),flip(a)].
% 1.25/1.55 2800 multiply(multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))),c_0) = inverse(A). [para(2733(a,1),2322(a,1,1,2,1,1)),rewrite([2317(7),2733(16)])].
% 1.25/1.55 2802 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(2715),rewrite([2791(11)])].
% 1.25/1.55 2806 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(2708),rewrite([2791(10)])].
% 1.25/1.55 2810 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(2622),rewrite([2791(4)])].
% 1.25/1.55 2812 multiply(inverse(multiply(A,c_0)),inverse(multiply(inverse(inverse(c_0)),inverse(inverse(c_0))))) = multiply(c_0,inverse(A)). [back_rewrite(2601),rewrite([2791(7)])].
% 1.25/1.55 2818 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(2474),rewrite([2791(13)])].
% 1.25/1.55 2842 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(2311),rewrite([2793(5),2317(6)])].
% 1.25/1.55 2844 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(2309),rewrite([2793(19),2317(20)])].
% 1.25/1.55 2845 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(2308),rewrite([2793(7),2317(8)])].
% 1.25/1.55 2851 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(2295),rewrite([2793(23),2317(24)])].
% 1.25/1.55 2853 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(2287),rewrite([2793(11),2317(12)])].
% 1.25/1.55 2856 multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))) = inverse(A). [back_rewrite(2270),rewrite([2793(6),2317(7)])].
% 1.25/1.55 2858 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(2800),rewrite([2856(10)])].
% 1.25/1.55 2870 inverse(multiply(inverse(A),inverse(c_0))) = inverse(multiply(c_0,inverse(A))). [back_rewrite(2761),rewrite([2858(3)])].
% 1.25/1.55 2875 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(2858(a,1),124(a,1,1,2,2))].
% 1.25/1.55 2887 multiply(multiply(inverse(A),inverse(multiply(inverse(B),inverse(inverse(c_0))))),inverse(B)) = inverse(A). [para(2858(a,1),103(a,1,1,2,1,1,2,1)),rewrite([2741(7),1179(21)])].
% 1.25/1.55 2888 inverse(multiply(c_0,inverse(A))) = multiply(inverse(inverse(inverse(inverse(A)))),inverse(inverse(c_0))). [para(2858(a,1),2317(a,1,1,2))].
% 1.25/1.55 2892 multiply(c_0,c_0) = c_0. [para(2733(a,1),2858(a,1,1)),rewrite([2733(9)])].
% 1.25/1.55 2900 multiply(inverse(A),inverse(c_0)) = inverse(A). [back_rewrite(1492),rewrite([2875(24),2741(9),2440(21),2539(25),2887(12)])].
% 1.25/1.55 2912 multiply(inverse(c_0),inverse(multiply(inverse(A),multiply(B,c_0)))) = multiply(inverse(B),inverse(inverse(A))). [back_rewrite(2739),rewrite([2892(13),2858(12)])].
% 1.25/1.55 2919 multiply(inverse(A),inverse(inverse(c_0))) = inverse(A). [back_rewrite(2322),rewrite([2892(5),2858(4),2741(6)])].
% 1.25/1.55 2952 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(2165),rewrite([2892(34)])].
% 1.25/1.55 2961 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(2045),rewrite([2892(13)])].
% 1.25/1.55 2963 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(2015),rewrite([2892(17)])].
% 1.25/1.55 2967 inverse(inverse(inverse(inverse(A)))) = inverse(inverse(A)). [back_rewrite(2870),rewrite([2900(4),2888(6),2919(10)]),flip(a)].
% 1.25/1.55 2970 inverse(multiply(A,c_0)) = inverse(A). [back_rewrite(2802),rewrite([2888(5),2967(5),2919(7),2919(12),2248(14),2912(11),2967(6),2919(5)]),flip(a)].
% 1.25/1.55 2974 inverse(c_0) = c_0. [back_rewrite(2389),rewrite([2888(5),2967(5),2919(7),2741(6),2919(5),1170(2)]),flip(a)].
% 1.25/1.55 2981 multiply(A,multiply(multiply(inverse(A),inverse(multiply(inverse(B),C))),inverse(B))) = inverse(C). [back_rewrite(2818),rewrite([2974(11),2974(11),2974(12),2974(12),2892(12),2974(11),2858(11)])].
% 1.25/1.55 2984 multiply(c_0,inverse(A)) = inverse(A). [back_rewrite(2812),rewrite([2970(3),2974(3),2974(3),2974(4),2974(4),2892(4),2974(3),2858(3)]),flip(a)].
% 1.25/1.55 2986 multiply(inverse(multiply(A,inverse(B))),inverse(C)) = multiply(multiply(inverse(inverse(B)),inverse(A)),inverse(C)). [back_rewrite(2810),rewrite([2974(2),2974(2),2974(3),2974(3),2892(3),2974(2),2974(2),2970(4),2984(5),2970(10)])].
% 1.25/1.55 2987 inverse(multiply(multiply(inverse(A),inverse(multiply(B,C))),B)) = inverse(multiply(inverse(A),inverse(multiply(c_0,C)))). [back_rewrite(2806),rewrite([2974(8),2974(8),2974(9),2974(9),2892(9),2974(8),2858(8),2984(14)])].
% 1.25/1.55 3009 inverse(inverse(multiply(c_0,A))) = inverse(inverse(A)). [back_rewrite(2785),rewrite([2987(7),2984(8),2986(8),2741(9),2974(6),2974(6),2858(6),2974(10),2974(11),2892(11),2970(11),2981(13)])].
% 1.25/1.55 3015 multiply(A,c_0) = inverse(inverse(A)). [back_rewrite(2764),rewrite([2974(2),2974(3),2892(3),2984(5),2984(4)]),flip(a)].
% 1.25/1.55 3016 multiply(A,multiply(inverse(A),inverse(B))) = inverse(B). [back_rewrite(2762),rewrite([2974(2),2974(3),3015(3),2974(2),2974(2),2984(4),2984(3)]),flip(a)].
% 1.25/1.55 3018 multiply(A,multiply(multiply(inverse(A),inverse(B)),inverse(C))) = multiply(c_0,multiply(inverse(B),inverse(C))). [back_rewrite(2754),rewrite([2974(2),2974(3),3015(3),2974(2),2974(2),2984(4)]),flip(a)].
% 1.25/1.55 3019 inverse(inverse(A)) = A. [back_rewrite(2751),rewrite([2974(2),2974(3),3015(3),2974(2),2974(2),2987(8),2984(9),2986(9),3009(5),2741(8),2974(5),2974(5),3015(5),2967(5),2984(4)])].
% 1.25/1.55 3027 multiply(A,inverse(multiply(inverse(B),A))) = multiply(c_0,B). [back_rewrite(2452),rewrite([2974(3),3015(3),3019(2),3019(2),3019(2),2974(3),2974(3),3015(3),3019(2),3015(3),3019(3),3015(7),3019(7)])].
% 1.25/1.55 3040 multiply(c_0,A) = A. [back_rewrite(2085),rewrite([2974(3),3015(3),3019(2),3019(2),2974(2),3015(2),3019(2),2984(5),3027(6)])].
% 1.25/1.55 3043 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(2066),rewrite([3015(4),3019(4),3016(6),2974(6),3015(6),3019(5)])].
% 1.25/1.55 3045 inverse(multiply(multiply(inverse(A),inverse(B)),C)) = multiply(multiply(inverse(C),B),A). [back_rewrite(2063),rewrite([2974(3),3015(3),3019(2),3015(4),3019(4),3043(5),3043(3),2974(9),3015(9),3019(8),3019(8)]),flip(a)].
% 1.25/1.55 3062 inverse(multiply(multiply(inverse(A),B),multiply(inverse(B),C))) = multiply(inverse(C),A). [back_rewrite(1497),rewrite([3019(3),2974(4),3015(6),3019(6),3043(6),3040(6),2974(9),3015(9),3019(8),3043(9)])].
% 1.25/1.55 3064 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(1289),rewrite([2974(3),3015(3),3019(2),3019(2),3015(3),3019(3),3043(3)])].
% 1.25/1.55 3071 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(2845),rewrite([2974(2),2974(3),2974(3),2974(3),2974(4),2974(4),3015(4),2974(3),2974(3),3015(4),3019(4),3040(3),3040(4),3043(5),3019(7),3015(8),3043(7),3043(7),3062(8),3040(5)])].
% 1.25/1.55 3072 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(2844),rewrite([3019(7),2974(12),2974(13),2974(13),2974(13),2974(14),2974(14),3015(14),2974(13),2974(13),3040(14),3015(15),3019(15),3043(15),3040(15)])].
% 1.25/1.55 3083 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(1873),rewrite([3072(11),3019(2),2974(4),3043(9),3015(21),3072(20),3019(11),3040(15)]),flip(a)].
% 1.25/1.55 3098 multiply(multiply(A,multiply(B,inverse(C))),C) = multiply(A,B). [back_rewrite(1844),rewrite([2974(2),3015(4),3019(4),3043(4),3040(4),3062(10),3019(5),3045(10),3071(7)])].
% 1.25/1.55 3101 multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(A)),C))) = C. [back_rewrite(1820),rewrite([2974(2),3043(11),3015(23),3072(22),3019(13),3083(16),3040(8)])].
% 1.25/1.55 3135 multiply(multiply(inverse(A),B),multiply(C,D)) = multiply(inverse(A),multiply(B,multiply(C,D))). [back_rewrite(1219),rewrite([3043(8),3072(12),3043(3),2974(6),3015(10),3019(10),3043(10),3040(10)])].
% 1.25/1.55 3149 multiply(A,multiply(multiply(inverse(A),multiply(multiply(inverse(B),C),D)),inverse(D))) = multiply(inverse(B),C). [back_rewrite(2160),rewrite([3019(3),3015(5),3019(5),3135(8),3101(7),3043(3),3135(8),3101(7),3043(3),3045(8)]),flip(a)].
% 1.25/1.55 3174 inverse(multiply(multiply(A,multiply(B,C)),D)) = multiply(multiply(inverse(D),inverse(multiply(B,C))),inverse(A)). [back_rewrite(2853),rewrite([2974(8),2974(8),2974(8),2974(9),2974(9),3015(9),2974(8),2974(8),3015(8),3045(7),3019(2)])].
% 1.25/1.55 3175 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))) = multiply(inverse(D),C). [back_rewrite(2851),rewrite([3045(14),3149(16),2974(12),2974(12),2974(12),2974(13),2974(13),3015(13),2974(12),2974(12),3015(12),3043(11),3043(11)])].
% 1.25/1.55 3176 inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))). [back_rewrite(2842),rewrite([2974(2),2974(2),2974(2),2974(3),2974(3),3015(3),2974(2),2974(2),3040(6),3019(6),3015(6),3019(6)])].
% 1.25/1.55 3182 multiply(multiply(inverse(A),inverse(B)),inverse(C)) = multiply(inverse(A),inverse(multiply(C,B))). [back_rewrite(2701),rewrite([2974(8),2974(8),3015(8),3019(7),3018(8),3040(7),3043(6),3019(4),3174(6),3019(7),3149(10),2974(10),2974(10),3015(10),3019(9)]),flip(a)].
% 1.25/1.55 3184 multiply(multiply(A,inverse(multiply(multiply(inverse(B),C),A))),inverse(D)) = multiply(inverse(C),inverse(multiply(D,inverse(B)))). [back_rewrite(2597),rewrite([3045(8),3071(5),3040(8),3176(7),1189(6),3015(4),3019(3),3019(7),3045(10),3174(12),3019(7),2974(14),2974(14),3015(14),3019(14)]),flip(a)].
% 1.25/1.55 3185 multiply(multiply(inverse(A),multiply(B,C)),inverse(C)) = multiply(inverse(A),B). [back_rewrite(2596),rewrite([3064(6),3040(4),3045(7),3071(4),2974(10),2974(10),3015(10),3019(9),3045(11),3149(13)])].
% 1.25/1.55 3187 inverse(multiply(multiply(A,inverse(B)),C)) = inverse(multiply(A,multiply(inverse(B),C))). [back_rewrite(2585),rewrite([3175(9),3135(9),3101(8),3043(4),3040(5),3019(6),3045(9),3174(11),3019(6),3184(11),2974(11),2974(11),3015(11),3043(10),3019(8)]),flip(a)].
% 1.25/1.55 3192 inverse(multiply(A,inverse(multiply(B,C)))) = multiply(B,inverse(multiply(A,inverse(C)))). [back_rewrite(2547),rewrite([3182(6),3064(6),3040(5),3019(6),3187(9),3176(9),2974(10),2974(10),3015(10),3019(10)])].
% 1.25/1.55 3196 multiply(inverse(multiply(A,B)),A) = inverse(B). [back_rewrite(2531),rewrite([2974(2),3043(6),3019(4),3019(5),2974(5),2974(5),3015(5),3019(5),3015(6),3043(5),3043(5),3043(5),3040(5),3187(9),3043(9),3043(7),3185(10),3064(8),3135(6),3064(5)])].
% 1.25/1.55 3199 inverse(multiply(multiply(inverse(A),B),C)) = multiply(inverse(multiply(B,C)),A). [back_rewrite(2520),rewrite([3175(8),3015(4),3019(4),3043(9),3019(7),3019(8),2974(8),2974(8),3015(8),3019(8),3015(9),3043(8),3043(8),3043(8)])].
% 1.25/1.55 3202 multiply(multiply(A,multiply(B,C)),inverse(C)) = multiply(A,B). [back_rewrite(2505),rewrite([3019(2),3187(6),3196(4),3043(4),3019(2),3019(7),2974(8),2974(8),3015(8),3019(7),3015(9),3043(8),3019(6),3019(7)])].
% 1.25/1.55 3205 multiply(multiply(A,B),inverse(multiply(C,multiply(D,B)))) = multiply(A,inverse(multiply(C,D))). [back_rewrite(2492),rewrite([3019(3),2974(4),2974(4),3015(4),3019(3),3015(5),3043(4),3019(2),3019(3),3019(7),3015(7),3019(7)])].
% 1.25/1.55 3217 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,C). [back_rewrite(1556),rewrite([3015(3),3019(3),3192(8),3043(7),3019(5),3040(7),3205(6),3176(6),3043(4),3187(10),3196(8),3043(8),3019(6)])].
% 1.25/1.55 3222 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(1283),rewrite([3019(2),3015(5),3019(5),3187(5),3043(5),3043(3),3019(7),3040(6)])].
% 1.25/1.55 3241 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(2963),rewrite([3019(4),3199(5),3202(7),3064(5),3015(5),3019(5),3015(5),3019(5)])].
% 1.25/1.55 3242 multiply(multiply(inverse(A),multiply(inverse(B),multiply(C,D))),inverse(D)) = multiply(inverse(A),multiply(inverse(B),C)). [back_rewrite(2961),rewrite([3241(4),3222(8),3222(6),3015(5),3241(4),3019(4),3241(4),3019(4),3015(5),3241(4),3019(4),3241(4),3019(4),3241(4),3019(4),3241(10),3241(10),3019(8),3019(8)]),flip(a)].
% 1.25/1.55 3247 multiply(multiply(inverse(A),inverse(B)),C) = multiply(inverse(A),multiply(inverse(B),C)). [back_rewrite(2952),rewrite([3222(5),3241(9),3241(9),3019(7),3019(7),3242(10),3064(8),3222(8),3135(6),3222(5),3241(4),3241(2),3019(5),3241(8),3222(12),3222(10),3015(9),3241(8),3019(8),3241(8),3019(8),3015(9),3241(8),3019(8),3241(8),3019(8),3241(8),3019(8)])].
% 1.25/1.55 3266 multiply(multiply(inverse(A),B),C) = multiply(inverse(A),multiply(B,C)). [back_rewrite(2409),rewrite([3247(6),3241(7),3241(5),3019(5),3019(6),3202(8),3064(6),3241(4),3019(4),3241(5),3241(3),3019(3),3019(4),3015(6),3019(6),3241(6),3019(6),3217(6),3241(7),3098(10),3241(8),3019(6),3019(6)])].
% 1.25/1.55 3287 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [back_rewrite(1485),rewrite([3241(4),3266(7),3266(6),3064(8),3064(6),3241(4),3019(4),3266(4),3241(5),3241(3),3019(6),3266(5),3241(9),3266(12),3266(11),3217(10),3064(10),3064(8),3241(6),3241(4),3019(2),3019(2),3019(3),3241(6),3019(4),3019(4),3241(5),3015(8),3019(8),3266(7),3241(8),3241(6),3019(6),3019(7),3266(6),3217(7)])].
% 1.25/1.55 3288 $F # answer(prove_these_axioms_3). [resolve(3287,a,2,a)].
% 1.25/1.55
% 1.25/1.55 % SZS output end Refutation
% 1.25/1.55 ============================== end of proof ==========================
% 1.25/1.55
% 1.25/1.55 ============================== STATISTICS ============================
% 1.25/1.55
% 1.25/1.55 Given=47. Generated=5635. Kept=3287. proofs=1.
% 1.25/1.55 Usable=15. Sos=622. Demods=555. Limbo=301, Disabled=2350. Hints=0.
% 1.25/1.55 Megabytes=5.70.
% 1.25/1.55 User_CPU=0.55, System_CPU=0.01, Wall_clock=1.
% 1.25/1.55
% 1.25/1.55 ============================== end of statistics =====================
% 1.25/1.55
% 1.25/1.55 ============================== end of search =========================
% 1.25/1.55
% 1.25/1.55 THEOREM PROVED
% 1.25/1.55 % SZS status Unsatisfiable
% 1.25/1.55
% 1.25/1.55 Exiting with 1 proof.
% 1.25/1.55
% 1.25/1.55 Process 23629 exit (max_proofs) Mon Jun 13 21:08:24 2022
% 1.25/1.55 Prover9 interrupted
%------------------------------------------------------------------------------