TSTP Solution File: GRP410-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP410-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:18:58 EDT 2022
% Result : Unsatisfiable 2.63s 2.93s
% Output : Refutation 2.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP410-1 : TPTP v8.1.0. Released v2.6.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.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 05:11:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.63/2.93 ============================== Prover9 ===============================
% 2.63/2.93 Prover9 (32) version 2009-11A, November 2009.
% 2.63/2.93 Process 25827 was started by sandbox on n025.cluster.edu,
% 2.63/2.93 Mon Jun 13 05:11:39 2022
% 2.63/2.93 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25674_n025.cluster.edu".
% 2.63/2.93 ============================== end of head ===========================
% 2.63/2.93
% 2.63/2.93 ============================== INPUT =================================
% 2.63/2.93
% 2.63/2.93 % Reading from file /tmp/Prover9_25674_n025.cluster.edu
% 2.63/2.93
% 2.63/2.93 set(prolog_style_variables).
% 2.63/2.93 set(auto2).
% 2.63/2.93 % set(auto2) -> set(auto).
% 2.63/2.93 % set(auto) -> set(auto_inference).
% 2.63/2.93 % set(auto) -> set(auto_setup).
% 2.63/2.93 % set(auto_setup) -> set(predicate_elim).
% 2.63/2.93 % set(auto_setup) -> assign(eq_defs, unfold).
% 2.63/2.93 % set(auto) -> set(auto_limits).
% 2.63/2.93 % set(auto_limits) -> assign(max_weight, "100.000").
% 2.63/2.93 % set(auto_limits) -> assign(sos_limit, 20000).
% 2.63/2.93 % set(auto) -> set(auto_denials).
% 2.63/2.93 % set(auto) -> set(auto_process).
% 2.63/2.93 % set(auto2) -> assign(new_constants, 1).
% 2.63/2.93 % set(auto2) -> assign(fold_denial_max, 3).
% 2.63/2.93 % set(auto2) -> assign(max_weight, "200.000").
% 2.63/2.93 % set(auto2) -> assign(max_hours, 1).
% 2.63/2.93 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.63/2.93 % set(auto2) -> assign(max_seconds, 0).
% 2.63/2.93 % set(auto2) -> assign(max_minutes, 5).
% 2.63/2.93 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.63/2.93 % set(auto2) -> set(sort_initial_sos).
% 2.63/2.93 % set(auto2) -> assign(sos_limit, -1).
% 2.63/2.93 % set(auto2) -> assign(lrs_ticks, 3000).
% 2.63/2.93 % set(auto2) -> assign(max_megs, 400).
% 2.63/2.93 % set(auto2) -> assign(stats, some).
% 2.63/2.93 % set(auto2) -> clear(echo_input).
% 2.63/2.93 % set(auto2) -> set(quiet).
% 2.63/2.93 % set(auto2) -> clear(print_initial_clauses).
% 2.63/2.93 % set(auto2) -> clear(print_given).
% 2.63/2.93 assign(lrs_ticks,-1).
% 2.63/2.93 assign(sos_limit,10000).
% 2.63/2.93 assign(order,kbo).
% 2.63/2.93 set(lex_order_vars).
% 2.63/2.93 clear(print_given).
% 2.63/2.93
% 2.63/2.93 % formulas(sos). % not echoed (2 formulas)
% 2.63/2.93
% 2.63/2.93 ============================== end of input ==========================
% 2.63/2.93
% 2.63/2.93 % From the command line: assign(max_seconds, 300).
% 2.63/2.93
% 2.63/2.93 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.63/2.93
% 2.63/2.93 % Formulas that are not ordinary clauses:
% 2.63/2.93
% 2.63/2.93 ============================== end of process non-clausal formulas ===
% 2.63/2.93
% 2.63/2.93 ============================== PROCESS INITIAL CLAUSES ===============
% 2.63/2.93
% 2.63/2.93 ============================== PREDICATE ELIMINATION =================
% 2.63/2.93
% 2.63/2.93 ============================== end predicate elimination =============
% 2.63/2.93
% 2.63/2.93 Auto_denials:
% 2.63/2.93 % copying label prove_these_axioms_2 to answer in negative clause
% 2.63/2.93
% 2.63/2.93 Term ordering decisions:
% 2.63/2.93
% 2.63/2.93 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 2.63/2.93 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 2.63/2.93
% 2.63/2.93 ============================== end of process initial clauses ========
% 2.63/2.93
% 2.63/2.93 ============================== CLAUSES FOR SEARCH ====================
% 2.63/2.93
% 2.63/2.93 ============================== end of clauses for search =============
% 2.63/2.93
% 2.63/2.93 ============================== SEARCH ================================
% 2.63/2.93
% 2.63/2.93 % Starting search at 0.01 seconds.
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=151.000, iters=3340
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=67.000, iters=3370
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=66.000, iters=3340
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=63.000, iters=3345
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=58.000, iters=3479
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=56.000, iters=3384
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=48.000, iters=3398
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=47.000, iters=3587
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=41.000, iters=3418
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=39.000, iters=3452
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=37.000, iters=3340
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=34.000, iters=3387
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=33.000, iters=3494
% 2.63/2.93
% 2.63/2.93 Low Water (keep): wt=32.000, iters=3384
% 2.63/2.93
% 2.63/2.93 ============================== PROOF =================================
% 2.63/2.93 % SZS status Unsatisfiable
% 2.63/2.93 % SZS output start Refutation
% 2.63/2.93
% 2.63/2.93 % Proof 1 at 1.91 (+ 0.03) seconds: prove_these_axioms_2.
% 2.63/2.93 % Length of proof is 146.
% 2.63/2.93 % Level of proof is 38.
% 2.63/2.93 % Maximum clause weight is 152.000.
% 2.63/2.93 % Given clauses 152.
% 2.63/2.93
% 2.63/2.93 1 multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))) = B # label(single_axiom) # label(axiom). [assumption].
% 2.63/2.93 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 2.63/2.93 3 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))). [para(1(a,1),1(a,1,1,1,1,2,1)),flip(a)].
% 2.63/2.93 4 multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))),inverse(multiply(inverse(C),C))) = inverse(C). [para(1(a,1),1(a,1,1,1,1))].
% 2.63/2.93 5 multiply(multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(D,multiply(inverse(C),C))))),B),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))) = D. [para(1(a,1),1(a,1,1,2))].
% 2.63/2.93 7 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = B. [para(3(a,1),1(a,1,1))].
% 2.63/2.93 8 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(C),C))))) = multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(E,inverse(multiply(B,C)))),multiply(E,inverse(C)))))),multiply(D,inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))). [para(3(a,2),1(a,1,1,1,1,2,1)),flip(a)].
% 2.63/2.93 9 multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C)))),multiply(multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))) = inverse(inverse(multiply(inverse(C),C))). [para(3(a,2),1(a,1,1,1,1))].
% 2.63/2.93 11 multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),C)))),multiply(A,inverse(C))) = B. [para(3(a,2),1(a,1))].
% 2.63/2.93 12 multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(inverse(C)))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))). [para(1(a,1),3(a,1,1,1))].
% 2.63/2.93 21 multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(multiply(B,C)))),multiply(D,inverse(C))). [para(3(a,2),3(a,2))].
% 2.63/2.93 22 multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))),inverse(multiply(inverse(multiply(C,inverse(D))),multiply(C,inverse(D))))) = inverse(multiply(C,inverse(multiply(multiply(B,inverse(multiply(inverse(D),D))),D)))). [para(11(a,1),1(a,1,1,1,1,2,1))].
% 2.63/2.93 23 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(multiply(D,inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))),multiply(inverse(C),C))))),B) = D. [para(1(a,1),11(a,1,2))].
% 2.63/2.93 34 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(multiply(C,inverse(D))))) = multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(multiply(C,inverse(D))))). [para(11(a,1),21(a,1,1,1,2,1)),rewrite([11(19)])].
% 2.63/2.93 36 multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A))),inverse(A))),inverse(A))),inverse(multiply(inverse(A),A))) = inverse(A). [para(4(a,1),1(a,1,1,1,1))].
% 2.63/2.93 39 multiply(inverse(multiply(A,inverse(inverse(B)))),multiply(A,inverse(inverse(multiply(inverse(B),B))))) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),inverse(B)))))),multiply(C,inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))),inverse(multiply(inverse(inverse(multiply(inverse(B),B))),inverse(multiply(inverse(B),B))))))). [para(4(a,1),3(a,1,1,1,2,1))].
% 2.63/2.93 40 multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A))),inverse(A))),inverse(A))) = multiply(multiply(inverse(multiply(D,inverse(inverse(A)))),multiply(D,inverse(inverse(multiply(inverse(A),A))))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))). [para(4(a,1),3(a,1,1,1))].
% 2.63/2.93 54 multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A))),inverse(A))),inverse(A))),inverse(A))),inverse(multiply(inverse(A),A))) = inverse(A). [para(4(a,1),4(a,1,1,2,1,1,1))].
% 2.63/2.93 56 inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C)))) = B. [para(34(a,1),1(a,1,1)),rewrite([22(19)])].
% 2.63/2.93 59 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(C))) = multiply(inverse(multiply(D,inverse(B))),multiply(D,inverse(C))). [para(1(a,1),34(a,1,2,2,1)),rewrite([1(20)])].
% 2.63/2.93 76 multiply(inverse(A),multiply(multiply(inverse(multiply(multiply(inverse(multiply(B,inverse(multiply(C,D)))),multiply(B,inverse(D))),inverse(multiply(A,multiply(inverse(D),D))))),C),inverse(multiply(inverse(D),D)))) = multiply(multiply(inverse(multiply(E,inverse(inverse(multiply(inverse(D),D))))),multiply(E,inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))),inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))). [para(5(a,1),3(a,1,1,1))].
% 2.63/2.93 137 multiply(inverse(multiply(A,B)),multiply(A,inverse(C))) = multiply(inverse(multiply(D,B)),multiply(D,inverse(C))). [para(56(a,1),59(a,1,1,1,2)),rewrite([56(16)])].
% 2.63/2.93 141 inverse(multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(B,C)),multiply(B,inverse(D))),inverse(multiply(inverse(D),D))),D)))) = inverse(multiply(A,C)). [para(137(a,1),1(a,1,1,1,1,2,1)),rewrite([22(21)])].
% 2.63/2.93 151 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(56(a,1),137(a,1,2,2)),rewrite([56(17)])].
% 2.63/2.93 159 multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,D))))),multiply(A,inverse(multiply(C,D)))) = multiply(multiply(inverse(multiply(E,inverse(B))),multiply(E,inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))),inverse(multiply(inverse(multiply(F,D)),multiply(F,D)))))). [para(151(a,1),3(a,2,2,1,2,1))].
% 2.63/2.93 178 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(151(a,1),151(a,1,1,1))].
% 2.63/2.93 179 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(151(a,1),151(a,1,2))].
% 2.63/2.93 181 multiply(inverse(A),multiply(multiply(multiply(inverse(multiply(B,inverse(A))),multiply(B,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(inverse(C)))),multiply(D,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))). [para(7(a,1),3(a,1,1,1))].
% 2.63/2.93 187 multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(multiply(multiply(inverse(multiply(C,inverse(B))),multiply(C,inverse(inverse(multiply(inverse(A),A))))),inverse(multiply(inverse(inverse(multiply(inverse(A),A))),inverse(multiply(inverse(A),A))))),inverse(A))),inverse(A))),inverse(multiply(inverse(A),A))) = inverse(A). [para(7(a,1),4(a,1,1,2,1,1,1))].
% 2.63/2.93 191 multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = multiply(D,inverse(multiply(multiply(multiply(B,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E))). [para(56(a,1),7(a,1,1,1,1,1,2))].
% 2.63/2.93 229 inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))). [para(151(a,1),141(a,2,1)),rewrite([141(16)])].
% 2.63/2.93 230 multiply(A,inverse(multiply(multiply(multiply(inverse(multiply(B,C)),multiply(B,inverse(D))),inverse(multiply(inverse(D),D))),D))) = multiply(A,C). [para(141(a,1),7(a,1,1,1,1,1,2)),rewrite([7(24)]),flip(a)].
% 2.63/2.93 232 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,inverse(E))),inverse(multiply(inverse(E),E))),E))),D))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,inverse(E))),inverse(multiply(inverse(E),E))),E))),D))),inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,inverse(E))),inverse(multiply(inverse(E),E))),E))),D))))),inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,inverse(E))),inverse(multiply(inverse(E),E))),E))),D))) = B. [para(141(a,1),7(a,1,1,1,2,2,1)),rewrite([230(44),230(59),230(76)])].
% 2.63/2.93 270 multiply(A,inverse(multiply(multiply(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,D)))),multiply(C,inverse(D))),inverse(E))),inverse(multiply(inverse(E),E))),E))) = multiply(A,inverse(multiply(inverse(D),D))). [para(1(a,1),230(a,1,2,1,1,1,1,1))].
% 2.63/2.93 394 inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(multiply(C,inverse(inverse(multiply(inverse(D),D))))))),inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(F,inverse(multiply(inverse(multiply(inverse(D),D)),D)))),multiply(F,inverse(D)))))),multiply(E,inverse(inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))),inverse(multiply(inverse(inverse(multiply(inverse(D),D))),inverse(multiply(inverse(D),D))))))))),multiply(C,inverse(inverse(multiply(inverse(D),D)))))))) = B. [para(8(a,1),56(a,1,1,2,1,1,2,1))].
% 2.63/2.93 397 multiply(inverse(multiply(A,B)),multiply(A,inverse(inverse(multiply(inverse(C),C))))) = multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(E,inverse(multiply(multiply(F,inverse(multiply(multiply(multiply(B,multiply(F,inverse(V6))),inverse(multiply(inverse(V6),V6))),V6))),C)))),multiply(E,inverse(C)))))),multiply(D,inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))). [para(56(a,1),8(a,1,1,1,2))].
% 2.63/2.93 411 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))))) = multiply(multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(F,inverse(multiply(B,multiply(C,D))))),multiply(F,inverse(multiply(C,D))))))),multiply(E,inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))),inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))),inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,D)),multiply(C,D)))),inverse(multiply(inverse(multiply(V6,D)),multiply(V6,D)))))))). [para(151(a,1),8(a,2,2,1,2,1,2,1))].
% 2.63/2.93 474 multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,multiply(D,E)))))),multiply(A,inverse(multiply(C,multiply(D,E))))) = multiply(multiply(inverse(multiply(F,inverse(B))),multiply(F,inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,V6)),multiply(D,E))),multiply(inverse(multiply(V7,V6)),multiply(V7,E))))))). [para(179(a,2),3(a,2,2,1,2,1))].
% 2.63/2.93 512 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,F)),multiply(D,E))),multiply(inverse(multiply(V6,F)),multiply(V6,E))))))),inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))) = B. [para(179(a,2),7(a,1,1,2,1,2,1))].
% 2.63/2.93 561 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))))) = multiply(multiply(inverse(multiply(F,inverse(multiply(inverse(multiply(V6,inverse(multiply(B,multiply(C,multiply(D,E)))))),multiply(V6,inverse(multiply(C,multiply(D,E)))))))),multiply(F,inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))),inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))),inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))),inverse(multiply(inverse(multiply(inverse(multiply(D,V7)),multiply(D,E))),multiply(inverse(multiply(V8,V7)),multiply(V8,E))))))))). [para(179(a,2),8(a,2,2,1,2,1,2,1))].
% 2.63/2.93 807 inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,B)))) = inverse(inverse(multiply(inverse(multiply(C,B)),multiply(C,B)))). [para(151(a,1),9(a,2,1,1)),rewrite([9(43)])].
% 2.63/2.93 895 inverse(inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C)))))) = inverse(inverse(multiply(inverse(D),D))). [para(11(a,1),807(a,1,1,1,1,1)),rewrite([11(12)]),flip(a)].
% 2.63/2.93 959 inverse(inverse(multiply(inverse(A),A))) = inverse(inverse(multiply(inverse(B),B))). [para(11(a,1),895(a,1,1,1,1,1)),rewrite([11(12)])].
% 2.63/2.93 974 inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C))))) = inverse(multiply(inverse(D),D)). [para(895(a,1),7(a,1,1,1,1,1,2)),rewrite([7(26)]),flip(a)].
% 2.63/2.93 993 inverse(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C))),B))) = inverse(inverse(multiply(inverse(multiply(D,multiply(E,inverse(F)))),multiply(D,multiply(E,inverse(F)))))). [para(230(a,1),895(a,2,1,1)),flip(a)].
% 2.63/2.93 1015 multiply(inverse(multiply(A,inverse(B))),multiply(A,inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))) = multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(inverse(C),C)))))),multiply(E,inverse(inverse(multiply(inverse(C),C)))))))),multiply(D,inverse(inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))))),inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(C),C))),inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(inverse(multiply(inverse(multiply(F,multiply(V6,inverse(V7)))),multiply(F,multiply(V6,inverse(V7)))))),inverse(multiply(inverse(C),C))))))))). [para(895(a,2),8(a,2,2,1,2,1,2,1,1))].
% 2.63/2.93 1043 inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,inverse(C)))),multiply(A,multiply(B,inverse(C)))))),inverse(multiply(inverse(D),D))))) = inverse(inverse(multiply(inverse(multiply(E,multiply(F,inverse(V6)))),multiply(E,multiply(F,inverse(V6)))))). [para(895(a,2),895(a,2,1,1,1)),flip(a)].
% 2.63/2.93 1044 inverse(inverse(multiply(inverse(A),A))) = c_0. [new_symbol(959)].
% 2.63/2.93 1045 inverse(inverse(multiply(c_0,inverse(multiply(inverse(A),A))))) = c_0. [back_rewrite(1043),rewrite([1044(10),1044(17)])].
% 2.63/2.93 1056 multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(inverse(E),E)))))),multiply(D,c_0))))),multiply(C,inverse(inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(E),E))))))))),inverse(multiply(inverse(inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(E),E))))))),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(E),E))))))))). [back_rewrite(1015),rewrite([1044(7),1045(10),1044(17),1044(23),1045(26),1044(24),1044(35),1045(38),1044(36),1044(45),1045(48),1044(52)])].
% 2.63/2.93 1061 inverse(inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C))),B))) = c_0. [back_rewrite(993),rewrite([1044(25)])].
% 2.63/2.93 1216 multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(E,multiply(F,V6)))))),multiply(D,inverse(multiply(E,multiply(F,V6)))))))),multiply(C,c_0)),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(F,V7)),multiply(F,V6))),multiply(inverse(multiply(V8,V7)),multiply(V8,V6))))))))). [back_rewrite(561),rewrite([1044(11),1044(28),1045(31),1044(31),1045(34),1044(32)])].
% 2.63/2.93 1227 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,E))),multiply(inverse(multiply(F,D)),multiply(F,E))))))),inverse(multiply(inverse(multiply(V6,multiply(C,E))),multiply(V6,multiply(C,E))))) = B. [back_rewrite(512),rewrite([1044(11),1044(14)])].
% 2.63/2.93 1240 multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,multiply(D,E)))))),multiply(A,inverse(multiply(C,multiply(D,E))))) = multiply(multiply(inverse(multiply(F,inverse(B))),multiply(F,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(multiply(inverse(multiply(D,V6)),multiply(D,E))),multiply(inverse(multiply(V7,V6)),multiply(V7,E))))))). [back_rewrite(474),rewrite([1044(22),1044(25)])].
% 2.63/2.93 1280 multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(B,multiply(E,F))))),multiply(D,inverse(multiply(E,F))))))),multiply(C,c_0)),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(multiply(V6,F)),multiply(V6,F)))))))). [back_rewrite(411),rewrite([1044(9),1044(24),1045(27),1044(27),1045(30),1044(28)])].
% 2.63/2.93 1288 multiply(inverse(multiply(A,B)),multiply(A,c_0)) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(E,inverse(multiply(multiply(multiply(B,multiply(E,inverse(F))),inverse(multiply(inverse(F),F))),F))),V6)))),multiply(D,inverse(V6)))))),multiply(C,c_0)),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(V6),V6))))))). [back_rewrite(397),rewrite([1044(6),1044(29),1045(32),1044(32),1045(35),1044(33)])].
% 2.63/2.93 1291 inverse(multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(multiply(C,c_0)))),inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(multiply(inverse(F),F)),F)))),multiply(E,inverse(F)))))),multiply(D,c_0)),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(F),F))))))))),multiply(C,c_0))))) = B. [back_rewrite(394),rewrite([1044(4),1044(22),1045(25),1044(25),1045(28),1044(26),1044(37)])].
% 2.63/2.93 1355 multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(C),C))))),inverse(multiply(inverse(C),C))) = multiply(D,inverse(multiply(multiply(multiply(B,multiply(D,inverse(E))),inverse(multiply(inverse(E),E))),E))). [back_rewrite(191),rewrite([1044(6),1044(9)])].
% 2.63/2.93 1359 multiply(multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(multiply(multiply(inverse(multiply(C,inverse(B))),multiply(C,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(A),A))))),inverse(A))),inverse(A))),inverse(multiply(inverse(A),A))) = inverse(A). [back_rewrite(187),rewrite([1044(10),1044(13)])].
% 2.63/2.93 1364 multiply(inverse(A),multiply(multiply(multiply(inverse(multiply(B,inverse(A))),multiply(B,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(C),C))))),inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(inverse(C)))),multiply(D,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(C),C))))). [back_rewrite(181),rewrite([1044(8),1044(11),1044(25),1044(28)])].
% 2.63/2.93 1369 multiply(inverse(multiply(A,inverse(multiply(B,multiply(C,D))))),multiply(A,inverse(multiply(C,D)))) = multiply(multiply(inverse(multiply(E,inverse(B))),multiply(E,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(multiply(F,D)),multiply(F,D)))))). [back_rewrite(159),rewrite([1044(18),1044(21)])].
% 2.63/2.93 1388 multiply(inverse(A),multiply(multiply(inverse(multiply(multiply(inverse(multiply(B,inverse(multiply(C,D)))),multiply(B,inverse(D))),inverse(multiply(A,multiply(inverse(D),D))))),C),inverse(multiply(inverse(D),D)))) = multiply(multiply(inverse(multiply(E,c_0)),multiply(E,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(multiply(inverse(D),D)),multiply(inverse(D),D)))))). [back_rewrite(76),rewrite([1044(24),1044(31),1044(34)])].
% 2.63/2.93 1399 multiply(inverse(inverse(A)),multiply(multiply(inverse(B),multiply(multiply(inverse(multiply(C,inverse(multiply(B,A)))),multiply(C,inverse(A))),inverse(A))),inverse(A))) = multiply(multiply(inverse(multiply(D,inverse(inverse(A)))),multiply(D,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(A),A))))). [back_rewrite(40),rewrite([1044(24),1044(27)])].
% 2.63/2.93 1400 multiply(inverse(multiply(A,inverse(inverse(B)))),multiply(A,c_0)) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,B)))),multiply(E,inverse(B))),inverse(B)))))),multiply(C,c_0)),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(B),B))))))). [back_rewrite(39),rewrite([1044(8),1044(25),1045(28),1044(28),1045(31),1044(29)])].
% 2.63/2.93 1412 multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(C))) = multiply(multiply(inverse(multiply(D,inverse(inverse(C)))),multiply(D,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(C),C))))). [back_rewrite(12),rewrite([1044(19),1044(22)])].
% 2.63/2.93 1415 multiply(multiply(multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,inverse(E))),inverse(multiply(inverse(E),E))),E))),D))))),inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(C,D)),multiply(C,inverse(E))),inverse(multiply(inverse(E),E))),E))),D))) = B. [back_rewrite(232),rewrite([1061(18),1061(21)])].
% 2.63/2.93 1433 inverse(inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(A),A))))))) = c_0. [para(1045(a,1),1044(a,1,1,1,1))].
% 2.63/2.93 1441 multiply(inverse(multiply(A,inverse(B))),multiply(A,c_0)) = multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(inverse(E),E)))))),multiply(D,c_0))))),multiply(C,c_0)),inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(E),E))))))))). [back_rewrite(1056),rewrite([1433(29),1433(32)])].
% 2.63/2.93 1499 inverse(multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(C),C))),C)))) = multiply(multiply(inverse(multiply(D,c_0)),multiply(D,inverse(multiply(A,inverse(C))))),inverse(multiply(inverse(multiply(A,inverse(C))),multiply(A,inverse(C))))). [para(1045(a,1),22(a,1,1,1,1,2)),flip(a)].
% 2.63/2.93 1556 inverse(multiply(inverse(A),A)) = inverse(multiply(inverse(B),B)). [para(11(a,1),974(a,1,1,1,1)),rewrite([11(12)])].
% 2.63/2.93 1646 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C))))),B) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,multiply(inverse(C),C))))),multiply(E,inverse(multiply(inverse(C),C)))),inverse(multiply(inverse(C),C)))). [para(4(a,1),23(a,1,1,1,2,1,1))].
% 2.63/2.93 1729 multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(inverse(D),D))) = B. [para(1556(a,1),1(a,1,2))].
% 2.63/2.93 1731 multiply(inverse(multiply(A,inverse(multiply(multiply(B,inverse(multiply(inverse(C),C))),D)))),multiply(A,inverse(D))) = B. [para(1556(a,1),11(a,1,1,1,2,1,1,2))].
% 2.63/2.93 1751 inverse(multiply(inverse(inverse(multiply(multiply(multiply(inverse(multiply(A,B)),multiply(A,inverse(C))),inverse(multiply(inverse(C),C))),C))),B)) = inverse(multiply(inverse(D),D)). [para(230(a,1),1556(a,1,1))].
% 2.63/2.93 1763 inverse(multiply(inverse(A),A)) = inverse(multiply(c_0,inverse(multiply(inverse(B),B)))). [para(1044(a,1),1556(a,1,1,1)),flip(a)].
% 2.63/2.93 1773 multiply(inverse(A),A) = multiply(inverse(B),B). [back_rewrite(1646),rewrite([1729(15),1729(18)])].
% 2.63/2.93 1780 multiply(multiply(inverse(A),A),a2) != a2 # answer(prove_these_axioms_2). [para(1773(a,1),2(a,1,1))].
% 2.63/2.93 1781 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(C),C)) = multiply(inverse(multiply(D,B)),multiply(D,A)). [para(1773(a,1),151(a,1,2))].
% 2.63/2.93 1799 multiply(inverse(A),A) = multiply(c_0,inverse(multiply(inverse(B),B))). [para(1044(a,1),1773(a,1,1)),flip(a)].
% 2.63/2.93 1800 multiply(inverse(A),A) = multiply(c_0,inverse(multiply(c_0,inverse(multiply(inverse(B),B))))). [para(1045(a,1),1773(a,1,1)),flip(a)].
% 2.63/2.93 1804 multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)) = multiply(inverse(C),C). [para(1556(a,1),1773(a,1,1))].
% 2.63/2.93 2011 multiply(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),multiply(inverse(multiply(D,B)),multiply(D,C))),a2) != a2 # answer(prove_these_axioms_2). [para(229(a,1),1780(a,1,1,1))].
% 2.63/2.93 2359 multiply(multiply(c_0,multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B)))),inverse(multiply(inverse(C),C))) = inverse(multiply(inverse(B),B)). [para(1804(a,1),36(a,1,2,1)),rewrite([1044(4),1729(17)])].
% 2.63/2.93 4628 multiply(multiply(c_0,inverse(multiply(inverse(A),A))),inverse(multiply(inverse(B),B))) = inverse(multiply(inverse(A),A)). [para(1804(a,1),54(a,1,2,1)),rewrite([1044(4),1044(5),1729(18),2359(13)])].
% 2.63/2.93 5538 inverse(multiply(inverse(A),A)) = multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))). [para(1799(a,2),4628(a,1,1)),flip(a)].
% 2.63/2.93 5618 inverse(inverse(multiply(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B))),multiply(inverse(C),C)))) = c_0. [para(5538(a,1),1044(a,1,1,1,1))].
% 2.63/2.93 5619 inverse(multiply(multiply(inverse(A),A),inverse(multiply(inverse(B),B)))) = c_0. [para(5538(a,1),1044(a,1,1))].
% 2.63/2.93 5620 inverse(multiply(c_0,inverse(multiply(inverse(A),A)))) = multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))). [para(1044(a,1),5538(a,1,1,1))].
% 2.63/2.93 5657 inverse(multiply(inverse(A),A)) = inverse(multiply(c_0,multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))))). [para(5538(a,1),1763(a,2,1,2))].
% 2.63/2.93 5843 inverse(multiply(multiply(inverse(A),A),inverse(multiply(c_0,inverse(multiply(inverse(B),B)))))) = c_0. [para(1044(a,1),5619(a,1,1,2,1,1))].
% 2.63/2.93 5849 inverse(multiply(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)),inverse(multiply(inverse(C),C)))) = c_0. [para(1556(a,1),5619(a,1,1,1,1))].
% 2.63/2.93 5948 inverse(multiply(multiply(inverse(A),A),multiply(multiply(inverse(B),B),inverse(multiply(inverse(C),C))))) = c_0. [para(5538(a,1),5619(a,1,1,2))].
% 2.63/2.93 9204 multiply(inverse(multiply(inverse(A),B)),multiply(c_0,multiply(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(D),D)),inverse(multiply(inverse(E),E))))) = multiply(inverse(multiply(F,B)),multiply(F,A)). [para(5849(a,1),1781(a,1,2,1))].
% 2.63/2.93 9480 multiply(multiply(inverse(multiply(inverse(A),A)),multiply(c_0,inverse(B))),inverse(multiply(inverse(C),C))) = inverse(B). [para(1799(a,2),1729(a,1,1,1,1))].
% 2.63/2.93 9491 multiply(multiply(inverse(multiply(inverse(A),A)),multiply(c_0,c_0)),inverse(multiply(inverse(B),B))) = c_0. [para(1800(a,2),1729(a,1,1,1,1)),rewrite([1044(8)])].
% 2.63/2.93 9536 multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(B),B)))),multiply(inverse(C),C)) = multiply(inverse(D),multiply(multiply(inverse(multiply(E,inverse(multiply(D,F)))),multiply(E,inverse(F))),A)). [para(1729(a,1),1781(a,2,1,1))].
% 2.63/2.93 9548 multiply(inverse(A),A) = multiply(multiply(inverse(multiply(B,c_0)),multiply(B,c_0)),inverse(multiply(inverse(C),C))). [para(5538(a,2),1729(a,1,1,1,1,2,1)),rewrite([1044(4),1044(7)]),flip(a)].
% 2.63/2.93 9549 multiply(multiply(c_0,multiply(multiply(inverse(A),A),inverse(B))),inverse(multiply(inverse(C),C))) = inverse(B). [para(5538(a,2),1729(a,1,1,1,1)),rewrite([1044(4)])].
% 2.63/2.93 9556 multiply(multiply(inverse(multiply(A,inverse(multiply(B,multiply(multiply(inverse(C),C),inverse(multiply(c_0,inverse(multiply(inverse(D),D))))))))),multiply(A,c_0)),inverse(multiply(inverse(E),E))) = B. [para(5843(a,1),1729(a,1,1,2,2))].
% 2.63/2.93 9574 multiply(multiply(inverse(A),multiply(multiply(inverse(multiply(B,inverse(multiply(A,C)))),multiply(B,inverse(C))),inverse(D))),inverse(multiply(inverse(E),E))) = inverse(D). [para(1729(a,1),1729(a,1,1,1,1))].
% 2.63/2.93 9575 multiply(multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,C)))),multiply(A,inverse(C))),inverse(multiply(D,multiply(inverse(E),E))))),B),inverse(multiply(inverse(F),F))) = D. [para(1729(a,1),1729(a,1,1,2))].
% 2.63/2.93 9577 multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(inverse(C),C))). [back_rewrite(270),rewrite([9574(15)])].
% 2.63/2.93 9586 multiply(inverse(A),A) = multiply(multiply(inverse(multiply(B,c_0)),multiply(B,c_0)),inverse(multiply(c_0,inverse(multiply(inverse(multiply(inverse(C),C)),multiply(inverse(C),C)))))). [back_rewrite(1388),rewrite([9575(19)])].
% 2.63/2.93 9594 multiply(A,inverse(multiply(inverse(B),B))) = multiply(A,inverse(multiply(c_0,inverse(multiply(inverse(C),C))))). [para(1044(a,1),9577(a,1,2,1,1)),flip(a)].
% 2.63/2.93 10074 multiply(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),C))))),multiply(inverse(multiply(multiply(inverse(multiply(inverse(D),D)),multiply(c_0,c_0)),B)),c_0)),a2) != a2 # answer(prove_these_axioms_2). [para(9491(a,1),2011(a,1,1,2,2))].
% 2.63/2.93 10102 multiply(multiply(inverse(multiply(c_0,multiply(multiply(inverse(multiply(inverse(A),A)),multiply(inverse(B),B)),inverse(multiply(inverse(C),C))))),multiply(c_0,c_0)),inverse(multiply(inverse(D),D))) = c_0. [para(5849(a,1),9491(a,1,1,1,1,1))].
% 2.63/2.93 10564 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(c_0,multiply(inverse(B),C)). [para(9548(a,1),151(a,1,1,1)),rewrite([5619(11)]),flip(a)].
% 2.63/2.93 10567 multiply(inverse(multiply(multiply(c_0,multiply(inverse(c_0),c_0)),inverse(multiply(inverse(A),A)))),multiply(inverse(B),C)) = multiply(c_0,multiply(inverse(B),C)). [para(9548(a,1),151(a,2,1,1)),rewrite([10564(4),10564(10)]),flip(a)].
% 2.63/2.93 10576 multiply(inverse(multiply(c_0,multiply(inverse(A),B))),multiply(inverse(multiply(C,A)),D)) = multiply(c_0,multiply(inverse(multiply(C,B)),D)). [para(9548(a,1),178(a,1,1,1,1,1)),rewrite([10564(6),10567(14),10564(14)])].
% 2.63/2.93 10760 inverse(multiply(inverse(A),A)) = c_0. [para(9548(a,2),5619(a,1,1))].
% 2.63/2.93 10805 inverse(multiply(multiply(inverse(A),A),multiply(inverse(B),B))) = c_0. [para(9548(a,2),5948(a,1,1,2))].
% 2.63/2.93 10811 inverse(c_0) = c_0. [para(9548(a,2),5618(a,1,1,1,1)),rewrite([10805(6)])].
% 2.63/2.93 10817 inverse(multiply(c_0,c_0)) = multiply(inverse(A),A). [para(9548(a,2),5620(a,2)),rewrite([10760(4)])].
% 2.63/2.93 10844 inverse(multiply(c_0,multiply(inverse(A),A))) = c_0. [para(9548(a,2),5657(a,2,1,2)),rewrite([10760(3)]),flip(a)].
% 2.63/2.93 10868 multiply(inverse(multiply(c_0,c_0)),c_0) = inverse(multiply(c_0,c_0)). [para(9548(a,2),1729(a,1,1,1,1,2,1)),rewrite([10760(3),10760(6),10811(5),10817(6,R),10760(7),10817(12,R)])].
% 2.63/2.93 10871 inverse(multiply(c_0,c_0)) = multiply(c_0,c_0). [para(9548(a,1),9577(a,1)),rewrite([10817(6,R),10760(7),10868(6),10760(7),10811(6),10760(8)])].
% 2.63/2.93 10873 multiply(multiply(c_0,c_0),c_0) = multiply(c_0,c_0). [para(9548(a,1),9577(a,2)),rewrite([10760(3),10811(2),10760(4),10817(9,R),10871(7),10760(9)]),flip(a)].
% 2.63/2.93 10888 multiply(multiply(c_0,multiply(inverse(A),A)),c_0) = c_0. [para(9548(a,2),9549(a,1,1,2)),rewrite([10760(7),10760(9)])].
% 2.63/2.93 10889 multiply(c_0,multiply(c_0,c_0)) = multiply(c_0,c_0). [para(9548(a,1),9594(a,1)),rewrite([10817(6,R),10871(4),10760(6),10873(5),10760(6),10811(5),10760(8),10871(8)]),flip(a)].
% 2.63/2.93 10890 multiply(A,multiply(c_0,c_0)) = multiply(A,c_0). [para(9548(a,1),9594(a,2,2,1,2,1)),rewrite([10760(3),10817(9,R),10871(7),10760(9),10873(8),10871(7),10889(7),10871(6)]),flip(a)].
% 2.63/2.93 10898 multiply(multiply(c_0,multiply(c_0,inverse(A))),c_0) = inverse(A). [para(9548(a,1),9480(a,1,2,1)),rewrite([10760(3),10817(11,R),10871(9),10760(11),10873(10),10871(9),10890(9)])].
% 2.63/2.93 10927 multiply(c_0,c_0) = c_0. [back_rewrite(10102),rewrite([10760(4),10760(8),10888(7),10871(4),10890(7),10873(5),10760(6),10873(5)])].
% 2.63/2.93 10928 multiply(c_0,a2) != a2 # answer(prove_these_axioms_2). [back_rewrite(10074),rewrite([10760(5),10564(5),10760(9),10927(10),10927(9),10576(12),10927(4),10811(3),10927(4),10927(3)])].
% 2.63/2.93 10938 multiply(inverse(A),A) = c_0. [back_rewrite(9586),rewrite([10817(8,R),10927(5),10811(4),10760(7),10844(9),10927(6),10811(5),10927(5)])].
% 2.63/2.93 10943 multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,c_0))),c_0)),c_0) = A. [back_rewrite(9556),rewrite([10938(2),10938(4),10811(4),10927(4),10811(3),10927(3),10564(8),10938(10),10811(10)])].
% 2.63/2.93 10947 multiply(inverse(A),multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,B))),inverse(B))),C)) = multiply(inverse(multiply(inverse(C),c_0)),c_0). [back_rewrite(9536),rewrite([10938(3),10811(3),10938(6),10564(14)]),flip(a)].
% 2.63/2.93 10952 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(9204),rewrite([10938(6),10811(6),10938(7),10927(7),10938(7),10811(7),10927(7),10927(6),10564(9)])].
% 2.63/2.93 11033 inverse(multiply(inverse(inverse(multiply(multiply(multiply(c_0,multiply(inverse(A),inverse(B))),c_0),B))),A)) = c_0. [back_rewrite(1751),rewrite([10564(5),10938(7),10811(7),10938(14),10811(14)])].
% 2.63/2.93 11038 multiply(c_0,multiply(inverse(inverse(multiply(multiply(A,c_0),B))),inverse(B))) = A. [back_rewrite(1731),rewrite([10938(2),10811(2),10564(9)])].
% 2.63/2.93 11083 inverse(multiply(A,inverse(multiply(c_0,B)))) = inverse(multiply(A,inverse(B))). [back_rewrite(1499),rewrite([10938(3),10811(3),10927(3),10811(2),10938(3),10811(3),10927(3),10564(13),10811(8),10817(18,R),10927(15),10811(14),10811(14),10898(14)])].
% 2.63/2.93 11118 multiply(c_0,multiply(inverse(inverse(A)),c_0)) = inverse(inverse(multiply(A,c_0))). [back_rewrite(1441),rewrite([10564(6),10938(8),10811(8),10564(14),11083(17),10564(18),10938(23),10811(23),10927(23),10811(22),10927(22),10811(21),10927(21),10811(20),10943(20)])].
% 2.63/2.93 11132 multiply(multiply(inverse(inverse(multiply(A,c_0))),c_0),c_0) = A. [back_rewrite(1415),rewrite([10564(6),11118(6),10564(10),10938(12),10811(12),11033(17),10927(7),10811(6),10564(11),10938(13),10811(13),11033(18)])].
% 2.63/2.93 11134 multiply(inverse(inverse(multiply(inverse(A),c_0))),c_0) = multiply(c_0,multiply(c_0,inverse(A))). [back_rewrite(1412),rewrite([10564(8),10947(11),10952(7),10811(3),10564(12),11118(12),10938(13),10811(13),10927(13),10811(12)]),flip(a)].
% 2.63/2.93 11141 multiply(c_0,multiply(c_0,inverse(A))) = inverse(inverse(multiply(inverse(A),c_0))). [back_rewrite(1400),rewrite([10564(7),11118(7),10564(13),10947(16),10952(12),10811(8),11083(13),11083(11),10564(12),11118(12),10938(14),10811(14),10927(14),10811(13),10927(13),10811(12),11134(12)]),flip(a)].
% 2.63/2.94 11142 multiply(inverse(inverse(A)),multiply(inverse(inverse(multiply(inverse(A),c_0))),inverse(A))) = inverse(inverse(multiply(inverse(A),c_0))). [back_rewrite(1399),rewrite([10564(10),10947(13),10952(9),10811(5),11141(7),10564(17),11118(17),10938(18),10811(18),10927(18),10811(17),11134(17),11141(15)])].
% 2.63/2.94 11160 multiply(c_0,multiply(inverse(inverse(multiply(A,multiply(B,C)))),inverse(multiply(B,C)))) = multiply(inverse(inverse(multiply(A,c_0))),c_0). [back_rewrite(1369),rewrite([10564(9),10564(15),11118(15),10817(18,R),10927(17),10811(16),10811(16),10927(16),10811(15)])].
% 2.63/2.94 11164 multiply(inverse(A),multiply(multiply(inverse(inverse(multiply(A,c_0))),c_0),inverse(B))) = inverse(inverse(multiply(inverse(B),c_0))). [back_rewrite(1364),rewrite([10564(7),11118(7),10938(8),10811(8),10927(8),10811(7),10564(17),11118(17),10938(18),10811(18),10927(18),10811(17),11134(17),11141(15)])].
% 2.63/2.94 11165 inverse(inverse(multiply(inverse(A),c_0))) = inverse(A). [back_rewrite(1359),rewrite([10564(9),11118(9),10938(10),10811(10),10927(10),10811(9),11164(12),11142(10),10938(7),10811(7),11134(7),11141(5)])].
% 2.63/2.94 11168 multiply(A,inverse(multiply(multiply(multiply(B,multiply(A,inverse(C))),c_0),C))) = multiply(multiply(multiply(c_0,multiply(inverse(B),c_0)),c_0),c_0). [back_rewrite(1355),rewrite([10564(5),10938(8),10811(8),10927(8),10811(7),10938(9),10811(9),10938(14),10811(14)]),flip(a)].
% 2.63/2.94 11192 inverse(multiply(multiply(multiply(c_0,multiply(inverse(A),c_0)),c_0),c_0)) = A. [back_rewrite(1291),rewrite([10938(7),10811(7),11083(10),10817(11,R),10927(8),10811(7),10811(7),10817(11,R),10927(8),10811(7),10938(10),10811(10),10927(10),10811(9),10927(9),10811(8),10927(8),10811(7),11168(12)])].
% 2.63/2.94 11194 multiply(c_0,multiply(inverse(A),c_0)) = multiply(inverse(A),c_0). [back_rewrite(1288),rewrite([10564(5),10938(10),10811(10),11168(13),10564(21),11038(21),10564(18),11118(18),11192(15),10938(10),10811(10),10927(10),10811(9),10927(9),10811(8)])].
% 2.63/2.94 11200 multiply(inverse(inverse(A)),c_0) = A. [back_rewrite(1280),rewrite([10564(6),11194(6),10564(13),11160(13),10564(16),11165(13),11194(12),10817(16,R),10927(15),10811(14),10811(14),10927(14),10811(13),10927(13),10811(12),11132(12)])].
% 2.63/2.94 11229 multiply(multiply(c_0,A),c_0) = multiply(A,c_0). [back_rewrite(1240),rewrite([10564(11),11160(11),11200(6),10564(8),11200(7),10564(9),10564(14),10817(15,R),10927(8),10811(7),10811(7),10927(7),10811(6)]),flip(a)].
% 2.63/2.94 11242 multiply(multiply(A,c_0),c_0) = A. [back_rewrite(1227),rewrite([10564(6),11200(5),10564(7),10564(12),10817(13,R),10927(6),10811(5),10811(5),10927(5),10811(4),11229(4),10817(8,R),10927(5),10811(4),10811(4)])].
% 2.63/2.94 11250 multiply(c_0,A) = A. [back_rewrite(1216),rewrite([10564(6),11200(5),10564(13),11160(13),11200(8),10564(10),11200(9),10564(12),10564(17),10817(18,R),10927(11),10811(10),10811(10),10927(10),10811(9),10927(9),10811(8),11229(8),11242(6)])].
% 2.63/2.94 11251 $F # answer(prove_these_axioms_2). [resolve(11250,a,10928,a)].
% 2.63/2.94
% 2.63/2.94 % SZS output end Refutation
% 2.63/2.94 ============================== end of proof ==========================
% 2.63/2.94
% 2.63/2.94 ============================== STATISTICS ============================
% 2.63/2.94
% 2.63/2.94 Given=152. Generated=39423. Kept=11250. proofs=1.
% 2.63/2.94 Usable=109. Sos=4918. Demods=1550. Limbo=686, Disabled=5538. Hints=0.
% 2.63/2.94 Megabytes=20.16.
% 2.63/2.94 User_CPU=1.91, System_CPU=0.03, Wall_clock=2.
% 2.63/2.94
% 2.63/2.94 ============================== end of statistics =====================
% 2.63/2.94
% 2.63/2.94 ============================== end of search =========================
% 2.63/2.94
% 2.63/2.94 THEOREM PROVED
% 2.63/2.94 % SZS status Unsatisfiable
% 2.63/2.94
% 2.63/2.94 Exiting with 1 proof.
% 2.63/2.94
% 2.63/2.94 Process 25827 exit (max_proofs) Mon Jun 13 05:11:41 2022
% 2.63/2.94 Prover9 interrupted
%------------------------------------------------------------------------------