TSTP Solution File: GRP105-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP105-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:17:10 EDT 2022
% Result : Unsatisfiable 0.81s 1.09s
% Output : Refutation 0.81s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP105-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.09/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 13 11:49:42 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.81/1.09 ============================== Prover9 ===============================
% 0.81/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.09 Process 27995 was started by sandbox2 on n021.cluster.edu,
% 0.81/1.09 Mon Jun 13 11:49:42 2022
% 0.81/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27842_n021.cluster.edu".
% 0.81/1.09 ============================== end of head ===========================
% 0.81/1.09
% 0.81/1.09 ============================== INPUT =================================
% 0.81/1.09
% 0.81/1.09 % Reading from file /tmp/Prover9_27842_n021.cluster.edu
% 0.81/1.09
% 0.81/1.09 set(prolog_style_variables).
% 0.81/1.09 set(auto2).
% 0.81/1.09 % set(auto2) -> set(auto).
% 0.81/1.09 % set(auto) -> set(auto_inference).
% 0.81/1.09 % set(auto) -> set(auto_setup).
% 0.81/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.09 % set(auto) -> set(auto_limits).
% 0.81/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.09 % set(auto) -> set(auto_denials).
% 0.81/1.09 % set(auto) -> set(auto_process).
% 0.81/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.09 % set(auto2) -> assign(stats, some).
% 0.81/1.09 % set(auto2) -> clear(echo_input).
% 0.81/1.09 % set(auto2) -> set(quiet).
% 0.81/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.09 % set(auto2) -> clear(print_given).
% 0.81/1.09 assign(lrs_ticks,-1).
% 0.81/1.09 assign(sos_limit,10000).
% 0.81/1.09 assign(order,kbo).
% 0.81/1.09 set(lex_order_vars).
% 0.81/1.09 clear(print_given).
% 0.81/1.09
% 0.81/1.09 % formulas(sos). % not echoed (3 formulas)
% 0.81/1.09
% 0.81/1.09 ============================== end of input ==========================
% 0.81/1.09
% 0.81/1.09 % From the command line: assign(max_seconds, 300).
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.09
% 0.81/1.09 % Formulas that are not ordinary clauses:
% 0.81/1.09
% 0.81/1.09 ============================== end of process non-clausal formulas ===
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.09
% 0.81/1.09 ============================== PREDICATE ELIMINATION =================
% 0.81/1.09
% 0.81/1.09 ============================== end predicate elimination =============
% 0.81/1.09
% 0.81/1.09 Auto_denials:
% 0.81/1.09 % copying label prove_these_axioms to answer in negative clause
% 0.81/1.09
% 0.81/1.09 Term ordering decisions:
% 0.81/1.09
% 0.81/1.09 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.81/1.09 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.
% 0.81/1.09
% 0.81/1.09 ============================== end of process initial clauses ========
% 0.81/1.09
% 0.81/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.81/1.09
% 0.81/1.09 ============================== end of clauses for search =============
% 0.81/1.09
% 0.81/1.09 ============================== SEARCH ================================
% 0.81/1.09
% 0.81/1.09 % Starting search at 0.01 seconds.
% 0.81/1.09
% 0.81/1.09 ============================== PROOF =================================
% 0.81/1.09 % SZS status Unsatisfiable
% 0.81/1.09 % SZS output start Refutation
% 0.81/1.09
% 0.81/1.09 % Proof 1 at 0.05 (+ 0.00) seconds: prove_these_axioms.
% 0.81/1.09 % Length of proof is 41.
% 0.81/1.09 % Level of proof is 14.
% 0.81/1.09 % Maximum clause weight is 45.000.
% 0.81/1.09 % Given clauses 40.
% 0.81/1.09
% 0.81/1.09 1 multiply(A,B) = inverse(double_divide(B,A)) # label(multiply) # label(axiom). [assumption].
% 0.81/1.09 2 double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C # label(single_axiom) # label(axiom). [assumption].
% 0.81/1.09 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].
% 0.81/1.09 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)].
% 0.81/1.09 5 double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(B,C),inverse(double_divide(B,inverse(A))))),inverse(D))))),C) = D. [para(2(a,1),2(a,1,1,1,1))].
% 0.81/1.09 10 double_divide(inverse(double_divide(A,inverse(A))),inverse(B)) = B. [para(2(a,1),5(a,1,1,1,2,1))].
% 0.81/1.09 13 double_divide(inverse(double_divide(A,inverse(B))),inverse(A)) = B. [para(10(a,1),2(a,1,1,1,1)),rewrite([10(5)])].
% 0.81/1.09 15 double_divide(inverse(double_divide(A,inverse(double_divide(inverse(double_divide(B,inverse(A))),inverse(C))))),inverse(B)) = C. [para(10(a,1),5(a,1,1,1,2,1,1,1,1)),rewrite([10(5)])].
% 0.81/1.09 18 double_divide(inverse(inverse(double_divide(A,inverse(A)))),inverse(B)) = B. [para(10(a,1),10(a,1,1,1))].
% 0.81/1.09 25 double_divide(inverse(A),inverse(inverse(double_divide(B,inverse(B))))) = A. [para(10(a,1),13(a,1,1,1))].
% 0.81/1.09 31 double_divide(inverse(A),inverse(inverse(inverse(double_divide(B,inverse(B)))))) = A. [para(18(a,1),13(a,1,1,1))].
% 0.81/1.09 33 double_divide(A,inverse(double_divide(inverse(A),inverse(B)))) = B. [para(25(a,1),2(a,1,1,1,1)),rewrite([25(11)])].
% 0.81/1.09 36 double_divide(inverse(double_divide(inverse(double_divide(double_divide(inverse(A),B),inverse(A))),inverse(C))),B) = C. [para(25(a,1),5(a,1,1,1,2,1,1,1,2,1)),rewrite([10(12)])].
% 0.81/1.09 38 double_divide(A,inverse(A)) = inverse(double_divide(B,inverse(B))). [para(25(a,1),10(a,1))].
% 0.81/1.09 41 double_divide(A,inverse(A)) = c_0. [new_symbol(38)].
% 0.81/1.09 42 inverse(double_divide(a2,inverse(c_0))) != 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). [back_unit_del(4),rewrite([41(4),41(6),41(10)]),xx(a)].
% 0.81/1.09 44 inverse(c_0) = c_0. [back_rewrite(38),rewrite([41(2),41(3)]),flip(a)].
% 0.81/1.09 49 double_divide(inverse(A),c_0) = A. [back_rewrite(31),rewrite([41(3),44(3),44(3),44(3)])].
% 0.81/1.09 53 inverse(double_divide(a2,c_0)) != 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). [back_rewrite(42),rewrite([44(3)])].
% 0.81/1.09 96 double_divide(inverse(double_divide(A,c_0)),inverse(B)) = inverse(double_divide(B,inverse(A))). [para(41(a,1),15(a,1,1,1,2,1)),rewrite([44(2)])].
% 0.81/1.09 109 double_divide(inverse(A),inverse(B)) = double_divide(inverse(B),inverse(A)). [para(33(a,1),13(a,1,1,1))].
% 0.81/1.09 111 double_divide(A,c_0) = inverse(A). [para(41(a,1),33(a,1,2,1)),rewrite([44(2)])].
% 0.81/1.09 113 double_divide(inverse(A),inverse(double_divide(B,inverse(C)))) = double_divide(inverse(C),inverse(inverse(double_divide(A,inverse(B))))). [para(33(a,1),15(a,1,1,1,2,1)),rewrite([109(5),109(11)])].
% 0.81/1.09 115 double_divide(inverse(A),inverse(inverse(B))) = double_divide(B,inverse(A)). [para(33(a,1),33(a,1,2,1)),rewrite([109(6)]),flip(a)].
% 0.81/1.09 126 inverse(double_divide(A,inverse(B))) = double_divide(inverse(A),inverse(inverse(B))). [back_rewrite(96),rewrite([111(2),109(4)]),flip(a)].
% 0.81/1.09 135 double_divide(double_divide(double_divide(inverse(inverse(inverse(A))),inverse(inverse(double_divide(inverse(A),B)))),inverse(inverse(C))),B) = C. [back_rewrite(36),rewrite([126(5),109(6),126(9),126(7)])].
% 0.81/1.09 149 inverse(inverse(a2)) != a2 | inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(inverse(c3),inverse(inverse(double_divide(b3,a3)))) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(53),rewrite([111(3),126(19)])].
% 0.81/1.09 150 inverse(inverse(A)) = A. [back_rewrite(49),rewrite([111(3)])].
% 0.81/1.09 163 double_divide(inverse(A),double_divide(inverse(B),C)) = double_divide(inverse(C),inverse(double_divide(inverse(A),B))). [back_rewrite(113),rewrite([126(4),150(4),126(8),150(8)])].
% 0.81/1.09 168 double_divide(A,double_divide(A,B)) = B. [back_rewrite(33),rewrite([126(4),150(2),150(2)])].
% 0.81/1.09 172 inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != double_divide(inverse(c3),double_divide(b3,a3)) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(149),rewrite([150(3),150(17)]),xx(a)].
% 0.81/1.09 183 double_divide(double_divide(A,B),A) = B. [back_rewrite(135),rewrite([150(2),150(5),168(4),150(2)])].
% 0.81/1.09 191 inverse(double_divide(A,inverse(B))) = double_divide(inverse(A),B). [back_rewrite(126),rewrite([150(6)])].
% 0.81/1.09 192 double_divide(inverse(A),B) = double_divide(B,inverse(A)). [back_rewrite(115),rewrite([150(3)])].
% 0.81/1.09 193 inverse(double_divide(A,inverse(B))) = double_divide(B,inverse(A)). [back_rewrite(191),rewrite([192(5)])].
% 0.81/1.09 202 double_divide(inverse(c3),double_divide(b3,a3)) != double_divide(inverse(a3),double_divide(c3,b3)) | inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4)) # answer(prove_these_axioms). [back_rewrite(172),rewrite([192(6),193(7),192(6,R)]),flip(a)].
% 0.81/1.09 205 double_divide(inverse(A),double_divide(B,inverse(C))) = double_divide(inverse(B),double_divide(A,inverse(C))). [back_rewrite(163),rewrite([192(3),192(7),193(8)])].
% 0.81/1.09 224 double_divide(A,B) = double_divide(B,A). [para(168(a,1),183(a,1,1))].
% 0.81/1.09 236 double_divide(inverse(c3),double_divide(a3,b3)) != double_divide(inverse(a3),double_divide(b3,c3)) # answer(prove_these_axioms). [back_rewrite(202),rewrite([224(5),224(11),224(16)]),xx(b)].
% 0.81/1.09 277 double_divide(inverse(A),double_divide(B,C)) = double_divide(inverse(B),double_divide(A,C)). [para(150(a,1),205(a,1,2,2)),rewrite([150(6)])].
% 0.81/1.09 314 $F # answer(prove_these_axioms). [para(277(a,1),236(a,1)),rewrite([224(5)]),xx(a)].
% 0.81/1.09
% 0.81/1.09 % SZS output end Refutation
% 0.81/1.09 ============================== end of proof ==========================
% 0.81/1.09
% 0.81/1.09 ============================== STATISTICS ============================
% 0.81/1.09
% 0.81/1.09 Given=40. Generated=762. Kept=312. proofs=1.
% 0.81/1.09 Usable=16. Sos=25. Demods=41. Limbo=4, Disabled=270. Hints=0.
% 0.81/1.09 Megabytes=0.33.
% 0.81/1.09 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.81/1.09
% 0.81/1.09 ============================== end of statistics =====================
% 0.81/1.09
% 0.81/1.09 ============================== end of search =========================
% 0.81/1.09
% 0.81/1.09 THEOREM PROVED
% 0.81/1.09 % SZS status Unsatisfiable
% 0.81/1.09
% 0.81/1.09 Exiting with 1 proof.
% 0.81/1.09
% 0.81/1.09 Process 27995 exit (max_proofs) Mon Jun 13 11:49:42 2022
% 0.81/1.09 Prover9 interrupted
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