TSTP Solution File: GRP106-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP106-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:17:11 EDT 2022
% Result : Unsatisfiable 0.73s 1.06s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP106-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 07:22:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.73/1.06 ============================== Prover9 ===============================
% 0.73/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.06 Process 15077 was started by sandbox2 on n018.cluster.edu,
% 0.73/1.06 Tue Jun 14 07:22:14 2022
% 0.73/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_14924_n018.cluster.edu".
% 0.73/1.06 ============================== end of head ===========================
% 0.73/1.06
% 0.73/1.06 ============================== INPUT =================================
% 0.73/1.06
% 0.73/1.06 % Reading from file /tmp/Prover9_14924_n018.cluster.edu
% 0.73/1.06
% 0.73/1.06 set(prolog_style_variables).
% 0.73/1.06 set(auto2).
% 0.73/1.06 % set(auto2) -> set(auto).
% 0.73/1.06 % set(auto) -> set(auto_inference).
% 0.73/1.06 % set(auto) -> set(auto_setup).
% 0.73/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.06 % set(auto) -> set(auto_limits).
% 0.73/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.06 % set(auto) -> set(auto_denials).
% 0.73/1.06 % set(auto) -> set(auto_process).
% 0.73/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.06 % set(auto2) -> assign(stats, some).
% 0.73/1.06 % set(auto2) -> clear(echo_input).
% 0.73/1.06 % set(auto2) -> set(quiet).
% 0.73/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.06 % set(auto2) -> clear(print_given).
% 0.73/1.06 assign(lrs_ticks,-1).
% 0.73/1.06 assign(sos_limit,10000).
% 0.73/1.06 assign(order,kbo).
% 0.73/1.06 set(lex_order_vars).
% 0.73/1.06 clear(print_given).
% 0.73/1.06
% 0.73/1.06 % formulas(sos). % not echoed (3 formulas)
% 0.73/1.06
% 0.73/1.06 ============================== end of input ==========================
% 0.73/1.06
% 0.73/1.06 % From the command line: assign(max_seconds, 300).
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.06
% 0.73/1.06 % Formulas that are not ordinary clauses:
% 0.73/1.06
% 0.73/1.06 ============================== end of process non-clausal formulas ===
% 0.73/1.06
% 0.73/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.06
% 0.73/1.06 ============================== PREDICATE ELIMINATION =================
% 0.73/1.06
% 0.73/1.06 ============================== end predicate elimination =============
% 0.73/1.06
% 0.73/1.06 Auto_denials:
% 0.73/1.06 % copying label prove_these_axioms to answer in negative clause
% 0.73/1.06
% 0.73/1.06 Term ordering decisions:
% 0.73/1.06
% 0.73/1.06 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.73/1.06 Function symbol KB weights: a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. double_divide=1. multiply=1. inverse=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of process initial clauses ========
% 0.73/1.06
% 0.73/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.06
% 0.73/1.06 ============================== end of clauses for search =============
% 0.73/1.06
% 0.73/1.06 ============================== SEARCH ================================
% 0.73/1.06
% 0.73/1.06 % Starting search at 0.01 seconds.
% 0.73/1.06
% 0.73/1.06 ============================== PROOF =================================
% 0.73/1.06 % SZS status Unsatisfiable
% 0.73/1.06 % SZS output start Refutation
% 0.73/1.06
% 0.73/1.06 % Proof 1 at 0.08 (+ 0.00) seconds: prove_these_axioms.
% 0.73/1.06 % Length of proof is 97.
% 0.73/1.06 % Level of proof is 25.
% 0.73/1.06 % Maximum clause weight is 45.000.
% 0.73/1.06 % Given clauses 21.
% 0.73/1.06
% 0.73/1.06 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.73/1.06 2 inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.73/1.06 3 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)) | multiply(a4,b4) != multiply(b4,a4) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.73/1.06 4 inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) | inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [copy(3),rewrite([1(4),1(9),1(15),1(18),1(24),1(27),1(32),1(34),1(39),1(43)]),flip(a),flip(c)].
% 0.73/1.06 5 inverse(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),inverse(double_divide(A,C)))) = double_divide(B,D). [para(2(a,1),2(a,1,1,2,1,2))].
% 0.73/1.06 6 inverse(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C)) = A. [para(2(a,1),2(a,1,1,2))].
% 0.73/1.06 7 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(A,double_divide(D,E))))) = double_divide(B,inverse(double_divide(D,inverse(double_divide(C,E))))). [para(5(a,1),2(a,1,1,2,1,2))].
% 0.73/1.06 8 inverse(double_divide(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),C),double_divide(B,D))) = A. [para(5(a,1),2(a,1,1,2))].
% 0.73/1.06 16 double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)),C) = A. [para(6(a,1),5(a,1)),flip(a)].
% 0.73/1.06 20 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)) = inverse(double_divide(double_divide(D,C),inverse(double_divide(D,inverse(A))))). [para(16(a,1),2(a,1,1,2,1,2,1)),flip(a)].
% 0.73/1.06 21 inverse(double_divide(double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),B)),D),inverse(A))) = C. [para(16(a,1),2(a,1,1,2,1))].
% 0.73/1.06 24 inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,C)))) = double_divide(inverse(double_divide(double_divide(B,inverse(double_divide(D,inverse(double_divide(C,E))))),D)),E). [para(16(a,1),5(a,1,1,1,2,1))].
% 0.73/1.06 28 double_divide(double_divide(inverse(double_divide(A,B)),C),inverse(double_divide(B,C))) = A. [para(5(a,1),16(a,1,1))].
% 0.73/1.06 33 inverse(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(C,D))))),B)) = double_divide(inverse(double_divide(A,C)),D). [para(16(a,1),16(a,1,1,1,1)),flip(a)].
% 0.73/1.06 35 inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,C)))) = double_divide(double_divide(inverse(double_divide(B,C)),D),D). [back_rewrite(24),rewrite([33(13)])].
% 0.73/1.06 36 inverse(double_divide(double_divide(double_divide(inverse(double_divide(A,B)),C),C),inverse(A))) = B. [back_rewrite(21),rewrite([33(7)])].
% 0.73/1.06 38 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(A,inverse(D))))) = double_divide(inverse(double_divide(D,B)),C). [para(28(a,1),2(a,1,1,2,1,2,1))].
% 0.73/1.06 46 double_divide(double_divide(A,B),inverse(double_divide(C,B))) = double_divide(double_divide(A,D),inverse(double_divide(C,D))). [para(6(a,1),28(a,1,1,1))].
% 0.73/1.06 52 double_divide(double_divide(inverse(double_divide(A,double_divide(inverse(double_divide(B,C)),D))),inverse(double_divide(C,D))),inverse(B)) = A. [para(28(a,1),28(a,1,2,1))].
% 0.73/1.06 57 inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) = double_divide(double_divide(double_divide(inverse(double_divide(double_divide(C,D),B)),E),E),D). [para(36(a,1),5(a,1,1,1,2))].
% 0.73/1.06 58 inverse(double_divide(double_divide(double_divide(double_divide(inverse(double_divide(A,B)),C),C),inverse(double_divide(D,inverse(double_divide(inverse(A),E))))),B)) = double_divide(D,E). [para(36(a,1),5(a,1,1,2))].
% 0.73/1.06 63 double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(A),C))) = double_divide(B,C). [para(36(a,1),16(a,1,1)),flip(a)].
% 0.73/1.06 65 double_divide(double_divide(inverse(double_divide(A,B)),C),C) = double_divide(double_divide(B,D),inverse(double_divide(inverse(A),D))). [para(36(a,1),28(a,1,1,1)),flip(a)].
% 0.73/1.06 71 double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(double_divide(double_divide(B,C),D)),C))))) = double_divide(A,D). [para(7(a,1),5(a,1))].
% 0.73/1.06 73 inverse(double_divide(double_divide(double_divide(A,inverse(double_divide(B,double_divide(C,D)))),double_divide(E,inverse(double_divide(C,inverse(double_divide(F,D)))))),double_divide(B,inverse(double_divide(E,F))))) = A. [para(7(a,1),6(a,1,1,1,2))].
% 0.73/1.06 77 inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,double_divide(C,D))))) = double_divide(inverse(double_divide(double_divide(B,inverse(double_divide(E,F))),E)),inverse(double_divide(C,inverse(double_divide(F,D))))). [para(16(a,1),7(a,1,1,1,2,1))].
% 0.73/1.06 79 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(A,D)))) = double_divide(B,inverse(double_divide(inverse(double_divide(double_divide(D,inverse(double_divide(E,F))),E)),inverse(double_divide(C,F))))). [para(16(a,1),7(a,1,1,2,1,2))].
% 0.73/1.06 85 inverse(double_divide(double_divide(A,B),inverse(double_divide(A,double_divide(C,D))))) = double_divide(double_divide(double_divide(inverse(double_divide(E,B)),F),F),inverse(double_divide(C,inverse(double_divide(inverse(E),D))))). [para(36(a,1),7(a,1,1,1,2))].
% 0.73/1.06 88 double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B) = inverse(double_divide(C,A)). [para(63(a,1),2(a,1,1,2,1,2,1)),rewrite([38(10)])].
% 0.73/1.06 89 double_divide(inverse(double_divide(A,inverse(double_divide(B,C)))),D) = double_divide(B,inverse(double_divide(inverse(double_divide(A,C)),D))). [para(2(a,1),63(a,1,1)),flip(a)].
% 0.73/1.06 98 double_divide(inverse(double_divide(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C),D)),inverse(double_divide(A,E))) = double_divide(D,E). [para(6(a,1),63(a,1,2,1,1))].
% 0.73/1.06 104 inverse(double_divide(double_divide(double_divide(inverse(double_divide(A,B)),C),C),inverse(inverse(double_divide(D,A))))) = inverse(double_divide(inverse(D),B)). [para(63(a,1),36(a,1,1,1,1,1,1))].
% 0.73/1.06 121 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),A)) = double_divide(B,C). [para(2(a,1),88(a,1,1)),flip(a)].
% 0.73/1.06 132 inverse(double_divide(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C),D)) = double_divide(inverse(double_divide(double_divide(D,E),A)),E). [para(6(a,1),88(a,1,1,1,2)),flip(a)].
% 0.73/1.06 133 inverse(double_divide(A,double_divide(B,C))) = double_divide(B,inverse(double_divide(inverse(A),C))). [para(6(a,1),88(a,1,1)),flip(a)].
% 0.73/1.06 134 double_divide(double_divide(A,B),B) = A. [para(6(a,1),88(a,2)),rewrite([89(9),89(7),71(9)])].
% 0.73/1.06 136 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(D))) = double_divide(inverse(double_divide(inverse(double_divide(D,A)),B)),C). [para(88(a,1),16(a,1,1,1,1)),flip(a)].
% 0.73/1.06 142 double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(B,C)),D),C)),D))) = inverse(A). [para(28(a,1),88(a,2,1)),rewrite([89(10)])].
% 0.73/1.06 151 double_divide(inverse(double_divide(double_divide(inverse(double_divide(A,B)),C),D)),C) = double_divide(D,inverse(inverse(double_divide(A,B)))). [para(88(a,1),7(a,2,2,1)),rewrite([136(9),134(9),136(11),121(7)])].
% 0.73/1.06 157 double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),inverse(double_divide(inverse(D),B))) = inverse(double_divide(C,inverse(double_divide(D,A)))). [para(63(a,1),88(a,1,1,1,1))].
% 0.73/1.06 165 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,inverse(double_divide(inverse(A),D))))) = double_divide(C,inverse(double_divide(B,D))). [back_rewrite(85),rewrite([133(4),133(7),63(6),134(7)]),flip(a)].
% 0.73/1.06 170 double_divide(inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)),inverse(double_divide(D,inverse(double_divide(C,E))))) = double_divide(D,inverse(double_divide(inverse(A),E))). [back_rewrite(77),rewrite([133(5),133(8),63(7)]),flip(a)].
% 0.73/1.06 173 double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(double_divide(B,C),B)),D)),inverse(double_divide(A,C)))) = D. [back_rewrite(73),rewrite([133(3),133(16),133(12),133(6),136(13),121(5),157(8),136(9)])].
% 0.73/1.06 179 double_divide(double_divide(double_divide(inverse(double_divide(A,B)),inverse(double_divide(inverse(C),D))),inverse(double_divide(B,D))),inverse(A)) = C. [back_rewrite(52),rewrite([133(5)])].
% 0.73/1.06 190 double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(B,inverse(double_divide(A,inverse(double_divide(C,D))))),C)),D))) = B. [back_rewrite(8),rewrite([133(9)])].
% 0.73/1.06 193 inverse(double_divide(inverse(double_divide(A,B)),inverse(inverse(double_divide(C,A))))) = inverse(double_divide(inverse(C),B)). [back_rewrite(104),rewrite([134(4)])].
% 0.73/1.06 196 double_divide(double_divide(A,B),inverse(double_divide(inverse(C),B))) = inverse(double_divide(C,A)). [back_rewrite(65),rewrite([134(4)]),flip(a)].
% 0.73/1.06 199 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)) = double_divide(A,C). [back_rewrite(58),rewrite([134(4),165(8)])].
% 0.73/1.06 200 inverse(double_divide(double_divide(A,B),inverse(double_divide(A,C)))) = double_divide(inverse(double_divide(double_divide(C,D),B)),D). [back_rewrite(57),rewrite([134(10)])].
% 0.73/1.06 204 inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,C)))) = inverse(double_divide(B,C)). [back_rewrite(35),rewrite([134(10)])].
% 0.73/1.06 207 double_divide(A,inverse(double_divide(double_divide(B,C),inverse(double_divide(D,C))))) = inverse(double_divide(double_divide(A,D),B)). [back_rewrite(79),rewrite([204(7),199(8)]),flip(a)].
% 0.73/1.06 208 inverse(double_divide(double_divide(A,B),inverse(C))) = double_divide(inverse(double_divide(C,A)),B). [back_rewrite(38),rewrite([204(8)])].
% 0.73/1.06 213 double_divide(inverse(double_divide(A,B)),inverse(double_divide(C,inverse(inverse(double_divide(B,C)))))) = inverse(A). [back_rewrite(142),rewrite([151(8)])].
% 0.73/1.06 221 double_divide(double_divide(A,B),inverse(double_divide(C,inverse(double_divide(B,D))))) = double_divide(C,inverse(double_divide(inverse(A),D))). [back_rewrite(170),rewrite([199(5)])].
% 0.73/1.06 225 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))). [back_rewrite(33),rewrite([199(7)]),flip(a)].
% 0.73/1.06 226 double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,C))) = double_divide(B,C). [back_rewrite(20),rewrite([199(5),208(7),225(6)]),flip(a)].
% 0.73/1.06 227 double_divide(A,double_divide(double_divide(B,C),inverse(double_divide(D,C)))) = inverse(double_divide(double_divide(A,B),D)). [back_rewrite(207),rewrite([208(5),225(4)])].
% 0.73/1.06 228 double_divide(double_divide(A,B),inverse(double_divide(C,B))) = double_divide(double_divide(D,A),inverse(double_divide(D,C))). [back_rewrite(200),rewrite([208(5),225(4),225(8)]),flip(a)].
% 0.73/1.06 230 double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(inverse(D),C))) = inverse(double_divide(A,inverse(double_divide(D,B)))). [back_rewrite(157),rewrite([208(4),225(3)])].
% 0.73/1.06 235 double_divide(double_divide(A,inverse(double_divide(B,C))),C) = inverse(double_divide(A,B)). [back_rewrite(88),rewrite([208(4),225(3)])].
% 0.73/1.06 245 double_divide(A,inverse(double_divide(B,inverse(double_divide(C,inverse(inverse(double_divide(B,C)))))))) = inverse(A). [back_rewrite(213),rewrite([225(8)])].
% 0.73/1.06 247 inverse(double_divide(double_divide(A,B),inverse(C))) = double_divide(C,inverse(double_divide(A,B))). [back_rewrite(208),rewrite([225(7)])].
% 0.73/1.06 248 inverse(double_divide(A,inverse(double_divide(B,inverse(inverse(double_divide(C,A))))))) = inverse(double_divide(inverse(C),B)). [back_rewrite(193),rewrite([225(6)])].
% 0.73/1.06 250 double_divide(A,inverse(inverse(double_divide(B,A)))) = B. [back_rewrite(190),rewrite([225(8),235(8)])].
% 0.73/1.06 255 double_divide(double_divide(double_divide(A,inverse(double_divide(B,inverse(double_divide(inverse(C),D))))),inverse(double_divide(B,D))),inverse(A)) = C. [back_rewrite(179),rewrite([225(6)])].
% 0.73/1.06 256 double_divide(A,double_divide(double_divide(double_divide(B,C),inverse(double_divide(B,D))),inverse(double_divide(A,D)))) = C. [back_rewrite(173),rewrite([225(4),247(5)])].
% 0.73/1.06 267 double_divide(double_divide(A,inverse(double_divide(B,C))),inverse(double_divide(D,C))) = double_divide(D,inverse(inverse(double_divide(A,B)))). [back_rewrite(151),rewrite([225(3),225(6)])].
% 0.73/1.06 271 inverse(double_divide(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C),D)) = double_divide(double_divide(D,E),inverse(double_divide(A,E))). [back_rewrite(132),rewrite([225(11)])].
% 0.73/1.06 276 double_divide(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C),inverse(double_divide(D,inverse(double_divide(A,E))))) = double_divide(D,E). [back_rewrite(98),rewrite([225(10)])].
% 0.73/1.06 280 double_divide(A,inverse(inverse(double_divide(double_divide(B,C),B)))) = double_divide(A,C). [back_rewrite(71),rewrite([225(4),247(5),227(5)])].
% 0.73/1.06 282 inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) | inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([225(27)]),xx(c)].
% 0.73/1.06 287 double_divide(A,inverse(double_divide(B,inverse(B)))) = inverse(A). [back_rewrite(245),rewrite([250(4)])].
% 0.73/1.06 289 double_divide(A,double_divide(A,B)) = B. [back_rewrite(256),rewrite([267(7),280(5)])].
% 0.73/1.06 290 inverse(double_divide(A,inverse(double_divide(B,C)))) = double_divide(inverse(B),inverse(inverse(double_divide(A,C)))). [back_rewrite(230),rewrite([267(7)]),flip(a)].
% 0.73/1.06 292 inverse(double_divide(b1,inverse(b1))) != inverse(double_divide(a1,inverse(a1))) | inverse(inverse(a2)) != a2 | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(282),rewrite([287(18)])].
% 0.73/1.06 297 double_divide(double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),C),double_divide(inverse(A),inverse(inverse(double_divide(D,E))))) = double_divide(D,E). [back_rewrite(276),rewrite([290(9)])].
% 0.73/1.06 311 double_divide(double_divide(double_divide(A,double_divide(inverse(inverse(B)),inverse(inverse(double_divide(C,D))))),inverse(double_divide(C,D))),inverse(A)) = B. [back_rewrite(255),rewrite([290(5)])].
% 0.73/1.06 314 inverse(double_divide(inverse(A),B)) = double_divide(inverse(B),inverse(inverse(A))). [back_rewrite(248),rewrite([290(7),250(5)]),flip(a)].
% 0.73/1.06 325 double_divide(double_divide(A,B),double_divide(inverse(B),inverse(inverse(double_divide(C,D))))) = double_divide(C,double_divide(inverse(D),inverse(inverse(A)))). [back_rewrite(221),rewrite([290(5),314(10)])].
% 0.73/1.06 352 double_divide(double_divide(A,B),double_divide(inverse(B),inverse(inverse(C)))) = inverse(double_divide(C,A)). [back_rewrite(196),rewrite([314(4)])].
% 0.73/1.06 357 inverse(double_divide(double_divide(A,B),C)) = double_divide(A,double_divide(inverse(B),inverse(inverse(C)))). [back_rewrite(325),rewrite([352(7)])].
% 0.73/1.06 367 double_divide(double_divide(double_divide(A,B),inverse(double_divide(C,B))),double_divide(inverse(C),inverse(inverse(D)))) = double_divide(double_divide(D,E),inverse(double_divide(A,E))). [back_rewrite(271),rewrite([357(7)])].
% 0.73/1.06 376 double_divide(double_divide(A,B),A) = B. [para(134(a,1),289(a,1,2))].
% 0.73/1.06 380 double_divide(double_divide(A,B),double_divide(C,double_divide(inverse(D),inverse(inverse(B))))) = double_divide(double_divide(A,D),inverse(C)). [para(134(a,1),46(a,1,2,1)),rewrite([357(7)]),flip(a)].
% 0.73/1.06 383 double_divide(double_divide(A,double_divide(B,C)),inverse(C)) = double_divide(double_divide(A,D),inverse(double_divide(B,D))). [para(289(a,1),46(a,1,2,1))].
% 0.73/1.06 385 double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(inverse(D)))) = double_divide(double_divide(A,C),inverse(D)). [para(46(a,1),46(a,1,2,1)),rewrite([290(8),134(6),357(12),380(15)])].
% 0.73/1.06 389 double_divide(double_divide(A,B),inverse(double_divide(C,B))) = double_divide(C,inverse(A)). [back_rewrite(367),rewrite([385(9),134(2)]),flip(a)].
% 0.73/1.06 392 double_divide(double_divide(A,double_divide(B,C)),inverse(C)) = double_divide(B,inverse(A)). [back_rewrite(383),rewrite([389(8)])].
% 0.73/1.06 397 inverse(inverse(double_divide(A,B))) = double_divide(A,B). [back_rewrite(297),rewrite([389(4),376(3),289(7)])].
% 0.73/1.06 398 double_divide(double_divide(A,B),inverse(double_divide(A,C))) = double_divide(C,inverse(B)). [back_rewrite(228),rewrite([389(4)]),flip(a)].
% 0.73/1.06 409 inverse(inverse(A)) = A. [back_rewrite(311),rewrite([397(5),392(8),134(6)])].
% 0.73/1.06 436 double_divide(A,B) = double_divide(B,A). [back_rewrite(226),rewrite([398(5),409(2)])].
% 0.73/1.06 456 inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)). [back_rewrite(314),rewrite([436(2),409(6),436(5)])].
% 0.73/1.06 457 double_divide(b1,inverse(b1)) != double_divide(a1,inverse(a1)) # answer(prove_these_axioms). [back_rewrite(292),rewrite([456(5),456(9),409(12),436(15)]),xx(b),xx(c)].
% 0.73/1.06 474 double_divide(A,double_divide(B,inverse(B))) = inverse(A). [back_rewrite(287),rewrite([456(3)])].
% 0.73/1.06 489 double_divide(A,inverse(A)) = double_divide(B,inverse(B)). [para(474(a,1),289(a,1,2))].
% 0.73/1.06 490 $F # answer(prove_these_axioms). [resolve(489,a,457,a)].
% 0.73/1.06
% 0.73/1.06 % SZS output end Refutation
% 0.73/1.06 ============================== end of proof ==========================
% 0.73/1.06
% 0.73/1.06 ============================== STATISTICS ============================
% 0.73/1.06
% 0.73/1.06 Given=21. Generated=768. Kept=488. proofs=1.
% 0.73/1.06 Usable=8. Sos=40. Demods=35. Limbo=0, Disabled=442. Hints=0.
% 0.73/1.06 Megabytes=0.47.
% 0.73/1.06 User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.73/1.06
% 0.73/1.06 ============================== end of statistics =====================
% 0.73/1.06
% 0.73/1.06 ============================== end of search =========================
% 0.73/1.06
% 0.73/1.06 THEOREM PROVED
% 0.73/1.06 % SZS status Unsatisfiable
% 0.73/1.06
% 0.73/1.06 Exiting with 1 proof.
% 0.73/1.06
% 0.73/1.06 Process 15077 exit (max_proofs) Tue Jun 14 07:22:14 2022
% 0.73/1.06 Prover9 interrupted
%------------------------------------------------------------------------------