TSTP Solution File: GRP097-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP097-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 11:17:08 EDT 2022
% Result : Unsatisfiable 0.75s 1.04s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP097-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 08:40:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.75/1.04 ============================== Prover9 ===============================
% 0.75/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.04 Process 27744 was started by sandbox2 on n006.cluster.edu,
% 0.75/1.04 Mon Jun 13 08:40:27 2022
% 0.75/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27591_n006.cluster.edu".
% 0.75/1.04 ============================== end of head ===========================
% 0.75/1.04
% 0.75/1.04 ============================== INPUT =================================
% 0.75/1.04
% 0.75/1.04 % Reading from file /tmp/Prover9_27591_n006.cluster.edu
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% 0.75/1.04 set(prolog_style_variables).
% 0.75/1.04 set(auto2).
% 0.75/1.04 % set(auto2) -> set(auto).
% 0.75/1.04 % set(auto) -> set(auto_inference).
% 0.75/1.04 % set(auto) -> set(auto_setup).
% 0.75/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.04 % set(auto) -> set(auto_limits).
% 0.75/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.04 % set(auto) -> set(auto_denials).
% 0.75/1.04 % set(auto) -> set(auto_process).
% 0.75/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.04 % set(auto2) -> assign(stats, some).
% 0.75/1.04 % set(auto2) -> clear(echo_input).
% 0.75/1.04 % set(auto2) -> set(quiet).
% 0.75/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.04 % set(auto2) -> clear(print_given).
% 0.75/1.04 assign(lrs_ticks,-1).
% 0.75/1.04 assign(sos_limit,10000).
% 0.75/1.04 assign(order,kbo).
% 0.75/1.04 set(lex_order_vars).
% 0.75/1.04 clear(print_given).
% 0.75/1.04
% 0.75/1.04 % formulas(sos). % not echoed (3 formulas)
% 0.75/1.04
% 0.75/1.04 ============================== end of input ==========================
% 0.75/1.04
% 0.75/1.04 % From the command line: assign(max_seconds, 300).
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.04
% 0.75/1.04 % Formulas that are not ordinary clauses:
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% 0.75/1.04 ============================== end of process non-clausal formulas ===
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.75/1.04 ============================== PREDICATE ELIMINATION =================
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% 0.75/1.04 ============================== end predicate elimination =============
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% 0.75/1.04 Auto_denials:
% 0.75/1.04 % copying label prove_these_axioms to answer in negative clause
% 0.75/1.04
% 0.75/1.04 Term ordering decisions:
% 0.75/1.04
% 0.75/1.04 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.75/1.04 Function symbol KB weights: a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. divide=1. multiply=1. inverse=0.
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% 0.75/1.04 ============================== end of process initial clauses ========
% 0.75/1.04
% 0.75/1.04 ============================== CLAUSES FOR SEARCH ====================
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% 0.75/1.04 ============================== end of clauses for search =============
% 0.75/1.04
% 0.75/1.04 ============================== SEARCH ================================
% 0.75/1.04
% 0.75/1.04 % Starting search at 0.01 seconds.
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% 0.75/1.04 ============================== PROOF =================================
% 0.75/1.04 % SZS status Unsatisfiable
% 0.75/1.04 % SZS output start Refutation
% 0.75/1.04
% 0.75/1.04 % Proof 1 at 0.03 (+ 0.00) seconds: prove_these_axioms.
% 0.75/1.04 % Length of proof is 38.
% 0.75/1.04 % Level of proof is 17.
% 0.75/1.04 % Maximum clause weight is 45.000.
% 0.75/1.04 % Given clauses 31.
% 0.75/1.04
% 0.75/1.04 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.75/1.04 2 divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B # label(single_axiom) # label(axiom). [assumption].
% 0.75/1.04 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].
% 0.75/1.04 4 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) | divide(b4,inverse(a4)) != divide(a4,inverse(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(d)].
% 0.75/1.04 5 divide(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(D,C))))))) = D. [para(2(a,1),2(a,1,2,1,1))].
% 0.75/1.04 6 divide(A,inverse(divide(divide(B,inverse(divide(divide(C,D),divide(A,D)))),C))) = B. [para(2(a,1),2(a,1,2,1,2))].
% 0.75/1.04 10 divide(A,inverse(divide(B,B))) = A. [para(2(a,1),5(a,1,2,1,2))].
% 0.75/1.04 13 divide(A,inverse(divide(B,A))) = B. [para(10(a,1),2(a,1,2,1,1)),rewrite([10(3)])].
% 0.75/1.04 14 divide(A,inverse(divide(B,divide(A,inverse(divide(B,C)))))) = C. [para(10(a,1),5(a,1,2,1,2,2,1,1)),rewrite([10(3)])].
% 0.75/1.04 20 divide(divide(A,B),inverse(divide(C,divide(C,B)))) = A. [para(13(a,1),5(a,1,2,1,2))].
% 0.75/1.04 22 divide(inverse(divide(A,A)),inverse(B)) = B. [para(10(a,1),13(a,1,2,1))].
% 0.75/1.04 28 divide(divide(A,inverse(B)),B) = A. [para(22(a,1),2(a,1,2,1,2)),rewrite([22(7)])].
% 0.75/1.04 32 inverse(divide(A,A)) = divide(B,B). [para(22(a,1),10(a,1)),flip(a)].
% 0.75/1.04 35 inverse(divide(A,A)) = c_0. [new_symbol(32)].
% 0.75/1.04 37 divide(A,A) = c_0. [back_rewrite(32),rewrite([35(2)]),flip(a)].
% 0.75/1.04 43 divide(inverse(c_0),inverse(A)) = A. [back_rewrite(22),rewrite([37(1)])].
% 0.75/1.04 46 inverse(c_0) = c_0. [back_rewrite(35),rewrite([37(1)])].
% 0.75/1.04 47 divide(c_0,inverse(a2)) != a2 | divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) | divide(b4,inverse(a4)) != divide(a4,inverse(b4)) # answer(prove_these_axioms). [back_rewrite(4),rewrite([37(5),37(6),37(8)]),xx(a)].
% 0.75/1.04 49 divide(c_0,inverse(A)) = A. [back_rewrite(43),rewrite([46(2)])].
% 0.75/1.04 53 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))) | divide(b4,inverse(a4)) != divide(a4,inverse(b4)) # answer(prove_these_axioms). [back_rewrite(47),rewrite([49(4)]),xx(a)].
% 0.75/1.04 68 inverse(divide(divide(A,B),divide(C,B))) = divide(C,inverse(divide(c_0,A))). [para(37(a,1),6(a,1,2,1,1)),flip(a)].
% 0.75/1.04 87 divide(A,divide(A,inverse(divide(c_0,B)))) = B. [back_rewrite(2),rewrite([68(4)])].
% 0.75/1.04 90 divide(A,divide(A,B)) = B. [para(14(a,1),49(a,1)),rewrite([49(4)]),flip(a)].
% 0.75/1.04 100 inverse(divide(c_0,A)) = A. [back_rewrite(87),rewrite([90(5)])].
% 0.75/1.04 101 divide(divide(A,B),inverse(B)) = A. [back_rewrite(20),rewrite([90(3)])].
% 0.75/1.04 118 inverse(divide(divide(A,B),divide(C,B))) = divide(C,A). [back_rewrite(68),rewrite([100(7)])].
% 0.75/1.04 119 inverse(divide(A,B)) = divide(B,A). [para(13(a,1),90(a,1,2)),flip(a)].
% 0.75/1.04 121 divide(divide(A,B),divide(C,B)) = divide(A,C). [back_rewrite(118),rewrite([119(4)])].
% 0.75/1.04 137 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(c3),b3)) | divide(b4,inverse(a4)) != divide(a4,inverse(b4)) # answer(prove_these_axioms). [back_rewrite(53),rewrite([119(13)])].
% 0.75/1.04 139 divide(divide(A,B),A) = inverse(B). [para(101(a,1),90(a,1,2))].
% 0.75/1.04 141 divide(A,divide(B,inverse(A))) = inverse(B). [para(28(a,1),119(a,1,1)),flip(a)].
% 0.75/1.04 143 divide(inverse(A),B) = divide(inverse(B),A). [para(139(a,1),28(a,1,1))].
% 0.75/1.04 145 divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,divide(inverse(b3),c3)) | divide(b4,inverse(a4)) != divide(a4,inverse(b4)) # answer(prove_these_axioms). [back_rewrite(137),rewrite([143(12)])].
% 0.75/1.04 146 divide(A,inverse(B)) = divide(B,inverse(A)). [para(141(a,1),90(a,1,2))].
% 0.75/1.04 148 divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(145),rewrite([146(7),119(6),143(5),146(17)]),xx(b)].
% 0.75/1.04 154 divide(A,divide(B,C)) = divide(C,divide(B,A)). [para(139(a,1),121(a,1,2)),rewrite([146(3),119(2)])].
% 0.75/1.04 157 divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(148),rewrite([154(6)])].
% 0.75/1.04 158 $F # answer(prove_these_axioms). [para(154(a,1),157(a,2)),rewrite([143(11),154(12)]),xx(a)].
% 0.75/1.04
% 0.75/1.04 % SZS output end Refutation
% 0.75/1.04 ============================== end of proof ==========================
% 0.75/1.04
% 0.75/1.04 ============================== STATISTICS ============================
% 0.75/1.04
% 0.75/1.04 Given=31. Generated=496. Kept=156. proofs=1.
% 0.75/1.04 Usable=13. Sos=2. Demods=14. Limbo=0, Disabled=144. Hints=0.
% 0.75/1.04 Megabytes=0.16.
% 0.75/1.04 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.75/1.04
% 0.75/1.04 ============================== end of statistics =====================
% 0.75/1.04
% 0.75/1.04 ============================== end of search =========================
% 0.75/1.04
% 0.75/1.04 THEOREM PROVED
% 0.75/1.04 % SZS status Unsatisfiable
% 0.75/1.04
% 0.75/1.04 Exiting with 1 proof.
% 0.75/1.04
% 0.75/1.04 Process 27744 exit (max_proofs) Mon Jun 13 08:40:27 2022
% 0.75/1.05 Prover9 interrupted
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