TSTP Solution File: SET355+4 by Prover9---1109a

View Problem - Process Solution

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% File     : Prover9---1109a
% Problem  : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n029.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 : Tue Jul 19 04:29:07 EDT 2022

% Result   : Theorem 0.76s 1.06s
% Output   : Refutation 0.76s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 03:17:31 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.46/1.02  ============================== Prover9 ===============================
% 0.46/1.02  Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.02  Process 2887 was started by sandbox2 on n029.cluster.edu,
% 0.46/1.02  Sun Jul 10 03:17:31 2022
% 0.46/1.02  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2733_n029.cluster.edu".
% 0.46/1.02  ============================== end of head ===========================
% 0.46/1.02  
% 0.46/1.02  ============================== INPUT =================================
% 0.46/1.02  
% 0.46/1.02  % Reading from file /tmp/Prover9_2733_n029.cluster.edu
% 0.46/1.02  
% 0.46/1.02  set(prolog_style_variables).
% 0.46/1.02  set(auto2).
% 0.46/1.02      % set(auto2) -> set(auto).
% 0.46/1.02      % set(auto) -> set(auto_inference).
% 0.46/1.02      % set(auto) -> set(auto_setup).
% 0.46/1.02      % set(auto_setup) -> set(predicate_elim).
% 0.46/1.02      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.02      % set(auto) -> set(auto_limits).
% 0.46/1.02      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.02      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.02      % set(auto) -> set(auto_denials).
% 0.46/1.02      % set(auto) -> set(auto_process).
% 0.46/1.02      % set(auto2) -> assign(new_constants, 1).
% 0.46/1.02      % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.02      % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.02      % set(auto2) -> assign(max_hours, 1).
% 0.46/1.02      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.02      % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.02      % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.02      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.02      % set(auto2) -> set(sort_initial_sos).
% 0.46/1.02      % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.02      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.02      % set(auto2) -> assign(max_megs, 400).
% 0.46/1.02      % set(auto2) -> assign(stats, some).
% 0.46/1.02      % set(auto2) -> clear(echo_input).
% 0.46/1.02      % set(auto2) -> set(quiet).
% 0.46/1.02      % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.02      % set(auto2) -> clear(print_given).
% 0.46/1.02  assign(lrs_ticks,-1).
% 0.46/1.02  assign(sos_limit,10000).
% 0.46/1.02  assign(order,kbo).
% 0.46/1.02  set(lex_order_vars).
% 0.46/1.02  clear(print_given).
% 0.46/1.02  
% 0.46/1.02  % formulas(sos).  % not echoed (12 formulas)
% 0.46/1.02  
% 0.46/1.02  ============================== end of input ==========================
% 0.46/1.02  
% 0.46/1.02  % From the command line: assign(max_seconds, 300).
% 0.46/1.02  
% 0.46/1.02  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.02  
% 0.46/1.02  % Formulas that are not ordinary clauses:
% 0.46/1.02  1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  4 (all X all A all B (member(X,intersection(A,B)) <-> member(X,A) & member(X,B))) # label(intersection) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  5 (all X all A all B (member(X,union(A,B)) <-> member(X,A) | member(X,B))) # label(union) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  7 (all B all A all E (member(B,difference(E,A)) <-> member(B,E) & -member(B,A))) # label(difference) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  9 (all X all A all B (member(X,unordered_pair(A,B)) <-> X = A | X = B)) # label(unordered_pair) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  10 (all X all A (member(X,sum(A)) <-> (exists Y (member(Y,A) & member(X,Y))))) # label(sum) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  11 (all X all A (member(X,product(A)) <-> (all Y (member(Y,A) -> member(X,Y))))) # label(product) # label(axiom) # label(non_clause).  [assumption].
% 0.46/1.02  12 -(all A all X (member(X,A) -> subset(X,sum(A)))) # label(thI43) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.46/1.02  
% 0.46/1.02  ============================== end of process non-clausal formulas ===
% 0.46/1.02  
% 0.46/1.02  ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.02  
% 0.46/1.02  ============================== PREDICATE ELIMINATION =================
% 0.46/1.02  13 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom).  [clausify(2)].
% 0.46/1.02  14 -equal_set(A,B) | subset(A,B) # label(equal_set) # label(axiom).  [clausify(2)].
% 0.76/1.06  15 -equal_set(A,B) | subset(B,A) # label(equal_set) # label(axiom).  [clausify(2)].
% 0.76/1.06  
% 0.76/1.06  ============================== end predicate elimination =============
% 0.76/1.06  
% 0.76/1.06  Auto_denials:  (non-Horn, no changes).
% 0.76/1.06  
% 0.76/1.06  Term ordering decisions:
% 0.76/1.06  Function symbol KB weights:  empty_set=1. c1=1. c2=1. intersection=1. union=1. unordered_pair=1. difference=1. f1=1. f2=1. f3=1. product=1. sum=1. power_set=1. singleton=1.
% 0.76/1.06  
% 0.76/1.06  ============================== end of process initial clauses ========
% 0.76/1.06  
% 0.76/1.06  ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.06  
% 0.76/1.06  ============================== end of clauses for search =============
% 0.76/1.06  
% 0.76/1.06  ============================== SEARCH ================================
% 0.76/1.06  
% 0.76/1.06  % Starting search at 0.01 seconds.
% 0.76/1.06  
% 0.76/1.06  ============================== PROOF =================================
% 0.76/1.06  % SZS status Theorem
% 0.76/1.06  % SZS output start Refutation
% 0.76/1.06  
% 0.76/1.06  % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.76/1.06  % Length of proof is 11.
% 0.76/1.06  % Level of proof is 3.
% 0.76/1.06  % Maximum clause weight is 10.000.
% 0.76/1.06  % Given clauses 87.
% 0.76/1.06  
% 0.76/1.06  1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.06  10 (all X all A (member(X,sum(A)) <-> (exists Y (member(Y,A) & member(X,Y))))) # label(sum) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.06  12 -(all A all X (member(X,A) -> subset(X,sum(A)))) # label(thI43) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.76/1.06  16 member(c2,c1) # label(thI43) # label(negated_conjecture).  [clausify(12)].
% 0.76/1.06  17 subset(A,B) | member(f1(A,B),A) # label(subset) # label(axiom).  [clausify(1)].
% 0.76/1.06  20 -subset(c2,sum(c1)) # label(thI43) # label(negated_conjecture).  [clausify(12)].
% 0.76/1.06  26 subset(A,B) | -member(f1(A,B),B) # label(subset) # label(axiom).  [clausify(1)].
% 0.76/1.06  38 member(A,sum(B)) | -member(C,B) | -member(A,C) # label(sum) # label(axiom).  [clausify(10)].
% 0.76/1.06  49 member(f1(c2,sum(c1)),c2).  [resolve(20,a,17,a)].
% 0.76/1.06  57 -member(f1(c2,sum(c1)),sum(c1)).  [ur(26,a,20,a)].
% 0.76/1.06  945 $F.  [ur(38,a,57,a,c,49,a),unit_del(a,16)].
% 0.76/1.06  
% 0.76/1.06  % SZS output end Refutation
% 0.76/1.06  ============================== end of proof ==========================
% 0.76/1.06  
% 0.76/1.06  ============================== STATISTICS ============================
% 0.76/1.06  
% 0.76/1.06  Given=87. Generated=1308. Kept=929. proofs=1.
% 0.76/1.06  Usable=86. Sos=782. Demods=1. Limbo=33, Disabled=59. Hints=0.
% 0.76/1.06  Megabytes=0.64.
% 0.76/1.06  User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.76/1.06  
% 0.76/1.06  ============================== end of statistics =====================
% 0.76/1.06  
% 0.76/1.06  ============================== end of search =========================
% 0.76/1.06  
% 0.76/1.06  THEOREM PROVED
% 0.76/1.06  % SZS status Theorem
% 0.76/1.06  
% 0.76/1.06  Exiting with 1 proof.
% 0.76/1.06  
% 0.76/1.06  Process 2887 exit (max_proofs) Sun Jul 10 03:17:31 2022
% 0.76/1.06  Prover9 interrupted
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