TSTP Solution File: GRP057-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP057-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:16:58 EDT 2022
% Result : Unsatisfiable 1.54s 1.81s
% Output : Refutation 1.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP057-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 04:12:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.54/1.81 ============================== Prover9 ===============================
% 1.54/1.81 Prover9 (32) version 2009-11A, November 2009.
% 1.54/1.81 Process 30868 was started by sandbox2 on n019.cluster.edu,
% 1.54/1.81 Tue Jun 14 04:12:10 2022
% 1.54/1.81 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_30625_n019.cluster.edu".
% 1.54/1.81 ============================== end of head ===========================
% 1.54/1.81
% 1.54/1.81 ============================== INPUT =================================
% 1.54/1.81
% 1.54/1.81 % Reading from file /tmp/Prover9_30625_n019.cluster.edu
% 1.54/1.81
% 1.54/1.81 set(prolog_style_variables).
% 1.54/1.81 set(auto2).
% 1.54/1.81 % set(auto2) -> set(auto).
% 1.54/1.81 % set(auto) -> set(auto_inference).
% 1.54/1.81 % set(auto) -> set(auto_setup).
% 1.54/1.81 % set(auto_setup) -> set(predicate_elim).
% 1.54/1.81 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.54/1.81 % set(auto) -> set(auto_limits).
% 1.54/1.81 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.54/1.81 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.54/1.81 % set(auto) -> set(auto_denials).
% 1.54/1.81 % set(auto) -> set(auto_process).
% 1.54/1.81 % set(auto2) -> assign(new_constants, 1).
% 1.54/1.81 % set(auto2) -> assign(fold_denial_max, 3).
% 1.54/1.81 % set(auto2) -> assign(max_weight, "200.000").
% 1.54/1.81 % set(auto2) -> assign(max_hours, 1).
% 1.54/1.81 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.54/1.81 % set(auto2) -> assign(max_seconds, 0).
% 1.54/1.81 % set(auto2) -> assign(max_minutes, 5).
% 1.54/1.81 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.54/1.81 % set(auto2) -> set(sort_initial_sos).
% 1.54/1.81 % set(auto2) -> assign(sos_limit, -1).
% 1.54/1.81 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.54/1.81 % set(auto2) -> assign(max_megs, 400).
% 1.54/1.81 % set(auto2) -> assign(stats, some).
% 1.54/1.81 % set(auto2) -> clear(echo_input).
% 1.54/1.81 % set(auto2) -> set(quiet).
% 1.54/1.81 % set(auto2) -> clear(print_initial_clauses).
% 1.54/1.81 % set(auto2) -> clear(print_given).
% 1.54/1.81 assign(lrs_ticks,-1).
% 1.54/1.81 assign(sos_limit,10000).
% 1.54/1.81 assign(order,kbo).
% 1.54/1.81 set(lex_order_vars).
% 1.54/1.81 clear(print_given).
% 1.54/1.81
% 1.54/1.81 % formulas(sos). % not echoed (2 formulas)
% 1.54/1.81
% 1.54/1.81 ============================== end of input ==========================
% 1.54/1.81
% 1.54/1.81 % From the command line: assign(max_seconds, 300).
% 1.54/1.81
% 1.54/1.81 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.54/1.81
% 1.54/1.81 % Formulas that are not ordinary clauses:
% 1.54/1.81
% 1.54/1.81 ============================== end of process non-clausal formulas ===
% 1.54/1.81
% 1.54/1.81 ============================== PROCESS INITIAL CLAUSES ===============
% 1.54/1.81
% 1.54/1.81 ============================== PREDICATE ELIMINATION =================
% 1.54/1.81
% 1.54/1.81 ============================== end predicate elimination =============
% 1.54/1.81
% 1.54/1.81 Auto_denials:
% 1.54/1.81 % copying label prove_these_axioms to answer in negative clause
% 1.54/1.81
% 1.54/1.81 Term ordering decisions:
% 1.54/1.81
% 1.54/1.81 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 1.54/1.81 Function symbol KB weights: a1=1. a2=1. a3=1. b1=1. b2=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.54/1.81
% 1.54/1.81 ============================== end of process initial clauses ========
% 1.54/1.81
% 1.54/1.81 ============================== CLAUSES FOR SEARCH ====================
% 1.54/1.81
% 1.54/1.81 ============================== end of clauses for search =============
% 1.54/1.81
% 1.54/1.81 ============================== SEARCH ================================
% 1.54/1.81
% 1.54/1.81 % Starting search at 0.01 seconds.
% 1.54/1.81
% 1.54/1.81 ============================== PROOF =================================
% 1.54/1.81 % SZS status Unsatisfiable
% 1.54/1.81 % SZS output start Refutation
% 1.54/1.81
% 1.54/1.81 % Proof 1 at 0.80 (+ 0.01) seconds: prove_these_axioms.
% 1.54/1.81 % Length of proof is 150.
% 1.54/1.81 % Level of proof is 36.
% 1.54/1.81 % Maximum clause weight is 72.000.
% 1.54/1.81 % Given clauses 56.
% 1.54/1.81
% 1.54/1.81 1 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),D),inverse(multiply(B,D))))) = C # label(single_axiom) # label(axiom). [assumption].
% 1.54/1.81 2 multiply(inverse(a1),a1) != multiply(inverse(b1),b1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 1.54/1.81 3 multiply(inverse(b1),b1) != multiply(inverse(a1),a1) | multiply(multiply(inverse(b2),b2),a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [copy(2),flip(a)].
% 1.54/1.81 4 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(inverse(A)),C))),F),inverse(multiply(E,F)))). [para(1(a,1),1(a,1,2,1,1,1,1,2))].
% 1.54/1.81 5 multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(A),E)))),B))),F),inverse(multiply(D,F))))))))) = E. [para(1(a,1),1(a,1,2,1,1))].
% 1.54/1.81 7 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(inverse(A))),D))),E),inverse(multiply(C,E)))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))). [para(4(a,1),1(a,1,2,1,1,1,1,2))].
% 1.54/1.81 9 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(A),C))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(B)),E))),V7),inverse(multiply(V6,V7)))))))) = C. [para(4(a,1),1(a,1,2,1,2,1))].
% 1.54/1.81 11 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),multiply(inverse(B),C)))),D),inverse(multiply(A,D)))) = C. [para(4(a,1),1(a,1))].
% 1.54/1.81 15 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D)))))) = C. [para(4(a,2),1(a,1,2))].
% 1.54/1.81 82 multiply(inverse(inverse(A)),multiply(inverse(A),B)) = multiply(inverse(C),multiply(C,B)). [para(11(a,1),15(a,1,2,2)),flip(a)].
% 1.54/1.81 86 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),D),inverse(multiply(A,D)))) = C. [para(11(a,1),11(a,1,1,1,1,1,2,1,1)),rewrite([11(15)])].
% 1.54/1.81 88 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(inverse(A),D))))) = C. [para(82(a,1),1(a,1,2,1,1,1,1))].
% 1.54/1.81 110 multiply(inverse(A),multiply(A,B)) = multiply(inverse(C),multiply(C,B)). [para(82(a,1),82(a,1))].
% 1.54/1.81 120 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(E,D)))))) = multiply(E,C). [para(110(a,1),15(a,1,2,2,1,1,1,1))].
% 1.54/1.81 121 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(B),multiply(B,C)),inverse(multiply(D,multiply(multiply(inverse(D),E),C))))))) = E. [para(110(a,1),15(a,1,2,2,1,1))].
% 1.54/1.81 123 multiply(inverse(inverse(A)),multiply(inverse(B),multiply(B,C))) = multiply(inverse(D),multiply(D,multiply(A,C))). [para(110(a,1),110(a,1,2))].
% 1.54/1.81 187 multiply(inverse(inverse(A)),multiply(inverse(B),multiply(B,C))) = multiply(inverse(inverse(A)),multiply(inverse(D),multiply(D,C))). [para(110(a,1),123(a,2,2))].
% 1.54/1.81 224 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,multiply(multiply(inverse(C),multiply(inverse(D),multiply(D,E))),B))))) = E. [para(110(a,1),86(a,1,1,1))].
% 1.54/1.81 261 multiply(A,inverse(multiply(multiply(inverse(B),multiply(B,C)),inverse(multiply(inverse(A),multiply(multiply(inverse(D),multiply(D,E)),C)))))) = E. [para(110(a,1),88(a,1,2,1,1))].
% 1.54/1.81 418 multiply(inverse(A),multiply(inverse(B),multiply(B,C))) = multiply(inverse(A),multiply(inverse(D),multiply(D,C))). [para(86(a,1),187(a,1,1,1)),rewrite([86(16)])].
% 1.54/1.81 438 multiply(A,multiply(inverse(B),multiply(B,C))) = multiply(A,multiply(inverse(D),multiply(D,C))). [para(86(a,1),418(a,1,1)),rewrite([86(15)])].
% 1.54/1.81 445 multiply(inverse(A),multiply(A,multiply(inverse(B),multiply(B,C)))) = multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,C)))). [para(438(a,1),110(a,1,2))].
% 1.54/1.81 511 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(inverse(A))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F))))))),V6),inverse(multiply(C,V6)))))),V7),inverse(multiply(B,V7))))) = inverse(multiply(multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(V8),multiply(inverse(inverse(inverse(V9))),E))),V10),inverse(multiply(V8,V10))))),V11),inverse(multiply(V9,V11)))). [para(4(a,1),7(a,2,1,1,1,1))].
% 1.54/1.81 774 multiply(inverse(A),multiply(A,inverse(inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(multiply(inverse(multiply(inverse(C),multiply(C,D))),inverse(multiply(E,F))))),V6))),V7),inverse(multiply(B,V7))))))) = multiply(multiply(inverse(multiply(inverse(E),V6)),F),D). [para(4(a,1),120(a,1,2,2,1))].
% 1.54/1.81 793 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(E,D)))))) = multiply(E,inverse(multiply(F,inverse(multiply(V6,inverse(multiply(multiply(inverse(multiply(inverse(V7),multiply(inverse(inverse(multiply(inverse(V6),multiply(inverse(B),C)))),F))),V8),inverse(multiply(V7,V8))))))))). [para(5(a,1),120(a,1,2,2,1,1,1,1,2))].
% 1.54/1.81 805 multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),D),E) = multiply(inverse(F),multiply(F,inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(V6,E))),inverse(multiply(A,D))),C)))). [para(86(a,1),120(a,1,2,2,1,2)),flip(a)].
% 1.54/1.81 1173 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(inverse(inverse(C)),multiply(multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,F)))),B))))) = multiply(C,F). [para(445(a,1),224(a,1,1,2,1,2,1))].
% 1.54/1.81 1236 multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,inverse(C)))) = B. [para(15(a,1),261(a,1,2,1,2,1)),rewrite([15(14)])].
% 1.54/1.81 1303 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(inverse(C),multiply(multiply(inverse(D),multiply(D,E)),B))))) = inverse(multiply(multiply(inverse(F),multiply(F,V6)),inverse(multiply(V7,multiply(multiply(inverse(V7),multiply(inverse(C),E)),V6))))). [para(261(a,1),224(a,1,1,2,1,2,1,2,2)),flip(a)].
% 1.54/1.81 1313 multiply(A,inverse(multiply(B,inverse(B)))) = inverse(multiply(multiply(inverse(multiply(inverse(C),A)),D),inverse(multiply(C,D)))). [para(4(a,1),1236(a,1,1,2)),rewrite([1(13)])].
% 1.54/1.81 1323 multiply(inverse(inverse(A)),multiply(inverse(multiply(inverse(B),multiply(B,C))),C)) = multiply(inverse(D),multiply(D,multiply(A,inverse(multiply(E,inverse(E)))))). [para(1236(a,1),123(a,1,2,2))].
% 1.54/1.81 1336 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,inverse(multiply(F,inverse(F))))))). [para(1236(a,1),445(a,1,2,2,2))].
% 1.54/1.81 1350 multiply(inverse(multiply(inverse(A),multiply(A,B))),B) = multiply(inverse(multiply(inverse(C),multiply(C,D))),D). [para(1236(a,1),120(a,1,2))].
% 1.54/1.81 1357 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),C),inverse(multiply(D,multiply(multiply(inverse(D),E),inverse(multiply(F,inverse(F)))))))))) = E. [para(1236(a,1),121(a,1,2,2,1,1,2))].
% 1.54/1.81 1507 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(E),F))),inverse(multiply(multiply(inverse(multiply(inverse(V6),V7)),V8),inverse(multiply(V6,V8))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V9),multiply(inverse(inverse(D)),V7))),V10),inverse(multiply(V9,V10)))))))),inverse(F))))) = multiply(E,C). [para(9(a,1),120(a,1,2,2,1,2,1))].
% 1.54/1.81 1586 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),C),inverse(multiply(D,E)))))) = multiply(D,E). [para(1350(a,1),15(a,1,2,2,1,1))].
% 1.54/1.81 1588 multiply(inverse(inverse(A)),multiply(inverse(multiply(inverse(B),multiply(B,C))),C)) = A. [para(1350(a,1),15(a,1,2)),rewrite([15(11)])].
% 1.54/1.81 1650 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(C,inverse(C))))) = B. [back_rewrite(1357),rewrite([1586(18)])].
% 1.54/1.81 1652 multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,inverse(C)))))) = B. [back_rewrite(1323),rewrite([1588(8)]),flip(a)].
% 1.54/1.81 1743 multiply(inverse(A),multiply(A,multiply(B,multiply(C,inverse(multiply(D,inverse(D))))))) = multiply(inverse(inverse(B)),C). [para(1652(a,1),110(a,1,2)),flip(a)].
% 1.54/1.81 1764 multiply(inverse(inverse(inverse(A))),A) = multiply(inverse(inverse(inverse(B))),B). [para(1652(a,1),445(a,1,2)),rewrite([1743(13)])].
% 1.54/1.81 1798 multiply(A,inverse(multiply(B,inverse(B)))) = multiply(A,inverse(multiply(C,inverse(C)))). [para(1652(a,1),1236(a,1,1))].
% 1.54/1.81 1800 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = inverse(multiply(inverse(D),multiply(D,inverse(multiply(E,inverse(E)))))). [para(1350(a,1),1652(a,1,2,2))].
% 1.54/1.81 1802 multiply(inverse(inverse(inverse(A))),A) = multiply(inverse(B),multiply(B,multiply(inverse(multiply(inverse(C),multiply(C,D))),D))). [back_rewrite(1336),rewrite([1743(17)]),flip(a)].
% 1.54/1.81 1803 multiply(inverse(inverse(inverse(A))),A) = c_0. [new_symbol(1764)].
% 1.54/1.81 1804 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = c_0. [back_rewrite(1802),rewrite([1803(4)]),flip(a)].
% 1.54/1.81 1806 inverse(multiply(inverse(A),multiply(A,inverse(multiply(B,inverse(B)))))) = c_0. [back_rewrite(1800),rewrite([1804(8)]),flip(a)].
% 1.54/1.81 1823 multiply(inverse(A),multiply(A,B)) = multiply(inverse(inverse(inverse(inverse(B)))),c_0). [para(1803(a,1),110(a,1,2)),flip(a)].
% 1.54/1.81 1828 multiply(inverse(inverse(inverse(inverse(multiply(A,B))))),c_0) = multiply(inverse(inverse(A)),multiply(inverse(inverse(inverse(inverse(B)))),c_0)). [para(1803(a,1),123(a,1,2,2)),rewrite([1823(13)]),flip(a)].
% 1.54/1.81 1848 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),B),inverse(c_0))))))),c_0) = multiply(inverse(inverse(inverse(B))),A). [para(1803(a,1),120(a,1,2,2,1,2,1)),rewrite([1823(4),1823(15)])].
% 1.54/1.81 1857 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(B,multiply(multiply(inverse(B),C),A))))))))),c_0) = C. [para(1803(a,1),121(a,1,2,2,1,1,2)),rewrite([1823(16)])].
% 1.54/1.81 1863 multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),B))),inverse(multiply(multiply(inverse(inverse(inverse(inverse(B)))),c_0),inverse(c_0)))) = A. [para(1803(a,1),261(a,1,2,1,2,1)),rewrite([1823(3),1823(12)])].
% 1.54/1.81 1866 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(B,inverse(B))))) = A. [para(1803(a,1),1650(a,1,2,1))].
% 1.54/1.81 1871 inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0)) = c_0. [back_rewrite(1806),rewrite([1823(6)])].
% 1.54/1.81 2032 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(C),D))),inverse(multiply(multiply(inverse(multiply(inverse(E),F)),V6),inverse(multiply(E,V6))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V7),multiply(inverse(inverse(B)),F))),V8),inverse(multiply(V7,V8)))))))),inverse(D))))))),c_0) = multiply(C,A). [back_rewrite(1507),rewrite([1823(4),1823(42)])].
% 1.54/1.81 2134 inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(inverse(B),multiply(multiply(inverse(inverse(inverse(inverse(C)))),c_0),A))))) = inverse(multiply(multiply(inverse(inverse(inverse(inverse(D)))),c_0),inverse(multiply(E,multiply(multiply(inverse(E),multiply(inverse(B),C)),D))))). [back_rewrite(1303),rewrite([1823(3),1823(10),1823(21)])].
% 1.54/1.81 2252 inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(inverse(inverse(B)),multiply(multiply(inverse(inverse(inverse(inverse(inverse(inverse(C)))))),multiply(inverse(inverse(inverse(inverse(c_0)))),c_0)),A))))) = multiply(B,C). [back_rewrite(1173),rewrite([1823(3),1823(12),1823(17),1828(20)])].
% 1.54/1.81 2484 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),inverse(multiply(B,C))),D)))))),c_0) = multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(inverse(inverse(D)))),c_0))),C),A). [back_rewrite(805),rewrite([1823(4),1823(15),1823(26)]),flip(a)].
% 1.54/1.81 2493 multiply(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(D,C)))))))),c_0) = multiply(D,inverse(multiply(E,inverse(multiply(F,inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(multiply(inverse(F),multiply(inverse(A),B)))),E))),V7),inverse(multiply(V6,V7))))))))). [back_rewrite(793),rewrite([1823(11)])].
% 1.54/1.81 2510 multiply(inverse(inverse(inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(B)))),c_0)),inverse(multiply(C,D))))),E))),F),inverse(multiply(A,F))))))))),c_0) = multiply(multiply(inverse(multiply(inverse(C),E)),D),B). [back_rewrite(774),rewrite([1823(5),1823(25)])].
% 1.54/1.81 2849 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(B),C))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F)))))),multiply(inverse(inverse(inverse(inverse(inverse(C))))),c_0))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(A)),E))),V7),inverse(multiply(V6,V7)))))),V8) = multiply(B,V8). [back_rewrite(2032),rewrite([2484(45)])].
% 1.54/1.81 2936 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(c_0,inverse(multiply(C,inverse(C)))))),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),A)),F),inverse(multiply(E,F)))). [para(1866(a,1),4(a,2,1,1,1,1,2))].
% 1.54/1.81 2937 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(E))),multiply(inverse(inverse(A)),C))),multiply(c_0,inverse(multiply(F,inverse(F))))),inverse(E))). [para(1866(a,1),4(a,2,1,2,1))].
% 1.54/1.81 2939 multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),C))),D),inverse(multiply(A,D))) = multiply(inverse(multiply(B,inverse(multiply(multiply(inverse(multiply(inverse(E),C)),F),inverse(multiply(E,F)))))),multiply(c_0,inverse(multiply(V6,inverse(V6))))). [para(4(a,2),1866(a,1,1,1)),flip(a)].
% 1.54/1.81 2941 multiply(inverse(A),inverse(multiply(B,inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(C),A))),B))),E),inverse(multiply(D,E))))))))) = multiply(c_0,inverse(multiply(F,inverse(F)))). [para(1866(a,1),5(a,1,2,1,2,1,2,1,1,1,1,2,1,1,1,2))].
% 1.54/1.81 2945 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(inverse(A))),D))),multiply(c_0,inverse(multiply(E,inverse(E))))),inverse(C))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))). [para(1866(a,1),7(a,1,2,1,1,1,1,2,1,2,1))].
% 1.54/1.81 2949 multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))) = multiply(inverse(multiply(D,inverse(multiply(multiply(inverse(multiply(inverse(E),inverse(multiply(multiply(inverse(multiply(inverse(F),multiply(inverse(inverse(inverse(D))),B))),V6),inverse(multiply(F,V6)))))),V7),inverse(multiply(E,V7)))))),multiply(c_0,inverse(multiply(V8,inverse(V8))))). [para(7(a,2),1866(a,1,1,1)),flip(a)].
% 1.54/1.81 2956 multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0) = multiply(c_0,inverse(multiply(B,inverse(B)))). [para(1866(a,1),1650(a,1,2,1)),rewrite([1823(6)])].
% 1.54/1.81 2957 inverse(multiply(c_0,inverse(multiply(A,inverse(A))))) = c_0. [para(1866(a,1),1803(a,1))].
% 1.54/1.81 2969 multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(c_0),C))),F),inverse(multiply(E,F)))). [para(2957(a,1),4(a,2,1,1,1,1,2,1,1))].
% 1.54/1.81 2970 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(c_0),multiply(inverse(inverse(A)),C))),inverse(multiply(E,inverse(E)))),c_0)). [para(2957(a,1),4(a,2,1,2))].
% 1.54/1.81 2979 multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(c_0)),D))),E),inverse(multiply(C,E)))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(inverse(V6),D)),V7),inverse(multiply(V6,V7)))). [para(2957(a,1),7(a,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1))].
% 1.54/1.81 2981 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(c_0),inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(inverse(inverse(inverse(A))),C))),D),inverse(multiply(B,D)))))),inverse(multiply(E,inverse(E)))),c_0))) = inverse(multiply(multiply(inverse(multiply(inverse(F),C)),V6),inverse(multiply(F,V6)))). [para(2957(a,1),7(a,1,2,1,2))].
% 1.54/1.81 2982 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),inverse(multiply(multiply(inverse(multiply(inverse(C),multiply(inverse(inverse(inverse(A))),D))),E),inverse(multiply(C,E)))))),F),inverse(multiply(B,F))))) = inverse(multiply(multiply(inverse(multiply(c_0,D)),V6),inverse(multiply(multiply(c_0,inverse(multiply(V7,inverse(V7)))),V6)))). [para(2957(a,1),7(a,2,1,1,1,1,1))].
% 1.54/1.81 2992 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(multiply(c_0,inverse(multiply(C,inverse(C)))),c_0)))) = B. [para(2957(a,1),1650(a,1,2,2,1,2))].
% 1.54/1.81 2998 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(multiply(c_0,inverse(multiply(B,inverse(B)))),c_0)))) = A. [para(2957(a,1),1866(a,1,2,2,1,2))].
% 1.54/1.81 3008 multiply(c_0,multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),B)) = multiply(inverse(inverse(inverse(inverse(B)))),c_0). [para(2957(a,1),1823(a,1,1))].
% 1.54/1.81 3011 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(multiply(B,inverse(B)))))))),multiply(inverse(A),C))),c_0),c_0))) = C. [para(1871(a,1),1(a,1,2,1,2))].
% 1.54/1.81 3012 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),C),inverse(multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(D,inverse(D))))))),c_0),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(inverse(A)),B))),F),inverse(multiply(E,F)))). [para(1871(a,1),4(a,1,2,1,1,1,1,1))].
% 1.54/1.81 3014 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(inverse(inverse(multiply(B,inverse(B)))))))),C)),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(A)),C))),E),inverse(multiply(D,E)))). [para(1871(a,1),4(a,1,2,1,2))].
% 1.54/1.81 3016 multiply(multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0),inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D))))) = inverse(multiply(multiply(inverse(multiply(inverse(E),multiply(inverse(c_0),C))),F),inverse(multiply(E,F)))). [para(1871(a,1),4(a,2,1,1,1,1,2,1,1))].
% 1.54/1.81 3198 inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))). [para(1798(a,1),1(a,1,2,1,1,1,1,2)),rewrite([1(14)])].
% 1.54/1.81 3226 multiply(inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))),inverse(multiply(B,inverse(B)))) = c_0. [para(1798(a,1),1803(a,1))].
% 1.54/1.81 3232 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))))) = A. [para(1798(a,1),1866(a,1,2,2,1))].
% 1.54/1.81 3268 multiply(inverse(inverse(inverse(multiply(A,inverse(A))))),multiply(B,inverse(B))) = c_0. [para(3198(a,1),1803(a,1,1,1,1))].
% 1.54/1.81 3274 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(3198(a,1),1866(a,1,1,1)),rewrite([1866(10)])].
% 1.54/1.81 3305 multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)). [para(3274(a,1),1650(a,1,2))].
% 1.54/1.81 3309 multiply(inverse(inverse(inverse(inverse(inverse(A))))),c_0) = inverse(inverse(inverse(A))). [para(3274(a,1),1823(a,1,2)),rewrite([3305(4)]),flip(a)].
% 1.54/1.81 3310 inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))) = c_0. [para(3274(a,1),1871(a,1,1,1,1,1,1,1,1)),rewrite([3309(9)])].
% 1.54/1.81 3311 multiply(multiply(inverse(c_0),c_0),c_0) = multiply(A,inverse(A)). [para(1871(a,1),3274(a,1,2)),rewrite([3310(6)])].
% 1.54/1.81 3324 inverse(c_0) = c_0. [back_rewrite(3268),rewrite([3305(8),3310(6)])].
% 1.54/1.81 3356 multiply(multiply(c_0,c_0),inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(c_0,B))),E),inverse(multiply(D,E)))). [back_rewrite(3016),rewrite([3310(6),3324(2),3324(15)])].
% 1.54/1.81 3358 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),C),inverse(multiply(multiply(c_0,c_0),C))))) = inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(A)),B))),E),inverse(multiply(D,E)))). [back_rewrite(3012),rewrite([3310(10),3324(6)])].
% 1.54/1.81 3363 multiply(c_0,inverse(multiply(A,inverse(A)))) = multiply(c_0,c_0). [back_rewrite(2956),rewrite([3310(6),3324(2)]),flip(a)].
% 1.54/1.81 3364 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(B),C))),inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(D,F)))))),inverse(inverse(inverse(C))))),inverse(inverse(multiply(multiply(inverse(multiply(inverse(V6),multiply(inverse(inverse(A)),E))),V7),inverse(multiply(V6,V7)))))),V8) = multiply(B,V8). [back_rewrite(2849),rewrite([3309(22)])].
% 1.54/1.81 3411 inverse(inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(B)))),c_0)),inverse(multiply(C,D))))),E))),F),inverse(multiply(A,F))))))) = multiply(multiply(inverse(multiply(inverse(C),E)),D),B). [back_rewrite(2510),rewrite([3309(28)])].
% 1.54/1.81 3420 multiply(A,inverse(multiply(B,inverse(multiply(C,inverse(multiply(multiply(inverse(multiply(inverse(D),multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(E),F)))),B))),V6),inverse(multiply(D,V6))))))))) = inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(E),F)),V7),inverse(multiply(A,V7)))))). [back_rewrite(2493),rewrite([3309(14)]),flip(a)].
% 1.54/1.81 3518 inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(B,multiply(multiply(inverse(B),C),A))))))) = C. [back_rewrite(1857),rewrite([3309(19)])].
% 1.54/1.81 3519 inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(inverse(A)))),c_0)),B),c_0)))) = multiply(inverse(inverse(inverse(B))),A). [back_rewrite(1848),rewrite([3324(10),3309(17)])].
% 1.54/1.81 3522 multiply(c_0,c_0) = c_0. [back_rewrite(3226),rewrite([3310(6),3363(5)])].
% 1.54/1.81 3538 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),C))),D),inverse(multiply(A,D)))) = multiply(B,inverse(multiply(multiply(inverse(multiply(c_0,C)),c_0),c_0))). [back_rewrite(3014),rewrite([3310(6),3324(2),3324(2)]),flip(a)].
% 1.54/1.81 3539 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,multiply(inverse(A),B))),c_0),c_0))) = B. [back_rewrite(3011),rewrite([3310(6),3324(2),3324(2)])].
% 1.54/1.81 3541 multiply(A,inverse(A)) = c_0. [back_rewrite(3311),rewrite([3324(2),3522(3),3522(3)]),flip(a)].
% 1.54/1.81 3550 inverse(multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C)))) = inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0)). [back_rewrite(2981),rewrite([3324(2),3538(13),3541(15),3324(15),3539(19)]),flip(a)].
% 1.54/1.81 3552 multiply(c_0,inverse(multiply(multiply(inverse(multiply(c_0,inverse(multiply(multiply(inverse(multiply(c_0,multiply(c_0,A))),c_0),c_0)))),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)). [back_rewrite(2979),rewrite([3541(3),3324(3),3522(3),3324(5),3324(5),3550(12),3550(19),3550(28)])].
% 1.54/1.81 3553 inverse(multiply(multiply(inverse(multiply(c_0,multiply(inverse(inverse(A)),B))),c_0),c_0)) = multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0))). [back_rewrite(2970),rewrite([3550(8),3324(11),3541(17),3324(17)]),flip(a)].
% 1.54/1.81 3554 inverse(multiply(multiply(inverse(multiply(c_0,multiply(c_0,A))),c_0),c_0)) = multiply(c_0,inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0))). [back_rewrite(2969),rewrite([3541(3),3324(3),3522(3),3550(9),3324(13),3550(20)]),flip(a)].
% 1.54/1.81 3561 inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(inverse(inverse(B)),multiply(inverse(inverse(inverse(inverse(C)))),A))))) = multiply(B,C). [back_rewrite(2252),rewrite([3324(16),3324(16),3324(16),3324(16),3522(17),3309(16)])].
% 1.54/1.81 3565 multiply(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),B))),inverse(multiply(multiply(inverse(inverse(inverse(inverse(B)))),c_0),c_0))) = A. [back_rewrite(1863),rewrite([3324(17)])].
% 1.54/1.81 3597 multiply(c_0,multiply(c_0,A)) = multiply(inverse(inverse(inverse(inverse(A)))),c_0). [back_rewrite(3008),rewrite([3541(4),3324(4),3522(4)])].
% 1.54/1.81 3598 multiply(inverse(inverse(A)),c_0) = A. [back_rewrite(2998),rewrite([3541(6),3324(6),3522(6),3522(6),3324(5),3522(5)])].
% 1.54/1.81 3602 multiply(A,multiply(multiply(inverse(A),B),c_0)) = B. [back_rewrite(2992),rewrite([3541(5),3324(5),3522(5),3522(5),3324(4)])].
% 1.54/1.81 3608 inverse(multiply(multiply(inverse(multiply(c_0,A)),B),inverse(multiply(c_0,B)))) = inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)). [back_rewrite(2982),rewrite([3550(13),3553(13),3550(18),3539(19),3541(15),3324(15),3522(15)]),flip(a)].
% 1.54/1.81 3620 multiply(multiply(inverse(multiply(inverse(A),B)),C),inverse(multiply(A,C))) = multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0). [back_rewrite(2949),rewrite([3550(20),3553(20),3550(25),3539(26),3541(19),3324(19),3522(19),3598(18)])].
% 1.54/1.81 3623 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(B))),multiply(inverse(inverse(inverse(A))),C))),c_0),inverse(B))))),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(c_0,C)),c_0),c_0)). [back_rewrite(2945),rewrite([3541(13),3324(13),3522(13),3620(21),3620(30)])].
% 1.54/1.81 3627 multiply(inverse(A),inverse(multiply(B,inverse(multiply(C,multiply(multiply(inverse(C),A),inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0)))))))) = c_0. [back_rewrite(2941),rewrite([3620(13),3553(14),3541(20),3324(20),3522(20)])].
% 1.54/1.81 3628 multiply(inverse(multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0)))),c_0) = multiply(multiply(inverse(multiply(c_0,multiply(inverse(inverse(A)),B))),c_0),c_0). [back_rewrite(2939),rewrite([3620(10),3620(17),3541(23),3324(23),3522(23)]),flip(a)].
% 1.54/1.81 3629 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,B)),c_0),c_0))) = inverse(multiply(multiply(inverse(multiply(inverse(inverse(inverse(C))),multiply(inverse(inverse(A)),B))),c_0),inverse(C))). [back_rewrite(2937),rewrite([3620(7),3541(20),3324(20),3522(20)])].
% 1.54/1.81 3630 inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)) = multiply(A,c_0). [back_rewrite(2936),rewrite([3541(4),3324(4),3522(4),3620(8),3522(3),3324(2),3522(3),3522(3),3324(2),3620(9)]),flip(a)].
% 1.54/1.81 3671 inverse(inverse(inverse(multiply(multiply(inverse(inverse(multiply(inverse(inverse(inverse(A))),inverse(multiply(B,C))))),D),c_0)))) = multiply(multiply(inverse(multiply(inverse(B),D)),C),A). [back_rewrite(3411),rewrite([3598(7),3620(16),3630(17)])].
% 1.54/1.81 3684 multiply(multiply(inverse(inverse(A)),B),c_0) = multiply(A,multiply(B,c_0)). [back_rewrite(3358),rewrite([3522(7),3608(9),3630(8),3620(13),3630(14)]),flip(a)].
% 1.54/1.81 3685 multiply(c_0,multiply(A,c_0)) = inverse(multiply(inverse(A),c_0)). [back_rewrite(3356),rewrite([3522(3),3620(8),3630(9),3620(13),3597(8),3598(10),3598(9)])].
% 1.54/1.81 3766 inverse(multiply(multiply(inverse(A),c_0),c_0)) = multiply(multiply(A,c_0),c_0). [back_rewrite(511),rewrite([3620(12),3630(13),3620(14),3630(15),3684(9),3620(13),3630(14),3602(9),3620(15),3630(16),3684(10),3620(13),3685(8),3598(11)]),flip(a)].
% 1.54/1.81 3810 multiply(A,inverse(multiply(B,inverse(multiply(C,multiply(multiply(multiply(c_0,multiply(inverse(inverse(multiply(inverse(C),multiply(inverse(D),E)))),B)),c_0),c_0)))))) = inverse(inverse(inverse(multiply(multiply(inverse(multiply(inverse(D),E)),F),inverse(multiply(A,F)))))). [back_rewrite(3420),rewrite([3620(14),3766(15)])].
% 1.54/1.81 3835 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(A),multiply(inverse(B),C))),multiply(multiply(multiply(c_0,D),c_0),c_0))),inverse(inverse(inverse(C))))),inverse(multiply(multiply(multiply(c_0,multiply(inverse(inverse(A)),D)),c_0),c_0))),E) = multiply(B,E). [back_rewrite(3364),rewrite([3620(12),3766(13),3620(28),3766(29)])].
% 1.54/1.81 3938 multiply(A,c_0) = inverse(inverse(A)). [back_rewrite(3305),rewrite([3541(2)])].
% 1.54/1.81 3949 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(3232),rewrite([3541(5),3541(6),3324(6),3938(6),3324(5),3324(5),3324(5),3938(5),3324(4),3324(4),3938(4)])].
% 1.54/1.81 3989 inverse(inverse(multiply(c_0,A))) = inverse(inverse(A)). [back_rewrite(1313),rewrite([3541(2),3324(2),3938(2),3620(9),3938(7),3938(9),3949(8)]),flip(a)].
% 1.54/1.81 3994 multiply(c_0,inverse(inverse(A))) = inverse(inverse(A)). [back_rewrite(3552),rewrite([3597(6),3949(6),3938(4),3938(7),3949(6),3938(5),3949(6),3938(6),3989(5),3938(6),3949(5),3938(9),3989(8),3938(9),3949(8)])].
% 1.54/1.81 3996 inverse(inverse(A)) = A. [back_rewrite(3554),rewrite([3597(4),3949(4),3938(2),3938(5),3949(4),3938(3),3949(4),3938(6),3989(5),3938(6),3949(5),3994(4)]),flip(a)].
% 1.54/1.81 4000 multiply(multiply(A,B),inverse(B)) = A. [back_rewrite(3565),rewrite([3996(2),3996(2),3938(2),3996(2),3996(3),3996(3),3996(3),3938(3),3996(3),3938(3),3996(3)])].
% 1.54/1.81 4003 inverse(multiply(A,inverse(multiply(B,multiply(C,A))))) = multiply(B,C). [back_rewrite(3561),rewrite([3996(2),3996(2),3938(2),3996(2),3996(2),3996(2),3996(2)])].
% 1.54/1.81 4005 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(3519),rewrite([3996(2),3996(2),3938(2),3996(2),3938(4),3996(4),3996(4),3996(5)])].
% 1.54/1.81 4006 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(3518),rewrite([3996(2),3996(2),3938(2),3996(2),4003(7),3996(5)])].
% 1.54/1.81 4049 inverse(multiply(A,multiply(inverse(multiply(B,A)),C))) = multiply(inverse(C),B). [back_rewrite(2134),rewrite([3996(2),3996(2),3938(2),3996(2),3996(3),3996(3),3938(3),3996(3),4005(4),3996(7),3996(7),3938(7),3996(7),4003(14),4006(10)])].
% 1.54/1.81 4052 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(1823),rewrite([3996(5),3996(5),3938(5),3996(5)])].
% 1.54/1.81 4059 multiply(A,multiply(c_0,B)) = multiply(A,B). [back_rewrite(3629),rewrite([3938(5),3996(4),3938(5),3996(4),3996(4),3996(5),3996(6),4005(7),3938(8),4005(7),4005(7),4000(8),3996(6)])].
% 1.54/1.81 4060 inverse(multiply(c_0,multiply(A,B))) = inverse(multiply(A,B)). [back_rewrite(3628),rewrite([3938(5),3996(4),3938(5),3996(4),3996(4),4059(3),3938(4),3996(3),3996(5),3938(8),3996(7),3938(8),3996(7)]),flip(a)].
% 1.54/1.81 4061 multiply(inverse(A),A) = c_0. [back_rewrite(3627),rewrite([3938(8),3996(7),3938(8),3996(7),3996(7),4059(6),4003(8),4006(4)])].
% 1.54/1.81 4062 multiply(c_0,A) = A. [back_rewrite(3623),rewrite([3996(3),3996(4),4005(6),4005(4),3938(6),3996(6),4000(6),4005(4),4060(5),4005(3),3938(4),4005(3),4005(3),3938(4),4005(3),4005(3),4005(3),4006(3),3938(5),3996(4),3938(5),3996(4),3996(4)]),flip(a)].
% 1.54/1.81 4074 multiply(multiply(multiply(inverse(A),B),C),D) = multiply(inverse(A),multiply(multiply(B,C),D)). [back_rewrite(3671),rewrite([3996(2),4005(5),3996(3),3938(6),4005(5),4005(5),4005(5),4005(5),4005(5),4005(7)]),flip(a)].
% 1.54/1.81 4088 multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(B,C))),D) = multiply(A,D). [back_rewrite(3835),rewrite([4005(5),4005(3),4062(5),3938(5),3996(5),3938(5),3996(5),4074(4),4005(5),3996(6),4000(6),3996(4),3996(5),4062(5),3938(5),3996(5),3938(5),3996(5)])].
% 1.54/1.81 4089 multiply(inverse(multiply(multiply(A,B),inverse(multiply(C,B)))),D) = multiply(C,multiply(inverse(A),D)). [back_rewrite(3810),rewrite([4005(6),4005(4),4062(7),3938(7),4005(6),4005(6),3938(7),4005(6),4005(6),4049(7),4006(5),4005(3),4005(6),4074(9),4005(10),4005(10),4005(10)]),flip(a)].
% 1.54/1.81 4117 multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # answer(prove_these_axioms). [back_rewrite(3),rewrite([4061(4),4061(5),4061(7),4062(6)]),xx(a),xx(b)].
% 1.54/1.81 4124 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(4052(a,1),4000(a,1,1))].
% 1.54/1.81 4127 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(4000(a,1),4124(a,1,2,1)),flip(a)].
% 1.54/1.81 4145 multiply(multiply(multiply(A,B),multiply(inverse(B),inverse(C))),D) = multiply(A,multiply(inverse(C),D)). [back_rewrite(4089),rewrite([4127(3),4127(6),4127(4),3996(2),3996(2),4127(3)])].
% 1.54/1.81 4146 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,C). [back_rewrite(4088),rewrite([4127(4),4145(7)])].
% 1.54/1.81 4162 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(4000(a,1),4146(a,1,1)),rewrite([3996(2)]),flip(a)].
% 1.54/1.81 4163 $F # answer(prove_these_axioms). [resolve(4162,a,4117,a)].
% 1.54/1.81
% 1.54/1.81 % SZS output end Refutation
% 1.54/1.81 ============================== end of proof ==========================
% 1.54/1.81
% 1.54/1.81 ============================== STATISTICS ============================
% 1.54/1.81
% 1.54/1.81 Given=56. Generated=8290. Kept=4161. proofs=1.
% 1.54/1.81 Usable=12. Sos=5. Demods=16. Limbo=0, Disabled=4145. Hints=0.
% 1.54/1.81 Megabytes=8.00.
% 1.54/1.81 User_CPU=0.80, System_CPU=0.01, Wall_clock=1.
% 1.54/1.81
% 1.54/1.81 ============================== end of statistics =====================
% 1.54/1.81
% 1.54/1.81 ============================== end of search =========================
% 1.54/1.81
% 1.54/1.81 THEOREM PROVED
% 1.54/1.81 % SZS status Unsatisfiable
% 1.54/1.81
% 1.54/1.81 Exiting with 1 proof.
% 1.54/1.81
% 1.54/1.81 Process 30868 exit (max_proofs) Tue Jun 14 04:12:11 2022
% 1.54/1.81 Prover9 interrupted
%------------------------------------------------------------------------------