TSTP Solution File: SET628+3 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n028.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 04:30:57 EDT 2022

% Result   : Theorem 0.72s 0.97s
% Output   : Refutation 0.72s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n028.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 : Mon Jul 11 02:34:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.72/0.97  ============================== Prover9 ===============================
% 0.72/0.97  Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.97  Process 7296 was started by sandbox on n028.cluster.edu,
% 0.72/0.97  Mon Jul 11 02:34:58 2022
% 0.72/0.97  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7113_n028.cluster.edu".
% 0.72/0.97  ============================== end of head ===========================
% 0.72/0.97  
% 0.72/0.97  ============================== INPUT =================================
% 0.72/0.97  
% 0.72/0.97  % Reading from file /tmp/Prover9_7113_n028.cluster.edu
% 0.72/0.97  
% 0.72/0.97  set(prolog_style_variables).
% 0.72/0.97  set(auto2).
% 0.72/0.97      % set(auto2) -> set(auto).
% 0.72/0.97      % set(auto) -> set(auto_inference).
% 0.72/0.97      % set(auto) -> set(auto_setup).
% 0.72/0.97      % set(auto_setup) -> set(predicate_elim).
% 0.72/0.97      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.97      % set(auto) -> set(auto_limits).
% 0.72/0.97      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.97      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.97      % set(auto) -> set(auto_denials).
% 0.72/0.97      % set(auto) -> set(auto_process).
% 0.72/0.97      % set(auto2) -> assign(new_constants, 1).
% 0.72/0.97      % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.97      % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.97      % set(auto2) -> assign(max_hours, 1).
% 0.72/0.97      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.97      % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.97      % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.97      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.97      % set(auto2) -> set(sort_initial_sos).
% 0.72/0.97      % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.97      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.97      % set(auto2) -> assign(max_megs, 400).
% 0.72/0.97      % set(auto2) -> assign(stats, some).
% 0.72/0.97      % set(auto2) -> clear(echo_input).
% 0.72/0.97      % set(auto2) -> set(quiet).
% 0.72/0.97      % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.97      % set(auto2) -> clear(print_given).
% 0.72/0.97  assign(lrs_ticks,-1).
% 0.72/0.97  assign(sos_limit,10000).
% 0.72/0.97  assign(order,kbo).
% 0.72/0.97  set(lex_order_vars).
% 0.72/0.97  clear(print_given).
% 0.72/0.97  
% 0.72/0.97  % formulas(sos).  % not echoed (7 formulas)
% 0.72/0.97  
% 0.72/0.97  ============================== end of input ==========================
% 0.72/0.97  
% 0.72/0.97  % From the command line: assign(max_seconds, 300).
% 0.72/0.97  
% 0.72/0.97  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.97  
% 0.72/0.97  % Formulas that are not ordinary clauses:
% 0.72/0.97  1 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  3 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  4 (all B all C (not_equal(B,C) <-> B != C)) # label(not_equal_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  5 (all B all C (intersect(B,C) -> intersect(C,B))) # label(symmetry_of_intersect) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  6 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  7 -(all B (intersect(B,B) <-> not_equal(B,empty_set))) # label(prove_th110) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.72/0.97  
% 0.72/0.97  ============================== end of process non-clausal formulas ===
% 0.72/0.97  
% 0.72/0.97  ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/0.97  
% 0.72/0.97  ============================== PREDICATE ELIMINATION =================
% 0.72/0.97  8 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom).  [clausify(6)].
% 0.72/0.97  9 empty(A) | member(f3(A),A) # label(empty_defn) # label(axiom).  [clausify(6)].
% 0.72/0.97  Derived: -member(A,B) | member(f3(B),B).  [resolve(8,a,9,a)].
% 0.72/0.97  
% 0.72/0.97  ============================== end predicate elimination =============
% 0.72/0.97  
% 0.72/0.97  Auto_denials:  (non-Horn, no changes).
% 0.72/0.97  
% 0.72/0.97  Term ordering decisions:
% 0.72/0.97  
% 0.72/0.97  % Assigning unary symbol f3 kb_weight 0 and highest precedence (9).
% 0.72/0.97  Function symbol KB weights:  empty_set=1. c1=1. f1=1. f2=1. f3=0.
% 0.72/0.97  
% 0.72/0.97  ============================== end of process initial clauses ========
% 0.72/0.97  
% 0.72/0.97  ============================== CLAUSES FOR SEARCH ====================
% 0.72/0.97  
% 0.72/0.97  ============================== end of clauses for search =============
% 0.72/0.97  
% 0.72/0.97  ============================== SEARCH ================================
% 0.72/0.97  
% 0.72/0.97  % Starting search at 0.01 seconds.
% 0.72/0.97  
% 0.72/0.97  ============================== PROOF =================================
% 0.72/0.97  % SZS status Theorem
% 0.72/0.97  % SZS output start Refutation
% 0.72/0.97  
% 0.72/0.97  % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.72/0.97  % Length of proof is 21.
% 0.72/0.97  % Level of proof is 5.
% 0.72/0.97  % Maximum clause weight is 13.000.
% 0.72/0.97  % Given clauses 22.
% 0.72/0.97  
% 0.72/0.97  1 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  3 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  4 (all B all C (not_equal(B,C) <-> B != C)) # label(not_equal_defn) # label(axiom) # label(non_clause).  [assumption].
% 0.72/0.97  7 -(all B (intersect(B,B) <-> not_equal(B,empty_set))) # label(prove_th110) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.72/0.97  10 not_equal(A,B) | B = A # label(not_equal_defn) # label(axiom).  [clausify(4)].
% 0.72/0.97  11 intersect(c1,c1) | not_equal(c1,empty_set) # label(prove_th110) # label(negated_conjecture).  [clausify(7)].
% 0.72/0.97  12 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom).  [clausify(3)].
% 0.72/0.97  13 -member(A,empty_set) # label(empty_set_defn) # label(axiom).  [clausify(2)].
% 0.72/0.97  14 -not_equal(A,B) | B != A # label(not_equal_defn) # label(axiom).  [clausify(4)].
% 0.72/0.97  15 -intersect(c1,c1) | -not_equal(c1,empty_set) # label(prove_th110) # label(negated_conjecture).  [clausify(7)].
% 0.72/0.97  18 -intersect(A,B) | member(f1(A,B),B) # label(intersect_defn) # label(axiom).  [clausify(1)].
% 0.72/0.97  19 intersect(A,B) | -member(C,A) | -member(C,B) # label(intersect_defn) # label(axiom).  [clausify(1)].
% 0.72/0.97  24 intersect(A,A) | -member(B,A).  [factor(19,b,c)].
% 0.72/0.97  25 empty_set = A | member(f2(A,empty_set),A).  [resolve(13,a,12,c)].
% 0.72/0.97  27 c1 != empty_set | intersect(c1,c1).  [resolve(14,a,11,b),flip(a)].
% 0.72/0.97  29 -intersect(c1,c1) | c1 = empty_set.  [resolve(15,b,10,a),flip(b)].
% 0.72/0.97  31 -intersect(A,empty_set).  [ur(18,b,13,a)].
% 0.72/0.97  46 empty_set = A | intersect(A,A).  [resolve(25,b,24,b)].
% 0.72/0.97  52 c1 = empty_set.  [resolve(46,b,29,a),flip(a),merge(b)].
% 0.72/0.97  54 $F.  [back_rewrite(27),rewrite([52(1),52(4),52(5)]),xx(a),unit_del(a,31)].
% 0.72/0.97  
% 0.72/0.97  % SZS output end Refutation
% 0.72/0.97  ============================== end of proof ==========================
% 0.72/0.97  
% 0.72/0.97  ============================== STATISTICS ============================
% 0.72/0.97  
% 0.72/0.97  Given=22. Generated=70. Kept=44. proofs=1.
% 0.72/0.97  Usable=20. Sos=20. Demods=1. Limbo=2, Disabled=18. Hints=0.
% 0.72/0.97  Megabytes=0.06.
% 0.72/0.97  User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.72/0.97  
% 0.72/0.97  ============================== end of statistics =====================
% 0.72/0.97  
% 0.72/0.97  ============================== end of search =========================
% 0.72/0.97  
% 0.72/0.97  THEOREM PROVED
% 0.72/0.97  % SZS status Theorem
% 0.72/0.97  
% 0.72/0.97  Exiting with 1 proof.
% 0.72/0.97  
% 0.72/0.97  Process 7296 exit (max_proofs) Mon Jul 11 02:34:58 2022
% 0.72/0.97  Prover9 interrupted
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