TSTP Solution File: GRP429-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP429-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:19:03 EDT 2022
% Result : Unsatisfiable 1.58s 1.84s
% Output : Refutation 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP429-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 05:29:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.58/1.84 ============================== Prover9 ===============================
% 1.58/1.84 Prover9 (32) version 2009-11A, November 2009.
% 1.58/1.84 Process 27072 was started by sandbox on n026.cluster.edu,
% 1.58/1.84 Tue Jun 14 05:29:52 2022
% 1.58/1.84 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26712_n026.cluster.edu".
% 1.58/1.84 ============================== end of head ===========================
% 1.58/1.84
% 1.58/1.84 ============================== INPUT =================================
% 1.58/1.84
% 1.58/1.84 % Reading from file /tmp/Prover9_26712_n026.cluster.edu
% 1.58/1.84
% 1.58/1.84 set(prolog_style_variables).
% 1.58/1.84 set(auto2).
% 1.58/1.84 % set(auto2) -> set(auto).
% 1.58/1.84 % set(auto) -> set(auto_inference).
% 1.58/1.84 % set(auto) -> set(auto_setup).
% 1.58/1.84 % set(auto_setup) -> set(predicate_elim).
% 1.58/1.84 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.58/1.84 % set(auto) -> set(auto_limits).
% 1.58/1.84 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.58/1.84 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.58/1.84 % set(auto) -> set(auto_denials).
% 1.58/1.84 % set(auto) -> set(auto_process).
% 1.58/1.84 % set(auto2) -> assign(new_constants, 1).
% 1.58/1.84 % set(auto2) -> assign(fold_denial_max, 3).
% 1.58/1.84 % set(auto2) -> assign(max_weight, "200.000").
% 1.58/1.84 % set(auto2) -> assign(max_hours, 1).
% 1.58/1.84 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.58/1.84 % set(auto2) -> assign(max_seconds, 0).
% 1.58/1.84 % set(auto2) -> assign(max_minutes, 5).
% 1.58/1.84 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.58/1.84 % set(auto2) -> set(sort_initial_sos).
% 1.58/1.84 % set(auto2) -> assign(sos_limit, -1).
% 1.58/1.84 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.58/1.84 % set(auto2) -> assign(max_megs, 400).
% 1.58/1.84 % set(auto2) -> assign(stats, some).
% 1.58/1.84 % set(auto2) -> clear(echo_input).
% 1.58/1.84 % set(auto2) -> set(quiet).
% 1.58/1.84 % set(auto2) -> clear(print_initial_clauses).
% 1.58/1.84 % set(auto2) -> clear(print_given).
% 1.58/1.84 assign(lrs_ticks,-1).
% 1.58/1.84 assign(sos_limit,10000).
% 1.58/1.84 assign(order,kbo).
% 1.58/1.84 set(lex_order_vars).
% 1.58/1.84 clear(print_given).
% 1.58/1.84
% 1.58/1.84 % formulas(sos). % not echoed (2 formulas)
% 1.58/1.84
% 1.58/1.84 ============================== end of input ==========================
% 1.58/1.84
% 1.58/1.84 % From the command line: assign(max_seconds, 300).
% 1.58/1.84
% 1.58/1.84 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.58/1.84
% 1.58/1.84 % Formulas that are not ordinary clauses:
% 1.58/1.84
% 1.58/1.84 ============================== end of process non-clausal formulas ===
% 1.58/1.84
% 1.58/1.84 ============================== PROCESS INITIAL CLAUSES ===============
% 1.58/1.84
% 1.58/1.84 ============================== PREDICATE ELIMINATION =================
% 1.58/1.84
% 1.58/1.84 ============================== end predicate elimination =============
% 1.58/1.84
% 1.58/1.84 Auto_denials:
% 1.58/1.84 % copying label prove_these_axioms_3 to answer in negative clause
% 1.58/1.84
% 1.58/1.84 Term ordering decisions:
% 1.58/1.84
% 1.58/1.84 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.58/1.84 Function symbol KB weights: a3=1. b3=1. c3=1. multiply=1. inverse=0.
% 1.58/1.84
% 1.58/1.84 ============================== end of process initial clauses ========
% 1.58/1.84
% 1.58/1.84 ============================== CLAUSES FOR SEARCH ====================
% 1.58/1.84
% 1.58/1.84 ============================== end of clauses for search =============
% 1.58/1.84
% 1.58/1.84 ============================== SEARCH ================================
% 1.58/1.84
% 1.58/1.84 % Starting search at 0.01 seconds.
% 1.58/1.84
% 1.58/1.84 ============================== PROOF =================================
% 1.58/1.84 % SZS status Unsatisfiable
% 1.58/1.84 % SZS output start Refutation
% 1.58/1.84
% 1.58/1.84 % Proof 1 at 0.77 (+ 0.01) seconds: prove_these_axioms_3.
% 1.58/1.84 % Length of proof is 145.
% 1.58/1.84 % Level of proof is 36.
% 1.58/1.84 % Maximum clause weight is 72.000.
% 1.58/1.84 % Given clauses 55.
% 1.58/1.84
% 1.58/1.84 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].
% 1.58/1.84 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].
% 1.58/1.84 3 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))].
% 1.58/1.84 4 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))].
% 1.58/1.84 6 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(3(a,1),1(a,1,2,1,1,1,1,2))].
% 1.58/1.84 8 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(3(a,1),1(a,1,2,1,2,1))].
% 1.58/1.84 10 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(inverse(B)),multiply(inverse(B),C)))),D),inverse(multiply(A,D)))) = C. [para(3(a,1),1(a,1))].
% 1.58/1.84 14 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),C)),D),inverse(multiply(B,D)))))) = C. [para(3(a,2),1(a,1,2))].
% 1.58/1.84 81 multiply(inverse(inverse(A)),multiply(inverse(A),B)) = multiply(inverse(C),multiply(C,B)). [para(10(a,1),14(a,1,2,2)),flip(a)].
% 1.58/1.84 85 inverse(multiply(multiply(inverse(multiply(inverse(A),multiply(inverse(B),multiply(B,C)))),D),inverse(multiply(A,D)))) = C. [para(10(a,1),10(a,1,1,1,1,1,2,1,1)),rewrite([10(15)])].
% 1.58/1.84 87 multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(inverse(A),D))))) = C. [para(81(a,1),1(a,1,2,1,1,1,1))].
% 1.58/1.84 109 multiply(inverse(A),multiply(A,B)) = multiply(inverse(C),multiply(C,B)). [para(81(a,1),81(a,1))].
% 1.58/1.84 119 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),D),inverse(multiply(E,D)))))) = multiply(E,C). [para(109(a,1),14(a,1,2,2,1,1,1,1))].
% 1.58/1.84 120 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(B),multiply(B,C)),inverse(multiply(D,multiply(multiply(inverse(D),E),C))))))) = E. [para(109(a,1),14(a,1,2,2,1,1))].
% 1.58/1.84 122 multiply(inverse(inverse(A)),multiply(inverse(B),multiply(B,C))) = multiply(inverse(D),multiply(D,multiply(A,C))). [para(109(a,1),109(a,1,2))].
% 1.58/1.84 186 multiply(inverse(inverse(A)),multiply(inverse(B),multiply(B,C))) = multiply(inverse(inverse(A)),multiply(inverse(D),multiply(D,C))). [para(109(a,1),122(a,2,2))].
% 1.58/1.84 223 inverse(multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,multiply(multiply(inverse(C),multiply(inverse(D),multiply(D,E))),B))))) = E. [para(109(a,1),85(a,1,1,1))].
% 1.58/1.84 260 multiply(A,inverse(multiply(multiply(inverse(B),multiply(B,C)),inverse(multiply(inverse(A),multiply(multiply(inverse(D),multiply(D,E)),C)))))) = E. [para(109(a,1),87(a,1,2,1,1))].
% 1.58/1.84 417 multiply(inverse(A),multiply(inverse(B),multiply(B,C))) = multiply(inverse(A),multiply(inverse(D),multiply(D,C))). [para(85(a,1),186(a,1,1,1)),rewrite([85(16)])].
% 1.58/1.84 437 multiply(A,multiply(inverse(B),multiply(B,C))) = multiply(A,multiply(inverse(D),multiply(D,C))). [para(85(a,1),417(a,1,1)),rewrite([85(15)])].
% 1.58/1.84 444 multiply(inverse(A),multiply(A,multiply(inverse(B),multiply(B,C)))) = multiply(inverse(D),multiply(D,multiply(inverse(E),multiply(E,C)))). [para(437(a,1),109(a,1,2))].
% 1.58/1.84 510 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(3(a,1),6(a,2,1,1,1,1))].
% 1.58/1.84 773 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(3(a,1),119(a,1,2,2,1))].
% 1.58/1.84 792 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(4(a,1),119(a,1,2,2,1,1,1,1,2))].
% 1.58/1.84 804 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(85(a,1),119(a,1,2,2,1,2)),flip(a)].
% 1.58/1.84 1172 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(444(a,1),223(a,1,1,2,1,2,1))].
% 1.58/1.84 1235 multiply(multiply(inverse(A),multiply(A,B)),inverse(multiply(C,inverse(C)))) = B. [para(14(a,1),260(a,1,2,1,2,1)),rewrite([14(14)])].
% 1.58/1.84 1302 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(260(a,1),223(a,1,1,2,1,2,1,2,2)),flip(a)].
% 1.58/1.84 1312 multiply(A,inverse(multiply(B,inverse(B)))) = inverse(multiply(multiply(inverse(multiply(inverse(C),A)),D),inverse(multiply(C,D)))). [para(3(a,1),1235(a,1,1,2)),rewrite([1(13)])].
% 1.58/1.84 1322 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(1235(a,1),122(a,1,2,2))].
% 1.58/1.84 1335 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(1235(a,1),444(a,1,2,2,2))].
% 1.58/1.84 1349 multiply(inverse(multiply(inverse(A),multiply(A,B))),B) = multiply(inverse(multiply(inverse(C),multiply(C,D))),D). [para(1235(a,1),119(a,1,2))].
% 1.58/1.84 1356 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(1235(a,1),120(a,1,2,2,1,1,2))].
% 1.58/1.84 1506 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(8(a,1),119(a,1,2,2,1,2,1))].
% 1.58/1.84 1585 multiply(inverse(A),multiply(A,inverse(multiply(multiply(inverse(multiply(inverse(B),multiply(B,C))),C),inverse(multiply(D,E)))))) = multiply(D,E). [para(1349(a,1),14(a,1,2,2,1,1))].
% 1.58/1.84 1587 multiply(inverse(inverse(A)),multiply(inverse(multiply(inverse(B),multiply(B,C))),C)) = A. [para(1349(a,1),14(a,1,2)),rewrite([14(11)])].
% 1.58/1.84 1649 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(C,inverse(C))))) = B. [back_rewrite(1356),rewrite([1585(18)])].
% 1.58/1.84 1651 multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,inverse(C)))))) = B. [back_rewrite(1322),rewrite([1587(8)]),flip(a)].
% 1.58/1.84 1742 multiply(inverse(A),multiply(A,multiply(B,multiply(C,inverse(multiply(D,inverse(D))))))) = multiply(inverse(inverse(B)),C). [para(1651(a,1),109(a,1,2)),flip(a)].
% 1.58/1.84 1763 multiply(inverse(inverse(inverse(A))),A) = multiply(inverse(inverse(inverse(B))),B). [para(1651(a,1),444(a,1,2)),rewrite([1742(13)])].
% 1.58/1.84 1797 multiply(A,inverse(multiply(B,inverse(B)))) = multiply(A,inverse(multiply(C,inverse(C)))). [para(1651(a,1),1235(a,1,1))].
% 1.58/1.84 1799 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(1349(a,1),1651(a,1,2,2))].
% 1.58/1.84 1801 multiply(inverse(inverse(inverse(A))),A) = multiply(inverse(B),multiply(B,multiply(inverse(multiply(inverse(C),multiply(C,D))),D))). [back_rewrite(1335),rewrite([1742(17)]),flip(a)].
% 1.58/1.84 1802 multiply(inverse(inverse(inverse(A))),A) = c_0. [new_symbol(1763)].
% 1.58/1.84 1803 multiply(inverse(A),multiply(A,multiply(inverse(multiply(inverse(B),multiply(B,C))),C))) = c_0. [back_rewrite(1801),rewrite([1802(4)]),flip(a)].
% 1.58/1.84 1805 inverse(multiply(inverse(A),multiply(A,inverse(multiply(B,inverse(B)))))) = c_0. [back_rewrite(1799),rewrite([1803(8)]),flip(a)].
% 1.58/1.84 1822 multiply(inverse(A),multiply(A,B)) = multiply(inverse(inverse(inverse(inverse(B)))),c_0). [para(1802(a,1),109(a,1,2)),flip(a)].
% 1.58/1.84 1827 multiply(inverse(inverse(inverse(inverse(multiply(A,B))))),c_0) = multiply(inverse(inverse(A)),multiply(inverse(inverse(inverse(inverse(B)))),c_0)). [para(1802(a,1),122(a,1,2,2)),rewrite([1822(13)]),flip(a)].
% 1.58/1.84 1847 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(1802(a,1),119(a,1,2,2,1,2,1)),rewrite([1822(4),1822(15)])].
% 1.58/1.84 1856 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(1802(a,1),120(a,1,2,2,1,1,2)),rewrite([1822(16)])].
% 1.58/1.84 1862 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(1802(a,1),260(a,1,2,1,2,1)),rewrite([1822(3),1822(12)])].
% 1.58/1.84 1865 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(B,inverse(B))))) = A. [para(1802(a,1),1649(a,1,2,1))].
% 1.58/1.84 1870 inverse(multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0)) = c_0. [back_rewrite(1805),rewrite([1822(6)])].
% 1.58/1.84 2031 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(1506),rewrite([1822(4),1822(42)])].
% 1.58/1.84 2133 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(1302),rewrite([1822(3),1822(10),1822(21)])].
% 1.58/1.84 2251 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(1172),rewrite([1822(3),1822(12),1822(17),1827(20)])].
% 1.58/1.84 2483 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(804),rewrite([1822(4),1822(15),1822(26)]),flip(a)].
% 1.58/1.84 2492 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(792),rewrite([1822(11)])].
% 1.58/1.84 2509 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(773),rewrite([1822(5),1822(25)])].
% 1.58/1.84 2848 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(2031),rewrite([2483(45)])].
% 1.58/1.84 2935 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(1865(a,1),3(a,2,1,1,1,1,2))].
% 1.58/1.84 2936 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(1865(a,1),3(a,2,1,2,1))].
% 1.58/1.84 2938 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(3(a,2),1865(a,1,1,1)),flip(a)].
% 1.58/1.84 2944 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(1865(a,1),6(a,1,2,1,1,1,1,2,1,2,1))].
% 1.58/1.84 2948 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(6(a,2),1865(a,1,1,1)),flip(a)].
% 1.58/1.84 2955 multiply(inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))),c_0) = multiply(c_0,inverse(multiply(B,inverse(B)))). [para(1865(a,1),1649(a,1,2,1)),rewrite([1822(6)])].
% 1.58/1.84 2956 inverse(multiply(c_0,inverse(multiply(A,inverse(A))))) = c_0. [para(1865(a,1),1802(a,1))].
% 1.58/1.84 2968 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(2956(a,1),3(a,2,1,1,1,1,2,1,1))].
% 1.58/1.84 2969 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(2956(a,1),3(a,2,1,2))].
% 1.58/1.84 2978 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(2956(a,1),6(a,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1))].
% 1.58/1.84 2980 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(2956(a,1),6(a,1,2,1,2))].
% 1.58/1.84 2981 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(2956(a,1),6(a,2,1,1,1,1,1))].
% 1.58/1.84 2991 multiply(A,multiply(multiply(inverse(A),B),inverse(multiply(multiply(c_0,inverse(multiply(C,inverse(C)))),c_0)))) = B. [para(2956(a,1),1649(a,1,2,2,1,2))].
% 1.58/1.84 2997 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(multiply(c_0,inverse(multiply(B,inverse(B)))),c_0)))) = A. [para(2956(a,1),1865(a,1,2,2,1,2))].
% 1.58/1.84 3007 multiply(c_0,multiply(multiply(c_0,inverse(multiply(A,inverse(A)))),B)) = multiply(inverse(inverse(inverse(inverse(B)))),c_0). [para(2956(a,1),1822(a,1,1))].
% 1.58/1.84 3010 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(1870(a,1),1(a,1,2,1,2))].
% 1.58/1.84 3011 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(1870(a,1),3(a,1,2,1,1,1,1,1))].
% 1.58/1.84 3013 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(1870(a,1),3(a,1,2,1,2))].
% 1.58/1.84 3015 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(1870(a,1),3(a,2,1,1,1,1,2,1,1))].
% 1.58/1.84 3197 inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))). [para(1797(a,1),1(a,1,2,1,1,1,1,2)),rewrite([1(14)])].
% 1.58/1.84 3225 multiply(inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))),inverse(multiply(B,inverse(B)))) = c_0. [para(1797(a,1),1802(a,1))].
% 1.58/1.84 3231 multiply(inverse(inverse(A)),multiply(c_0,inverse(multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C))))))) = A. [para(1797(a,1),1865(a,1,2,2,1))].
% 1.58/1.84 3267 multiply(inverse(inverse(inverse(multiply(A,inverse(A))))),multiply(B,inverse(B))) = c_0. [para(3197(a,1),1802(a,1,1,1,1))].
% 1.58/1.84 3273 multiply(A,inverse(A)) = multiply(B,inverse(B)). [para(3197(a,1),1865(a,1,1,1)),rewrite([1865(10)])].
% 1.58/1.84 3304 multiply(A,multiply(B,inverse(B))) = inverse(inverse(A)). [para(3273(a,1),1649(a,1,2))].
% 1.58/1.84 3308 multiply(inverse(inverse(inverse(inverse(inverse(A))))),c_0) = inverse(inverse(inverse(A))). [para(3273(a,1),1822(a,1,2)),rewrite([3304(4)]),flip(a)].
% 1.58/1.84 3309 inverse(inverse(inverse(inverse(multiply(A,inverse(A)))))) = c_0. [para(3273(a,1),1870(a,1,1,1,1,1,1,1,1)),rewrite([3308(9)])].
% 1.58/1.84 3310 multiply(multiply(inverse(c_0),c_0),c_0) = multiply(A,inverse(A)). [para(1870(a,1),3273(a,1,2)),rewrite([3309(6)])].
% 1.58/1.84 3323 inverse(c_0) = c_0. [back_rewrite(3267),rewrite([3304(8),3309(6)])].
% 1.58/1.84 3355 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(3015),rewrite([3309(6),3323(2),3323(15)])].
% 1.58/1.84 3357 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(3011),rewrite([3309(10),3323(6)])].
% 1.58/1.84 3362 multiply(c_0,inverse(multiply(A,inverse(A)))) = multiply(c_0,c_0). [back_rewrite(2955),rewrite([3309(6),3323(2)]),flip(a)].
% 1.58/1.84 3363 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(2848),rewrite([3308(22)])].
% 1.58/1.84 3410 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(2509),rewrite([3308(28)])].
% 1.58/1.84 3419 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(2492),rewrite([3308(14)]),flip(a)].
% 1.58/1.84 3517 inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(inverse(A)))),c_0),inverse(multiply(B,multiply(multiply(inverse(B),C),A))))))) = C. [back_rewrite(1856),rewrite([3308(19)])].
% 1.58/1.84 3518 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(1847),rewrite([3323(10),3308(17)])].
% 1.58/1.84 3521 multiply(c_0,c_0) = c_0. [back_rewrite(3225),rewrite([3309(6),3362(5)])].
% 1.58/1.84 3537 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(3013),rewrite([3309(6),3323(2),3323(2)]),flip(a)].
% 1.58/1.84 3538 multiply(A,inverse(multiply(multiply(inverse(multiply(c_0,multiply(inverse(A),B))),c_0),c_0))) = B. [back_rewrite(3010),rewrite([3309(6),3323(2),3323(2)])].
% 1.58/1.84 3540 multiply(A,inverse(A)) = c_0. [back_rewrite(3310),rewrite([3323(2),3521(3),3521(3)]),flip(a)].
% 1.58/1.84 3549 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(2980),rewrite([3323(2),3537(13),3540(15),3323(15),3538(19)]),flip(a)].
% 1.58/1.84 3551 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(2978),rewrite([3540(3),3323(3),3521(3),3323(5),3323(5),3549(12),3549(19),3549(28)])].
% 1.58/1.84 3552 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(2969),rewrite([3549(8),3323(11),3540(17),3323(17)]),flip(a)].
% 1.58/1.84 3553 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(2968),rewrite([3540(3),3323(3),3521(3),3549(9),3323(13),3549(20)]),flip(a)].
% 1.58/1.84 3560 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(2251),rewrite([3323(16),3323(16),3323(16),3323(16),3521(17),3308(16)])].
% 1.58/1.84 3564 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(1862),rewrite([3323(17)])].
% 1.58/1.84 3596 multiply(c_0,multiply(c_0,A)) = multiply(inverse(inverse(inverse(inverse(A)))),c_0). [back_rewrite(3007),rewrite([3540(4),3323(4),3521(4)])].
% 1.58/1.84 3597 multiply(inverse(inverse(A)),c_0) = A. [back_rewrite(2997),rewrite([3540(6),3323(6),3521(6),3521(6),3323(5),3521(5)])].
% 1.58/1.84 3601 multiply(A,multiply(multiply(inverse(A),B),c_0)) = B. [back_rewrite(2991),rewrite([3540(5),3323(5),3521(5),3521(5),3323(4)])].
% 1.58/1.84 3607 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(2981),rewrite([3549(13),3552(13),3549(18),3538(19),3540(15),3323(15),3521(15)]),flip(a)].
% 1.58/1.84 3619 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(2948),rewrite([3549(20),3552(20),3549(25),3538(26),3540(19),3323(19),3521(19),3597(18)])].
% 1.58/1.84 3622 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(2944),rewrite([3540(13),3323(13),3521(13),3619(21),3619(30)])].
% 1.58/1.84 3627 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(2938),rewrite([3619(10),3619(17),3540(23),3323(23),3521(23)]),flip(a)].
% 1.58/1.84 3628 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(2936),rewrite([3619(7),3540(20),3323(20),3521(20)])].
% 1.58/1.84 3629 inverse(multiply(multiply(inverse(multiply(c_0,A)),c_0),c_0)) = multiply(A,c_0). [back_rewrite(2935),rewrite([3540(4),3323(4),3521(4),3619(8),3521(3),3323(2),3521(3),3521(3),3323(2),3619(9)]),flip(a)].
% 1.58/1.84 3670 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(3410),rewrite([3597(7),3619(16),3629(17)])].
% 1.58/1.84 3683 multiply(multiply(inverse(inverse(A)),B),c_0) = multiply(A,multiply(B,c_0)). [back_rewrite(3357),rewrite([3521(7),3607(9),3629(8),3619(13),3629(14)]),flip(a)].
% 1.58/1.84 3684 multiply(c_0,multiply(A,c_0)) = inverse(multiply(inverse(A),c_0)). [back_rewrite(3355),rewrite([3521(3),3619(8),3629(9),3619(13),3596(8),3597(10),3597(9)])].
% 1.58/1.84 3765 inverse(multiply(multiply(inverse(A),c_0),c_0)) = multiply(multiply(A,c_0),c_0). [back_rewrite(510),rewrite([3619(12),3629(13),3619(14),3629(15),3683(9),3619(13),3629(14),3601(9),3619(15),3629(16),3683(10),3619(13),3684(8),3597(11)]),flip(a)].
% 1.58/1.84 3809 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(3419),rewrite([3619(14),3765(15)])].
% 1.58/1.84 3834 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(3363),rewrite([3619(12),3765(13),3619(28),3765(29)])].
% 1.58/1.84 3937 multiply(A,c_0) = inverse(inverse(A)). [back_rewrite(3304),rewrite([3540(2)])].
% 1.58/1.84 3948 inverse(inverse(inverse(inverse(A)))) = A. [back_rewrite(3231),rewrite([3540(5),3540(6),3323(6),3937(6),3323(5),3323(5),3323(5),3937(5),3323(4),3323(4),3937(4)])].
% 1.58/1.84 3988 inverse(inverse(multiply(c_0,A))) = inverse(inverse(A)). [back_rewrite(1312),rewrite([3540(2),3323(2),3937(2),3619(9),3937(7),3937(9),3948(8)]),flip(a)].
% 1.58/1.84 3993 multiply(c_0,inverse(inverse(A))) = inverse(inverse(A)). [back_rewrite(3551),rewrite([3596(6),3948(6),3937(4),3937(7),3948(6),3937(5),3948(6),3937(6),3988(5),3937(6),3948(5),3937(9),3988(8),3937(9),3948(8)])].
% 1.58/1.84 3995 inverse(inverse(A)) = A. [back_rewrite(3553),rewrite([3596(4),3948(4),3937(2),3937(5),3948(4),3937(3),3948(4),3937(6),3988(5),3937(6),3948(5),3993(4)]),flip(a)].
% 1.58/1.84 3999 multiply(multiply(A,B),inverse(B)) = A. [back_rewrite(3564),rewrite([3995(2),3995(2),3937(2),3995(2),3995(3),3995(3),3995(3),3937(3),3995(3),3937(3),3995(3)])].
% 1.58/1.84 4002 inverse(multiply(A,inverse(multiply(B,multiply(C,A))))) = multiply(B,C). [back_rewrite(3560),rewrite([3995(2),3995(2),3937(2),3995(2),3995(2),3995(2),3995(2)])].
% 1.58/1.84 4004 inverse(multiply(inverse(A),B)) = multiply(inverse(B),A). [back_rewrite(3518),rewrite([3995(2),3995(2),3937(2),3995(2),3937(4),3995(4),3995(4),3995(5)])].
% 1.58/1.84 4005 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(3517),rewrite([3995(2),3995(2),3937(2),3995(2),4002(7),3995(5)])].
% 1.58/1.84 4048 inverse(multiply(A,multiply(inverse(multiply(B,A)),C))) = multiply(inverse(C),B). [back_rewrite(2133),rewrite([3995(2),3995(2),3937(2),3995(2),3995(3),3995(3),3937(3),3995(3),4004(4),3995(7),3995(7),3937(7),3995(7),4002(14),4005(10)])].
% 1.58/1.84 4051 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(1822),rewrite([3995(5),3995(5),3937(5),3995(5)])].
% 1.58/1.84 4058 multiply(A,multiply(c_0,B)) = multiply(A,B). [back_rewrite(3628),rewrite([3937(5),3995(4),3937(5),3995(4),3995(4),3995(5),3995(6),4004(7),3937(8),4004(7),4004(7),3999(8),3995(6)])].
% 1.58/1.84 4059 inverse(multiply(c_0,multiply(A,B))) = inverse(multiply(A,B)). [back_rewrite(3627),rewrite([3937(5),3995(4),3937(5),3995(4),3995(4),4058(3),3937(4),3995(3),3995(5),3937(8),3995(7),3937(8),3995(7)]),flip(a)].
% 1.58/1.84 4061 multiply(c_0,A) = A. [back_rewrite(3622),rewrite([3995(3),3995(4),4004(6),4004(4),3937(6),3995(6),3999(6),4004(4),4059(5),4004(3),3937(4),4004(3),4004(3),3937(4),4004(3),4004(3),4004(3),4005(3),3937(5),3995(4),3937(5),3995(4),3995(4)]),flip(a)].
% 1.58/1.84 4073 multiply(multiply(multiply(inverse(A),B),C),D) = multiply(inverse(A),multiply(multiply(B,C),D)). [back_rewrite(3670),rewrite([3995(2),4004(5),3995(3),3937(6),4004(5),4004(5),4004(5),4004(5),4004(5),4004(7)]),flip(a)].
% 1.58/1.84 4087 multiply(multiply(multiply(multiply(A,B),C),inverse(multiply(B,C))),D) = multiply(A,D). [back_rewrite(3834),rewrite([4004(5),4004(3),4061(5),3937(5),3995(5),3937(5),3995(5),4073(4),4004(5),3995(6),3999(6),3995(4),3995(5),4061(5),3937(5),3995(5),3937(5),3995(5)])].
% 1.58/1.84 4088 multiply(inverse(multiply(multiply(A,B),inverse(multiply(C,B)))),D) = multiply(C,multiply(inverse(A),D)). [back_rewrite(3809),rewrite([4004(6),4004(4),4061(7),3937(7),4004(6),4004(6),3937(7),4004(6),4004(6),4048(7),4005(5),4004(3),4004(6),4073(9),4004(10),4004(10),4004(10)]),flip(a)].
% 1.58/1.84 4122 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(4051(a,1),3999(a,1,1))].
% 1.58/1.84 4125 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(3999(a,1),4122(a,1,2,1)),flip(a)].
% 1.58/1.84 4143 multiply(multiply(multiply(A,B),multiply(inverse(B),inverse(C))),D) = multiply(A,multiply(inverse(C),D)). [back_rewrite(4088),rewrite([4125(3),4125(6),4125(4),3995(2),3995(2),4125(3)])].
% 1.58/1.84 4144 multiply(multiply(A,B),multiply(inverse(B),C)) = multiply(A,C). [back_rewrite(4087),rewrite([4125(4),4143(7)])].
% 1.58/1.84 4160 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)). [para(3999(a,1),4144(a,1,1)),rewrite([3995(2)]),flip(a)].
% 1.58/1.84 4161 $F # answer(prove_these_axioms_3). [resolve(4160,a,2,a)].
% 1.58/1.84
% 1.58/1.84 % SZS output end Refutation
% 1.58/1.84 ============================== end of proof ==========================
% 1.58/1.84
% 1.58/1.84 ============================== STATISTICS ============================
% 1.58/1.84
% 1.58/1.84 Given=55. Generated=8289. Kept=4160. proofs=1.
% 1.58/1.84 Usable=12. Sos=5. Demods=16. Limbo=0, Disabled=4144. Hints=0.
% 1.58/1.84 Megabytes=7.98.
% 1.58/1.84 User_CPU=0.77, System_CPU=0.01, Wall_clock=1.
% 1.58/1.84
% 1.58/1.84 ============================== end of statistics =====================
% 1.58/1.84
% 1.58/1.84 ============================== end of search =========================
% 1.58/1.84
% 1.58/1.84 THEOREM PROVED
% 1.58/1.84 % SZS status Unsatisfiable
% 1.58/1.84
% 1.58/1.84 Exiting with 1 proof.
% 1.58/1.84
% 1.58/1.84 Process 27072 exit (max_proofs) Tue Jun 14 05:29:53 2022
% 1.58/1.84 Prover9 interrupted
%------------------------------------------------------------------------------