TSTP Solution File: SET959+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n027.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 04:33:42 EDT 2022

% Result   : Theorem 0.76s 1.03s
% Output   : Refutation 0.76s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.13/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.36  % Computer : n027.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jul 10 17:22:33 EDT 2022
% 0.21/0.36  % CPUTime  : 
% 0.76/1.03  ============================== Prover9 ===============================
% 0.76/1.03  Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03  Process 2457 was started by sandbox on n027.cluster.edu,
% 0.76/1.03  Sun Jul 10 17:22:33 2022
% 0.76/1.03  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2304_n027.cluster.edu".
% 0.76/1.03  ============================== end of head ===========================
% 0.76/1.03  
% 0.76/1.03  ============================== INPUT =================================
% 0.76/1.03  
% 0.76/1.03  % Reading from file /tmp/Prover9_2304_n027.cluster.edu
% 0.76/1.03  
% 0.76/1.03  set(prolog_style_variables).
% 0.76/1.03  set(auto2).
% 0.76/1.03      % set(auto2) -> set(auto).
% 0.76/1.03      % set(auto) -> set(auto_inference).
% 0.76/1.03      % set(auto) -> set(auto_setup).
% 0.76/1.03      % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03      % set(auto) -> set(auto_limits).
% 0.76/1.03      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03      % set(auto) -> set(auto_denials).
% 0.76/1.03      % set(auto) -> set(auto_process).
% 0.76/1.03      % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03      % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03      % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03      % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03      % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03      % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03      % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03      % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03      % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03      % set(auto2) -> assign(stats, some).
% 0.76/1.03      % set(auto2) -> clear(echo_input).
% 0.76/1.03      % set(auto2) -> set(quiet).
% 0.76/1.03      % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03      % set(auto2) -> clear(print_given).
% 0.76/1.03  assign(lrs_ticks,-1).
% 0.76/1.03  assign(sos_limit,10000).
% 0.76/1.03  assign(order,kbo).
% 0.76/1.03  set(lex_order_vars).
% 0.76/1.03  clear(print_given).
% 0.76/1.03  
% 0.76/1.03  % formulas(sos).  % not echoed (8 formulas)
% 0.76/1.03  
% 0.76/1.03  ============================== end of input ==========================
% 0.76/1.03  
% 0.76/1.03  % From the command line: assign(max_seconds, 300).
% 0.76/1.03  
% 0.76/1.03  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03  
% 0.76/1.03  % Formulas that are not ordinary clauses:
% 0.76/1.03  1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  3 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  4 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  5 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  6 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  7 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  8 -(all A all B ((all C -(in(C,A) & (all D all E C != ordered_pair(D,E)))) & (all C -(in(C,B) & (all D all E C != ordered_pair(D,E)))) & (all C all D (in(ordered_pair(C,D),A) <-> in(ordered_pair(C,D),B))) -> A = B)) # label(t112_zfmisc_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.76/1.03  
% 0.76/1.03  ============================== end of process non-clausal formulas ===
% 0.76/1.03  
% 0.76/1.03  ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.03  
% 0.76/1.03  ============================== PREDICATE ELIMINATION =================
% 0.76/1.03  
% 0.76/1.03  ============================== end predicate elimination =============
% 0.76/1.03  
% 0.76/1.03  Auto_denials:  (non-Horn, no changes).
% 0.76/1.03  
% 0.76/1.03  Term ordering decisions:
% 0.76/1.03  Function symbol KB weights:  c1=1. c2=1. c3=1. c4=1. ordered_pair=1. unordered_pair=1. f1=1. singleton=1. f2=1. f3=1. f4=1. f5=1.
% 0.76/1.03  
% 0.76/1.03  ============================== end of process initial clauses ========
% 0.76/1.03  
% 0.76/1.03  ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.03  
% 0.76/1.03  ============================== end of clauses for search =============
% 0.76/1.03  
% 0.76/1.03  ============================== SEARCH ================================
% 0.76/1.03  
% 0.76/1.03  % Starting search at 0.01 seconds.
% 0.76/1.03  
% 0.76/1.03  ============================== PROOF =================================
% 0.76/1.03  % SZS status Theorem
% 0.76/1.03  % SZS output start Refutation
% 0.76/1.03  
% 0.76/1.03  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.76/1.03  % Length of proof is 29.
% 0.76/1.03  % Level of proof is 13.
% 0.76/1.03  % Maximum clause weight is 41.000.
% 0.76/1.03  % Given clauses 39.
% 0.76/1.03  
% 0.76/1.03  2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  3 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  7 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  8 -(all A all B ((all C -(in(C,A) & (all D all E C != ordered_pair(D,E)))) & (all C -(in(C,B) & (all D all E C != ordered_pair(D,E)))) & (all C all D (in(ordered_pair(C,D),A) <-> in(ordered_pair(C,D),B))) -> A = B)) # label(t112_zfmisc_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.76/1.03  10 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom).  [clausify(2)].
% 0.76/1.03  11 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom).  [clausify(3)].
% 0.76/1.03  12 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)).  [copy(11),rewrite([10(4)])].
% 0.76/1.03  13 in(f1(A,B),A) | in(f1(A,B),B) | B = A # label(t2_tarski) # label(axiom).  [clausify(7)].
% 0.76/1.03  15 c4 != c3 # label(t112_zfmisc_1) # label(negated_conjecture).  [clausify(8)].
% 0.76/1.03  19 -in(A,c3) | ordered_pair(f2(A),f3(A)) = A # label(t112_zfmisc_1) # label(negated_conjecture).  [clausify(8)].
% 0.76/1.03  20 -in(A,c3) | unordered_pair(singleton(f2(A)),unordered_pair(f2(A),f3(A))) = A.  [copy(19),rewrite([12(5)])].
% 0.76/1.03  21 -in(A,c4) | ordered_pair(f4(A),f5(A)) = A # label(t112_zfmisc_1) # label(negated_conjecture).  [clausify(8)].
% 0.76/1.03  22 -in(A,c4) | unordered_pair(singleton(f4(A)),unordered_pair(f4(A),f5(A))) = A.  [copy(21),rewrite([12(5)])].
% 0.76/1.03  23 -in(ordered_pair(A,B),c3) | in(ordered_pair(A,B),c4) # label(t112_zfmisc_1) # label(negated_conjecture).  [clausify(8)].
% 0.76/1.03  24 -in(unordered_pair(singleton(A),unordered_pair(A,B)),c3) | in(unordered_pair(singleton(A),unordered_pair(A,B)),c4).  [copy(23),rewrite([12(1),12(6)])].
% 0.76/1.03  25 in(ordered_pair(A,B),c3) | -in(ordered_pair(A,B),c4) # label(t112_zfmisc_1) # label(negated_conjecture).  [clausify(8)].
% 0.76/1.03  26 in(unordered_pair(singleton(A),unordered_pair(A,B)),c3) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),c4).  [copy(25),rewrite([12(1),12(6)])].
% 0.76/1.03  27 -in(f1(A,B),A) | -in(f1(A,B),B) | B = A # label(t2_tarski) # label(axiom).  [clausify(7)].
% 0.76/1.03  31 unordered_pair(singleton(f2(f1(A,c3))),unordered_pair(f2(f1(A,c3)),f3(f1(A,c3)))) = f1(A,c3) | in(f1(A,c3),A) | c3 = A.  [resolve(20,a,13,b)].
% 0.76/1.03  35 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | unordered_pair(singleton(f4(f1(c4,c3))),unordered_pair(f4(f1(c4,c3)),f5(f1(c4,c3)))) = f1(c4,c3).  [resolve(31,b,22,a),flip(b),unit_del(b,15)].
% 0.76/1.03  46 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | in(unordered_pair(singleton(f4(f1(c4,c3))),unordered_pair(f4(f1(c4,c3)),f5(f1(c4,c3)))),c3) | -in(f1(c4,c3),c4).  [para(35(b,1),26(b,1))].
% 0.76/1.03  57 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | in(unordered_pair(singleton(f4(f1(c4,c3))),unordered_pair(f4(f1(c4,c3)),f5(f1(c4,c3)))),c3).  [resolve(46,c,31,b),flip(d),merge(c),unit_del(c,15)].
% 0.76/1.03  61 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | in(f1(c4,c3),c3).  [para(35(b,1),57(b,1)),merge(b)].
% 0.76/1.03  63 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3).  [resolve(61,b,20,a),merge(b)].
% 0.76/1.03  67 -in(f1(c4,c3),c3) | in(f1(c4,c3),c4).  [para(63(a,1),24(a,1)),rewrite([63(20)])].
% 0.76/1.03  69 in(f1(c4,c3),c3) | -in(f1(c4,c3),c4).  [para(63(a,1),26(b,1)),rewrite([63(15)])].
% 0.76/1.03  71 in(f1(c4,c3),c4).  [resolve(67,a,13,b),flip(c),merge(b),unit_del(b,15)].
% 0.76/1.03  72 in(f1(c4,c3),c3).  [back_unit_del(69),unit_del(b,71)].
% 0.76/1.03  73 $F.  [resolve(71,a,27,a),flip(b),unit_del(a,72),unit_del(b,15)].
% 0.76/1.03  
% 0.76/1.03  % SZS output end Refutation
% 0.76/1.03  ============================== end of proof ==========================
% 0.76/1.03  
% 0.76/1.03  ============================== STATISTICS ============================
% 0.76/1.03  
% 0.76/1.03  Given=39. Generated=137. Kept=58. proofs=1.
% 0.76/1.03  Usable=29. Sos=9. Demods=3. Limbo=0, Disabled=33. Hints=0.
% 0.76/1.03  Megabytes=0.18.
% 0.76/1.03  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.76/1.03  
% 0.76/1.03  ============================== end of statistics =====================
% 0.76/1.03  
% 0.76/1.03  ============================== end of search =========================
% 0.76/1.03  
% 0.76/1.03  THEOREM PROVED
% 0.76/1.03  % SZS status Theorem
% 0.76/1.03  
% 0.76/1.03  Exiting with 1 proof.
% 0.76/1.03  
% 0.76/1.03  Process 2457 exit (max_proofs) Sun Jul 10 17:22:33 2022
% 0.76/1.03  Prover9 interrupted
%------------------------------------------------------------------------------