TSTP Solution File: GRP091-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP091-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 11:17:07 EDT 2022
% Result : Unsatisfiable 0.43s 0.99s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP091-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 00:49:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 16434 was started by sandbox2 on n027.cluster.edu,
% 0.43/0.99 Tue Jun 14 00:49:03 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16151_n027.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_16151_n027.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (5 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
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% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.43/0.99 ============================== PREDICATE ELIMINATION =================
% 0.43/0.99
% 0.43/0.99 ============================== end predicate elimination =============
% 0.43/0.99
% 0.43/0.99 Auto_denials:
% 0.43/0.99 % copying label prove_these_axioms to answer in negative clause
% 0.43/0.99
% 0.43/0.99 Term ordering decisions:
% 0.43/0.99
% 0.43/0.99 % Assigning unary symbol inverse kb_weight 0 and highest precedence (14).
% 0.43/0.99 Function symbol KB weights: identity=1. a1=1. a2=1. a3=1. a4=1. b1=1. b2=1. b3=1. b4=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.43/0.99
% 0.43/0.99 ============================== end of process initial clauses ========
% 0.43/0.99
% 0.43/0.99 ============================== CLAUSES FOR SEARCH ====================
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% 0.43/0.99 ============================== end of clauses for search =============
% 0.43/0.99
% 0.43/0.99 ============================== SEARCH ================================
% 0.43/0.99
% 0.43/0.99 % Starting search at 0.01 seconds.
% 0.43/0.99
% 0.43/0.99 ============================== PROOF =================================
% 0.43/0.99 % SZS status Unsatisfiable
% 0.43/0.99 % SZS output start Refutation
% 0.43/0.99
% 0.43/0.99 % Proof 1 at 0.01 (+ 0.00) seconds: prove_these_axioms.
% 0.43/0.99 % Length of proof is 26.
% 0.43/0.99 % Level of proof is 11.
% 0.43/0.99 % Maximum clause weight is 29.000.
% 0.43/0.99 % Given clauses 23.
% 0.43/0.99
% 0.43/0.99 1 identity = divide(A,A) # label(identity) # label(axiom). [assumption].
% 0.43/0.99 2 divide(A,A) = identity. [copy(1),flip(a)].
% 0.43/0.99 3 inverse(A) = divide(divide(B,B),A) # label(inverse) # label(axiom). [assumption].
% 0.43/0.99 4 divide(identity,A) = inverse(A). [copy(3),rewrite([2(2)]),flip(a)].
% 0.43/0.99 5 divide(divide(A,divide(divide(A,B),C)),B) = C # label(single_axiom) # label(axiom). [assumption].
% 0.43/0.99 6 multiply(A,B) = divide(A,divide(divide(C,C),B)) # label(multiply) # label(axiom). [assumption].
% 0.43/0.99 7 multiply(A,B) = divide(A,inverse(B)). [copy(6),rewrite([2(2),4(3)])].
% 0.43/0.99 8 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].
% 0.43/0.99 9 inverse(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(8),rewrite([7(4),2(5),7(5),2(6),7(7),2(8),7(6),4(7),7(11),7(14),7(19),7(21),7(26),7(30)]),flip(d),xx(a)].
% 0.43/0.99 11 divide(divide(A,inverse(B)),A) = B. [para(2(a,1),5(a,1,1,2,1)),rewrite([4(2)])].
% 0.43/0.99 13 divide(inverse(divide(inverse(A),B)),A) = B. [para(4(a,1),5(a,1,1,2,1)),rewrite([4(4)])].
% 0.43/0.99 15 divide(divide(A,B),divide(divide(A,C),B)) = C. [para(5(a,1),5(a,1,1,2))].
% 0.43/0.99 16 inverse(inverse(A)) = A. [para(2(a,1),11(a,1,1)),rewrite([4(3)])].
% 0.43/0.99 17 divide(A,identity) = A. [para(4(a,1),11(a,1,1)),rewrite([16(2)])].
% 0.43/0.99 22 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(9),rewrite([16(3)]),xx(a)].
% 0.43/0.99 23 divide(divide(A,B),A) = inverse(B). [para(16(a,1),11(a,1,1,2))].
% 0.43/0.99 24 divide(A,divide(A,B)) = B. [para(17(a,1),5(a,1,1,2,1)),rewrite([17(4)])].
% 0.43/0.99 29 divide(inverse(A),B) = divide(inverse(B),A). [para(24(a,1),13(a,1,1,1))].
% 0.43/0.99 32 inverse(divide(A,B)) = divide(B,A). [para(24(a,1),23(a,1,1)),flip(a)].
% 0.43/0.99 35 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(22),rewrite([32(13),29(12)])].
% 0.43/0.99 52 divide(A,inverse(B)) = divide(B,inverse(A)). [para(29(a,1),32(a,1,1)),rewrite([32(3)])].
% 0.43/0.99 54 divide(c3,divide(inverse(a3),b3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [para(29(a,1),35(a,2,2)),rewrite([52(7),32(6),29(5),29(11),52(17)]),xx(b)].
% 0.43/0.99 60 divide(A,divide(B,C)) = divide(C,divide(B,A)). [para(15(a,1),23(a,1,1)),rewrite([32(5)])].
% 0.43/0.99 66 divide(b3,divide(inverse(a3),c3)) != divide(a3,divide(inverse(b3),c3)) # answer(prove_these_axioms). [back_rewrite(54),rewrite([60(6)])].
% 0.43/0.99 72 divide(A,divide(inverse(B),C)) = divide(B,divide(inverse(A),C)). [para(29(a,1),60(a,1,2)),rewrite([29(5)])].
% 0.43/0.99 73 $F # answer(prove_these_axioms). [resolve(72,a,66,a)].
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% 0.43/0.99 % SZS output end Refutation
% 0.43/0.99 ============================== end of proof ==========================
% 0.43/0.99
% 0.43/0.99 ============================== STATISTICS ============================
% 0.43/0.99
% 0.43/0.99 Given=23. Generated=333. Kept=68. proofs=1.
% 0.43/0.99 Usable=11. Sos=7. Demods=17. Limbo=0, Disabled=54. Hints=0.
% 0.43/0.99 Megabytes=0.08.
% 0.43/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.43/0.99
% 0.43/0.99 ============================== end of statistics =====================
% 0.43/0.99
% 0.43/0.99 ============================== end of search =========================
% 0.43/0.99
% 0.43/0.99 THEOREM PROVED
% 0.43/0.99 % SZS status Unsatisfiable
% 0.43/0.99
% 0.43/0.99 Exiting with 1 proof.
% 0.43/0.99
% 0.43/0.99 Process 16434 exit (max_proofs) Tue Jun 14 00:49:03 2022
% 0.43/0.99 Prover9 interrupted
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