TSTP Solution File: GRP052-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP052-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:16:57 EDT 2022
% Result : Unsatisfiable 3.42s 3.75s
% Output : Refutation 3.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP052-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.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 04:16:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.42/3.75 ============================== Prover9 ===============================
% 3.42/3.75 Prover9 (32) version 2009-11A, November 2009.
% 3.42/3.75 Process 20939 was started by sandbox on n021.cluster.edu,
% 3.42/3.75 Mon Jun 13 04:16:27 2022
% 3.42/3.75 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20782_n021.cluster.edu".
% 3.42/3.75 ============================== end of head ===========================
% 3.42/3.75
% 3.42/3.75 ============================== INPUT =================================
% 3.42/3.75
% 3.42/3.75 % Reading from file /tmp/Prover9_20782_n021.cluster.edu
% 3.42/3.75
% 3.42/3.75 set(prolog_style_variables).
% 3.42/3.75 set(auto2).
% 3.42/3.75 % set(auto2) -> set(auto).
% 3.42/3.75 % set(auto) -> set(auto_inference).
% 3.42/3.75 % set(auto) -> set(auto_setup).
% 3.42/3.75 % set(auto_setup) -> set(predicate_elim).
% 3.42/3.75 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.42/3.75 % set(auto) -> set(auto_limits).
% 3.42/3.75 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.42/3.75 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.42/3.75 % set(auto) -> set(auto_denials).
% 3.42/3.75 % set(auto) -> set(auto_process).
% 3.42/3.75 % set(auto2) -> assign(new_constants, 1).
% 3.42/3.75 % set(auto2) -> assign(fold_denial_max, 3).
% 3.42/3.75 % set(auto2) -> assign(max_weight, "200.000").
% 3.42/3.75 % set(auto2) -> assign(max_hours, 1).
% 3.42/3.75 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.42/3.75 % set(auto2) -> assign(max_seconds, 0).
% 3.42/3.75 % set(auto2) -> assign(max_minutes, 5).
% 3.42/3.75 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.42/3.75 % set(auto2) -> set(sort_initial_sos).
% 3.42/3.75 % set(auto2) -> assign(sos_limit, -1).
% 3.42/3.75 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.42/3.75 % set(auto2) -> assign(max_megs, 400).
% 3.42/3.75 % set(auto2) -> assign(stats, some).
% 3.42/3.75 % set(auto2) -> clear(echo_input).
% 3.42/3.75 % set(auto2) -> set(quiet).
% 3.42/3.75 % set(auto2) -> clear(print_initial_clauses).
% 3.42/3.75 % set(auto2) -> clear(print_given).
% 3.42/3.75 assign(lrs_ticks,-1).
% 3.42/3.75 assign(sos_limit,10000).
% 3.42/3.75 assign(order,kbo).
% 3.42/3.75 set(lex_order_vars).
% 3.42/3.75 clear(print_given).
% 3.42/3.75
% 3.42/3.75 % formulas(sos). % not echoed (2 formulas)
% 3.42/3.75
% 3.42/3.75 ============================== end of input ==========================
% 3.42/3.75
% 3.42/3.75 % From the command line: assign(max_seconds, 300).
% 3.42/3.75
% 3.42/3.75 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.42/3.75
% 3.42/3.75 % Formulas that are not ordinary clauses:
% 3.42/3.75
% 3.42/3.75 ============================== end of process non-clausal formulas ===
% 3.42/3.75
% 3.42/3.75 ============================== PROCESS INITIAL CLAUSES ===============
% 3.42/3.75
% 3.42/3.75 ============================== PREDICATE ELIMINATION =================
% 3.42/3.75
% 3.42/3.75 ============================== end predicate elimination =============
% 3.42/3.75
% 3.42/3.75 Auto_denials:
% 3.42/3.75 % copying label prove_these_axioms to answer in negative clause
% 3.42/3.75
% 3.42/3.75 Term ordering decisions:
% 3.42/3.75
% 3.42/3.75 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 3.42/3.75 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 3.42/3.75
% 3.42/3.75 ============================== end of process initial clauses ========
% 3.42/3.75
% 3.42/3.75 ============================== CLAUSES FOR SEARCH ====================
% 3.42/3.75
% 3.42/3.75 ============================== end of clauses for search =============
% 3.42/3.75
% 3.42/3.75 ============================== SEARCH ================================
% 3.42/3.75
% 3.42/3.75 % Starting search at 0.01 seconds.
% 3.42/3.75
% 3.42/3.75 ============================== PROOF =================================
% 3.42/3.75 % SZS status Unsatisfiable
% 3.42/3.75 % SZS output start Refutation
% 3.42/3.75
% 3.42/3.75 % Proof 1 at 2.76 (+ 0.02) seconds: prove_these_axioms.
% 3.42/3.75 % Length of proof is 156.
% 3.42/3.75 % Level of proof is 35.
% 3.42/3.75 % Maximum clause weight is 145.000.
% 3.42/3.75 % Given clauses 73.
% 3.42/3.75
% 3.42/3.75 1 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C # label(single_axiom) # label(axiom). [assumption].
% 3.42/3.75 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 3.42/3.75 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [copy(2),flip(a)].
% 3.42/3.75 4 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(multiply(inverse(C),D))),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = D. [para(1(a,1),1(a,1,2,1,1,2,1,1,1))].
% 3.42/3.75 5 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),C))),D)). [para(1(a,1),1(a,1,2,1,1,2,1))].
% 3.42/3.75 7 inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A)),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A)),inverse(multiply(inverse(D),E))),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),D))),A))) = multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(E)),C))). [para(4(a,1),1(a,1,2,1,1,2,1)),flip(a)].
% 3.42/3.75 9 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),D))),E)). [para(1(a,1),4(a,1,2,1,1,2,1))].
% 3.42/3.75 12 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)),inverse(D)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E)),inverse(multiply(inverse(F),D))),multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(C),inverse(E))),F))),E))). [para(4(a,1),4(a,1,2,1,1,2,1))].
% 3.42/3.75 15 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(D))),inverse(C))),E))),C)))),B))) = inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D)). [para(5(a,1),1(a,1,2,1,1,2,1))].
% 3.42/3.75 20 multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(inverse(A)))),D))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))),E))),A))) = E. [para(5(a,2),1(a,1,2,1,1,2,1,1))].
% 3.42/3.75 21 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))) = C. [para(5(a,2),1(a,1,2))].
% 3.42/3.75 22 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(A))),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(C),C),inverse(D))),E))),D)))),A)) = multiply(B,inverse(multiply(E,C))). [para(1(a,1),5(a,1,2,1,1)),flip(a)].
% 3.42/3.75 36 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(B),inverse(A))),multiply(inverse(B),C)))),A)) = C. [para(5(a,1),4(a,1)),rewrite([1(13)])].
% 3.42/3.75 102 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),A)) = C. [para(36(a,1),36(a,1,1,1,2,1,1,1,1)),rewrite([36(18)])].
% 3.42/3.75 120 inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))),inverse(multiply(inverse(multiply(D,inverse(inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B))))),multiply(D,E)))),inverse(B))),inverse(A))),C))),A))) = E. [para(5(a,1),102(a,1,1))].
% 3.42/3.75 127 multiply(inverse(multiply(A,inverse(B))),multiply(A,C)) = multiply(inverse(multiply(D,inverse(B))),multiply(D,C)). [para(102(a,1),21(a,1,2,2))].
% 3.42/3.75 139 multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),D))),B)))),multiply(A,E)) = multiply(inverse(D),multiply(C,E)). [para(1(a,1),127(a,1,1,1)),flip(a)].
% 3.42/3.75 151 multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))),multiply(A,D)) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(B))),inverse(E))),C))),E))),multiply(F,D)). [para(5(a,1),127(a,1,1,1)),flip(a)].
% 3.42/3.75 153 multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))),multiply(A,E)) = multiply(inverse(D),multiply(inverse(multiply(B,inverse(C))),E)). [para(5(a,2),127(a,1,1,1,2)),rewrite([139(28)])].
% 3.42/3.75 157 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(102(a,1),127(a,1,1,1,2)),rewrite([102(15)])].
% 3.42/3.75 174 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))) = multiply(inverse(multiply(D,B)),E). [para(1(a,1),157(a,1,2)),flip(a)].
% 3.42/3.75 185 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(D,C)),multiply(D,C)),inverse(E)),multiply(B,C))))) = E. [para(157(a,1),21(a,1,2,2,1,1,1))].
% 3.42/3.75 186 multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))) = multiply(inverse(multiply(inverse(multiply(C,inverse(D))),B)),E). [para(21(a,1),157(a,1,2)),flip(a)].
% 3.42/3.75 188 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,C)),inverse(A))),multiply(inverse(multiply(D,C)),multiply(D,E))))),A)) = multiply(B,E). [para(157(a,1),102(a,1,1,1,2,1,2))].
% 3.42/3.75 189 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(E,inverse(B))),multiply(E,D)))),C)). [para(102(a,1),157(a,1,1)),flip(a)].
% 3.42/3.75 196 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)). [para(157(a,1),157(a,1,1,1))].
% 3.42/3.75 197 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,E))). [para(157(a,1),157(a,1,2))].
% 3.42/3.75 201 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),D) = multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),D). [para(1(a,1),196(a,1,2)),rewrite([174(23)])].
% 3.42/3.75 306 multiply(A,inverse(multiply(multiply(multiply(B,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,B)))),C)),inverse(E)),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,B)))),C)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(F))),V6))),F)),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(F))),V6))),F)),inverse(multiply(inverse(V6),E))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(F))),V6))),F))). [para(102(a,1),7(a,1,1,1,1,1,1,1,2,1,1,1,1,1,2)),rewrite([102(25),102(41),102(52)]),flip(a)].
% 3.42/3.75 336 multiply(inverse(A),multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(inverse(A),multiply(inverse(multiply(E,C)),multiply(E,D))). [para(1(a,1),197(a,1,1,1)),rewrite([139(23)])].
% 3.42/3.75 342 multiply(inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),B)))),multiply(A,multiply(D,E))) = multiply(inverse(inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(D,V6)),inverse(B))),inverse(F))),C))),F))),multiply(inverse(multiply(V7,V6)),multiply(V7,E))). [para(5(a,1),197(a,1,1,1)),flip(a)].
% 3.42/3.75 366 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D))) = multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,D))). [para(197(a,1),196(a,1))].
% 3.42/3.75 377 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),E)),multiply(inverse(multiply(F,multiply(inverse(multiply(B,V6)),D))),multiply(F,V7))) = multiply(inverse(multiply(V8,E)),multiply(V8,multiply(inverse(multiply(inverse(multiply(V9,V6)),multiply(V9,C))),V7))). [para(196(a,1),197(a,1,1,1,1,1))].
% 3.42/3.75 431 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D))) = multiply(A,multiply(inverse(multiply(E,C)),multiply(E,D))). [para(102(a,1),336(a,1,1)),rewrite([102(16)])].
% 3.42/3.75 854 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(multiply(C,inverse(D))))))),E) = multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(F,A)),multiply(F,E)))),D))). [para(189(a,2),1(a,1,2,1,1,2,1)),flip(a)].
% 3.42/3.75 867 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C)))) = multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(V6,inverse(B))),multiply(V6,E)))),inverse(C))),inverse(F))),D))),F))). [para(5(a,1),189(a,2,2))].
% 3.42/3.75 874 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,inverse(A))),multiply(B,C)))),D) = inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(C,inverse(E))),multiply(inverse(multiply(F,A)),multiply(F,D))))),E)). [para(189(a,2),102(a,1,1,1,2,1,2)),flip(a)].
% 3.42/3.75 876 multiply(inverse(multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,D)))),B))),multiply(A,E)) = multiply(F,multiply(multiply(multiply(D,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,D)))),B)),inverse(multiply(inverse(multiply(V6,D)),multiply(V6,F)))),E)). [para(102(a,1),189(a,2,2,1,1,1)),rewrite([102(36)])].
% 3.42/3.75 914 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(B,C)),multiply(B,C)),inverse(D)),multiply(B,C)))) = multiply(A,inverse(multiply(multiply(multiply(E,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(F,inverse(C))),multiply(F,E)))),C)),inverse(D)),multiply(B,C)))). [para(189(a,1),7(a,2,2,1,1,1)),rewrite([7(47)])].
% 3.42/3.75 952 multiply(inverse(multiply(A,multiply(inverse(multiply(B,C)),multiply(B,D)))),multiply(A,multiply(E,F))) = multiply(inverse(multiply(V6,multiply(V7,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(V8,inverse(C))),multiply(V8,E)))),D)))),multiply(V6,multiply(V7,F))). [para(189(a,2),366(a,1,1,1,2))].
% 3.42/3.75 1087 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,C))),inverse(D))),E))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),F))),V7)). [para(201(a,1),9(a,1,2,1,2,1,2,1,1,1))].
% 3.42/3.75 1109 multiply(inverse(multiply(A,B)),inverse(multiply(multiply(multiply(multiply(A,C),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(A,B)),inverse(D))),multiply(inverse(multiply(E,B)),multiply(E,C))))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(V6,inverse(D))),multiply(V6,multiply(A,C))))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),inverse(V7))),F))),V7)). [para(197(a,1),9(a,1,2,1,2,1,2,1)),rewrite([188(18)])].
% 3.42/3.75 1185 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(multiply(A,inverse(B))))))),E)))),B)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(multiply(A,inverse(B))))))),E)))),B)),inverse(F)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(V6,C)),multiply(V6,E)))),B)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,inverse(multiply(A,inverse(B))))))),E)),inverse(V7))),F))),V7)). [para(189(a,2),9(a,1,2,1,2,1,2,1))].
% 3.42/3.75 1574 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(D))),E))),D)),inverse(F)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6,B)),multiply(V6,C))),inverse(D))),E))),D)))) = inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),V8))),V7)),multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),V8))),V7)),inverse(multiply(inverse(V8),F))),multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(E),inverse(V7))),V8))),V7))). [para(201(a,1),12(a,1,2,1,2,1,2,1,1,1))].
% 3.42/3.75 1925 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))),multiply(F,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(V6,inverse(B))),multiply(V6,F)))),V7))) = multiply(inverse(E),multiply(D,multiply(A,V7))). [para(189(a,1),139(a,1,2))].
% 3.42/3.75 1946 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(A))),C))),A)),multiply(inverse(multiply(D,inverse(B))),E)) = multiply(inverse(multiply(F,multiply(D,inverse(multiply(C,B))))),multiply(F,E)). [para(1(a,1),153(a,1,1,1,2,2,1,1)),flip(a)].
% 3.42/3.75 1963 multiply(inverse(multiply(A,multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),D),C))))),multiply(A,E)) = multiply(D,multiply(inverse(multiply(B,inverse(C))),E)). [para(102(a,1),153(a,1,1,1,2,2,1,1,2)),rewrite([102(21)])].
% 3.42/3.75 2163 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),C),B))))),D) = multiply(C,D). [para(1(a,1),1963(a,2,2)),rewrite([174(23)])].
% 3.42/3.75 2283 multiply(multiply(inverse(multiply(A,B)),multiply(A,C)),D) = multiply(multiply(inverse(multiply(E,B)),multiply(E,C)),D). [para(431(a,1),2163(a,1,1,1,2,2,1,1)),rewrite([2163(16)])].
% 3.42/3.75 2516 multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(B,inverse(inverse(A)))),multiply(B,C)))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(E))),inverse(D))),F))),D)))),A))) = inverse(multiply(multiply(multiply(inverse(E),E),inverse(F)),E)). [para(102(a,1),15(a,1,2,1,1,2,1,1,1,2,1,1,1,1,1,1))].
% 3.42/3.75 2519 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(C))),inverse(F))),inverse(D))),V6))),D)))),C)))) = multiply(inverse(multiply(E,B)),inverse(multiply(multiply(multiply(inverse(F),F),inverse(V6)),F))). [para(15(a,1),157(a,1,2)),flip(a)].
% 3.42/3.75 2550 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(E,inverse(F))),inverse(D))),V6))),D)))),inverse(C))),multiply(inverse(V6),V7)))),C)))),B))) = multiply(E,inverse(multiply(multiply(multiply(inverse(F),F),inverse(V7)),F))). [para(15(a,2),7(a,1))].
% 3.42/3.75 2571 multiply(A,multiply(inverse(multiply(B,C)),multiply(B,inverse(multiply(multiply(multiply(inverse(D),D),inverse(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(D))),inverse(V6))),inverse(E))),V7))),E)))),D))))) = multiply(A,multiply(inverse(multiply(F,C)),inverse(multiply(multiply(multiply(inverse(V6),V6),inverse(V7)),V6)))). [para(15(a,1),431(a,1,2,2)),flip(a)].
% 3.42/3.75 3452 multiply(inverse(multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(B,inverse(inverse(A)))),multiply(B,C)))),D)),E) = multiply(inverse(multiply(F,D)),multiply(F,inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(C,E))),A)))). [para(102(a,1),174(a,1,2,2,1,1,2,1,1)),flip(a)].
% 3.42/3.75 3456 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),E)) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),multiply(inverse(multiply(D,F)),E)). [para(174(a,1),196(a,2,1,1)),rewrite([174(14)])].
% 3.42/3.75 3492 multiply(inverse(multiply(A,multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(C,inverse(B))),multiply(C,A)))),D))),multiply(inverse(multiply(E,B)),inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(V6,inverse(F))),V7))),F)))) = multiply(inverse(multiply(V6,multiply(E,D))),V7). [para(189(a,1),174(a,1,1,1))].
% 3.42/3.75 3977 multiply(multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(inverse(B)),inverse(B)),inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(inverse(B)))),E))),inverse(B))),inverse(inverse(A)))),multiply(multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))),F)))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(F,V6))),A))) = V6. [para(20(a,1),20(a,1,2,1,1,2,1,1))].
% 3.42/3.75 3982 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(D,F)),inverse(E))),V6))),E)))) = multiply(inverse(multiply(inverse(multiply(A,F)),C)),V6). [para(1(a,1),3456(a,1,2)),flip(a)].
% 3.42/3.75 4313 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),C)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(multiply(inverse(B),B),inverse(D))),E))),D)) = multiply(inverse(multiply(F,C)),multiply(F,multiply(A,inverse(multiply(E,B))))). [para(1(a,1),186(a,1,2,2,2,1,1)),flip(a)].
% 3.42/3.75 4673 multiply(A,inverse(multiply(B,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),C))))) = multiply(A,inverse(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(E))),D))),E)))). [para(5(a,1),22(a,2,2,1)),rewrite([22(42)])].
% 3.42/3.75 4753 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))),A)) = inverse(A). [para(189(a,2),22(a,1,1,1,2,1)),rewrite([1(22)])].
% 3.42/3.75 4780 multiply(multiply(A,inverse(multiply(B,C))),multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),F))),D))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),F))),D))),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(inverse(multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(E,inverse(D))),F))),D))))),multiply(multiply(multiply(inverse(V6),V6),inverse(multiply(inverse(multiply(multiply(inverse(C),C),inverse(V6))),B))),V6)))),V7)) = multiply(inverse(F),multiply(E,V7)). [para(22(a,1),139(a,1,1))].
% 3.42/3.75 4879 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A)) = inverse(A). [para(1(a,1),4753(a,1,1,1,2,1,1,1)),rewrite([1(14)])].
% 3.42/3.75 4893 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(B,C)),multiply(B,C)))),A) = A. [para(4753(a,1),21(a,1,2,2,1,1,2)),rewrite([21(11)]),flip(a)].
% 3.42/3.75 4929 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(D)),multiply(B,C))))) = D. [para(4753(a,1),185(a,1,2,2,1,1,1,1)),rewrite([4893(14)])].
% 3.42/3.75 5022 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),A) = A. [para(4879(a,1),21(a,1,2,2,1,1,2)),rewrite([21(11)]),flip(a)].
% 3.42/3.75 5023 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(B))) = multiply(inverse(C),C). [para(4879(a,1),21(a,1,2,2))].
% 3.42/3.75 5028 multiply(inverse(multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C))),multiply(inverse(multiply(D,A)),E)) = multiply(inverse(multiply(F,multiply(D,C))),multiply(F,E)). [para(4879(a,1),196(a,1,1,1,1))].
% 3.42/3.75 5037 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(C),multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(F),F))),multiply(A,E))). [para(4879(a,1),197(a,2,1))].
% 3.42/3.75 5047 multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)) = multiply(D,multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(E,inverse(A))),multiply(E,D)))),C)). [para(4879(a,1),189(a,1,1))].
% 3.42/3.75 5077 multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),inverse(multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),E))),C)))) = multiply(inverse(multiply(D,A)),E). [para(4879(a,1),174(a,1,1))].
% 3.42/3.75 5089 multiply(inverse(A),multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),D))))) = multiply(inverse(multiply(inverse(multiply(C,inverse(D))),A)),E). [para(4879(a,1),186(a,1,1))].
% 3.42/3.75 5103 inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))),inverse(A))),B))),A)) = B. [para(5022(a,1),102(a,1,1,1,2,1,2))].
% 3.42/3.75 5106 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),A) = multiply(inverse(multiply(D,C)),multiply(D,A)). [para(5022(a,1),157(a,1,2))].
% 3.42/3.75 5112 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,D))),multiply(inverse(multiply(E,C)),multiply(E,D))))),A) = A. [para(196(a,2),5022(a,1,1,2,1))].
% 3.42/3.75 5117 multiply(inverse(multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,B)),inverse(multiply(inverse(C),C))),D)),multiply(A,B)) = multiply(inverse(multiply(inverse(multiply(A,E)),D)),multiply(inverse(multiply(F,E)),multiply(F,B))). [para(5022(a,1),197(a,2,2)),flip(a)].
% 3.42/3.75 5131 multiply(inverse(multiply(A,B)),multiply(A,B)) = multiply(inverse(B),B). [para(5022(a,1),189(a,2,2))].
% 3.42/3.75 5153 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,inverse(multiply(multiply(multiply(inverse(D),D),E),D))))),A) = multiply(E,multiply(inverse(multiply(C,inverse(D))),A)). [para(5022(a,1),1963(a,1,2))].
% 3.42/3.75 5160 multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(C,A)) = multiply(C,A). [para(2283(a,1),5022(a,1,1)),rewrite([5131(4)])].
% 3.42/3.75 5183 multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),A))),inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),A))),inverse(multiply(inverse(C),C))),inverse(A))),D)),B) = multiply(inverse(multiply(E,D)),multiply(E,inverse(multiply(multiply(multiply(inverse(A),A),inverse(B)),A)))). [para(5022(a,1),186(a,1,2,2)),flip(a)].
% 3.42/3.75 5199 multiply(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),C)),multiply(D,A)) = multiply(inverse(multiply(inverse(multiply(D,E)),C)),multiply(inverse(multiply(F,E)),multiply(F,A))). [back_rewrite(5117),rewrite([5131(4)])].
% 3.42/3.75 5210 multiply(inverse(inverse(A)),inverse(A)) = multiply(inverse(B),B). [back_rewrite(5023),rewrite([5131(6)])].
% 3.42/3.75 5924 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,C))),inverse(D))),V6))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(V8),E))),multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(V6),inverse(V7))),V8))),V7))). [back_rewrite(1574),rewrite([5131(35),5131(48)])].
% 3.42/3.75 6028 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(D,E)),multiply(D,F)))),B)))) = inverse(multiply(multiply(multiply(inverse(V6),V6),inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(E),E),inverse(multiply(inverse(multiply(V7,inverse(E))),multiply(V7,inverse(multiply(A,inverse(B))))))),F)),inverse(V6))),C))),V6)). [back_rewrite(1185),rewrite([5131(46)])].
% 3.42/3.75 6107 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(multiply(inverse(D),D),inverse(E)),multiply(multiply(multiply(inverse(D),D),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,C))),inverse(D))),V6))),D)))) = inverse(multiply(multiply(multiply(inverse(V7),V7),inverse(multiply(inverse(multiply(inverse(V6),inverse(V7))),E))),V7)). [back_rewrite(1087),rewrite([5131(35)])].
% 3.42/3.75 6196 multiply(A,inverse(multiply(multiply(multiply(B,multiply(multiply(multiply(inverse(C),C),inverse(multiply(inverse(multiply(D,inverse(C))),multiply(D,B)))),C)),inverse(E)),multiply(F,C)))) = multiply(A,inverse(multiply(multiply(multiply(inverse(C),C),inverse(E)),multiply(F,C)))). [back_rewrite(914),rewrite([5131(4)]),flip(a)].
% 3.42/3.75 6427 multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(C)),multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(D,inverse(B))),multiply(D,E)))),B)))) = inverse(multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(V6),C))),multiply(multiply(multiply(inverse(F),F),inverse(multiply(inverse(multiply(inverse(multiply(A,E)),inverse(F))),V6))),F))). [back_rewrite(306),rewrite([6196(26),5131(41)])].
% 3.42/3.75 6490 multiply(inverse(inverse(A)),inverse(A)) = c_0. [new_symbol(5210)].
% 3.42/3.75 6695 multiply(inverse(A),A) = c_0. [back_rewrite(5210),rewrite([6490(4)]),flip(a)].
% 3.42/3.75 6702 multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(multiply(c_0,inverse(C)),D)))) = multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(c_0)),inverse(D))),B)),C). [back_rewrite(5183),rewrite([6695(2),6695(8),6695(12),6695(3),6695(14)]),flip(a)].
% 3.42/3.75 6740 multiply(multiply(A,inverse(multiply(B,C))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(C))),inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(D,inverse(E))),F))),E))))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(c_0,inverse(V6))),B))),V6)))),V7)) = multiply(inverse(F),multiply(D,V7)). [back_rewrite(4780),rewrite([6695(5),6695(15),6695(23),6695(9),6695(21),6695(22)])].
% 3.42/3.75 6795 multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(inverse(C)))),D))),inverse(C))),inverse(inverse(E)))),multiply(multiply(A,inverse(multiply(multiply(c_0,inverse(D)),B))),F)))),inverse(multiply(multiply(c_0,inverse(multiply(F,V6))),E))) = V6. [back_rewrite(3977),rewrite([6695(4),6695(5),6695(21),6695(31)])].
% 3.42/3.75 6868 multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(inverse(B)))),multiply(A,C)))),D)),E) = multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(c_0)),inverse(B))),D)),multiply(C,E)). [back_rewrite(3452),rewrite([6695(4),6695(16),6702(22)])].
% 3.42/3.75 6955 multiply(multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(inverse(B)))),multiply(A,C)))),inverse(multiply(multiply(c_0,inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(C,inverse(D))),inverse(E))),F))),E)))),B))) = inverse(multiply(multiply(c_0,inverse(F)),D)). [back_rewrite(2516),rewrite([6695(4),6695(11),6695(12),6695(29)])].
% 3.42/3.75 7005 inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(c_0)),inverse(multiply(multiply(c_0,inverse(A)),B)))),inverse(B))),multiply(C,inverse(D)))),A))),D))) = C. [back_rewrite(120),rewrite([6695(2),6695(3),6695(9),6695(13),6695(4),6868(19)])].
% 3.42/3.75 7225 multiply(A,inverse(multiply(multiply(c_0,inverse(B)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,E)))),D)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(F),B))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,E)),inverse(V6))),F))),V6))). [back_rewrite(6427),rewrite([6695(2),6695(5),6695(17),6695(22)])].
% 3.42/3.75 7474 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(c_0,inverse(D)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),inverse(F))),V6))),F)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(V6),inverse(V7))),D))),V7)). [back_rewrite(6107),rewrite([6695(7),6695(10),6695(26)])].
% 3.42/3.75 7524 multiply(A,inverse(multiply(multiply(c_0,inverse(B)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(C,D)),multiply(C,E)))),F)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(V6,inverse(D))),multiply(V6,inverse(multiply(A,inverse(F))))))),E)),inverse(V7))),B))),V7)). [back_rewrite(6028),rewrite([6695(2),6695(5),6695(16),6695(17)])].
% 3.42/3.75 7616 multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(multiply(c_0,inverse(D)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,C))),inverse(F))),V6))),F)))) = inverse(multiply(multiply(c_0,inverse(multiply(inverse(V7),D))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(V6),inverse(V8))),V7))),V8))). [back_rewrite(5924),rewrite([6695(7),6695(10),6695(26),6695(31)])].
% 3.42/3.75 8022 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(D,B)),multiply(D,E))) = multiply(inverse(multiply(multiply(c_0,inverse(c_0)),C)),multiply(A,E)). [back_rewrite(5199),rewrite([6695(2),6695(3)]),flip(a)].
% 3.42/3.75 8052 multiply(multiply(c_0,inverse(c_0)),multiply(A,B)) = multiply(A,B). [back_rewrite(5160),rewrite([6695(2),6695(3)])].
% 3.42/3.75 8056 multiply(inverse(multiply(A,inverse(multiply(multiply(c_0,B),C)))),D) = multiply(B,multiply(inverse(multiply(A,inverse(C))),D)). [back_rewrite(5153),rewrite([6695(2),6695(3),6695(6),8052(10)])].
% 3.42/3.75 8077 multiply(multiply(c_0,inverse(c_0)),A) = A. [back_rewrite(5112),rewrite([6695(2),8022(11),8052(7),6695(5)])].
% 3.42/3.75 8079 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(B),C). [back_rewrite(5106),rewrite([6695(2),6695(3),8077(5)]),flip(a)].
% 3.42/3.75 8081 inverse(multiply(multiply(c_0,inverse(multiply(inverse(inverse(A)),B))),A)) = B. [back_rewrite(5103),rewrite([6695(2),6695(3),6695(4),8077(7)])].
% 3.42/3.75 8088 multiply(inverse(A),multiply(B,inverse(multiply(multiply(c_0,inverse(C)),D)))) = multiply(inverse(multiply(inverse(multiply(B,inverse(D))),A)),C). [back_rewrite(5089),rewrite([6695(3),6695(4),6695(7),8077(12)])].
% 3.42/3.75 8091 multiply(inverse(A),inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(B,inverse(C))),D))),C))) = multiply(inverse(multiply(B,A)),D). [back_rewrite(5077),rewrite([6695(3),6695(4),6695(7),8077(15)])].
% 3.42/3.75 8093 multiply(A,multiply(multiply(c_0,inverse(multiply(inverse(inverse(B)),A))),C)) = multiply(inverse(B),C). [back_rewrite(5047),rewrite([6695(3),6695(4),8077(6),6695(4),8079(8)]),flip(a)].
% 3.42/3.75 8094 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(B),D)) = multiply(inverse(C),multiply(A,D)). [back_rewrite(5037),rewrite([8079(8),6695(10),6695(11),8077(14)])].
% 3.42/3.75 8095 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,A)),D)) = multiply(inverse(multiply(C,B)),D). [back_rewrite(5028),rewrite([6695(3),6695(4),8077(6),8079(12)])].
% 3.42/3.75 8098 multiply(inverse(c_0),A) = A. [back_rewrite(4929),rewrite([6695(6),8088(12),6695(8)])].
% 3.42/3.75 8155 multiply(A,inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),inverse(D))),E))),D)))) = multiply(A,inverse(multiply(B,inverse(multiply(multiply(c_0,inverse(E)),C))))). [back_rewrite(4673),rewrite([6695(2),6695(10)]),flip(a)].
% 3.42/3.75 8274 multiply(inverse(multiply(inverse(multiply(A,inverse(B))),C)),multiply(multiply(c_0,inverse(multiply(inverse(multiply(c_0,inverse(D))),E))),D)) = multiply(inverse(C),multiply(A,inverse(multiply(E,B)))). [back_rewrite(4313),rewrite([6695(7),6695(8),8079(22)])].
% 3.42/3.75 8322 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(multiply(inverse(D),B)),E)) = multiply(inverse(multiply(inverse(multiply(A,D)),C)),E). [back_rewrite(3982),rewrite([6695(8),8091(18),8079(8)])].
% 3.42/3.75 8356 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(D,A))),E)) = multiply(inverse(multiply(C,multiply(D,B))),E). [back_rewrite(3492),rewrite([6695(2),8079(6),8093(8),6695(7),8091(15)])].
% 3.42/3.75 8416 multiply(A,multiply(inverse(multiply(B,C)),inverse(multiply(multiply(c_0,inverse(D)),E)))) = multiply(A,multiply(inverse(multiply(inverse(inverse(E)),multiply(B,C))),D)). [back_rewrite(2571),rewrite([6695(4),6695(5),8155(20),8088(18),8079(5),8088(14),8094(10),6695(11)]),flip(a)].
% 3.42/3.75 8420 multiply(A,inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(B,inverse(C))),multiply(A,inverse(D)))),E))),D))) = multiply(B,inverse(multiply(multiply(c_0,inverse(E)),C))). [back_rewrite(2550),rewrite([6695(2),6695(3),6695(7),8091(18),8094(17),8081(17),6695(16)])].
% 3.42/3.75 8427 multiply(inverse(multiply(A,B)),inverse(multiply(multiply(c_0,inverse(C)),D))) = multiply(inverse(multiply(inverse(inverse(D)),multiply(A,B))),C). [back_rewrite(2519),rewrite([6695(4),6695(5),8155(20),8088(18),8079(5),8416(14),8356(12),6695(10)]),flip(a)].
% 3.42/3.75 8499 multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(c_0,inverse(A))),B))),A)),multiply(inverse(multiply(C,inverse(D))),E)) = multiply(inverse(multiply(C,inverse(multiply(B,D)))),E). [back_rewrite(1946),rewrite([6695(2),6695(3),8079(22)])].
% 3.42/3.75 8503 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(inverse(C),E)) = multiply(inverse(D),multiply(A,multiply(B,E))). [back_rewrite(1925),rewrite([6695(4),8091(12),6695(7),8079(11),8093(13)])].
% 3.42/3.75 8524 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),B)),inverse(C))),D))),C)) = multiply(inverse(multiply(inverse(B),A)),D). [back_rewrite(1109),rewrite([6695(5),8079(13),8094(12),8093(12),6695(4),6695(7),8079(12),8427(16),8081(9),8079(4),6695(6),8079(9)]),flip(a)].
% 3.42/3.75 8529 multiply(inverse(multiply(multiply(c_0,inverse(multiply(inverse(inverse(A)),B))),C)),D) = multiply(inverse(multiply(inverse(A),C)),multiply(B,D)). [back_rewrite(952),rewrite([8079(4),8079(7),6695(7),8079(11),8079(18),8079(16)]),flip(a)].
% 3.42/3.75 8535 multiply(A,multiply(multiply(c_0,inverse(multiply(inverse(B),A))),C)) = multiply(B,C). [back_rewrite(876),rewrite([6695(2),8079(6),8079(11),8081(8),6695(3),8079(7),8093(9),6695(3),8079(6)]),flip(a)].
% 3.42/3.75 8536 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(A,inverse(B))),multiply(inverse(C),D)))),B)) = multiply(multiply(c_0,inverse(multiply(inverse(inverse(C)),A))),D). [back_rewrite(874),rewrite([6695(2),8079(6),6695(9),8079(15)]),flip(a)].
% 3.42/3.75 8539 multiply(inverse(A),inverse(multiply(multiply(c_0,inverse(B)),C))) = multiply(inverse(multiply(inverse(inverse(C)),A)),B). [back_rewrite(867),rewrite([6695(4),8088(9),8079(5),6695(7),6695(8),8079(12),8529(17),8420(20)]),flip(a)].
% 3.42/3.75 8543 multiply(multiply(c_0,inverse(multiply(inverse(inverse(A)),inverse(multiply(B,inverse(C)))))),D) = multiply(B,inverse(multiply(multiply(c_0,inverse(multiply(inverse(A),D))),C))). [back_rewrite(854),rewrite([6695(2),8079(9),6695(12),8079(15)])].
% 3.42/3.75 8550 multiply(inverse(inverse(multiply(multiply(c_0,inverse(A)),B))),multiply(C,D)) = multiply(inverse(A),multiply(inverse(inverse(B)),multiply(C,D))). [back_rewrite(342),rewrite([6695(2),8079(10),6695(10),8524(22),8079(19),8503(18)])].
% 3.42/3.75 8558 multiply(inverse(inverse(multiply(multiply(c_0,inverse(A)),B))),C) = multiply(inverse(A),multiply(inverse(inverse(B)),C)). [back_rewrite(151),rewrite([6695(2),8079(9),6695(9),8550(22),8094(20),8079(13)])].
% 3.42/3.75 8570 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(B))),inverse(C))),D))),C)) = multiply(A,inverse(multiply(multiply(c_0,inverse(D)),B))). [back_rewrite(5),rewrite([6695(2),6695(8)]),flip(a)].
% 3.42/3.75 8571 multiply(c_0,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3),rewrite([6695(4),6695(5),6695(7)]),xx(a)].
% 3.42/3.75 8573 multiply(multiply(c_0,inverse(multiply(inverse(inverse(inverse(A))),B))),inverse(multiply(multiply(c_0,inverse(multiply(B,C))),A))) = C. [back_rewrite(6795),rewrite([8570(15),8079(19)])].
% 3.42/3.75 8645 inverse(inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),c_0)),multiply(B,inverse(C)))),A))),C))) = B. [back_rewrite(7005),rewrite([8077(11),8558(9),6695(6)])].
% 3.42/3.75 8676 multiply(inverse(multiply(inverse(multiply(inverse(A),B)),C)),D) = multiply(inverse(C),multiply(inverse(multiply(inverse(B),A)),D)). [back_rewrite(377),rewrite([8079(5),8079(13),8322(12),8079(4),8079(12),8079(14)])].
% 3.42/3.75 8740 inverse(multiply(multiply(c_0,inverse(multiply(inverse(A),B))),multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(C),inverse(D))),A))),D))) = multiply(inverse(multiply(inverse(C),c_0)),B). [back_rewrite(7616),rewrite([8079(4),8079(11),8676(14),8539(20),8081(12),8094(8),6695(3)]),flip(a)].
% 3.42/3.75 8746 multiply(A,inverse(multiply(multiply(c_0,inverse(B)),multiply(multiply(c_0,inverse(multiply(inverse(C),D))),E)))) = multiply(A,inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(D),C)),B))),E))). [back_rewrite(7524),rewrite([8079(8),8079(22),8543(23),8056(24),8676(24),8536(28),8543(24)])].
% 3.42/3.75 8753 inverse(multiply(multiply(c_0,inverse(multiply(inverse(multiply(inverse(A),inverse(B))),C))),B)) = multiply(inverse(multiply(inverse(A),c_0)),C). [back_rewrite(7474),rewrite([8079(4),8079(11),8676(14),8746(20),8676(11),8539(18),8356(16),6695(7)]),flip(a)].
% 3.42/3.75 8767 multiply(inverse(multiply(inverse(multiply(A,B)),c_0)),C) = multiply(A,multiply(inverse(multiply(inverse(B),c_0)),C)). [back_rewrite(7225),rewrite([8079(9),8746(13),8753(10),8740(23)]),flip(a)].
% 3.42/3.75 8782 inverse(multiply(multiply(c_0,inverse(A)),B)) = multiply(inverse(multiply(inverse(inverse(B)),c_0)),A). [back_rewrite(6955),rewrite([8079(7),8753(20),8767(15),8573(20)]),flip(a)].
% 3.42/3.75 8831 multiply(inverse(multiply(inverse(multiply(A,c_0)),B)),C) = multiply(inverse(B),multiply(A,C)). [back_rewrite(6740),rewrite([8782(16),8095(17),8274(24),8535(18)])].
% 3.42/3.75 8982 inverse(multiply(inverse(multiply(A,c_0)),c_0)) = A. [back_rewrite(8645),rewrite([8831(10),6695(6),8782(10),8095(11)])].
% 3.42/3.76 9001 multiply(multiply(inverse(multiply(c_0,c_0)),A),multiply(inverse(multiply(B,inverse(C))),D)) = multiply(inverse(multiply(B,inverse(multiply(A,C)))),D). [back_rewrite(8499),rewrite([8782(10),8095(11)])].
% 3.42/3.76 9110 multiply(c_0,inverse(c_0)) = inverse(c_0). [para(8077(a,1),8982(a,1,1,1,1)),rewrite([6695(4)]),flip(a)].
% 3.42/3.76 9111 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(B),A). [para(6695(a,1),8079(a,1,2))].
% 3.42/3.76 9112 multiply(inverse(inverse(c_0)),multiply(c_0,A)) = multiply(inverse(inverse(c_0)),A). [para(9110(a,1),8079(a,1,1,1))].
% 3.42/3.76 9115 multiply(inverse(multiply(c_0,A)),B) = multiply(inverse(A),B). [para(9112(a,1),8079(a,1,1,1)),rewrite([8079(10)]),flip(a)].
% 3.42/3.76 9128 multiply(inverse(multiply(A,inverse(multiply(B,C)))),D) = multiply(B,multiply(inverse(multiply(A,inverse(C))),D)). [back_rewrite(9001),rewrite([9115(5),8098(3)]),flip(a)].
% 3.42/3.76 9212 inverse(c_0) = c_0. [para(9115(a,1),8982(a,1,1)),rewrite([6695(4)])].
% 3.42/3.76 9216 multiply(c_0,A) = A. [back_rewrite(8098),rewrite([9212(2)])].
% 3.42/3.76 9274 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(8571),rewrite([9216(3)]),xx(a)].
% 3.42/3.76 9275 multiply(A,multiply(inverse(multiply(inverse(B),A)),C)) = multiply(B,C). [back_rewrite(8535),rewrite([9216(5)])].
% 3.42/3.76 9338 multiply(A,multiply(inverse(A),B)) = multiply(B,c_0). [para(6695(a,1),9275(a,1,2)),flip(a)].
% 3.42/3.76 9345 multiply(inverse(multiply(inverse(A),B)),C) = multiply(multiply(inverse(B),A),C). [para(9111(a,1),9275(a,1,2,1,1)),rewrite([9216(6)])].
% 3.42/3.76 9356 multiply(A,c_0) = A. [para(9212(a,1),9275(a,1,2,1,1,1)),rewrite([9216(2),9338(3),9216(4)])].
% 3.42/3.76 9357 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(9275(a,1),9216(a,1)),rewrite([9356(4)]),flip(a)].
% 3.42/3.76 9359 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(9275(a,1),9275(a,1,2)),rewrite([9128(9),9345(8),9357(6),9338(7),9356(6)]),flip(a)].
% 3.42/3.76 9360 $F # answer(prove_these_axioms). [resolve(9359,a,9274,a)].
% 3.42/3.76
% 3.42/3.76 % SZS output end Refutation
% 3.42/3.76 ============================== end of proof ==========================
% 3.42/3.76
% 3.42/3.76 ============================== STATISTICS ============================
% 3.42/3.76
% 3.42/3.76 Given=73. Generated=22974. Kept=9358. proofs=1.
% 3.42/3.76 Usable=10. Sos=99. Demods=121. Limbo=21, Disabled=9229. Hints=0.
% 3.42/3.76 Megabytes=22.81.
% 3.42/3.76 User_CPU=2.76, System_CPU=0.02, Wall_clock=3.
% 3.42/3.76
% 3.42/3.76 ============================== end of statistics =====================
% 3.42/3.76
% 3.42/3.76 ============================== end of search =========================
% 3.42/3.76
% 3.42/3.76 THEOREM PROVED
% 3.42/3.76 % SZS status Unsatisfiable
% 3.42/3.76
% 3.42/3.76 Exiting with 1 proof.
% 3.42/3.76
% 3.42/3.76 Process 20939 exit (max_proofs) Mon Jun 13 04:16:30 2022
% 3.42/3.76 Prover9 interrupted
%------------------------------------------------------------------------------