TSTP Solution File: CAT010-4 by Prover9---1109a

View Problem - Process Solution

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% 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 ===========================
% 0.70/1.00  
% 0.70/1.00  ============================== INPUT =================================
% 0.70/1.00  
% 0.70/1.00  % Reading from file /tmp/Prover9_20459_n026.cluster.edu
% 0.70/1.00  
% 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)
% 0.70/1.00  
% 0.70/1.00  ============================== end of input ==========================
% 0.70/1.00  
% 0.70/1.00  % From the command line: assign(max_seconds, 300).
% 0.70/1.00  
% 0.70/1.00  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.00  
% 0.70/1.00  % Formulas that are not ordinary clauses:
% 0.70/1.00  
% 0.70/1.00  ============================== end of process non-clausal formulas ===
% 0.70/1.00  
% 0.70/1.00  ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.00  
% 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 =============
% 0.70/1.00  
% 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.
% 0.70/1.00  
% 0.70/1.00  ============================== end of process initial clauses ========
% 0.70/1.00  
% 0.70/1.00  ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.00  
% 0.70/1.00  ============================== end of clauses for search =============
% 0.70/1.00  
% 0.70/1.00  ============================== SEARCH ================================
% 0.70/1.00  
% 0.70/1.00  % Starting search at 0.01 seconds.
% 0.70/1.00  
% 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)].
% 0.70/1.00  
% 0.70/1.00  % SZS output end Refutation
% 0.70/1.00  ============================== end of proof ==========================
% 0.70/1.00  
% 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.
% 0.70/1.00  
% 0.70/1.00  ============================== end of statistics =====================
% 0.70/1.00  
% 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.
% 0.70/1.00  
% 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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