TSTP Solution File: GRP098-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP098-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 11:17:09 EDT 2022
% Result : Unsatisfiable 0.72s 1.00s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP098-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 04:35:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.00 ============================== Prover9 ===============================
% 0.72/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.00 Process 16326 was started by sandbox2 on n004.cluster.edu,
% 0.72/1.00 Tue Jun 14 04:35:09 2022
% 0.72/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16172_n004.cluster.edu".
% 0.72/1.00 ============================== end of head ===========================
% 0.72/1.00
% 0.72/1.00 ============================== INPUT =================================
% 0.72/1.00
% 0.72/1.00 % Reading from file /tmp/Prover9_16172_n004.cluster.edu
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% 0.72/1.00 set(prolog_style_variables).
% 0.72/1.00 set(auto2).
% 0.72/1.00 % set(auto2) -> set(auto).
% 0.72/1.00 % set(auto) -> set(auto_inference).
% 0.72/1.00 % set(auto) -> set(auto_setup).
% 0.72/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.00 % set(auto) -> set(auto_limits).
% 0.72/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.00 % set(auto) -> set(auto_denials).
% 0.72/1.00 % set(auto) -> set(auto_process).
% 0.72/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.00 % set(auto2) -> assign(stats, some).
% 0.72/1.00 % set(auto2) -> clear(echo_input).
% 0.72/1.00 % set(auto2) -> set(quiet).
% 0.72/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.00 % set(auto2) -> clear(print_given).
% 0.72/1.00 assign(lrs_ticks,-1).
% 0.72/1.00 assign(sos_limit,10000).
% 0.72/1.00 assign(order,kbo).
% 0.72/1.00 set(lex_order_vars).
% 0.72/1.00 clear(print_given).
% 0.72/1.00
% 0.72/1.00 % formulas(sos). % not echoed (3 formulas)
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% 0.72/1.00 ============================== end of input ==========================
% 0.72/1.00
% 0.72/1.00 % From the command line: assign(max_seconds, 300).
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% 0.72/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
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% 0.72/1.00 % Formulas that are not ordinary clauses:
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% 0.72/1.00 ============================== end of process non-clausal formulas ===
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% 0.72/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.72/1.00 ============================== PREDICATE ELIMINATION =================
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% 0.72/1.00 ============================== end predicate elimination =============
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% 0.72/1.00 Auto_denials:
% 0.72/1.00 % copying label prove_these_axioms to answer in negative clause
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% 0.72/1.00 Term ordering decisions:
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% 0.72/1.00 % Assigning unary symbol inverse kb_weight 0 and highest precedence (13).
% 0.72/1.00 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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% 0.72/1.00 ============================== end of process initial clauses ========
% 0.72/1.00
% 0.72/1.00 ============================== CLAUSES FOR SEARCH ====================
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% 0.72/1.00 ============================== end of clauses for search =============
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% 0.72/1.00 ============================== SEARCH ================================
% 0.72/1.00
% 0.72/1.00 % Starting search at 0.01 seconds.
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% 0.72/1.00 ============================== PROOF =================================
% 0.72/1.00 % SZS status Unsatisfiable
% 0.72/1.00 % SZS output start Refutation
% 0.72/1.00
% 0.72/1.00 % Proof 1 at 0.04 (+ 0.00) seconds: prove_these_axioms.
% 0.72/1.00 % Length of proof is 35.
% 0.72/1.00 % Level of proof is 14.
% 0.72/1.00 % Maximum clause weight is 45.000.
% 0.72/1.00 % Given clauses 31.
% 0.72/1.00
% 0.72/1.00 1 multiply(A,B) = divide(A,inverse(B)) # label(multiply) # label(axiom). [assumption].
% 0.72/1.00 2 divide(divide(divide(A,inverse(B)),C),divide(A,C)) = B # label(single_axiom) # label(axiom). [assumption].
% 0.72/1.00 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].
% 0.72/1.00 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)].
% 0.72/1.00 5 divide(A,divide(divide(B,inverse(A)),divide(B,inverse(C)))) = C. [para(2(a,1),2(a,1,1))].
% 0.72/1.00 6 divide(divide(divide(divide(divide(A,inverse(B)),C),inverse(D)),divide(A,C)),B) = D. [para(2(a,1),2(a,1,2))].
% 0.72/1.00 7 divide(A,divide(B,divide(divide(C,inverse(divide(B,inverse(D)))),divide(C,inverse(A))))) = D. [para(5(a,1),2(a,1,1))].
% 0.72/1.00 16 divide(divide(A,inverse(B)),A) = B. [para(6(a,1),6(a,1,1,1)),rewrite([2(6)])].
% 0.72/1.00 19 divide(A,divide(B,B)) = A. [para(16(a,1),2(a,1,1))].
% 0.72/1.00 28 divide(divide(A,A),inverse(B)) = B. [para(19(a,1),16(a,1))].
% 0.72/1.00 29 divide(inverse(b1),inverse(b1)) != divide(inverse(a1),inverse(a1)) | 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([28(19)]),xx(b)].
% 0.72/1.00 31 divide(divide(A,inverse(B)),B) = A. [para(28(a,1),2(a,1,2)),rewrite([28(3)])].
% 0.72/1.00 32 divide(A,divide(A,B)) = B. [para(28(a,1),5(a,1,2,1)),rewrite([28(3)])].
% 0.72/1.00 46 divide(A,divide(divide(B,B),divide(divide(C,inverse(D)),divide(C,inverse(A))))) = D. [para(28(a,1),7(a,1,2,2,1,2,1))].
% 0.72/1.00 49 divide(divide(divide(A,inverse(B)),C),B) = divide(A,C). [para(2(a,1),32(a,1,2))].
% 0.72/1.00 50 divide(divide(A,inverse(B)),divide(A,inverse(C))) = divide(B,C). [para(5(a,1),32(a,1,2)),flip(a)].
% 0.72/1.00 53 divide(A,A) = divide(B,B). [para(19(a,1),32(a,1,2))].
% 0.72/1.00 54 divide(divide(A,A),B) = inverse(B). [para(28(a,1),32(a,1,2))].
% 0.72/1.00 56 divide(A,inverse(divide(B,A))) = B. [back_rewrite(46),rewrite([50(6),54(3)])].
% 0.72/1.00 59 divide(A,A) = c_0. [new_symbol(53)].
% 0.72/1.00 60 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_unit_del(29),rewrite([59(5),59(6)]),xx(a)].
% 0.72/1.00 63 divide(c_0,inverse(A)) = A. [back_rewrite(28),rewrite([59(1)])].
% 0.72/1.00 64 divide(c_0,A) = inverse(A). [back_rewrite(54),rewrite([59(1)])].
% 0.72/1.00 67 inverse(inverse(A)) = A. [back_rewrite(63),rewrite([64(3)])].
% 0.72/1.00 83 divide(divide(A,B),A) = inverse(B). [para(67(a,1),16(a,1,1,2))].
% 0.72/1.00 94 inverse(divide(A,B)) = divide(B,A). [para(56(a,1),32(a,1,2)),flip(a)].
% 0.72/1.00 95 divide(A,inverse(B)) = divide(B,inverse(A)). [para(31(a,1),56(a,1,2,1))].
% 0.72/1.00 97 divide(c3,divide(inverse(b3),a3)) != divide(a3,divide(inverse(c3),b3)) # answer(prove_these_axioms). [back_rewrite(60),rewrite([95(7),94(6),94(12),95(17)]),xx(b)].
% 0.72/1.00 131 divide(inverse(A),B) = divide(inverse(B),A). [para(83(a,1),31(a,1,1))].
% 0.72/1.00 136 divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(97),rewrite([131(5),131(11)])].
% 0.72/1.00 139 divide(A,divide(B,inverse(A))) = inverse(B). [para(31(a,1),94(a,1,1)),flip(a)].
% 0.72/1.00 171 divide(A,divide(B,C)) = divide(C,divide(B,A)). [para(49(a,1),139(a,1,2)),rewrite([67(4),94(5)])].
% 0.72/1.00 179 divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(136),rewrite([171(6)])].
% 0.72/1.00 184 divide(A,divide(inverse(B),C)) = divide(B,divide(inverse(A),C)). [para(131(a,1),171(a,1,2)),rewrite([131(5)])].
% 0.72/1.00 185 $F # answer(prove_these_axioms). [resolve(184,a,179,a)].
% 0.72/1.00
% 0.72/1.00 % SZS output end Refutation
% 0.72/1.00 ============================== end of proof ==========================
% 0.72/1.00
% 0.72/1.00 ============================== STATISTICS ============================
% 0.72/1.00
% 0.72/1.00 Given=31. Generated=562. Kept=183. proofs=1.
% 0.72/1.00 Usable=12. Sos=7. Demods=18. Limbo=0, Disabled=166. Hints=0.
% 0.72/1.00 Megabytes=0.20.
% 0.72/1.00 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.72/1.00
% 0.72/1.00 ============================== end of statistics =====================
% 0.72/1.00
% 0.72/1.00 ============================== end of search =========================
% 0.72/1.00
% 0.72/1.00 THEOREM PROVED
% 0.72/1.00 % SZS status Unsatisfiable
% 0.72/1.00
% 0.72/1.00 Exiting with 1 proof.
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% 0.72/1.00 Process 16326 exit (max_proofs) Tue Jun 14 04:35:09 2022
% 0.72/1.00 Prover9 interrupted
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