TSTP Solution File: GRP500-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP500-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 11:19:21 EDT 2022
% Result : Unsatisfiable 1.26s 1.53s
% Output : Refutation 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP500-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n029.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 : Mon Jun 13 09:47:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.26/1.53 ============================== Prover9 ===============================
% 1.26/1.53 Prover9 (32) version 2009-11A, November 2009.
% 1.26/1.53 Process 32573 was started by sandbox on n029.cluster.edu,
% 1.26/1.53 Mon Jun 13 09:47:40 2022
% 1.26/1.53 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32420_n029.cluster.edu".
% 1.26/1.53 ============================== end of head ===========================
% 1.26/1.53
% 1.26/1.53 ============================== INPUT =================================
% 1.26/1.53
% 1.26/1.53 % Reading from file /tmp/Prover9_32420_n029.cluster.edu
% 1.26/1.53
% 1.26/1.53 set(prolog_style_variables).
% 1.26/1.53 set(auto2).
% 1.26/1.53 % set(auto2) -> set(auto).
% 1.26/1.53 % set(auto) -> set(auto_inference).
% 1.26/1.53 % set(auto) -> set(auto_setup).
% 1.26/1.53 % set(auto_setup) -> set(predicate_elim).
% 1.26/1.53 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.26/1.53 % set(auto) -> set(auto_limits).
% 1.26/1.53 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.26/1.53 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.26/1.53 % set(auto) -> set(auto_denials).
% 1.26/1.53 % set(auto) -> set(auto_process).
% 1.26/1.53 % set(auto2) -> assign(new_constants, 1).
% 1.26/1.53 % set(auto2) -> assign(fold_denial_max, 3).
% 1.26/1.53 % set(auto2) -> assign(max_weight, "200.000").
% 1.26/1.53 % set(auto2) -> assign(max_hours, 1).
% 1.26/1.53 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.26/1.53 % set(auto2) -> assign(max_seconds, 0).
% 1.26/1.53 % set(auto2) -> assign(max_minutes, 5).
% 1.26/1.53 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.26/1.53 % set(auto2) -> set(sort_initial_sos).
% 1.26/1.53 % set(auto2) -> assign(sos_limit, -1).
% 1.26/1.53 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.26/1.53 % set(auto2) -> assign(max_megs, 400).
% 1.26/1.53 % set(auto2) -> assign(stats, some).
% 1.26/1.53 % set(auto2) -> clear(echo_input).
% 1.26/1.53 % set(auto2) -> set(quiet).
% 1.26/1.53 % set(auto2) -> clear(print_initial_clauses).
% 1.26/1.53 % set(auto2) -> clear(print_given).
% 1.26/1.53 assign(lrs_ticks,-1).
% 1.26/1.53 assign(sos_limit,10000).
% 1.26/1.53 assign(order,kbo).
% 1.26/1.53 set(lex_order_vars).
% 1.26/1.53 clear(print_given).
% 1.26/1.53
% 1.26/1.53 % formulas(sos). % not echoed (3 formulas)
% 1.26/1.53
% 1.26/1.53 ============================== end of input ==========================
% 1.26/1.53
% 1.26/1.53 % From the command line: assign(max_seconds, 300).
% 1.26/1.53
% 1.26/1.53 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.26/1.53
% 1.26/1.53 % Formulas that are not ordinary clauses:
% 1.26/1.53
% 1.26/1.53 ============================== end of process non-clausal formulas ===
% 1.26/1.53
% 1.26/1.53 ============================== PROCESS INITIAL CLAUSES ===============
% 1.26/1.53
% 1.26/1.53 ============================== PREDICATE ELIMINATION =================
% 1.26/1.53
% 1.26/1.53 ============================== end predicate elimination =============
% 1.26/1.53
% 1.26/1.53 Auto_denials:
% 1.26/1.53 % copying label prove_these_axioms_2 to answer in negative clause
% 1.26/1.53
% 1.26/1.53 Term ordering decisions:
% 1.26/1.53
% 1.26/1.53 % Assigning unary symbol inverse kb_weight 0 and highest precedence (6).
% 1.26/1.53 Function symbol KB weights: a2=1. b2=1. double_divide=1. multiply=1. inverse=0.
% 1.26/1.53
% 1.26/1.53 ============================== end of process initial clauses ========
% 1.26/1.53
% 1.26/1.53 ============================== CLAUSES FOR SEARCH ====================
% 1.26/1.53
% 1.26/1.53 ============================== end of clauses for search =============
% 1.26/1.53
% 1.26/1.53 ============================== SEARCH ================================
% 1.26/1.53
% 1.26/1.53 % Starting search at 0.01 seconds.
% 1.26/1.53
% 1.26/1.53 ============================== PROOF =================================
% 1.26/1.53 % SZS status Unsatisfiable
% 1.26/1.53 % SZS output start Refutation
% 1.26/1.53
% 1.26/1.53 % Proof 1 at 0.53 (+ 0.01) seconds: prove_these_axioms_2.
% 1.26/1.53 % Length of proof is 132.
% 1.26/1.53 % Level of proof is 38.
% 1.26/1.53 % Maximum clause weight is 60.000.
% 1.26/1.53 % Given clauses 32.
% 1.26/1.53
% 1.26/1.53 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 1.26/1.53 2 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),double_divide(D,double_divide(B,D))))) = C # label(single_axiom) # label(axiom). [assumption].
% 1.26/1.53 3 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 1.26/1.53 4 inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 # answer(prove_these_axioms_2). [copy(3),rewrite([1(4),1(7)])].
% 1.26/1.53 5 inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),double_divide(D,double_divide(B,D)))) = double_divide(inverse(E),inverse(double_divide(inverse(double_divide(E,C)),double_divide(F,double_divide(inverse(A),F))))). [para(2(a,1),2(a,1,2,1,1,1,2)),flip(a)].
% 1.26/1.53 6 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(inverse(B),C))),double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(D,E))),double_divide(F,double_divide(D,F)))),E)))) = C. [para(2(a,1),2(a,1,2,1,2,2))].
% 1.26/1.53 7 inverse(inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),double_divide(D,double_divide(B,D))))) = inverse(double_divide(inverse(E),inverse(double_divide(inverse(double_divide(E,C)),double_divide(F,double_divide(inverse(A),F)))))). [para(5(a,2),1(a,2,1)),rewrite([1(9)]),flip(a)].
% 1.26/1.53 8 double_divide(double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(D,double_divide(E,B))),double_divide(F,double_divide(E,F))),double_divide(V6,V7))),double_divide(V8,double_divide(V6,V8))))) = V7. [para(5(a,1),2(a,1,1))].
% 1.26/1.53 9 double_divide(inverse(inverse(double_divide(A,double_divide(B,C)))),inverse(double_divide(double_divide(inverse(D),inverse(double_divide(inverse(double_divide(D,C)),double_divide(E,double_divide(inverse(A),E))))),double_divide(F,double_divide(V6,F))))) = double_divide(B,V6). [para(5(a,1),2(a,1,2,1,1))].
% 1.26/1.53 10 double_divide(inverse(A),double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,double_divide(inverse(A),D)))))) = C. [para(5(a,1),2(a,1,2))].
% 1.26/1.53 11 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C)))) = double_divide(inverse(E),inverse(double_divide(inverse(double_divide(E,inverse(double_divide(inverse(double_divide(D,double_divide(F,B))),double_divide(V6,double_divide(F,V6)))))),double_divide(V7,double_divide(inverse(A),V7))))). [para(5(a,2),2(a,1,2,1,1,1,2)),flip(a)].
% 1.26/1.53 13 inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),C)))),double_divide(D,double_divide(B,D)))) = C. [para(5(a,2),2(a,1))].
% 1.26/1.53 48 double_divide(inverse(A),double_divide(B,inverse(A))) = double_divide(C,double_divide(B,C)). [para(5(a,1),10(a,1,2,2,1,1)),rewrite([9(20)])].
% 1.26/1.53 54 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,double_divide(A,D)))))) = C. [para(13(a,1),10(a,1,1)),rewrite([13(12)])].
% 1.26/1.53 82 double_divide(A,double_divide(B,A)) = double_divide(C,double_divide(B,C)). [para(13(a,1),48(a,1,1)),rewrite([13(9)])].
% 1.26/1.53 85 inverse(double_divide(A,double_divide(B,A))) = inverse(double_divide(C,double_divide(B,C))). [para(82(a,1),1(a,2,1)),rewrite([1(2)])].
% 1.26/1.53 86 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(E,D))))) = double_divide(C,E). [para(82(a,1),2(a,1,2,1,1,1,2))].
% 1.26/1.53 87 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(B,double_divide(C,B))),double_divide(D,double_divide(C,D))))) = A. [para(82(a,1),2(a,1,2,1,1,1))].
% 1.26/1.53 90 inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),double_divide(C,double_divide(B,C)))) = double_divide(inverse(D),inverse(double_divide(inverse(double_divide(D,E)),double_divide(F,double_divide(inverse(E),F))))). [para(82(a,1),5(a,1,1,1,1))].
% 1.26/1.54 93 inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(A),B)))),double_divide(C,double_divide(D,C)))) = D. [para(82(a,1),13(a,1,1,1,1,2))].
% 1.26/1.54 95 double_divide(double_divide(A,B),double_divide(C,double_divide(A,C))) = double_divide(D,double_divide(B,D)). [para(82(a,1),82(a,1,2))].
% 1.26/1.54 108 inverse(double_divide(inverse(double_divide(A,double_divide(inverse(B),C))),double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(D,E))),double_divide(F,double_divide(D,F)))),E))) = inverse(double_divide(inverse(double_divide(A,double_divide(V6,C))),double_divide(V7,double_divide(V6,V7)))). [para(6(a,1),13(a,1,1,1,1,2,2)),flip(a)].
% 1.26/1.54 127 inverse(double_divide(inverse(double_divide(double_divide(A,double_divide(B,A)),double_divide(C,D))),double_divide(E,double_divide(C,E)))) = double_divide(inverse(F),inverse(double_divide(inverse(double_divide(F,D)),double_divide(V6,double_divide(inverse(double_divide(V7,double_divide(B,V7))),V6))))). [para(85(a,1),5(a,2,2,1,2,2,1))].
% 1.26/1.54 133 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(inverse(B),C))),double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(D,E))),double_divide(F,double_divide(D,F)))),E))),C)) = inverse(double_divide(V6,double_divide(inverse(A),V6))). [para(6(a,1),85(a,1,1,2))].
% 1.26/1.54 136 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(double_divide(B,C),double_divide(D,double_divide(B,D))))),double_divide(E,double_divide(F,E))))) = double_divide(C,F). [para(95(a,2),2(a,1,2,1,1,1,2))].
% 1.26/1.54 142 inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(C,B)))),double_divide(D,double_divide(double_divide(E,C),D)))) = double_divide(E,inverse(A)). [para(95(a,1),5(a,1,1,1,1,2)),rewrite([86(20)])].
% 1.26/1.54 145 inverse(double_divide(inverse(double_divide(A,double_divide(double_divide(B,C),double_divide(D,double_divide(B,D))))),double_divide(E,double_divide(F,E)))) = double_divide(inverse(V6),inverse(double_divide(inverse(double_divide(V6,double_divide(C,F))),double_divide(V7,double_divide(inverse(A),V7))))). [para(95(a,2),5(a,1,1,1,1,2))].
% 1.26/1.54 169 double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(inverse(C),D))),double_divide(inverse(double_divide(inverse(double_divide(C,double_divide(E,F))),double_divide(V6,double_divide(E,V6)))),F))),A)) = double_divide(D,double_divide(V7,double_divide(inverse(B),V7))). [para(6(a,1),95(a,1,1)),flip(a)].
% 1.26/1.54 215 inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,double_divide(F,E)))))))),double_divide(V6,double_divide(B,V6)))) = double_divide(inverse(F),inverse(double_divide(inverse(D),double_divide(V7,double_divide(inverse(A),V7))))). [para(54(a,1),5(a,2,2,1,1,1))].
% 1.26/1.54 233 double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,double_divide(E,D))))),A)) = double_divide(C,double_divide(F,double_divide(E,F))). [para(54(a,1),95(a,1,1)),flip(a)].
% 1.26/1.54 234 double_divide(double_divide(A,B),double_divide(double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,double_divide(A,E))))),D)) = double_divide(F,double_divide(B,F)). [para(54(a,1),95(a,1,2,2))].
% 1.26/1.54 235 double_divide(double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(D,C))))),B) = double_divide(double_divide(E,D),double_divide(F,double_divide(E,F))). [para(54(a,1),95(a,2,2)),flip(a)].
% 1.26/1.54 244 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(D,C))))) = double_divide(E,double_divide(inverse(D),inverse(double_divide(inverse(B),double_divide(F,double_divide(E,F)))))). [para(54(a,1),54(a,1,2,2,1,1,1)),flip(a)].
% 1.26/1.54 331 double_divide(inverse(A),double_divide(B,inverse(double_divide(C,double_divide(B,C))))) = A. [para(95(a,1),87(a,1,2,1,1,1,2)),rewrite([142(12)])].
% 1.26/1.54 354 inverse(double_divide(inverse(double_divide(A,double_divide(inverse(B),C))),double_divide(double_divide(D,inverse(double_divide(E,double_divide(D,E)))),B))) = double_divide(inverse(F),inverse(double_divide(inverse(double_divide(F,C)),double_divide(V6,double_divide(inverse(A),V6))))). [para(331(a,1),5(a,1,1,2,2))].
% 1.26/1.54 360 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C)))) = inverse(double_divide(D,double_divide(inverse(A),D))). [para(331(a,1),13(a,1,1,1,1,2))].
% 1.26/1.54 363 double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C) = double_divide(D,double_divide(inverse(C),D)). [para(331(a,1),82(a,1,2))].
% 1.26/1.54 364 double_divide(inverse(A),double_divide(B,inverse(double_divide(double_divide(C,B),double_divide(D,double_divide(C,D)))))) = A. [para(82(a,1),331(a,1,2,2,1,2))].
% 1.26/1.54 371 inverse(double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C)) = inverse(double_divide(D,double_divide(inverse(C),D))). [para(331(a,1),85(a,1,1,2))].
% 1.26/1.54 393 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(double_divide(B,inverse(double_divide(C,double_divide(B,C)))),D))),double_divide(E,double_divide(F,double_divide(inverse(E),F)))))) = D. [para(363(a,1),2(a,1,2,1,2,2))].
% 1.26/1.54 399 inverse(double_divide(inverse(double_divide(A,double_divide(B,double_divide(inverse(C),B)))),double_divide(D,double_divide(double_divide(E,inverse(double_divide(F,double_divide(E,F)))),D)))) = double_divide(inverse(V6),inverse(double_divide(inverse(double_divide(V6,C)),double_divide(V7,double_divide(inverse(A),V7))))). [para(363(a,1),5(a,1,1,1,1,2))].
% 1.26/1.54 401 inverse(double_divide(inverse(double_divide(A,double_divide(double_divide(B,inverse(double_divide(C,double_divide(B,C)))),D))),double_divide(E,double_divide(F,double_divide(inverse(E),F))))) = double_divide(inverse(V6),inverse(double_divide(inverse(double_divide(V6,D)),double_divide(V7,double_divide(inverse(A),V7))))). [para(363(a,1),5(a,1,1,2,2))].
% 1.26/1.54 460 double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,double_divide(F,double_divide(inverse(E),F))))))) = D. [para(363(a,1),54(a,1,2,2,1,2,2))].
% 1.26/1.54 463 double_divide(A,double_divide(inverse(B),inverse(double_divide(inverse(double_divide(double_divide(C,inverse(double_divide(D,double_divide(C,D)))),E)),double_divide(F,double_divide(A,F)))))) = double_divide(inverse(E),B). [para(363(a,2),54(a,1,2,2,1,1,1))].
% 1.26/1.54 478 double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,double_divide(inverse(F),E)))))) = double_divide(V6,double_divide(inverse(inverse(double_divide(inverse(double_divide(F,double_divide(V7,D))),double_divide(V8,double_divide(V7,V8))))),V6)). [para(7(a,2),363(a,2,2,1))].
% 1.26/1.54 549 double_divide(inverse(A),double_divide(B,inverse(double_divide(double_divide(double_divide(C,inverse(double_divide(D,double_divide(C,D)))),B),double_divide(E,double_divide(F,double_divide(inverse(E),F))))))) = A. [para(363(a,1),364(a,1,2,2,1,2,2))].
% 1.26/1.54 611 double_divide(double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(D,double_divide(E,B))),double_divide(double_divide(F,E),double_divide(double_divide(V6,F),double_divide(V7,double_divide(V6,V7))))),double_divide(V8,V9))),double_divide(V10,double_divide(V8,V10))))) = V9. [para(95(a,2),8(a,1,2,1,1,1,1,2,2))].
% 1.26/1.54 612 double_divide(double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(D,double_divide(E,B))),double_divide(F,double_divide(E,F))),double_divide(double_divide(V6,V7),double_divide(V8,double_divide(V6,V8))))),double_divide(V9,double_divide(V10,V9))))) = double_divide(V7,V10). [para(95(a,2),8(a,1,2,1,1,1,2))].
% 1.26/1.54 727 inverse(double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(B,C)))))) = A. [para(363(a,1),93(a,1,1,2)),rewrite([93(15)])].
% 1.26/1.54 741 inverse(double_divide(A,double_divide(B,A))) = double_divide(inverse(C),inverse(double_divide(C,double_divide(D,double_divide(B,D))))). [para(727(a,1),2(a,1,2,1,1)),flip(a)].
% 1.26/1.54 749 inverse(double_divide(A,double_divide(B,inverse(double_divide(double_divide(C,B),double_divide(D,double_divide(C,D))))))) = A. [para(82(a,1),727(a,1,1,2,2,1,2))].
% 1.26/1.54 843 inverse(double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(D,double_divide(E,D))))))),double_divide(F,double_divide(B,F)))) = double_divide(inverse(inverse(C)),inverse(double_divide(inverse(inverse(double_divide(V6,double_divide(E,V6)))),double_divide(V7,double_divide(inverse(A),V7))))). [para(741(a,2),5(a,2,2,1,1,1))].
% 1.26/1.54 855 inverse(double_divide(A,double_divide(B,A))) = double_divide(inverse(double_divide(B,C)),inverse(double_divide(D,double_divide(C,D)))). [para(82(a,1),741(a,2,2,1))].
% 1.26/1.54 903 double_divide(inverse(A),double_divide(B,double_divide(inverse(C),inverse(double_divide(C,double_divide(D,double_divide(B,D))))))) = A. [para(741(a,1),331(a,1,2,2))].
% 1.26/1.54 906 inverse(double_divide(A,double_divide(inverse(B),A))) = double_divide(inverse(C),inverse(double_divide(C,double_divide(double_divide(D,inverse(double_divide(E,double_divide(D,E)))),B)))). [para(331(a,1),741(a,2,2,1,2,2))].
% 1.26/1.54 940 inverse(double_divide(A,double_divide(B,double_divide(inverse(C),inverse(double_divide(C,double_divide(D,double_divide(B,D)))))))) = A. [para(741(a,1),727(a,1,1,2,2))].
% 1.26/1.54 974 double_divide(inverse(inverse(double_divide(A,double_divide(B,A)))),inverse(double_divide(double_divide(inverse(C),inverse(double_divide(inverse(double_divide(C,D)),double_divide(E,double_divide(inverse(D),E))))),double_divide(F,double_divide(V6,F))))) = double_divide(B,V6). [para(82(a,1),9(a,1,1,1,1))].
% 1.26/1.54 999 double_divide(inverse(inverse(double_divide(A,double_divide(B,C)))),inverse(double_divide(double_divide(inverse(D),inverse(double_divide(inverse(double_divide(D,C)),double_divide(E,double_divide(inverse(A),E))))),double_divide(double_divide(F,V6),double_divide(double_divide(V7,F),double_divide(V8,double_divide(V7,V8))))))) = double_divide(B,V6). [para(95(a,2),9(a,1,2,1,2,2))].
% 1.26/1.54 1014 double_divide(inverse(inverse(double_divide(A,double_divide(B,C)))),inverse(double_divide(double_divide(inverse(D),inverse(double_divide(inverse(double_divide(D,C)),double_divide(E,double_divide(inverse(A),E))))),double_divide(double_divide(inverse(F),inverse(double_divide(inverse(double_divide(F,V6)),double_divide(V7,double_divide(V8,V7))))),V6)))) = double_divide(B,V8). [para(54(a,1),9(a,1,2,1,2,2))].
% 1.26/1.54 1041 double_divide(inverse(inverse(double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C))),inverse(double_divide(double_divide(inverse(D),inverse(double_divide(inverse(double_divide(D,E)),double_divide(F,double_divide(inverse(E),F))))),double_divide(V6,double_divide(V7,V6))))) = double_divide(inverse(C),V7). [para(363(a,2),9(a,1,1,1,1))].
% 1.26/1.54 1163 double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(B,C)),inverse(double_divide(D,double_divide(C,D)))))) = A. [para(855(a,1),331(a,1,2,2))].
% 1.26/1.54 1173 inverse(double_divide(A,double_divide(B,A))) = double_divide(B,inverse(double_divide(C,double_divide(D,double_divide(inverse(C),D))))). [para(363(a,1),855(a,2,2,1,2)),rewrite([727(9)])].
% 1.26/1.54 1231 inverse(double_divide(A,double_divide(inverse(double_divide(B,C)),A))) = double_divide(inverse(inverse(double_divide(D,double_divide(B,D)))),inverse(double_divide(E,double_divide(inverse(double_divide(F,double_divide(C,F))),E)))). [para(855(a,2),855(a,2,1,1))].
% 1.26/1.54 1233 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C))))) = double_divide(D,double_divide(inverse(E),inverse(double_divide(E,double_divide(F,double_divide(D,F)))))). [para(903(a,1),2(a,1,2,1,1,1,2))].
% 1.26/1.54 1305 double_divide(inverse(A),double_divide(B,double_divide(inverse(inverse(double_divide(C,double_divide(D,double_divide(inverse(C),D))))),B))) = A. [para(93(a,1),903(a,1,2,2,2))].
% 1.26/1.54 1345 inverse(double_divide(A,double_divide(B,double_divide(C,B)))) = inverse(double_divide(A,double_divide(D,double_divide(C,D)))). [para(940(a,1),13(a,1,1,1))].
% 1.26/1.54 1423 double_divide(A,double_divide(B,double_divide(C,B))) = double_divide(A,double_divide(D,double_divide(C,D))). [para(1345(a,1),87(a,1,1)),rewrite([87(12)])].
% 1.26/1.54 1481 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,double_divide(inverse(D),E))),double_divide(inverse(double_divide(inverse(double_divide(D,double_divide(F,V6))),double_divide(V7,double_divide(F,V7)))),V6))),E))) = double_divide(inverse(V8),inverse(double_divide(inverse(double_divide(V8,inverse(double_divide(inverse(double_divide(C,double_divide(V9,B))),double_divide(V10,double_divide(V9,V10)))))),double_divide(V11,double_divide(inverse(A),V11))))). [para(6(a,1),11(a,1,1,2,2))].
% 1.26/1.54 1551 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(double_divide(D,inverse(double_divide(E,double_divide(D,E))))),C)))) = double_divide(inverse(F),inverse(double_divide(inverse(double_divide(F,inverse(double_divide(inverse(double_divide(V6,double_divide(inverse(double_divide(V7,B)),V6))),double_divide(V8,double_divide(V7,V8)))))),double_divide(V9,double_divide(inverse(A),V9))))). [para(363(a,1),11(a,2,2,1,1,1,2,1,1,1))].
% 1.26/1.54 1552 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C)))) = double_divide(inverse(E),inverse(double_divide(inverse(double_divide(E,inverse(double_divide(inverse(double_divide(D,double_divide(double_divide(F,inverse(double_divide(V6,double_divide(F,V6)))),B))),double_divide(V7,double_divide(V8,double_divide(inverse(V7),V8))))))),double_divide(V9,double_divide(inverse(A),V9))))). [para(363(a,1),11(a,2,2,1,1,1,2,1,2,2))].
% 1.26/1.54 1587 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(C,double_divide(D,C)))))),double_divide(E,double_divide(inverse(F),E))))) = inverse(double_divide(F,double_divide(B,D))). [para(93(a,1),11(a,2,2,1,1,1,2,1,1)),rewrite([1305(12)]),flip(a)].
% 1.26/1.54 1695 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(double_divide(D,inverse(double_divide(E,double_divide(D,E))))),C)))) = inverse(double_divide(A,double_divide(inverse(double_divide(F,double_divide(inverse(double_divide(V6,B)),F))),V6))). [back_rewrite(1551),rewrite([1587(29)])].
% 1.26/1.54 1727 inverse(double_divide(inverse(double_divide(A,B)),double_divide(inverse(double_divide(inverse(double_divide(C,double_divide(inverse(D),E))),double_divide(inverse(double_divide(inverse(double_divide(D,double_divide(F,V6))),double_divide(V7,double_divide(F,V7)))),V6))),E))) = inverse(double_divide(A,double_divide(inverse(double_divide(C,double_divide(V8,B))),V8))). [back_rewrite(1481),rewrite([1587(35)])].
% 1.26/1.54 1856 double_divide(A,double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(inverse(C),D))),double_divide(inverse(double_divide(inverse(double_divide(C,double_divide(E,F))),double_divide(V6,double_divide(E,V6)))),F))),D)) = double_divide(A,double_divide(V7,double_divide(inverse(B),V7))). [para(6(a,1),1423(a,1,2,2))].
% 1.26/1.54 1867 double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),double_divide(D,double_divide(E,D))))),C)) = double_divide(A,double_divide(F,double_divide(E,F))). [para(54(a,1),1423(a,1,2,2))].
% 1.26/1.54 1970 double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(inverse(double_divide(double_divide(C,inverse(double_divide(D,double_divide(C,D)))),E)),inverse(double_divide(F,double_divide(E,F))))),B))) = A. [para(363(a,1),1163(a,1,2))].
% 1.26/1.54 2041 inverse(double_divide(A,double_divide(B,A))) = double_divide(B,inverse(double_divide(C,double_divide(inverse(double_divide(inverse(double_divide(C,double_divide(D,E))),double_divide(F,double_divide(D,F)))),E)))). [para(2(a,1),1173(a,2,2,1,2,2))].
% 1.26/1.54 2055 inverse(double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(inverse(A),C)))))),double_divide(D,double_divide(B,D)))) = inverse(double_divide(E,double_divide(F,double_divide(inverse(E),F)))). [para(1173(a,2),13(a,1,1,1,1,2,2))].
% 1.26/1.54 2121 double_divide(inverse(A),double_divide(B,double_divide(C,double_divide(inverse(B),C)))) = A. [para(1173(a,2),364(a,1,2,2,1,1)),rewrite([87(14)])].
% 1.26/1.54 2145 inverse(double_divide(A,double_divide(B,double_divide(C,double_divide(inverse(B),C))))) = A. [para(1173(a,2),749(a,1,1,2,2,1,1)),rewrite([87(13)])].
% 1.26/1.54 2201 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(D),C)))) = double_divide(inverse(E),inverse(double_divide(inverse(double_divide(E,inverse(double_divide(D,double_divide(double_divide(F,inverse(double_divide(V6,double_divide(F,V6)))),B))))),double_divide(V7,double_divide(inverse(A),V7))))). [back_rewrite(1552),rewrite([2121(20)])].
% 1.26/1.54 2207 double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),double_divide(inverse(C),inverse(double_divide(C,D)))) = D. [back_rewrite(460),rewrite([2121(12)])].
% 1.26/1.54 2210 inverse(double_divide(A,double_divide(double_divide(B,inverse(double_divide(C,double_divide(B,C)))),D))) = double_divide(inverse(E),inverse(double_divide(inverse(double_divide(E,D)),double_divide(F,double_divide(inverse(A),F))))). [back_rewrite(401),rewrite([2121(12)])].
% 1.26/1.54 2211 double_divide(inverse(A),inverse(double_divide(A,double_divide(double_divide(B,inverse(double_divide(C,double_divide(B,C)))),D)))) = D. [back_rewrite(393),rewrite([2121(13)])].
% 1.26/1.54 2217 double_divide(inverse(A),double_divide(B,double_divide(double_divide(C,inverse(double_divide(D,double_divide(C,D)))),B))) = A. [back_rewrite(549),rewrite([2145(12)])].
% 1.26/1.54 2221 inverse(double_divide(A,double_divide(inverse(B),A))) = B. [back_rewrite(906),rewrite([2211(13)])].
% 1.26/1.54 2230 inverse(double_divide(A,double_divide(B,double_divide(inverse(C),B)))) = double_divide(inverse(D),inverse(double_divide(inverse(double_divide(D,C)),double_divide(E,double_divide(inverse(A),E))))). [back_rewrite(399),rewrite([2217(12)])].
% 1.26/1.54 2249 inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),double_divide(C,double_divide(B,C)))) = inverse(double_divide(D,double_divide(E,double_divide(inverse(D),E)))). [back_rewrite(2055),rewrite([2221(4)])].
% 1.26/1.54 2271 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(double_divide(D,inverse(double_divide(E,double_divide(D,E))))),C)))) = inverse(double_divide(A,double_divide(double_divide(F,B),F))). [back_rewrite(1695),rewrite([2221(16)])].
% 1.26/1.54 2281 double_divide(inverse(inverse(double_divide(A,double_divide(B,A)))),double_divide(C,double_divide(D,C))) = double_divide(B,D). [back_rewrite(1231),rewrite([2221(5),2221(11)]),flip(a)].
% 1.26/1.54 2332 inverse(double_divide(double_divide(A,inverse(double_divide(B,double_divide(A,B)))),C)) = C. [back_rewrite(371),rewrite([2221(10)])].
% 1.26/1.54 2333 inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(inverse(B),C)))) = A. [back_rewrite(360),rewrite([2221(11)])].
% 1.26/1.54 2341 inverse(double_divide(inverse(double_divide(inverse(double_divide(A,double_divide(inverse(B),C))),double_divide(inverse(double_divide(inverse(double_divide(B,double_divide(D,E))),double_divide(F,double_divide(D,F)))),E))),C)) = A. [back_rewrite(133),rewrite([2221(20)])].
% 1.26/1.54 2370 inverse(double_divide(inverse(double_divide(A,double_divide(B,inverse(double_divide(C,double_divide(D,double_divide(E,D))))))),double_divide(F,double_divide(B,F)))) = double_divide(inverse(inverse(C)),inverse(double_divide(E,inverse(A)))). [back_rewrite(843),rewrite([2281(21)])].
% 1.26/1.54 2376 double_divide(inverse(A),double_divide(B,double_divide(inverse(double_divide(C,inverse(double_divide(D,double_divide(C,D))))),B))) = A. [back_rewrite(1970),rewrite([2332(7)])].
% 1.26/1.54 2382 double_divide(inverse(A),inverse(double_divide(double_divide(inverse(B),B),double_divide(C,double_divide(D,C))))) = double_divide(inverse(A),D). [back_rewrite(1041),rewrite([2332(6),2333(9)])].
% 1.26/1.54 2388 double_divide(A,double_divide(inverse(B),inverse(double_divide(C,double_divide(D,double_divide(A,D)))))) = double_divide(inverse(C),B). [back_rewrite(463),rewrite([2332(7)])].
% 1.26/1.54 2401 double_divide(inverse(A),A) = double_divide(inverse(B),B). [back_rewrite(1233),rewrite([2333(8),2388(9)])].
% 1.26/1.54 2408 double_divide(inverse(inverse(double_divide(A,double_divide(B,A)))),C) = double_divide(B,C). [back_rewrite(974),rewrite([2333(12),2382(11)])].
% 1.26/1.54 2422 inverse(double_divide(inverse(double_divide(A,double_divide(B,A))),double_divide(C,double_divide(B,C)))) = double_divide(inverse(D),D). [back_rewrite(90),rewrite([2333(15)])].
% 1.26/1.54 2464 inverse(double_divide(A,double_divide(double_divide(B,C),B))) = inverse(double_divide(A,C)). [back_rewrite(2271),rewrite([2376(10)]),flip(a)].
% 1.26/1.54 2557 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),double_divide(C,double_divide(D,C))))) = double_divide(inverse(inverse(B)),D). [back_rewrite(244),rewrite([2388(16)])].
% 1.26/1.54 2564 double_divide(A,double_divide(inverse(inverse(B)),A)) = B. [back_rewrite(54),rewrite([2557(8)])].
% 1.26/1.54 2566 double_divide(inverse(A),A) = c_0. [new_symbol(2401)].
% 1.26/1.54 2568 double_divide(A,double_divide(B,double_divide(C,B))) = double_divide(A,C). [back_rewrite(2281),rewrite([2408(7)])].
% 1.26/1.54 2738 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),inverse(C)))) = inverse(double_divide(C,inverse(B))). [back_rewrite(2230),rewrite([2568(4),2568(10)]),flip(a)].
% 1.26/1.54 2740 inverse(double_divide(A,double_divide(double_divide(B,inverse(double_divide(C,double_divide(B,C)))),D))) = inverse(double_divide(A,inverse(D))). [back_rewrite(2210),rewrite([2568(14),2738(14)])].
% 1.26/1.54 2743 inverse(double_divide(inverse(double_divide(A,B)),inverse(C))) = inverse(double_divide(A,inverse(inverse(double_divide(C,inverse(B)))))). [back_rewrite(2201),rewrite([2568(6),2740(13),2568(15),2738(15)])].
% 1.26/1.54 2773 double_divide(A,double_divide(double_divide(inverse(B),inverse(double_divide(inverse(double_divide(B,C)),D))),C)) = double_divide(A,D). [back_rewrite(1867),rewrite([2568(6),2568(11)])].
% 1.26/1.54 2867 double_divide(inverse(inverse(double_divide(A,double_divide(B,C)))),inverse(double_divide(double_divide(inverse(D),inverse(double_divide(D,inverse(inverse(double_divide(A,inverse(C))))))),E))) = double_divide(B,E). [back_rewrite(1014),rewrite([2568(11),2743(10),2568(18),2773(20)])].
% 1.26/1.54 2873 double_divide(A,double_divide(double_divide(B,C),double_divide(double_divide(D,B),D))) = double_divide(A,C). [back_rewrite(999),rewrite([2568(11),2743(10),2568(17),2867(19)])].
% 1.26/1.54 2949 double_divide(double_divide(inverse(A),inverse(double_divide(A,inverse(inverse(double_divide(B,inverse(C))))))),inverse(double_divide(inverse(double_divide(double_divide(inverse(double_divide(B,double_divide(D,C))),D),E)),F))) = double_divide(E,F). [back_rewrite(612),rewrite([2568(7),2743(6),2568(14),2568(16),2464(16),2568(17)])].
% 1.26/1.54 2950 double_divide(double_divide(A,B),A) = B. [back_rewrite(611),rewrite([2568(7),2743(6),2568(16),2873(16),2568(18),2949(18)])].
% 1.26/1.54 2975 double_divide(inverse(double_divide(A,double_divide(B,C))),B) = inverse(inverse(double_divide(A,inverse(C)))). [back_rewrite(478),rewrite([2568(11),2743(10),2207(13),2568(10),2564(12)]),flip(a)].
% 1.26/1.54 2988 double_divide(inverse(A),inverse(double_divide(A,inverse(inverse(double_divide(B,inverse(C))))))) = inverse(inverse(inverse(double_divide(B,inverse(C))))). [back_rewrite(354),rewrite([2740(11),2975(6),2568(12),2743(11)]),flip(a)].
% 1.26/1.54 3010 double_divide(double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),C))),B) = C. [back_rewrite(235),rewrite([2568(6),2568(11),2950(9)])].
% 1.26/1.54 3011 double_divide(A,double_divide(B,A)) = B. [back_rewrite(234),rewrite([2568(7),3010(8),2950(2)]),flip(a)].
% 1.26/1.54 3012 double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,B)),C))) = double_divide(B,C). [back_rewrite(233),rewrite([3011(5),3011(8),3011(8)])].
% 1.26/1.54 3017 inverse(inverse(inverse(double_divide(A,inverse(double_divide(B,C)))))) = double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))). [back_rewrite(215),rewrite([3011(5),3012(6),3011(6),2975(5),3011(11)])].
% 1.26/1.54 3019 inverse(double_divide(inverse(double_divide(A,B)),C)) = double_divide(inverse(C),inverse(double_divide(inverse(B),inverse(A)))). [back_rewrite(145),rewrite([3011(3),2950(2),3011(4),3011(11),2743(11),2988(13),3017(10)])].
% 1.26/1.54 3022 double_divide(inverse(A),double_divide(inverse(B),inverse(double_divide(inverse(C),inverse(A))))) = double_divide(C,B). [back_rewrite(136),rewrite([3011(4),2950(3),3011(5),3019(5)])].
% 1.26/1.54 3023 inverse(inverse(inverse(double_divide(A,inverse(B))))) = double_divide(B,inverse(A)). [back_rewrite(127),rewrite([3011(2),3011(5),2975(4),3011(10),3011(11),3019(11),3022(14)])].
% 1.26/1.54 3030 inverse(inverse(A)) = A. [back_rewrite(2341),rewrite([3011(9),2975(8),3023(9),2950(7),2975(6),3023(5),2950(3)])].
% 1.26/1.54 3035 double_divide(A,double_divide(double_divide(double_divide(inverse(B),inverse(double_divide(B,inverse(C)))),double_divide(D,inverse(double_divide(inverse(E),C)))),E)) = double_divide(A,inverse(D)). [back_rewrite(1856),rewrite([3011(9),2975(8),3030(8),3019(10),3019(5),3030(3),3019(11),3030(7),3030(8),3011(15)])].
% 1.26/1.54 3038 inverse(double_divide(A,double_divide(B,inverse(C)))) = double_divide(B,inverse(double_divide(inverse(C),inverse(A)))). [back_rewrite(1727),rewrite([3011(11),2975(10),3030(10),3019(12),3019(7),3030(5),3019(13),3030(9),3030(10),3035(14),3019(5),3030(2),2975(9),3030(9)]),flip(a)].
% 1.26/1.54 3056 double_divide(double_divide(inverse(A),inverse(double_divide(A,inverse(B)))),double_divide(C,inverse(double_divide(inverse(D),B)))) = double_divide(D,inverse(C)). [back_rewrite(169),rewrite([3011(9),2975(8),3030(8),3019(10),3019(5),3030(3),3019(11),3030(7),3030(8),3011(12),3011(13)])].
% 1.26/1.54 3060 inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)). [back_rewrite(108),rewrite([3011(9),2975(8),3030(8),3019(10),3019(5),3030(3),3019(11),3030(7),3030(8),3056(10),3011(7),2975(6),3030(6)]),flip(a)].
% 1.26/1.54 3067 inverse(c_0) = c_0. [back_rewrite(2422),rewrite([3011(2),3011(3),2566(2),2566(4)])].
% 1.26/1.54 3073 inverse(double_divide(A,double_divide(B,C))) = double_divide(B,double_divide(A,inverse(C))). [back_rewrite(2370),rewrite([3011(2),3038(5),3060(5),3030(3),3011(5),2950(4),3030(5),3060(6)])].
% 1.26/1.54 3079 double_divide(A,inverse(A)) = c_0. [back_rewrite(2249),rewrite([3011(2),3011(3),2566(2),3067(2),3011(4),3060(4)]),flip(a)].
% 1.26/1.54 3085 double_divide(A,c_0) = inverse(A). [back_rewrite(2041),rewrite([3011(2),3073(4),3011(6),2950(5),3060(4),2950(4),3079(3),3067(3)]),flip(a)].
% 1.26/1.54 3140 $F # answer(prove_these_axioms_2). [back_rewrite(4),rewrite([3079(5),3067(3),3085(3),3030(3)]),xx(a)].
% 1.26/1.54
% 1.26/1.54 % SZS output end Refutation
% 1.26/1.54 ============================== end of proof ==========================
% 1.26/1.54
% 1.26/1.54 ============================== STATISTICS ============================
% 1.26/1.54
% 1.26/1.54 Given=32. Generated=6174. Kept=3138. proofs=1.
% 1.26/1.54 Usable=1. Sos=27. Demods=121. Limbo=94, Disabled=3019. Hints=0.
% 1.26/1.54 Megabytes=4.98.
% 1.26/1.54 User_CPU=0.53, System_CPU=0.01, Wall_clock=1.
% 1.26/1.54
% 1.26/1.54 ============================== end of statistics =====================
% 1.26/1.54
% 1.26/1.54 ============================== end of search =========================
% 1.26/1.54
% 1.26/1.54 THEOREM PROVED
% 1.26/1.54 % SZS status Unsatisfiable
% 1.26/1.54
% 1.26/1.54 Exiting with 1 proof.
% 1.26/1.54
% 1.26/1.54 Process 32573 exit (max_proofs) Mon Jun 13 09:47:41 2022
% 1.26/1.54 Prover9 interrupted
%------------------------------------------------------------------------------