TSTP Solution File: CAT010-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 : Fri Jul 15 00:06:15 EDT 2022
% Result : Unsatisfiable 0.70s 1.00s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : CAT010-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.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 : Sun May 29 18:02:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.00 ============================== Prover9 ===============================
% 0.70/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.00 Process 20612 was started by sandbox2 on n026.cluster.edu,
% 0.70/1.00 Sun May 29 18:02:40 2022
% 0.70/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_20459_n026.cluster.edu".
% 0.70/1.00 ============================== end of head ===========================
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% 0.70/1.00 ============================== INPUT =================================
% 0.70/1.00
% 0.70/1.00 % Reading from file /tmp/Prover9_20459_n026.cluster.edu
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% 0.70/1.00 set(prolog_style_variables).
% 0.70/1.00 set(auto2).
% 0.70/1.00 % set(auto2) -> set(auto).
% 0.70/1.00 % set(auto) -> set(auto_inference).
% 0.70/1.00 % set(auto) -> set(auto_setup).
% 0.70/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.00 % set(auto) -> set(auto_limits).
% 0.70/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.00 % set(auto) -> set(auto_denials).
% 0.70/1.00 % set(auto) -> set(auto_process).
% 0.70/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.00 % set(auto2) -> assign(stats, some).
% 0.70/1.00 % set(auto2) -> clear(echo_input).
% 0.70/1.00 % set(auto2) -> set(quiet).
% 0.70/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.00 % set(auto2) -> clear(print_given).
% 0.70/1.00 assign(lrs_ticks,-1).
% 0.70/1.00 assign(sos_limit,10000).
% 0.70/1.00 assign(order,kbo).
% 0.70/1.00 set(lex_order_vars).
% 0.70/1.00 clear(print_given).
% 0.70/1.00
% 0.70/1.00 % formulas(sos). % not echoed (13 formulas)
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% 0.70/1.00 ============================== end of input ==========================
% 0.70/1.00
% 0.70/1.00 % From the command line: assign(max_seconds, 300).
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% 0.70/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
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% 0.70/1.00 % Formulas that are not ordinary clauses:
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% 0.70/1.00 ============================== end of process non-clausal formulas ===
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% 0.70/1.00 ============================== PROCESS INITIAL CLAUSES ===============
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% 0.70/1.00 ============================== PREDICATE ELIMINATION =================
% 0.70/1.00 1 -there_exists(A) | A != B | equivalent(A,B) # label(existence_and_equality_implies_equivalence1) # label(axiom). [assumption].
% 0.70/1.00 2 -equivalent(A,B) | there_exists(A) # label(equivalence_implies_existence1) # label(axiom). [assumption].
% 0.70/1.00 3 -equivalent(A,B) | A = B # label(equivalence_implies_existence2) # label(axiom). [assumption].
% 0.70/1.00
% 0.70/1.00 ============================== end predicate elimination =============
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% 0.70/1.00 Auto_denials:
% 0.70/1.00 % copying label prove_codomain_of_ab_equals_codomain_of_a to answer in negative clause
% 0.70/1.00
% 0.70/1.00 Term ordering decisions:
% 0.70/1.00 Function symbol KB weights: a=1. b=1. compose=1. domain=1. codomain=1.
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% 0.70/1.00 ============================== end of process initial clauses ========
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% 0.70/1.00 ============================== CLAUSES FOR SEARCH ====================
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% 0.70/1.00 ============================== end of clauses for search =============
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% 0.70/1.00 ============================== SEARCH ================================
% 0.70/1.00
% 0.70/1.00 % Starting search at 0.01 seconds.
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% 0.70/1.00 ============================== PROOF =================================
% 0.70/1.00 % SZS status Unsatisfiable
% 0.70/1.00 % SZS output start Refutation
% 0.70/1.00
% 0.70/1.00 % Proof 1 at 0.04 (+ 0.00) seconds: prove_codomain_of_ab_equals_codomain_of_a.
% 0.70/1.00 % Length of proof is 17.
% 0.70/1.00 % Level of proof is 5.
% 0.70/1.00 % Maximum clause weight is 12.000.
% 0.70/1.00 % Given clauses 86.
% 0.70/1.00
% 0.70/1.00 4 there_exists(compose(a,b)) # label(ab_exists) # label(hypothesis). [assumption].
% 0.70/1.00 6 compose(codomain(A),A) = A # label(compose_codomain) # label(axiom). [assumption].
% 0.70/1.00 7 compose(A,compose(B,C)) = compose(compose(A,B),C) # label(associativity_of_compose) # label(axiom). [assumption].
% 0.70/1.00 8 compose(compose(A,B),C) = compose(A,compose(B,C)). [copy(7),flip(a)].
% 0.70/1.00 9 codomain(compose(a,b)) != codomain(a) # label(prove_codomain_of_ab_equals_codomain_of_a) # label(negated_conjecture) # answer(prove_codomain_of_ab_equals_codomain_of_a). [assumption].
% 0.70/1.00 10 -there_exists(domain(A)) | there_exists(A) # label(domain_has_elements) # label(axiom). [assumption].
% 0.70/1.00 12 -there_exists(compose(A,B)) | there_exists(domain(A)) # label(composition_implies_domain) # label(axiom). [assumption].
% 0.70/1.00 13 -there_exists(compose(A,B)) | domain(A) = codomain(B) # label(domain_codomain_composition1) # label(axiom). [assumption].
% 0.70/1.00 14 -there_exists(compose(A,B)) | codomain(B) = domain(A). [copy(13),flip(b)].
% 0.70/1.00 19 compose(codomain(A),compose(A,B)) = compose(A,B). [para(6(a,1),8(a,1,1)),flip(a)].
% 0.70/1.00 20 there_exists(domain(a)). [hyper(12,a,4,a)].
% 0.70/1.00 26 -there_exists(A) | domain(codomain(A)) = codomain(A). [para(6(a,1),14(a,1)),flip(b)].
% 0.70/1.00 31 there_exists(a). [hyper(10,a,20,a)].
% 0.70/1.00 47 -there_exists(compose(A,B)) | codomain(compose(A,B)) = domain(codomain(A)). [para(19(a,1),14(a,1))].
% 0.70/1.00 121 domain(codomain(a)) = codomain(a). [hyper(26,a,31,a)].
% 0.70/1.00 303 codomain(compose(a,b)) = codomain(a). [hyper(47,a,4,a),rewrite([121(7)])].
% 0.70/1.00 304 $F # answer(prove_codomain_of_ab_equals_codomain_of_a). [resolve(303,a,9,a)].
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% 0.70/1.00 % SZS output end Refutation
% 0.70/1.00 ============================== end of proof ==========================
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% 0.70/1.00 ============================== STATISTICS ============================
% 0.70/1.00
% 0.70/1.00 Given=86. Generated=1234. Kept=297. proofs=1.
% 0.70/1.00 Usable=71. Sos=156. Demods=93. Limbo=0, Disabled=82. Hints=0.
% 0.70/1.00 Megabytes=0.31.
% 0.70/1.00 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
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% 0.70/1.00 ============================== end of statistics =====================
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% 0.70/1.00 ============================== end of search =========================
% 0.70/1.00
% 0.70/1.00 THEOREM PROVED
% 0.70/1.00 % SZS status Unsatisfiable
% 0.70/1.00
% 0.70/1.00 Exiting with 1 proof.
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% 0.70/1.00 Process 20612 exit (max_proofs) Sun May 29 18:02:40 2022
% 0.70/1.00 Prover9 interrupted
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