TSTP Solution File: GRP596-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP596-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 11:19:46 EDT 2022
% Result : Unsatisfiable 0.76s 1.07s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP596-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 11:10:03 EDT 2022
% 0.21/0.35 % CPUTime :
% 0.76/1.07 ============================== Prover9 ===============================
% 0.76/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.07 Process 30615 was started by sandbox on n024.cluster.edu,
% 0.76/1.07 Mon Jun 13 11:10:04 2022
% 0.76/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30368_n024.cluster.edu".
% 0.76/1.07 ============================== end of head ===========================
% 0.76/1.07
% 0.76/1.07 ============================== INPUT =================================
% 0.76/1.07
% 0.76/1.07 % Reading from file /tmp/Prover9_30368_n024.cluster.edu
% 0.76/1.07
% 0.76/1.07 set(prolog_style_variables).
% 0.76/1.07 set(auto2).
% 0.76/1.07 % set(auto2) -> set(auto).
% 0.76/1.07 % set(auto) -> set(auto_inference).
% 0.76/1.07 % set(auto) -> set(auto_setup).
% 0.76/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.07 % set(auto) -> set(auto_limits).
% 0.76/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.07 % set(auto) -> set(auto_denials).
% 0.76/1.07 % set(auto) -> set(auto_process).
% 0.76/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.07 % set(auto2) -> assign(stats, some).
% 0.76/1.07 % set(auto2) -> clear(echo_input).
% 0.76/1.07 % set(auto2) -> set(quiet).
% 0.76/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.07 % set(auto2) -> clear(print_given).
% 0.76/1.07 assign(lrs_ticks,-1).
% 0.76/1.07 assign(sos_limit,10000).
% 0.76/1.07 assign(order,kbo).
% 0.76/1.07 set(lex_order_vars).
% 0.76/1.07 clear(print_given).
% 0.76/1.07
% 0.76/1.07 % formulas(sos). % not echoed (3 formulas)
% 0.76/1.07
% 0.76/1.07 ============================== end of input ==========================
% 0.76/1.07
% 0.76/1.07 % From the command line: assign(max_seconds, 300).
% 0.76/1.07
% 0.76/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.07
% 0.76/1.07 % Formulas that are not ordinary clauses:
% 0.76/1.07
% 0.76/1.07 ============================== end of process non-clausal formulas ===
% 0.76/1.07
% 0.76/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.07
% 0.76/1.07 ============================== PREDICATE ELIMINATION =================
% 0.76/1.07
% 0.76/1.07 ============================== end predicate elimination =============
% 0.76/1.07
% 0.76/1.07 Auto_denials:
% 0.76/1.07 % copying label prove_these_axioms_4 to answer in negative clause
% 0.76/1.07
% 0.76/1.07 Term ordering decisions:
% 0.76/1.07
% 0.76/1.07 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 0.76/1.07 Function symbol KB weights: a=1. b=1. double_divide=1. multiply=1. inverse=0.
% 0.76/1.07
% 0.76/1.07 ============================== end of process initial clauses ========
% 0.76/1.07
% 0.76/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.07
% 0.76/1.07 ============================== end of clauses for search =============
% 0.76/1.07
% 0.76/1.07 ============================== SEARCH ================================
% 0.76/1.07
% 0.76/1.07 % Starting search at 0.01 seconds.
% 0.76/1.07
% 0.76/1.07 ============================== PROOF =================================
% 0.76/1.07 % SZS status Unsatisfiable
% 0.76/1.07 % SZS output start Refutation
% 0.76/1.07
% 0.76/1.07 % Proof 1 at 0.06 (+ 0.00) seconds: prove_these_axioms_4.
% 0.76/1.07 % Length of proof is 87.
% 0.76/1.07 % Level of proof is 22.
% 0.76/1.07 % Maximum clause weight is 30.000.
% 0.76/1.07 % Given clauses 14.
% 0.76/1.07
% 0.76/1.07 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.76/1.07 2 inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C # label(single_axiom) # label(axiom). [assumption].
% 0.76/1.07 3 multiply(a,b) != multiply(b,a) # label(prove_these_axioms_4) # label(negated_conjecture) # answer(prove_these_axioms_4). [assumption].
% 0.76/1.07 4 inverse(double_divide(b,a)) != inverse(double_divide(a,b)) # answer(prove_these_axioms_4). [copy(3),rewrite([1(3),1(7)])].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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)].
% 0.76/1.07 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)].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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)].
% 0.76/1.07 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)])].
% 0.76/1.07 36 inverse(double_divide(double_divide(double_divide(inverse(double_divide(A,B)),C),C),inverse(A))) = B. [back_rewrite(21),rewrite([33(7)])].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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)].
% 0.76/1.07 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)].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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))].
% 0.76/1.07 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)])].
% 0.76/1.07 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)].
% 0.76/1.07 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))].
% 0.76/1.07 104 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))].
% 0.76/1.07 121 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)].
% 0.76/1.07 132 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)].
% 0.76/1.07 133 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)].
% 0.76/1.07 134 double_divide(double_divide(A,B),B) = A. [para(6(a,1),88(a,2)),rewrite([89(9),89(7),71(9)])].
% 0.76/1.07 136 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)].
% 0.76/1.07 151 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)])].
% 0.76/1.07 157 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))].
% 0.76/1.07 165 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)].
% 0.76/1.07 170 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)].
% 0.76/1.07 173 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)])].
% 0.76/1.07 179 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)])].
% 0.76/1.07 190 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)])].
% 0.76/1.07 193 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)])].
% 0.76/1.07 196 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)].
% 0.76/1.07 199 inverse(double_divide(double_divide(A,inverse(double_divide(B,C))),B)) = double_divide(A,C). [back_rewrite(58),rewrite([134(4),165(8)])].
% 0.76/1.07 200 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)])].
% 0.76/1.07 204 inverse(double_divide(double_divide(A,inverse(B)),inverse(double_divide(A,C)))) = inverse(double_divide(B,C)). [back_rewrite(35),rewrite([134(10)])].
% 0.76/1.07 207 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)].
% 0.76/1.07 208 inverse(double_divide(double_divide(A,B),inverse(C))) = double_divide(inverse(double_divide(C,A)),B). [back_rewrite(38),rewrite([204(8)])].
% 0.76/1.07 221 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)])].
% 0.76/1.07 225 double_divide(inverse(double_divide(A,B)),C) = double_divide(A,inverse(double_divide(B,C))). [back_rewrite(33),rewrite([199(7)]),flip(a)].
% 0.76/1.07 226 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)].
% 0.76/1.07 227 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)])].
% 0.76/1.07 228 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)].
% 0.76/1.07 230 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)])].
% 0.76/1.07 235 double_divide(double_divide(A,inverse(double_divide(B,C))),C) = inverse(double_divide(A,B)). [back_rewrite(88),rewrite([208(4),225(3)])].
% 0.76/1.07 247 inverse(double_divide(double_divide(A,B),inverse(C))) = double_divide(C,inverse(double_divide(A,B))). [back_rewrite(208),rewrite([225(7)])].
% 0.76/1.07 248 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)])].
% 0.76/1.07 250 double_divide(A,inverse(inverse(double_divide(B,A)))) = B. [back_rewrite(190),rewrite([225(8),235(8)])].
% 0.76/1.07 255 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)])].
% 0.76/1.07 256 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)])].
% 0.76/1.07 267 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)])].
% 0.76/1.07 271 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)])].
% 0.76/1.07 276 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)])].
% 0.76/1.07 280 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)])].
% 0.76/1.07 288 double_divide(A,double_divide(A,B)) = B. [back_rewrite(256),rewrite([267(7),280(5)])].
% 0.76/1.07 289 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)].
% 0.76/1.07 295 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([289(9)])].
% 0.76/1.07 309 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([289(5)])].
% 0.76/1.07 312 inverse(double_divide(inverse(A),B)) = double_divide(inverse(B),inverse(inverse(A))). [back_rewrite(248),rewrite([289(7),250(5)]),flip(a)].
% 0.76/1.07 323 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([289(5),312(10)])].
% 0.76/1.07 350 double_divide(double_divide(A,B),double_divide(inverse(B),inverse(inverse(C)))) = inverse(double_divide(C,A)). [back_rewrite(196),rewrite([312(4)])].
% 0.76/1.07 355 inverse(double_divide(double_divide(A,B),C)) = double_divide(A,double_divide(inverse(B),inverse(inverse(C)))). [back_rewrite(323),rewrite([350(7)])].
% 0.76/1.07 365 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([355(7)])].
% 0.76/1.07 374 double_divide(double_divide(A,B),A) = B. [para(134(a,1),288(a,1,2))].
% 0.76/1.07 378 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([355(7)]),flip(a)].
% 0.76/1.07 381 double_divide(double_divide(A,double_divide(B,C)),inverse(C)) = double_divide(double_divide(A,D),inverse(double_divide(B,D))). [para(288(a,1),46(a,1,2,1))].
% 0.76/1.07 383 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([289(8),134(6),355(12),378(15)])].
% 0.76/1.07 387 double_divide(double_divide(A,B),inverse(double_divide(C,B))) = double_divide(C,inverse(A)). [back_rewrite(365),rewrite([383(9),134(2)]),flip(a)].
% 0.76/1.07 390 double_divide(double_divide(A,double_divide(B,C)),inverse(C)) = double_divide(B,inverse(A)). [back_rewrite(381),rewrite([387(8)])].
% 0.76/1.07 395 inverse(inverse(double_divide(A,B))) = double_divide(A,B). [back_rewrite(295),rewrite([387(4),374(3),288(7)])].
% 0.76/1.07 396 double_divide(double_divide(A,B),inverse(double_divide(A,C))) = double_divide(C,inverse(B)). [back_rewrite(228),rewrite([387(4)]),flip(a)].
% 0.76/1.07 407 inverse(inverse(A)) = A. [back_rewrite(309),rewrite([395(5),390(8),134(6)])].
% 0.76/1.07 434 double_divide(A,B) = double_divide(B,A). [back_rewrite(226),rewrite([396(5),407(2)])].
% 0.76/1.07 468 $F # answer(prove_these_axioms_4). [back_rewrite(4),rewrite([434(3)]),xx(a)].
% 0.76/1.07
% 0.76/1.07 % SZS output end Refutation
% 0.76/1.07 ============================== end of proof ==========================
% 0.76/1.07
% 0.76/1.07 ============================== STATISTICS ============================
% 0.76/1.07
% 0.76/1.07 Given=14. Generated=700. Kept=466. proofs=1.
% 0.76/1.07 Usable=2. Sos=15. Demods=40. Limbo=34, Disabled=418. Hints=0.
% 0.76/1.07 Megabytes=0.44.
% 0.76/1.07 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.76/1.07
% 0.76/1.07 ============================== end of statistics =====================
% 0.76/1.07
% 0.76/1.07 ============================== end of search =========================
% 0.76/1.07
% 0.76/1.07 THEOREM PROVED
% 0.76/1.07 % SZS status Unsatisfiable
% 0.76/1.07
% 0.76/1.07 Exiting with 1 proof.
% 0.76/1.07
% 0.76/1.07 Process 30615 exit (max_proofs) Mon Jun 13 11:10:04 2022
% 0.76/1.07 Prover9 interrupted
%------------------------------------------------------------------------------