TSTP Solution File: GRP437-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 1.33s 1.66s
% Output : Refutation 1.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP437-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n032.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Mon Jun 13 20:56:42 EDT 2022
% 0.10/0.31 % CPUTime :
% 1.33/1.66 ============================== Prover9 ===============================
% 1.33/1.66 Prover9 (32) version 2009-11A, November 2009.
% 1.33/1.66 Process 3874 was started by sandbox on n032.cluster.edu,
% 1.33/1.66 Mon Jun 13 20:56:42 2022
% 1.33/1.66 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_3721_n032.cluster.edu".
% 1.33/1.66 ============================== end of head ===========================
% 1.33/1.66
% 1.33/1.66 ============================== INPUT =================================
% 1.33/1.66
% 1.33/1.66 % Reading from file /tmp/Prover9_3721_n032.cluster.edu
% 1.33/1.66
% 1.33/1.66 set(prolog_style_variables).
% 1.33/1.66 set(auto2).
% 1.33/1.66 % set(auto2) -> set(auto).
% 1.33/1.66 % set(auto) -> set(auto_inference).
% 1.33/1.66 % set(auto) -> set(auto_setup).
% 1.33/1.66 % set(auto_setup) -> set(predicate_elim).
% 1.33/1.66 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.33/1.66 % set(auto) -> set(auto_limits).
% 1.33/1.66 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.33/1.66 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.33/1.66 % set(auto) -> set(auto_denials).
% 1.33/1.66 % set(auto) -> set(auto_process).
% 1.33/1.66 % set(auto2) -> assign(new_constants, 1).
% 1.33/1.66 % set(auto2) -> assign(fold_denial_max, 3).
% 1.33/1.66 % set(auto2) -> assign(max_weight, "200.000").
% 1.33/1.66 % set(auto2) -> assign(max_hours, 1).
% 1.33/1.66 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.33/1.66 % set(auto2) -> assign(max_seconds, 0).
% 1.33/1.66 % set(auto2) -> assign(max_minutes, 5).
% 1.33/1.66 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.33/1.66 % set(auto2) -> set(sort_initial_sos).
% 1.33/1.66 % set(auto2) -> assign(sos_limit, -1).
% 1.33/1.66 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.33/1.66 % set(auto2) -> assign(max_megs, 400).
% 1.33/1.66 % set(auto2) -> assign(stats, some).
% 1.33/1.66 % set(auto2) -> clear(echo_input).
% 1.33/1.66 % set(auto2) -> set(quiet).
% 1.33/1.66 % set(auto2) -> clear(print_initial_clauses).
% 1.33/1.66 % set(auto2) -> clear(print_given).
% 1.33/1.66 assign(lrs_ticks,-1).
% 1.33/1.66 assign(sos_limit,10000).
% 1.33/1.66 assign(order,kbo).
% 1.33/1.66 set(lex_order_vars).
% 1.33/1.66 clear(print_given).
% 1.33/1.66
% 1.33/1.66 % formulas(sos). % not echoed (2 formulas)
% 1.33/1.66
% 1.33/1.66 ============================== end of input ==========================
% 1.33/1.66
% 1.33/1.66 % From the command line: assign(max_seconds, 300).
% 1.33/1.66
% 1.33/1.66 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.33/1.66
% 1.33/1.66 % Formulas that are not ordinary clauses:
% 1.33/1.66
% 1.33/1.66 ============================== end of process non-clausal formulas ===
% 1.33/1.66
% 1.33/1.66 ============================== PROCESS INITIAL CLAUSES ===============
% 1.33/1.66
% 1.33/1.66 ============================== PREDICATE ELIMINATION =================
% 1.33/1.66
% 1.33/1.66 ============================== end predicate elimination =============
% 1.33/1.66
% 1.33/1.66 Auto_denials:
% 1.33/1.66 % copying label prove_these_axioms_2 to answer in negative clause
% 1.33/1.66
% 1.33/1.66 Term ordering decisions:
% 1.33/1.66
% 1.33/1.66 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.33/1.66 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 1.33/1.66
% 1.33/1.66 ============================== end of process initial clauses ========
% 1.33/1.66
% 1.33/1.66 ============================== CLAUSES FOR SEARCH ====================
% 1.33/1.66
% 1.33/1.66 ============================== end of clauses for search =============
% 1.33/1.66
% 1.33/1.66 ============================== SEARCH ================================
% 1.33/1.66
% 1.33/1.66 % Starting search at 0.01 seconds.
% 1.33/1.66
% 1.33/1.66 ============================== PROOF =================================
% 1.33/1.66 % SZS status Unsatisfiable
% 1.33/1.66 % SZS output start Refutation
% 1.33/1.66
% 1.33/1.66 % Proof 1 at 0.67 (+ 0.01) seconds: prove_these_axioms_2.
% 1.33/1.66 % Length of proof is 172.
% 1.33/1.66 % Level of proof is 45.
% 1.33/1.66 % Maximum clause weight is 64.000.
% 1.33/1.66 % Given clauses 47.
% 1.33/1.66
% 1.33/1.66 1 multiply(A,inverse(multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),A))))) = D # label(single_axiom) # label(axiom). [assumption].
% 1.33/1.66 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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)].
% 1.33/1.66 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))].
% 1.33/1.66 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)].
% 1.33/1.66 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))].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 103 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)].
% 1.33/1.66 112 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))].
% 1.33/1.66 124 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)])].
% 1.33/1.66 136 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))].
% 1.33/1.66 174 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)].
% 1.33/1.66 193 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)])].
% 1.33/1.66 194 multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(C,multiply(A,multiply(D,B))))),C))) = D. [back_rewrite(93),rewrite([174(15)])].
% 1.33/1.66 202 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))].
% 1.33/1.66 204 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))].
% 1.33/1.66 228 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)].
% 1.33/1.66 333 multiply(A,inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),E))),inverse(C)),multiply(F,multiply(multiply(inverse(F),inverse(inverse(multiply(inverse(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(V8,V6))),D)))),multiply(V9,multiply(multiply(inverse(V9),inverse(V8)),E)))))),V10)))),multiply(V11,multiply(multiply(inverse(V11),inverse(B)),A))))) = V10. [para(6(a,1),6(a,1,2,1,1,1,1,1,2,2,1)),rewrite([124(10)])].
% 1.33/1.66 344 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)])].
% 1.33/1.66 384 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)].
% 1.33/1.66 403 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)].
% 1.33/1.66 408 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))].
% 1.33/1.66 444 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)])].
% 1.33/1.66 448 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))].
% 1.33/1.66 468 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))].
% 1.33/1.66 488 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)])].
% 1.33/1.66 660 inverse(multiply(A,multiply(B,inverse(multiply(inverse(multiply(C,multiply(D,multiply(multiply(inverse(D),inverse(multiply(E,C))),F)))),multiply(V6,multiply(A,B))))))) = inverse(multiply(multiply(inverse(V6),inverse(E)),F)). [para(1(a,1),403(a,1,1,1,2,1)),flip(a)].
% 1.33/1.66 708 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))].
% 1.33/1.66 775 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)].
% 1.33/1.66 779 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)])].
% 1.33/1.66 805 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))].
% 1.33/1.66 816 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))].
% 1.33/1.66 819 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)].
% 1.33/1.66 821 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)])].
% 1.33/1.66 852 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))].
% 1.33/1.66 873 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))].
% 1.33/1.66 928 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 1160 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(779(a,1),821(a,1,2)),rewrite([779(17)])].
% 1.33/1.66 1170 multiply(A,inverse(A)) = c_0. [new_symbol(1160)].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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)].
% 1.33/1.66 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))].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 1216 inverse(multiply(inverse(A),multiply(B,multiply(multiply(inverse(B),inverse(c_0)),multiply(inverse(C),inverse(multiply(D,E))))))) = multiply(inverse(multiply(inverse(F),inverse(D))),inverse(multiply(inverse(multiply(E,multiply(C,A))),multiply(F,c_0)))). [para(1170(a,1),10(a,1,1,2,2,1,2,1)),rewrite([1189(24)])].
% 1.33/1.66 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)])].
% 1.33/1.66 1222 multiply(A,multiply(inverse(A),inverse(inverse(B)))) = multiply(B,c_0). [para(1170(a,1),821(a,1,2)),flip(a)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 1289 multiply(inverse(multiply(inverse(A),inverse(c_0))),inverse(multiply(inverse(B),multiply(A,c_0)))) = B. [back_rewrite(1173),rewrite([1189(10)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 1606 inverse(multiply(multiply(inverse(A),inverse(c_0)),multiply(B,multiply(C,multiply(multiply(inverse(C),inverse(multiply(D,B))),E))))) = inverse(multiply(multiply(inverse(A),inverse(D)),E)). [back_rewrite(660),rewrite([1189(13),1210(16)])].
% 1.33/1.66 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)])].
% 1.33/1.66 1721 multiply(inverse(multiply(inverse(A),inverse(B))),inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),E))),inverse(C)),multiply(F,multiply(multiply(inverse(F),inverse(inverse(multiply(inverse(multiply(V6,multiply(V7,multiply(multiply(inverse(V7),inverse(multiply(V8,V6))),D)))),multiply(V9,multiply(multiply(inverse(V9),inverse(V8)),E)))))),V10)))),multiply(A,c_0)))) = V10. [back_rewrite(333),rewrite([1189(39)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 2038 multiply(inverse(multiply(inverse(A),inverse(B))),inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),inverse(multiply(multiply(inverse(C),inverse(D)),E))),inverse(C)),multiply(multiply(inverse(multiply(F,multiply(V6,multiply(multiply(inverse(V6),inverse(multiply(V7,F))),D)))),multiply(V8,multiply(multiply(inverse(V8),inverse(V7)),E))),multiply(c_0,V9)))),multiply(A,c_0)))) = V9. [back_rewrite(1721),rewrite([2013(35)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 2073 multiply(multiply(inverse(A),inverse(c_0)),c_0) = multiply(c_0,inverse(A)). [back_rewrite(2050),rewrite([2057(10),1170(6)])].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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))].
% 1.33/1.66 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)].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 2733 inverse(multiply(inverse(c_0),inverse(c_0))) = c_0. [para(1289(a,1),2322(a,1,1)),rewrite([1170(2)]),flip(a)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 2856 multiply(inverse(A),multiply(inverse(inverse(inverse(c_0))),inverse(inverse(c_0)))) = inverse(A). [back_rewrite(2270),rewrite([2793(6),2317(7)])].
% 1.33/1.66 2858 multiply(inverse(A),c_0) = inverse(A). [back_rewrite(2800),rewrite([2856(10)])].
% 1.33/1.66 2870 inverse(multiply(inverse(A),inverse(c_0))) = inverse(multiply(c_0,inverse(A))). [back_rewrite(2761),rewrite([2858(3)])].
% 1.33/1.66 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))].
% 1.33/1.66 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)])].
% 1.33/1.66 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))].
% 1.33/1.66 2892 multiply(c_0,c_0) = c_0. [para(2733(a,1),2858(a,1,1)),rewrite([2733(9)])].
% 1.33/1.66 2900 multiply(inverse(A),inverse(c_0)) = inverse(A). [back_rewrite(1492),rewrite([2875(24),2741(9),2440(21),2539(25),2887(12)])].
% 1.33/1.66 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)])].
% 1.33/1.66 2919 multiply(inverse(A),inverse(inverse(c_0))) = inverse(A). [back_rewrite(2322),rewrite([2892(5),2858(4),2741(6)])].
% 1.33/1.66 2967 inverse(inverse(inverse(inverse(A)))) = inverse(inverse(A)). [back_rewrite(2870),rewrite([2900(4),2888(6),2919(10)]),flip(a)].
% 1.33/1.66 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)].
% 1.33/1.66 2974 inverse(c_0) = c_0. [back_rewrite(2389),rewrite([2888(5),2967(5),2919(7),2741(6),2919(5),1170(2)]),flip(a)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 3015 multiply(A,c_0) = inverse(inverse(A)). [back_rewrite(2764),rewrite([2974(2),2974(3),2892(3),2984(5),2984(4)]),flip(a)].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 3056 multiply(inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),inverse(multiply(C,A))),D)))),E) = multiply(multiply(inverse(D),C),E). [back_rewrite(1606),rewrite([2974(3),3015(3),3019(2),3043(10),3045(14)])].
% 1.33/1.66 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)])].
% 1.33/1.66 3067 multiply(multiply(A,B),multiply(inverse(B),multiply(C,multiply(D,E)))) = multiply(multiply(multiply(A,C),D),E). [back_rewrite(1216),rewrite([2974(4),3015(4),3019(3),3064(8),3043(7),3043(5),3019(3),3043(7),3019(5),3015(9),3019(9),3043(9)]),flip(a)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 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)])].
% 1.33/1.66 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)])].
% 1.33/1.66 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)].
% 1.33/1.66 3153 multiply(multiply(inverse(A),A),B) = B. [back_rewrite(2038),rewrite([3043(4),3019(2),3045(7),3056(22),3135(16),3101(15),3040(12),3015(15),3019(15),3043(15),3067(15),3149(8),3135(5),3064(4)])].
% 1.33/1.66 3154 $F # answer(prove_these_axioms_2). [resolve(3153,a,2,a)].
% 1.33/1.66
% 1.33/1.66 % SZS output end Refutation
% 1.33/1.66 ============================== end of proof ==========================
% 1.33/1.66
% 1.33/1.66 ============================== STATISTICS ============================
% 1.33/1.66
% 1.33/1.66 Given=47. Generated=5125. Kept=3153. proofs=1.
% 1.33/1.66 Usable=18. Sos=1060. Demods=752. Limbo=236, Disabled=1840. Hints=0.
% 1.33/1.66 Megabytes=5.64.
% 1.33/1.66 User_CPU=0.67, System_CPU=0.01, Wall_clock=1.
% 1.33/1.66
% 1.33/1.66 ============================== end of statistics =====================
% 1.33/1.66
% 1.33/1.66 ============================== end of search =========================
% 1.33/1.66
% 1.33/1.66 THEOREM PROVED
% 1.33/1.66 % SZS status Unsatisfiable
% 1.33/1.66
% 1.33/1.66 Exiting with 1 proof.
% 1.33/1.66
% 1.33/1.66 Process 3874 exit (max_proofs) Mon Jun 13 20:56:43 2022
% 1.33/1.66 Prover9 interrupted
%------------------------------------------------------------------------------