TSTP Solution File: GRP420-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP420-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:19:01 EDT 2022
% Result : Unsatisfiable 1.67s 1.96s
% Output : Refutation 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP420-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 04:00:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.67/1.96 ============================== Prover9 ===============================
% 1.67/1.96 Prover9 (32) version 2009-11A, November 2009.
% 1.67/1.96 Process 18505 was started by sandbox on n016.cluster.edu,
% 1.67/1.96 Tue Jun 14 04:00:16 2022
% 1.67/1.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18349_n016.cluster.edu".
% 1.67/1.96 ============================== end of head ===========================
% 1.67/1.96
% 1.67/1.96 ============================== INPUT =================================
% 1.67/1.96
% 1.67/1.96 % Reading from file /tmp/Prover9_18349_n016.cluster.edu
% 1.67/1.96
% 1.67/1.96 set(prolog_style_variables).
% 1.67/1.96 set(auto2).
% 1.67/1.96 % set(auto2) -> set(auto).
% 1.67/1.96 % set(auto) -> set(auto_inference).
% 1.67/1.96 % set(auto) -> set(auto_setup).
% 1.67/1.96 % set(auto_setup) -> set(predicate_elim).
% 1.67/1.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.67/1.96 % set(auto) -> set(auto_limits).
% 1.67/1.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.67/1.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.67/1.96 % set(auto) -> set(auto_denials).
% 1.67/1.96 % set(auto) -> set(auto_process).
% 1.67/1.96 % set(auto2) -> assign(new_constants, 1).
% 1.67/1.96 % set(auto2) -> assign(fold_denial_max, 3).
% 1.67/1.96 % set(auto2) -> assign(max_weight, "200.000").
% 1.67/1.96 % set(auto2) -> assign(max_hours, 1).
% 1.67/1.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.67/1.96 % set(auto2) -> assign(max_seconds, 0).
% 1.67/1.96 % set(auto2) -> assign(max_minutes, 5).
% 1.67/1.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.67/1.96 % set(auto2) -> set(sort_initial_sos).
% 1.67/1.96 % set(auto2) -> assign(sos_limit, -1).
% 1.67/1.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.67/1.96 % set(auto2) -> assign(max_megs, 400).
% 1.67/1.96 % set(auto2) -> assign(stats, some).
% 1.67/1.96 % set(auto2) -> clear(echo_input).
% 1.67/1.96 % set(auto2) -> set(quiet).
% 1.67/1.96 % set(auto2) -> clear(print_initial_clauses).
% 1.67/1.96 % set(auto2) -> clear(print_given).
% 1.67/1.96 assign(lrs_ticks,-1).
% 1.67/1.96 assign(sos_limit,10000).
% 1.67/1.96 assign(order,kbo).
% 1.67/1.96 set(lex_order_vars).
% 1.67/1.96 clear(print_given).
% 1.67/1.96
% 1.67/1.96 % formulas(sos). % not echoed (2 formulas)
% 1.67/1.96
% 1.67/1.96 ============================== end of input ==========================
% 1.67/1.96
% 1.67/1.96 % From the command line: assign(max_seconds, 300).
% 1.67/1.96
% 1.67/1.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.67/1.96
% 1.67/1.96 % Formulas that are not ordinary clauses:
% 1.67/1.96
% 1.67/1.96 ============================== end of process non-clausal formulas ===
% 1.67/1.96
% 1.67/1.96 ============================== PROCESS INITIAL CLAUSES ===============
% 1.67/1.96
% 1.67/1.96 ============================== PREDICATE ELIMINATION =================
% 1.67/1.96
% 1.67/1.96 ============================== end predicate elimination =============
% 1.67/1.96
% 1.67/1.96 Auto_denials:
% 1.67/1.96 % copying label prove_these_axioms_3 to answer in negative clause
% 1.67/1.96
% 1.67/1.96 Term ordering decisions:
% 1.67/1.96
% 1.67/1.96 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.67/1.96 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.67/1.96
% 1.67/1.96 ============================== end of process initial clauses ========
% 1.67/1.96
% 1.67/1.96 ============================== CLAUSES FOR SEARCH ====================
% 1.67/1.96
% 1.67/1.96 ============================== end of clauses for search =============
% 1.67/1.96
% 1.67/1.96 ============================== SEARCH ================================
% 1.67/1.96
% 1.67/1.96 % Starting search at 0.01 seconds.
% 1.67/1.96
% 1.67/1.96 ============================== PROOF =================================
% 1.67/1.96 % SZS status Unsatisfiable
% 1.67/1.96 % SZS output start Refutation
% 1.67/1.96
% 1.67/1.96 % Proof 1 at 0.99 (+ 0.01) seconds: prove_these_axioms_3.
% 1.67/1.96 % Length of proof is 154.
% 1.67/1.96 % Level of proof is 31.
% 1.67/1.96 % Maximum clause weight is 158.000.
% 1.67/1.96 % Given clauses 50.
% 1.67/1.96
% 1.67/1.96 1 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))) = B # label(single_axiom) # label(axiom). [assumption].
% 1.67/1.96 2 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms_3) # label(negated_conjecture) # answer(prove_these_axioms_3). [assumption].
% 1.67/1.96 3 multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(B,inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),multiply(D,E))). [para(1(a,1),1(a,1,1,1,1,2,1,1)),flip(a)].
% 1.67/1.96 6 inverse(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))) = B. [para(3(a,1),1(a,1,1))].
% 1.67/1.96 7 multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(inverse(B),inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F)),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),multiply(D,V6))). [para(3(a,2),1(a,1,1,1,1,2,1,1)),flip(a)].
% 1.67/1.96 9 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = B. [para(3(a,2),1(a,1))].
% 1.67/1.96 12 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F)))) = inverse(multiply(inverse(multiply(V6,inverse(multiply(D,inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),multiply(V6,V7))). [para(3(a,1),3(a,1,2))].
% 1.67/1.96 27 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(B)),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),B)) = D. [para(9(a,1),1(a,1,1,2))].
% 1.67/1.96 87 multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))) = inverse(multiply(inverse(multiply(E,D)),multiply(E,B))). [para(27(a,1),1(a,1,1,1,1,2)),flip(a)].
% 1.67/1.96 176 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))) = B. [para(87(a,1),1(a,1,1,1,1)),rewrite([9(24)])].
% 1.67/1.96 210 multiply(inverse(inverse(multiply(inverse(multiply(A,inverse(B))),multiply(A,C)))),inverse(multiply(C,inverse(multiply(inverse(C),C))))) = B. [para(87(a,1),9(a,1,1,1)),rewrite([9(25)])].
% 1.67/1.96 271 inverse(multiply(inverse(multiply(A,B)),multiply(A,C))) = inverse(multiply(inverse(multiply(D,B)),multiply(D,C))). [para(87(a,1),87(a,1))].
% 1.67/1.96 344 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)). [para(271(a,1),1(a,1,1,1,1,2,1,1)),rewrite([1(17)])].
% 1.67/1.96 346 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(C,D),inverse(multiply(inverse(multiply(E,D)),multiply(E,D))))))))),multiply(A,multiply(C,D)))) = B. [para(271(a,1),1(a,1,1,1,1,2,1,2,1,2))].
% 1.67/1.96 388 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(inverse(inverse(multiply(C,inverse(multiply(inverse(C),C)))))),inverse(multiply(multiply(A,D),inverse(multiply(inverse(multiply(A,D)),multiply(A,D))))))))),inverse(multiply(inverse(E),inverse(multiply(multiply(inverse(multiply(A,B)),multiply(A,D)),inverse(multiply(inverse(multiply(inverse(multiply(F,B)),multiply(F,D))),multiply(inverse(multiply(A,B)),multiply(A,D))))))))) = inverse(multiply(inverse(multiply(V6,E)),multiply(V6,C))). [para(271(a,1),87(a,1,2,1,2,1,2,1,1))].
% 1.67/1.96 392 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(multiply(inverse(B),B)))))),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)),inverse(multiply(inverse(multiply(E,F)),multiply(E,B))))) = inverse(multiply(inverse(multiply(V6,D)),multiply(V6,inverse(multiply(inverse(F),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C)))))))))). [para(87(a,1),271(a,1,1,2))].
% 1.67/1.96 404 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(E,multiply(inverse(multiply(B,inverse(multiply(inverse(E),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)). [para(1(a,1),344(a,1,1)),flip(a)].
% 1.67/1.96 417 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(271(a,1),344(a,1,1))].
% 1.67/1.96 418 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(344(a,1),344(a,1,2))].
% 1.67/1.96 442 multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(inverse(B),B)))))),multiply(A,C)) = multiply(D,multiply(inverse(inverse(multiply(inverse(multiply(E,D)),multiply(E,B)))),C)). [para(176(a,1),344(a,1,1)),flip(a)].
% 1.67/1.96 621 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(inverse(B),B)))))),multiply(A,C))),multiply(D,E)) = multiply(inverse(multiply(F,multiply(inverse(inverse(multiply(inverse(multiply(V6,D)),multiply(V6,B)))),C))),multiply(F,E)). [para(176(a,1),417(a,1,2,1))].
% 1.67/1.96 676 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)),E)),multiply(inverse(multiply(F,D)),multiply(F,multiply(A,C)))) = multiply(inverse(multiply(V6,E)),multiply(V6,inverse(multiply(inverse(multiply(V7,inverse(multiply(B,inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(V7,V8))))). [para(3(a,1),418(a,2,2,2))].
% 1.67/1.96 677 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),D)),inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F)))) = multiply(inverse(multiply(inverse(multiply(A,V6)),D)),multiply(inverse(multiply(V7,V6)),multiply(V7,C))). [para(3(a,1),418(a,2,2)),flip(a)].
% 1.67/1.96 715 multiply(inverse(multiply(A,B)),multiply(inverse(multiply(C,inverse(multiply(D,inverse(multiply(inverse(D),D)))))),multiply(C,E))) = multiply(inverse(multiply(F,B)),multiply(F,multiply(inverse(inverse(multiply(inverse(multiply(V6,A)),multiply(V6,D)))),E))). [para(176(a,1),418(a,1,1,1,1))].
% 1.67/1.96 734 multiply(inverse(multiply(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)),D)),multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,V7))) = multiply(inverse(multiply(V8,D)),multiply(V8,multiply(inverse(multiply(F,inverse(multiply(multiply(inverse(multiply(V9,inverse(multiply(inverse(B),inverse(multiply(V10,inverse(multiply(inverse(V10),V10)))))))),multiply(V9,V10)),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),V7))). [para(7(a,2),418(a,1,1,1,1))].
% 1.67/1.96 747 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(418(a,1),417(a,1))].
% 1.67/1.96 848 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(inverse(multiply(E,multiply(F,C))),multiply(E,multiply(F,V6)))) = multiply(inverse(multiply(inverse(multiply(A,V7)),D)),multiply(inverse(multiply(V8,V7)),multiply(V8,multiply(B,V6)))). [para(747(a,1),418(a,2,2)),flip(a)].
% 1.67/1.96 1722 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))) = multiply(inverse(D),D). [para(9(a,1),404(a,2,2))].
% 1.67/1.96 1742 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,F))))),inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(A),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),F),inverse(multiply(inverse(multiply(inverse(multiply(D,inverse(multiply(inverse(A),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),F)),multiply(inverse(multiply(D,inverse(multiply(inverse(A),inverse(multiply(E,inverse(multiply(inverse(E),E)))))))),F))))))) = B. [para(404(a,2),176(a,1,1,1,1,1,2))].
% 1.67/1.96 1758 multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)) = inverse(multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(E,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(F,inverse(multiply(inverse(E),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),V7),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(multiply(inverse(E),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),V7)),multiply(inverse(multiply(F,inverse(multiply(inverse(E),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),V7))))))))),multiply(inverse(multiply(V8,multiply(F,V6))),multiply(V8,V7))),inverse(multiply(V9,inverse(multiply(inverse(V9),V9)))))))),multiply(D,V9))). [para(404(a,2),7(a,2,1,1,1,2,1,1,2))].
% 1.67/1.96 1785 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),multiply(inverse(multiply(inverse(multiply(E,F)),multiply(E,C))),V6)) = multiply(V7,multiply(inverse(multiply(inverse(multiply(B,F)),inverse(multiply(inverse(V7),inverse(multiply(D,inverse(multiply(inverse(D),D)))))))),V6)). [para(417(a,1),404(a,1,1,1))].
% 1.67/1.96 1797 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(E,multiply(inverse(multiply(B,inverse(multiply(inverse(E),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),F))) = multiply(inverse(multiply(inverse(multiply(A,V6)),D)),multiply(inverse(multiply(V7,V6)),multiply(V7,F))). [para(404(a,1),418(a,2,2)),flip(a)].
% 1.67/1.96 1819 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,D)))),multiply(inverse(multiply(E,multiply(F,C))),V6)) = multiply(V7,multiply(inverse(multiply(E,inverse(multiply(inverse(V7),inverse(multiply(multiply(F,D),inverse(multiply(inverse(multiply(F,D)),multiply(F,D))))))))),V6)). [para(747(a,1),404(a,1,1,1))].
% 1.67/1.96 1881 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(D,inverse(multiply(inverse(D),D)))))))),E),inverse(multiply(inverse(multiply(F,E)),multiply(F,E))))))))),multiply(inverse(multiply(V6,multiply(C,D))),multiply(V6,E)))) = B. [para(404(a,2),346(a,1,1,2))].
% 1.67/1.96 1999 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),inverse(multiply(inverse(E),inverse(multiply(inverse(multiply(inverse(multiply(F,inverse(multiply(multiply(inverse(multiply(V6,inverse(multiply(inverse(B),inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),multiply(V6,V7)),inverse(multiply(V8,inverse(multiply(inverse(V8),V8)))))))),multiply(F,V8))),inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C))),multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),multiply(A,C)))))))))),inverse(multiply(inverse(multiply(V9,inverse(multiply(D,inverse(multiply(V10,inverse(multiply(inverse(V10),V10)))))))),multiply(V9,V10)))) = inverse(multiply(inverse(multiply(V11,inverse(multiply(E,inverse(multiply(V12,inverse(multiply(inverse(V12),V12)))))))),multiply(V11,V12))). [para(7(a,1),12(a,1,1,1,2,1,2,1,1))].
% 1.67/1.96 2040 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,inverse(multiply(C,inverse(multiply(D,inverse(multiply(inverse(D),D)))))))),multiply(B,D))))),E)),multiply(F,multiply(inverse(multiply(inverse(multiply(V6,inverse(multiply(inverse(C),inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),inverse(multiply(inverse(F),inverse(multiply(multiply(V6,V7),inverse(multiply(inverse(multiply(V6,V7)),multiply(V6,V7))))))))),V8))) = multiply(inverse(multiply(V9,E)),multiply(V9,multiply(A,V8))). [para(12(a,1),418(a,1,2,1,1)),rewrite([6(29)])].
% 1.67/1.96 2046 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(multiply(inverse(multiply(inverse(multiply(E,inverse(multiply(inverse(F),inverse(multiply(V6,inverse(multiply(inverse(V6),V6)))))))),inverse(multiply(inverse(V7),inverse(multiply(multiply(E,V6),inverse(multiply(inverse(multiply(E,V6)),multiply(E,V6))))))))),inverse(multiply(inverse(multiply(V8,inverse(multiply(F,inverse(multiply(V9,inverse(multiply(inverse(V9),V9)))))))),multiply(V8,V9)))),multiply(inverse(multiply(B,inverse(multiply(V7,inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),V10))) = multiply(inverse(multiply(V11,D)),multiply(V11,multiply(A,V10))). [para(12(a,2),418(a,1,2,1))].
% 1.67/1.96 2157 multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(multiply(inverse(multiply(A,C)),multiply(A,C))))))))),inverse(multiply(inverse(multiply(E,inverse(multiply(B,inverse(multiply(F,inverse(multiply(inverse(F),F)))))))),multiply(E,F)))),multiply(inverse(multiply(V6,inverse(multiply(D,inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),V8)) = multiply(V9,multiply(inverse(multiply(V6,inverse(multiply(inverse(V9),inverse(multiply(V7,inverse(multiply(inverse(V7),V7)))))))),V8)). [para(12(a,2),404(a,1,1))].
% 1.67/1.96 2186 inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(inverse(B),inverse(multiply(A,inverse(multiply(inverse(A),A)))))))),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E))))) = B. [para(1722(a,2),1(a,1,1,2))].
% 1.67/1.96 2193 multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(B,multiply(C,D))),multiply(B,multiply(C,D)))))),multiply(A,E)) = multiply(E,inverse(multiply(inverse(E),E))). [para(1722(a,2),3(a,1,1,1,2,1)),rewrite([1(28)])].
% 1.67/1.96 2206 inverse(inverse(multiply(inverse(multiply(inverse(A),inverse(multiply(B,inverse(multiply(A,inverse(multiply(inverse(A),A)))))))),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))))) = B. [para(1722(a,2),6(a,1,1,1,2))].
% 1.67/1.96 2211 multiply(inverse(A),A) = multiply(inverse(B),B). [para(9(a,1),1722(a,1,1,1)),rewrite([9(14)])].
% 1.67/1.96 2232 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C)))),multiply(inverse(D),E)) = multiply(inverse(multiply(F,D)),multiply(F,E)). [para(1722(a,2),344(a,1,1,1))].
% 1.67/1.96 2233 multiply(inverse(multiply(inverse(A),B)),multiply(inverse(multiply(C,multiply(D,E))),multiply(C,multiply(D,E)))) = multiply(inverse(multiply(F,B)),multiply(F,A)). [para(1722(a,2),344(a,1,2))].
% 1.67/1.96 2241 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),inverse(multiply(D,inverse(multiply(inverse(D),D)))))) = D. [para(1722(a,2),176(a,1,1,1,1,1))].
% 1.67/1.96 2274 multiply(inverse(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,multiply(B,C))))),inverse(multiply(inverse(D),inverse(multiply(inverse(inverse(D)),inverse(D)))))) = D. [para(1722(a,2),210(a,1,1,1,1))].
% 1.67/1.96 2404 multiply(inverse(multiply(inverse(A),multiply(B,C))),multiply(inverse(multiply(D,multiply(E,F))),multiply(D,multiply(E,F)))) = multiply(V6,multiply(inverse(multiply(B,inverse(multiply(inverse(V6),inverse(multiply(C,inverse(multiply(inverse(C),C)))))))),A)). [para(1722(a,2),404(a,1,2))].
% 1.67/1.96 2406 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(inverse(multiply(C,inverse(multiply(inverse(C),C)))),multiply(inverse(multiply(B,inverse(multiply(inverse(multiply(E,multiply(F,V6))),multiply(E,multiply(F,V6)))))),D)). [para(1722(a,2),404(a,2,2,1,1,2,1))].
% 1.67/1.96 2417 multiply(inverse(A),A) = c_0. [new_symbol(2211)].
% 1.67/1.96 2424 multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D)) = multiply(inverse(multiply(C,inverse(c_0))),multiply(inverse(multiply(B,inverse(c_0))),D)). [back_rewrite(2406),rewrite([2417(7),2417(15)])].
% 1.67/1.96 2426 multiply(A,multiply(inverse(multiply(B,inverse(multiply(inverse(A),inverse(multiply(C,inverse(c_0))))))),D)) = multiply(inverse(multiply(inverse(D),multiply(B,C))),c_0). [back_rewrite(2404),rewrite([2417(10),2417(9)]),flip(a)].
% 1.67/1.96 2491 multiply(inverse(inverse(c_0)),inverse(multiply(inverse(A),inverse(c_0)))) = A. [back_rewrite(2274),rewrite([2417(6),2417(8)])].
% 1.67/1.96 2511 inverse(multiply(inverse(inverse(c_0)),inverse(multiply(A,inverse(c_0))))) = A. [back_rewrite(2241),rewrite([2417(6),2417(5)])].
% 1.67/1.96 2513 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(C),B)),c_0). [back_rewrite(2233),rewrite([2417(9)]),flip(a)].
% 1.67/1.96 2514 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(inverse(c_0),multiply(inverse(B),A)). [back_rewrite(2232),rewrite([2417(6),2513(9)]),flip(a)].
% 1.67/1.97 2519 inverse(inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(B,inverse(c_0)))))),B)))) = A. [back_rewrite(2206),rewrite([2417(3),2417(15),2514(11)])].
% 1.67/1.97 2526 multiply(inverse(c_0),multiply(inverse(inverse(c_0)),A)) = multiply(A,inverse(c_0)). [back_rewrite(2193),rewrite([2417(6),2513(6),2514(7),2417(9)])].
% 1.67/1.97 2528 inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(B,inverse(c_0)))))),B))) = A. [back_rewrite(2186),rewrite([2417(4),2417(16),2514(12)])].
% 1.67/1.97 2549 multiply(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(c_0))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(c_0))))))),inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(multiply(E,inverse(c_0)))))),E)))),multiply(inverse(multiply(F,inverse(multiply(D,inverse(multiply(V6,inverse(c_0))))))),V7)) = multiply(inverse(c_0),multiply(inverse(multiply(F,V6)),V7)). [back_rewrite(2157),rewrite([2417(3),2417(15),2417(21),2513(29),2514(30),2417(34),2417(45),2426(53),2514(48)])].
% 1.67/1.97 2630 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(inverse(c_0),multiply(inverse(multiply(B,C)),E))) = multiply(inverse(c_0),multiply(inverse(D),multiply(A,E))). [back_rewrite(2046),rewrite([2417(8),2417(20),2417(26),2513(34),2514(35),2417(39),2549(47),2513(17),2514(18)])].
% 1.67/1.97 2636 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(multiply(C,inverse(c_0)))))),C))))),D)),multiply(inverse(c_0),multiply(B,E))) = multiply(inverse(c_0),multiply(inverse(D),multiply(A,E))). [back_rewrite(2040),rewrite([2417(2),2513(10),2514(11),2417(19),2417(31),2426(37),2513(28),2514(29),2514(33),2528(31),2513(26),2514(27)])].
% 1.67/1.97 2668 multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(c_0))))))),inverse(multiply(inverse(D),inverse(multiply(multiply(A,C),inverse(c_0))))))),inverse(multiply(inverse(E),inverse(multiply(inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(B),inverse(multiply(F,inverse(c_0)))))),F)),inverse(multiply(V6,inverse(c_0)))))),V6))),inverse(c_0))))))),inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(D,inverse(multiply(V7,inverse(c_0)))))),V7)))) = inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(E,inverse(multiply(V8,inverse(c_0)))))),V8))). [back_rewrite(1999),rewrite([2417(2),2417(14),2417(22),2513(30),2514(31),2417(33),2513(41),2514(42),2417(45),2513(53),2514(54),2417(57),2513(65),2514(66),2417(67),2417(53),2513(61),2514(62),2417(66),2513(74),2514(75)])].
% 1.67/1.97 2723 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(D,inverse(c_0))))))),E),inverse(c_0))))))),multiply(inverse(c_0),multiply(inverse(multiply(C,D)),E)))) = B. [back_rewrite(1881),rewrite([2417(4),2417(15),2513(24),2514(25)])].
% 1.67/1.97 2736 multiply(inverse(multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(A),B)))),multiply(inverse(multiply(C,multiply(D,A))),E)) = multiply(inverse(c_0),multiply(inverse(multiply(C,multiply(D,B))),E)). [back_rewrite(1819),rewrite([2513(6),2513(4),2514(5),2514(8),2514(7),2417(20),2426(26),2514(21)])].
% 1.67/1.97 2743 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(inverse(c_0),multiply(inverse(B),D))) = multiply(inverse(c_0),multiply(inverse(C),multiply(A,D))). [back_rewrite(1797),rewrite([2417(8),2426(16),2514(11),2630(12),2513(14),2514(15)]),flip(a)].
% 1.67/1.97 2746 multiply(inverse(multiply(inverse(c_0),multiply(inverse(multiply(A,B)),C))),multiply(inverse(multiply(inverse(c_0),multiply(inverse(D),B))),E)) = multiply(inverse(c_0),multiply(inverse(multiply(inverse(multiply(A,D)),C)),E)). [back_rewrite(1785),rewrite([2513(5),2514(6),2513(11),2514(12),2417(20),2426(28),2514(23)])].
% 1.67/1.97 2757 multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(B,inverse(c_0)))))),B)) = inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(C),inverse(multiply(E,inverse(c_0))))))),F),inverse(c_0))))))),multiply(inverse(c_0),multiply(inverse(multiply(D,E)),F))),inverse(multiply(V6,inverse(c_0)))))),V6))). [back_rewrite(1758),rewrite([2417(2),2513(10),2514(11),2417(15),2417(25),2417(36),2417(44),2513(35),2514(36),2417(39),2513(47),2514(48)])].
% 1.67/1.97 2764 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(inverse(c_0),multiply(inverse(multiply(C,D)),E))))),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(D,inverse(c_0))))))),E),inverse(c_0))))) = B. [back_rewrite(1742),rewrite([2513(7),2514(8),2417(14),2417(24),2417(35),2417(43)])].
% 1.67/1.97 2979 multiply(inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(B,inverse(c_0)))))),B)),C)),multiply(inverse(c_0),multiply(inverse(multiply(D,E)),F))) = multiply(inverse(c_0),multiply(inverse(C),multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(V6,inverse(c_0)))))),V6)),inverse(multiply(E,inverse(c_0))))))),F))). [back_rewrite(734),rewrite([2417(2),2513(10),2514(11),2513(18),2514(19),2417(25),2513(33),2514(34),2417(36),2513(45),2514(46)])].
% 1.67/1.97 2984 multiply(inverse(multiply(A,B)),multiply(inverse(c_0),multiply(inverse(inverse(multiply(C,inverse(c_0)))),D))) = multiply(inverse(c_0),multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(c_0),multiply(inverse(A),C)))),D))). [back_rewrite(715),rewrite([2417(4),2513(10),2514(11),2513(18),2514(19),2513(24),2514(25)])].
% 1.67/1.97 2992 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(C,inverse(c_0))))))),D)),inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(multiply(E,inverse(c_0)))))),E)))) = multiply(inverse(c_0),multiply(inverse(D),multiply(A,C))). [back_rewrite(677),rewrite([2417(3),2417(13),2513(21),2514(22),2513(32),2514(33),2743(34)])].
% 1.67/1.97 2993 multiply(inverse(c_0),multiply(inverse(A),multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(B),inverse(multiply(C,inverse(c_0)))))),C)))) = multiply(inverse(multiply(B,A)),c_0). [back_rewrite(676),rewrite([2417(3),2513(18),2514(19),2743(20),2513(14),2514(15),2417(21),2513(29),2514(30),2513(33),2519(30)])].
% 1.67/1.97 3003 multiply(inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(c_0)))),B))),multiply(C,D)) = multiply(inverse(c_0),multiply(inverse(multiply(inverse(inverse(multiply(inverse(c_0),multiply(inverse(C),A)))),B)),D)). [back_rewrite(621),rewrite([2417(2),2513(8),2514(9),2513(16),2514(17),2513(24),2514(25)])].
% 1.67/1.97 3046 multiply(A,multiply(inverse(inverse(multiply(inverse(c_0),multiply(inverse(A),B)))),C)) = multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(c_0)))),C)). [back_rewrite(442),rewrite([2417(2),2513(8),2514(9),2513(13),2514(14)]),flip(a)].
% 1.67/1.97 3053 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,inverse(c_0))))),inverse(multiply(C,inverse(c_0))))))),D)),inverse(multiply(inverse(c_0),multiply(inverse(E),B))))) = inverse(multiply(inverse(c_0),multiply(inverse(D),inverse(multiply(inverse(E),inverse(multiply(multiply(A,C),inverse(c_0)))))))). [back_rewrite(392),rewrite([2417(2),2417(8),2513(20),2514(21),2417(32),2513(36),2514(37)])].
% 1.67/1.97 3057 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(inverse(inverse(multiply(C,inverse(c_0))))),inverse(multiply(multiply(A,D),inverse(c_0))))))),inverse(multiply(inverse(E),inverse(multiply(multiply(inverse(c_0),multiply(inverse(B),D)),inverse(c_0)))))) = inverse(multiply(inverse(c_0),multiply(inverse(E),C))). [back_rewrite(388),rewrite([2417(4),2417(13),2513(22),2514(23),2513(27),2514(28),2513(33),2514(34),2417(35),2513(34),2514(35)])].
% 1.67/1.97 3104 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(inverse(c_0),multiply(inverse(c_0),multiply(inverse(C),E)))) = multiply(inverse(c_0),multiply(inverse(D),multiply(A,multiply(B,E)))). [back_rewrite(848),rewrite([2513(11),2513(9),2514(10),2514(13),2514(12),2513(23),2514(24),2743(25)])].
% 1.67/1.97 3106 multiply(inverse(multiply(A,inverse(c_0))),multiply(inverse(multiply(B,inverse(c_0))),C)) = multiply(inverse(c_0),multiply(inverse(multiply(B,A)),C)). [back_rewrite(2424),rewrite([2513(5),2514(6)]),flip(a)].
% 1.67/1.97 3114 multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(c_0),multiply(inverse(B),C)). [back_rewrite(2513),rewrite([2514(9)])].
% 1.67/1.97 3122 multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(multiply(inverse(c_0),multiply(inverse(inverse(multiply(inverse(B),inverse(multiply(C,inverse(c_0)))))),C)),inverse(multiply(D,inverse(c_0)))))),D))),inverse(c_0)))))),multiply(inverse(c_0),multiply(inverse(inverse(multiply(B,inverse(multiply(E,inverse(c_0)))))),E)))) = inverse(multiply(inverse(c_0),multiply(inverse(inverse(multiply(A,inverse(multiply(F,inverse(c_0)))))),F))). [back_rewrite(2668),rewrite([2992(64),3114(44)])].
% 1.67/1.97 3123 inverse(c_0) = c_0. [para(2417(a,1),2491(a,1,2,1)),rewrite([2417(6)]),flip(a)].
% 1.67/1.97 3124 multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(inverse(multiply(c_0,multiply(inverse(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(B),inverse(multiply(C,c_0))))),C)),inverse(multiply(D,c_0))))),D))),c_0))))),multiply(c_0,multiply(inverse(inverse(multiply(B,inverse(multiply(E,c_0))))),E)))) = inverse(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(F,c_0))))),F))). [back_rewrite(3122),rewrite([3123(2),3123(4),3123(5),3123(7),3123(15),3123(24),3123(30),3123(31),3123(41),3123(42)])].
% 1.67/1.97 3138 multiply(inverse(multiply(A,c_0)),multiply(inverse(multiply(B,c_0)),C)) = multiply(c_0,multiply(inverse(multiply(B,A)),C)). [back_rewrite(3106),rewrite([3123(2),3123(5),3123(10)])].
% 1.67/1.97 3140 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(c_0,multiply(c_0,multiply(inverse(C),E)))) = multiply(c_0,multiply(inverse(D),multiply(A,multiply(B,E)))). [back_rewrite(3104),rewrite([3123(7),3123(8),3123(14)])].
% 1.67/1.97 3175 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(inverse(inverse(multiply(C,c_0)))),inverse(multiply(multiply(A,D),c_0)))))),inverse(multiply(inverse(E),inverse(multiply(multiply(c_0,multiply(inverse(B),D)),c_0))))) = inverse(multiply(c_0,multiply(inverse(E),C))). [back_rewrite(3057),rewrite([3123(4),3123(10),3123(18),3123(22),3123(28)])].
% 1.67/1.97 3177 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,c_0)))),inverse(multiply(C,c_0)))))),D)),inverse(multiply(c_0,multiply(inverse(E),B))))) = inverse(multiply(c_0,multiply(inverse(D),inverse(multiply(inverse(E),inverse(multiply(multiply(A,C),c_0))))))). [back_rewrite(3053),rewrite([3123(2),3123(7),3123(16),3123(23),3123(27)])].
% 1.67/1.97 3183 multiply(A,multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),B)))),C)) = multiply(c_0,multiply(inverse(inverse(multiply(B,c_0))),C)). [back_rewrite(3046),rewrite([3123(2),3123(10),3123(11)])].
% 1.67/1.97 3209 multiply(inverse(multiply(c_0,multiply(inverse(inverse(multiply(A,c_0))),B))),multiply(C,D)) = multiply(c_0,multiply(inverse(multiply(inverse(inverse(multiply(c_0,multiply(inverse(C),A)))),B)),D)). [back_rewrite(3003),rewrite([3123(2),3123(3),3123(12),3123(13)])].
% 1.67/1.97 3214 multiply(c_0,multiply(inverse(A),multiply(c_0,multiply(inverse(inverse(multiply(inverse(B),inverse(multiply(C,c_0))))),C)))) = multiply(inverse(multiply(B,A)),c_0). [back_rewrite(2993),rewrite([3123(2),3123(4),3123(6)])].
% 1.67/1.97 3223 multiply(inverse(multiply(A,B)),multiply(c_0,multiply(inverse(inverse(multiply(C,c_0))),D))) = multiply(c_0,multiply(inverse(B),multiply(inverse(inverse(multiply(c_0,multiply(inverse(A),C)))),D))). [back_rewrite(2984),rewrite([3123(4),3123(5),3123(12),3123(14)])].
% 1.67/1.97 3226 multiply(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B)),C)),multiply(c_0,multiply(inverse(multiply(D,E)),F))) = multiply(c_0,multiply(inverse(C),multiply(inverse(multiply(D,inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),inverse(multiply(V6,c_0))))),V6)),inverse(multiply(E,c_0)))))),F))). [back_rewrite(2979),rewrite([3123(2),3123(3),3123(13),3123(19),3123(21),3123(23),3123(31)])].
% 1.67/1.97 3292 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(c_0,multiply(inverse(multiply(C,D)),E))))),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(D,c_0)))))),E),c_0)))) = B. [back_rewrite(2764),rewrite([3123(4),3123(13),3123(21)])].
% 1.67/1.97 3295 multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B)) = inverse(multiply(c_0,multiply(inverse(inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(multiply(inverse(multiply(D,inverse(multiply(inverse(C),inverse(multiply(E,c_0)))))),F),c_0)))))),multiply(c_0,multiply(inverse(multiply(D,E)),F))),inverse(multiply(V6,c_0))))),V6))). [back_rewrite(2757),rewrite([3123(2),3123(3),3123(11),3123(14),3123(22),3123(29),3123(35)])].
% 1.67/1.97 3303 multiply(inverse(multiply(c_0,multiply(inverse(multiply(A,B)),C))),multiply(inverse(multiply(c_0,multiply(inverse(D),B))),E)) = multiply(c_0,multiply(inverse(multiply(inverse(multiply(A,D)),C)),E)). [back_rewrite(2746),rewrite([3123(2),3123(8),3123(15)])].
% 1.67/1.97 3304 multiply(inverse(multiply(inverse(multiply(A,B)),C)),multiply(c_0,multiply(inverse(B),D))) = multiply(c_0,multiply(inverse(C),multiply(A,D))). [back_rewrite(2743),rewrite([3123(6),3123(11)])].
% 1.67/1.97 3307 multiply(inverse(multiply(c_0,multiply(c_0,multiply(inverse(A),B)))),multiply(inverse(multiply(C,multiply(D,A))),E)) = multiply(c_0,multiply(inverse(multiply(C,multiply(D,B))),E)). [back_rewrite(2736),rewrite([3123(2),3123(3),3123(14)])].
% 1.67/1.97 3308 inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(D,c_0)))))),E),c_0)))))),multiply(c_0,multiply(inverse(multiply(C,D)),E)))) = B. [back_rewrite(2723),rewrite([3123(4),3123(12),3123(19)])].
% 1.67/1.97 3332 multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(c_0,multiply(inverse(inverse(multiply(B,inverse(multiply(C,c_0))))),C))))),D)),multiply(c_0,multiply(B,E))) = multiply(c_0,multiply(inverse(D),multiply(A,E))). [back_rewrite(2636),rewrite([3123(2),3123(3),3123(16),3123(20)])].
% 1.67/1.97 3337 multiply(c_0,multiply(c_0,A)) = multiply(A,c_0). [back_rewrite(2526),rewrite([3123(2),3123(3),3123(3),3123(6)])].
% 1.67/1.97 3344 multiply(inverse(multiply(inverse(A),B)),c_0) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(2514),rewrite([3123(7)])].
% 1.67/1.97 3345 inverse(multiply(c_0,inverse(multiply(A,c_0)))) = A. [back_rewrite(2511),rewrite([3123(2),3123(2),3123(3)])].
% 1.67/1.97 3348 multiply(c_0,inverse(multiply(inverse(A),c_0))) = A. [back_rewrite(2491),rewrite([3123(2),3123(2),3123(4)])].
% 1.67/1.97 3349 multiply(inverse(multiply(multiply(inverse(A),B),c_0)),multiply(inverse(multiply(C,multiply(D,A))),E)) = multiply(c_0,multiply(inverse(multiply(C,multiply(D,B))),E)). [back_rewrite(3307),rewrite([3337(6)])].
% 1.67/1.97 3362 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(multiply(inverse(C),E),c_0)) = multiply(c_0,multiply(inverse(D),multiply(A,multiply(B,E)))). [back_rewrite(3140),rewrite([3337(11)])].
% 1.67/1.97 3363 multiply(c_0,c_0) = c_0. [para(3123(a,1),2417(a,1,1))].
% 1.67/1.97 3371 inverse(multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B))) = multiply(c_0,multiply(inverse(inverse(multiply(inverse(A),c_0))),c_0)). [para(3123(a,1),3124(a,1,2,1,1,1,2,1,1,1,2,1,1,1,1,2,1,1,1,1)),rewrite([3345(10),2417(6),3363(6),3345(9),2417(5),3363(5),3123(4),3363(5),3123(4),3345(13),2417(9),3363(9)]),flip(a)].
% 1.67/1.97 3390 multiply(inverse(multiply(inverse(multiply(A,multiply(c_0,multiply(inverse(inverse(multiply(inverse(B),c_0))),c_0)))),C)),multiply(c_0,multiply(B,D))) = multiply(c_0,multiply(inverse(C),multiply(A,D))). [back_rewrite(3332),rewrite([3371(10)])].
% 1.67/1.97 3401 multiply(c_0,multiply(inverse(inverse(multiply(A,inverse(multiply(B,c_0))))),B)) = multiply(c_0,multiply(inverse(inverse(multiply(A,c_0))),c_0)). [back_rewrite(3295),rewrite([3371(42),3308(34)])].
% 1.67/1.97 3441 multiply(c_0,multiply(inverse(A),multiply(inverse(multiply(B,inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(C),c_0))),c_0)),inverse(multiply(D,c_0)))))),E))) = multiply(inverse(multiply(multiply(c_0,multiply(inverse(inverse(multiply(C,c_0))),c_0)),A)),multiply(c_0,multiply(inverse(multiply(B,D)),E))). [back_rewrite(3226),rewrite([3401(9),3401(28)]),flip(a)].
% 1.67/1.97 3443 multiply(c_0,multiply(inverse(A),multiply(c_0,multiply(inverse(inverse(multiply(inverse(B),c_0))),c_0)))) = multiply(inverse(multiply(B,A)),c_0). [back_rewrite(3214),rewrite([3401(12)])].
% 1.67/1.97 3451 multiply(multiply(c_0,A),c_0) = multiply(c_0,multiply(A,c_0)). [para(3337(a,1),3337(a,1,2)),flip(a)].
% 1.67/1.97 3464 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(inverse(inverse(multiply(C,c_0)))),inverse(multiply(multiply(A,D),c_0)))))),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(multiply(inverse(B),D),c_0)))))) = inverse(multiply(c_0,multiply(inverse(E),C))). [back_rewrite(3175),rewrite([3451(22)])].
% 1.67/1.97 3466 multiply(c_0,A) = multiply(A,c_0). [para(3348(a,1),3337(a,1,2)),rewrite([3344(8),3123(5),3337(6)])].
% 1.67/1.97 3467 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(inverse(inverse(multiply(C,c_0)))),inverse(multiply(c_0,multiply(A,D))))))),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(inverse(B),D)))))) = inverse(multiply(c_0,multiply(inverse(E),C))). [back_rewrite(3464),rewrite([3466(10,R),3466(21,R),3337(22),3466(20,R)])].
% 1.67/1.97 3482 multiply(c_0,multiply(inverse(A),multiply(c_0,inverse(inverse(multiply(inverse(B),c_0)))))) = multiply(c_0,inverse(multiply(B,A))). [back_rewrite(3443),rewrite([3466(10,R),3337(11),3466(9,R),3466(15,R)])].
% 1.67/1.97 3484 multiply(c_0,multiply(inverse(A),multiply(inverse(multiply(B,inverse(multiply(multiply(c_0,inverse(inverse(multiply(inverse(C),c_0)))),inverse(multiply(D,c_0)))))),E))) = multiply(inverse(multiply(multiply(c_0,inverse(inverse(multiply(C,c_0)))),A)),multiply(c_0,multiply(inverse(multiply(B,D)),E))). [back_rewrite(3441),rewrite([3466(10,R),3337(11),3466(9,R),3466(26,R),3337(27),3466(25,R)])].
% 1.67/1.97 3504 multiply(inverse(multiply(inverse(multiply(A,multiply(c_0,inverse(inverse(multiply(inverse(B),c_0)))))),C)),multiply(c_0,multiply(B,D))) = multiply(c_0,multiply(inverse(C),multiply(A,D))). [back_rewrite(3390),rewrite([3466(8,R),3337(9),3466(7,R)])].
% 1.67/1.97 3508 multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),multiply(c_0,multiply(inverse(C),E))) = multiply(c_0,multiply(inverse(D),multiply(A,multiply(B,E)))). [back_rewrite(3362),rewrite([3466(9,R)])].
% 1.67/1.97 3516 multiply(inverse(multiply(c_0,multiply(inverse(A),B))),multiply(inverse(multiply(C,multiply(D,A))),E)) = multiply(c_0,multiply(inverse(multiply(C,multiply(D,B))),E)). [back_rewrite(3349),rewrite([3466(4,R)])].
% 1.67/1.97 3517 multiply(c_0,inverse(multiply(inverse(A),B))) = multiply(c_0,multiply(inverse(B),A)). [back_rewrite(3344),rewrite([3466(5,R)])].
% 1.67/1.97 3518 multiply(c_0,multiply(A,c_0)) = multiply(A,c_0). [back_rewrite(3337),rewrite([3466(3)])].
% 1.67/1.97 3522 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(c_0,multiply(inverse(multiply(C,D)),E))))),inverse(multiply(c_0,multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(multiply(D,c_0)))))),E))))) = B. [back_rewrite(3292),rewrite([3466(21,R)])].
% 1.67/1.97 3523 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(multiply(B,c_0)))),inverse(multiply(C,c_0)))))),D)),inverse(multiply(c_0,multiply(inverse(E),B))))) = inverse(multiply(c_0,multiply(inverse(D),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(A,C)))))))). [back_rewrite(3177),rewrite([3466(27,R)])].
% 1.67/1.97 3547 multiply(A,c_0) = A. [back_rewrite(3348),rewrite([3517(6),3123(3),3466(3),3518(4)])].
% 1.67/1.97 3568 inverse(multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(inverse(inverse(B))),inverse(C))))),D)),inverse(multiply(c_0,multiply(inverse(E),B))))) = inverse(multiply(c_0,multiply(inverse(D),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(A,C)))))))). [back_rewrite(3523),rewrite([3547(2),3547(5)])].
% 1.67/1.97 3569 inverse(multiply(inverse(inverse(multiply(inverse(multiply(A,B)),multiply(c_0,multiply(inverse(multiply(C,D)),E))))),inverse(multiply(c_0,multiply(inverse(multiply(C,inverse(multiply(inverse(A),inverse(D))))),E))))) = B. [back_rewrite(3522),rewrite([3547(14)])].
% 1.67/1.97 3580 multiply(inverse(multiply(inverse(multiply(A,multiply(c_0,inverse(inverse(inverse(B)))))),C)),multiply(c_0,multiply(B,D))) = multiply(c_0,multiply(inverse(C),multiply(A,D))). [back_rewrite(3504),rewrite([3547(4)])].
% 1.67/1.97 3594 multiply(inverse(multiply(multiply(c_0,inverse(inverse(A))),B)),multiply(c_0,multiply(inverse(multiply(C,D)),E))) = multiply(c_0,multiply(inverse(B),multiply(inverse(multiply(C,inverse(multiply(multiply(c_0,inverse(inverse(inverse(A)))),inverse(D))))),E))). [back_rewrite(3484),rewrite([3547(6),3547(9),3547(18)]),flip(a)].
% 1.67/1.97 3596 multiply(c_0,multiply(inverse(A),multiply(c_0,inverse(inverse(inverse(B)))))) = multiply(c_0,inverse(multiply(B,A))). [back_rewrite(3482),rewrite([3547(6)])].
% 1.67/1.97 3600 multiply(inverse(multiply(inverse(multiply(A,B)),inverse(multiply(inverse(inverse(inverse(C))),inverse(multiply(c_0,multiply(A,D))))))),inverse(multiply(inverse(E),inverse(multiply(c_0,multiply(inverse(B),D)))))) = inverse(multiply(c_0,multiply(inverse(E),C))). [back_rewrite(3467),rewrite([3547(4)])].
% 1.67/1.97 3601 multiply(c_0,A) = A. [back_rewrite(3466),rewrite([3547(4)])].
% 1.67/1.97 3603 inverse(inverse(A)) = A. [back_rewrite(3345),rewrite([3547(3),3601(3)])].
% 1.67/1.97 3610 multiply(inverse(multiply(A,B)),multiply(C,D)) = multiply(inverse(B),multiply(multiply(inverse(A),C),D)). [back_rewrite(3223),rewrite([3547(5),3603(5),3601(5),3601(10),3603(10),3601(11)])].
% 1.67/1.97 3613 multiply(inverse(multiply(multiply(inverse(A),B),C)),D) = multiply(inverse(C),multiply(multiply(inverse(B),A),D)). [back_rewrite(3209),rewrite([3547(3),3603(3),3601(3),3610(4),3601(10),3603(10),3601(12)]),flip(a)].
% 1.67/1.97 3615 multiply(A,multiply(multiply(inverse(A),B),C)) = multiply(B,C). [back_rewrite(3183),rewrite([3601(4),3603(4),3547(7),3603(7),3601(7)])].
% 1.67/1.97 3618 multiply(inverse(multiply(A,B)),C) = multiply(inverse(B),multiply(inverse(A),C)). [back_rewrite(3138),rewrite([3547(2),3547(3),3601(9)]),flip(a)].
% 1.67/1.97 3622 multiply(multiply(inverse(A),inverse(multiply(B,C))),multiply(B,multiply(D,inverse(multiply(inverse(E),inverse(multiply(inverse(D),C))))))) = inverse(multiply(inverse(E),A)). [back_rewrite(3600),rewrite([3603(4),3601(6),3618(8),3601(15),3618(17),3603(10),3618(16),3603(6),3603(6),3601(17)])].
% 1.67/1.97 3625 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [back_rewrite(3596),rewrite([3603(5),3601(5),3601(5),3601(7)]),flip(a)].
% 1.67/1.97 3626 multiply(multiply(inverse(A),inverse(B)),multiply(multiply(inverse(C),inverse(D)),E)) = multiply(inverse(A),multiply(multiply(multiply(inverse(B),inverse(C)),inverse(D)),E)). [back_rewrite(3594),rewrite([3603(3),3601(2),3625(2),3625(6),3601(9),3603(13),3601(13),3625(14),3603(12),3603(12),3625(13),3625(12),3601(18)])].
% 1.67/1.97 3635 multiply(multiply(inverse(A),multiply(B,inverse(C))),multiply(C,D)) = multiply(inverse(A),multiply(B,D)). [back_rewrite(3580),rewrite([3603(3),3601(3),3625(3),3603(2),3625(4),3625(4),3603(3),3601(7),3601(11)])].
% 1.67/1.97 3637 multiply(multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),D),multiply(multiply(inverse(D),multiply(C,multiply(B,A))),E)) = E. [back_rewrite(3569),rewrite([3625(2),3625(6),3601(9),3626(8),3625(9),3625(7),3625(7),3603(3),3625(5),3603(3),3603(3),3603(6),3625(6),3625(6),3625(4),3625(3),3603(8),3625(13),3603(11),3603(11),3625(12),3625(11),3601(16),3625(15),3625(15),3603(11),3625(13),3603(11),3603(11),3625(14),3625(5),3625(3),3625(2),3603(7),3625(15),3625(13),3625(13),3603(9),3625(11),3603(9),3603(9),3603(12)])].
% 1.67/1.97 3638 multiply(multiply(inverse(A),B),multiply(multiply(multiply(inverse(B),inverse(C)),inverse(D)),E)) = multiply(multiply(inverse(A),multiply(inverse(C),inverse(D))),E). [back_rewrite(3568),rewrite([3603(2),3625(4),3603(2),3603(2),3625(3),3625(2),3625(7),3625(7),3603(3),3625(5),3603(3),3603(3),3601(8),3625(7),3603(7),3625(8),3625(3),3603(3),3625(7),3625(5),3625(4),3603(9),3601(15),3625(14),3625(17),3625(15),3603(13),3603(13),3603(14),3601(15),3625(14),3625(12),3625(12),3603(16)])].
% 1.67/1.97 3642 multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),D) = multiply(multiply(inverse(A),multiply(inverse(B),inverse(C))),D). [back_rewrite(3516),rewrite([3601(4),3625(3),3603(3),3625(5),3625(4),3638(9),3625(10),3625(9),3601(14)]),flip(a)].
% 1.67/1.97 3645 multiply(multiply(inverse(A),multiply(multiply(B,C),D)),multiply(inverse(D),E)) = multiply(inverse(A),multiply(B,multiply(C,E))). [back_rewrite(3508),rewrite([3625(3),3625(2),3642(6),3625(7),3625(7),3625(5),3603(3),3603(3),3603(4),3601(8),3601(13)])].
% 1.67/1.97 3647 multiply(multiply(inverse(A),multiply(B,C)),multiply(inverse(C),D)) = multiply(inverse(A),multiply(B,D)). [back_rewrite(3304),rewrite([3625(2),3625(5),3625(5),3603(3),3603(3),3601(7),3601(11)])].
% 1.67/1.97 3648 multiply(multiply(inverse(A),multiply(B,C)),multiply(multiply(inverse(C),D),E)) = multiply(multiply(inverse(A),multiply(B,D)),E). [back_rewrite(3303),rewrite([3625(3),3601(6),3625(5),3625(5),3603(3),3603(3),3601(7),3625(6),3603(6),3625(10),3625(13),3625(13),3603(11),3603(11),3601(13)])].
% 1.67/1.97 3658 multiply(multiply(inverse(A),multiply(inverse(B),C)),D) = multiply(inverse(A),multiply(multiply(inverse(B),C),D)). [back_rewrite(3613),rewrite([3625(4),3625(4),3603(4)])].
% 1.67/1.97 3662 multiply(inverse(A),multiply(inverse(B),multiply(B,C))) = multiply(inverse(A),C). [back_rewrite(3622),rewrite([3625(3),3625(9),3603(9),3625(10),3625(8),3603(8),3603(9),3615(9),3635(8),3625(8),3603(8)])].
% 1.67/1.97 3664 multiply(multiply(inverse(A),inverse(B)),C) = multiply(inverse(A),multiply(inverse(B),C)). [back_rewrite(3618),rewrite([3625(2)])].
% 1.67/1.97 3666 multiply(inverse(A),multiply(multiply(inverse(B),multiply(B,A)),C)) = C. [back_rewrite(3637),rewrite([3664(5),3658(6),3664(5),3658(12),3648(11),3662(7)])].
% 1.67/1.97 3667 multiply(inverse(A),multiply(multiply(B,C),D)) = multiply(inverse(A),multiply(B,multiply(C,D))). [back_rewrite(3645),rewrite([3647(7)])].
% 1.67/1.97 3673 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(3666),rewrite([3667(6),3667(5),3662(6)])].
% 1.67/1.97 3681 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(3673(a,1),3615(a,1,2,1)),flip(a)].
% 1.67/1.97 3682 $F # answer(prove_these_axioms_3). [resolve(3681,a,2,a)].
% 1.67/1.97
% 1.67/1.97 % SZS output end Refutation
% 1.67/1.97 ============================== end of proof ==========================
% 1.67/1.97
% 1.67/1.97 ============================== STATISTICS ============================
% 1.67/1.97
% 1.67/1.97 Given=50. Generated=8599. Kept=3681. proofs=1.
% 1.67/1.97 Usable=11. Sos=10. Demods=20. Limbo=0, Disabled=3661. Hints=0.
% 1.67/1.97 Megabytes=10.56.
% 1.67/1.97 User_CPU=0.99, System_CPU=0.01, Wall_clock=1.
% 1.67/1.97
% 1.67/1.97 ============================== end of statistics =====================
% 1.67/1.97
% 1.67/1.97 ============================== end of search =========================
% 1.67/1.97
% 1.67/1.97 THEOREM PROVED
% 1.67/1.97 % SZS status Unsatisfiable
% 1.67/1.97
% 1.67/1.97 Exiting with 1 proof.
% 1.67/1.97
% 1.67/1.97 Process 18505 exit (max_proofs) Tue Jun 14 04:00:17 2022
% 1.67/1.97 Prover9 interrupted
%------------------------------------------------------------------------------