TSTP Solution File: GRP067-1 by Prover9---1109a
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- Process Solution
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% File : Prover9---1109a
% Problem : GRP067-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:17:01 EDT 2022
% Result : Unsatisfiable 0.46s 0.93s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP067-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jun 14 00:57:24 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.46/0.92 ============================== Prover9 ===============================
% 0.46/0.92 Prover9 (32) version 2009-11A, November 2009.
% 0.46/0.92 Process 30041 was started by sandbox on n025.cluster.edu,
% 0.46/0.92 Tue Jun 14 00:57:24 2022
% 0.46/0.92 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29733_n025.cluster.edu".
% 0.46/0.92 ============================== end of head ===========================
% 0.46/0.92
% 0.46/0.92 ============================== INPUT =================================
% 0.46/0.92
% 0.46/0.92 % Reading from file /tmp/Prover9_29733_n025.cluster.edu
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% 0.46/0.92 set(prolog_style_variables).
% 0.46/0.92 set(auto2).
% 0.46/0.92 % set(auto2) -> set(auto).
% 0.46/0.92 % set(auto) -> set(auto_inference).
% 0.46/0.92 % set(auto) -> set(auto_setup).
% 0.46/0.92 % set(auto_setup) -> set(predicate_elim).
% 0.46/0.92 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/0.92 % set(auto) -> set(auto_limits).
% 0.46/0.92 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/0.92 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/0.92 % set(auto) -> set(auto_denials).
% 0.46/0.92 % set(auto) -> set(auto_process).
% 0.46/0.92 % set(auto2) -> assign(new_constants, 1).
% 0.46/0.92 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/0.92 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/0.92 % set(auto2) -> assign(max_hours, 1).
% 0.46/0.92 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/0.92 % set(auto2) -> assign(max_seconds, 0).
% 0.46/0.92 % set(auto2) -> assign(max_minutes, 5).
% 0.46/0.92 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/0.92 % set(auto2) -> set(sort_initial_sos).
% 0.46/0.92 % set(auto2) -> assign(sos_limit, -1).
% 0.46/0.92 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/0.92 % set(auto2) -> assign(max_megs, 400).
% 0.46/0.92 % set(auto2) -> assign(stats, some).
% 0.46/0.92 % set(auto2) -> clear(echo_input).
% 0.46/0.92 % set(auto2) -> set(quiet).
% 0.46/0.92 % set(auto2) -> clear(print_initial_clauses).
% 0.46/0.92 % set(auto2) -> clear(print_given).
% 0.46/0.92 assign(lrs_ticks,-1).
% 0.46/0.92 assign(sos_limit,10000).
% 0.46/0.92 assign(order,kbo).
% 0.46/0.92 set(lex_order_vars).
% 0.46/0.92 clear(print_given).
% 0.46/0.92
% 0.46/0.92 % formulas(sos). % not echoed (5 formulas)
% 0.46/0.92
% 0.46/0.92 ============================== end of input ==========================
% 0.46/0.92
% 0.46/0.92 % From the command line: assign(max_seconds, 300).
% 0.46/0.92
% 0.46/0.92 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/0.93
% 0.46/0.93 % Formulas that are not ordinary clauses:
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% 0.46/0.93 ============================== end of process non-clausal formulas ===
% 0.46/0.93
% 0.46/0.93 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.46/0.93 ============================== PREDICATE ELIMINATION =================
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% 0.46/0.93 ============================== end predicate elimination =============
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% 0.46/0.93 Auto_denials:
% 0.46/0.93 % copying label prove_these_axioms to answer in negative clause
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% 0.46/0.93 Term ordering decisions:
% 0.46/0.93
% 0.46/0.93 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 0.46/0.93 Function symbol KB weights: identity=1. a1=1. a2=1. a3=1. b3=1. c3=1. divide=1. multiply=1. inverse=0.
% 0.46/0.93
% 0.46/0.93 ============================== end of process initial clauses ========
% 0.46/0.93
% 0.46/0.93 ============================== CLAUSES FOR SEARCH ====================
% 0.46/0.93
% 0.46/0.93 ============================== end of clauses for search =============
% 0.46/0.93
% 0.46/0.93 ============================== SEARCH ================================
% 0.46/0.93
% 0.46/0.93 % Starting search at 0.00 seconds.
% 0.46/0.93
% 0.46/0.93 ============================== PROOF =================================
% 0.46/0.93 % SZS status Unsatisfiable
% 0.46/0.93 % SZS output start Refutation
% 0.46/0.93
% 0.46/0.93 % Proof 1 at 0.01 (+ 0.00) seconds: prove_these_axioms.
% 0.46/0.93 % Length of proof is 21.
% 0.46/0.93 % Level of proof is 11.
% 0.46/0.93 % Maximum clause weight is 26.000.
% 0.46/0.93 % Given clauses 18.
% 0.46/0.93
% 0.46/0.93 1 identity = divide(A,A) # label(identity) # label(axiom). [assumption].
% 0.46/0.93 2 divide(A,A) = identity. [copy(1),flip(a)].
% 0.46/0.93 3 inverse(A) = divide(identity,A) # label(inverse) # label(axiom). [assumption].
% 0.46/0.93 4 multiply(A,B) = divide(A,divide(identity,B)) # label(multiply) # label(axiom). [assumption].
% 0.46/0.93 5 divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B # label(single_axiom) # label(axiom). [assumption].
% 0.46/0.93 6 divide(divide(identity,divide(A,divide(B,divide(divide(identity,A),C)))),C) = B. [copy(5),rewrite([2(1)])].
% 0.46/0.93 7 multiply(inverse(a1),a1) != identity | multiply(identity,a2) != a2 | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) # label(prove_these_axioms) # label(negated_conjecture) # answer(prove_these_axioms). [assumption].
% 0.46/0.93 8 divide(identity,divide(identity,a2)) != a2 | divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) # answer(prove_these_axioms). [copy(7),rewrite([3(2),4(5),2(7),4(6),4(13),4(17),4(23),4(26)]),xx(a)].
% 0.46/0.93 9 divide(divide(identity,divide(identity,divide(A,divide(identity,B)))),B) = A. [para(2(a,1),6(a,1,1,2,2,2,1))].
% 0.46/0.93 10 divide(divide(identity,divide(A,divide(B,identity))),divide(identity,A)) = B. [para(2(a,1),6(a,1,1,2,2,2))].
% 0.46/0.93 16 divide(identity,divide(identity,divide(A,divide(identity,divide(divide(identity,B),C))))) = divide(divide(identity,divide(B,A)),C). [para(9(a,1),6(a,1,1,2,2)),flip(a)].
% 0.46/0.93 27 divide(identity,divide(identity,divide(A,identity))) = A. [para(2(a,1),10(a,1,1,2)),rewrite([2(3)])].
% 0.46/0.93 28 divide(A,identity) = A. [para(2(a,1),10(a,1,2)),rewrite([27(6)])].
% 0.46/0.93 29 divide(divide(identity,divide(A,B)),divide(identity,A)) = B. [para(10(a,1),4(a,2)),rewrite([28(3),4(4)])].
% 0.46/0.93 33 divide(divide(identity,divide(identity,A)),B) = divide(identity,divide(B,A)). [para(10(a,1),9(a,1,1,2,2)),rewrite([28(8)])].
% 0.46/0.93 34 divide(identity,divide(identity,A)) = A. [para(9(a,1),10(a,1,1,2,2)),rewrite([29(6),2(5),28(4)]),flip(a)].
% 0.46/0.93 41 divide(identity,divide(A,B)) = divide(B,A). [back_rewrite(33),rewrite([34(4)]),flip(a)].
% 0.46/0.93 43 divide(A,divide(B,divide(identity,C))) = divide(divide(A,C),B). [back_rewrite(16),rewrite([41(7),41(7),41(6),41(7)])].
% 0.46/0.93 44 divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(divide(identity,c3),b3)) # answer(prove_these_axioms). [back_rewrite(8),rewrite([41(5),28(3),43(20)]),xx(a)].
% 0.46/0.93 62 divide(divide(A,divide(identity,B)),C) = divide(A,divide(C,B)). [para(43(a,1),41(a,1,2)),rewrite([41(4)]),flip(a)].
% 0.46/0.93 63 $F # answer(prove_these_axioms). [resolve(62,a,44,a)].
% 0.46/0.93
% 0.46/0.93 % SZS output end Refutation
% 0.46/0.93 ============================== end of proof ==========================
% 0.46/0.93
% 0.46/0.93 ============================== STATISTICS ============================
% 0.46/0.93
% 0.46/0.93 Given=18. Generated=244. Kept=59. proofs=1.
% 0.46/0.93 Usable=12. Sos=12. Demods=24. Limbo=2, Disabled=37. Hints=0.
% 0.46/0.93 Megabytes=0.08.
% 0.46/0.93 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
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% 0.46/0.93 ============================== end of statistics =====================
% 0.46/0.93
% 0.46/0.93 ============================== end of search =========================
% 0.46/0.93
% 0.46/0.93 THEOREM PROVED
% 0.46/0.93 % SZS status Unsatisfiable
% 0.46/0.93
% 0.46/0.93 Exiting with 1 proof.
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% 0.46/0.93 Process 30041 exit (max_proofs) Tue Jun 14 00:57:24 2022
% 0.46/0.93 Prover9 interrupted
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