TSTP Solution File: SEU634^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n010.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  : 300s
% DateTime : Tue May 21 03:43:05 EDT 2024

% Result   : Theorem 13.17s 4.01s
% Output   : Refutation 13.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   41 (  12 unt;  11 typ;   3 def)
%            Number of atoms       :   80 (  14 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  302 (  19   ~;  15   |;   2   &; 249   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   49 (   0   ^  47   !;   2   ?;  49   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(setunion_type,type,
    setunion: $i > $i ).

thf(uniqinunit_type,type,
    uniqinunit: $o ).

thf(uniqinunit_def,definition,
    ( uniqinunit
    = ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) ) ) ) ).

thf(subset_type,type,
    subset: $i > $i > $o ).

thf(subsetI2_type,type,
    subsetI2: $o ).

thf(subsetI2_def,definition,
    ( subsetI2
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ A )
             => ( in @ C @ B ) )
         => ( subset @ A @ B ) ) ) ) ).

thf(setunionE2_type,type,
    setunionE2: $o ).

thf(setunionE2_def,definition,
    ( setunionE2
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( setunion @ A ) )
         => ? [C: $i] :
              ( ( in @ C @ A )
              & ( in @ B @ C ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i > $i > $i ).

thf(sk2_type,type,
    sk2: $i > $i > $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(1,conjecture,
    ( uniqinunit
   => ( subsetI2
     => ( setunionE2
       => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).

thf(2,negated_conjecture,
    ~ ( uniqinunit
     => ( subsetI2
       => ( setunionE2
         => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ( in @ A @ ( setadjoin @ B @ emptyset ) )
         => ( A = B ) )
     => ( ! [A: $i,B: $i] :
            ( ! [C: $i] :
                ( ( in @ C @ A )
               => ( in @ C @ B ) )
           => ( subset @ A @ B ) )
       => ( ! [A: $i,B: $i] :
              ( ( in @ B @ ( setunion @ A ) )
             => ? [C: $i] :
                  ( ( in @ C @ A )
                  & ( in @ B @ C ) ) )
         => ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[6]) ).

thf(4,plain,
    ~ ( subset @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 ),
    inference(cnf,[status(esa)],[3]) ).

thf(334,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ B @ A ) @ B )
      | ( ( subset @ A @ B )
       != ( subset @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,4]) ).

thf(335,plain,
    ~ ( in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ sk3 ),
    inference(pattern_uni,[status(thm)],[334:[bind(A,$thf( setunion @ ( setadjoin @ sk3 @ emptyset ) )),bind(B,$thf( sk3 ))]]) ).

thf(7,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( subset @ A @ B ) ),
    inference(simp,[status(thm)],[7]) ).

thf(242,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ A )
      | ( ( subset @ A @ B )
       != ( subset @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[13,4]) ).

thf(243,plain,
    in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ),
    inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( setunion @ ( setadjoin @ sk3 @ emptyset ) )),bind(B,$thf( sk3 ))]]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | ( in @ B @ ( sk2 @ B @ A ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | ( in @ B @ ( sk2 @ B @ A ) ) ),
    inference(simp,[status(thm)],[8]) ).

thf(695,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( sk2 @ B @ A ) )
      | ( ( in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) )
       != ( in @ B @ ( setunion @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[243,14]) ).

thf(696,plain,
    in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) ),
    inference(pattern_uni,[status(thm)],[695:[bind(A,$thf( setadjoin @ sk3 @ emptyset )),bind(B,$thf( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ))]]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | ( in @ ( sk2 @ B @ A ) @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( setunion @ A ) )
      | ( in @ ( sk2 @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[5]) ).

thf(346,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk2 @ B @ A ) @ A )
      | ( ( in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) )
       != ( in @ B @ ( setunion @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[243,10]) ).

thf(347,plain,
    in @ ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ),
    inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( setadjoin @ sk3 @ emptyset )),bind(B,$thf( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ))]]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
      | ( A = B ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(557,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( in @ ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) ) @ ( setadjoin @ sk3 @ emptyset ) )
       != ( in @ A @ ( setadjoin @ B @ emptyset ) ) ) ),
    inference(paramod_ordered,[status(thm)],[347,12]) ).

thf(558,plain,
    ( ( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) )
    = sk3 ),
    inference(pattern_uni,[status(thm)],[557:[bind(A,$thf( sk2 @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ ( setadjoin @ sk3 @ emptyset ) )),bind(B,$thf( sk3 ))]]) ).

thf(1064,plain,
    in @ ( sk1 @ sk3 @ ( setunion @ ( setadjoin @ sk3 @ emptyset ) ) ) @ sk3,
    inference(rewrite,[status(thm)],[696,558]) ).

thf(1065,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[335,1064]) ).

thf(1066,plain,
    $false,
    inference(simp,[status(thm)],[1065]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.08  % Problem  : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.10  % Command  : run_Leo-III %s %d
% 0.11/0.29  % Computer : n010.cluster.edu
% 0.11/0.29  % Model    : x86_64 x86_64
% 0.11/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29  % Memory   : 8042.1875MB
% 0.11/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30  % CPULimit : 300
% 0.11/0.30  % WCLimit  : 300
% 0.11/0.30  % DateTime : Sun May 19 15:27:39 EDT 2024
% 0.11/0.30  % CPUTime  : 
% 0.89/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.07  % [INFO] 	 Parsing done (151ms). 
% 1.28/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.86/1.43  % [INFO] 	 nitpick registered as external prover. 
% 1.86/1.44  % [INFO] 	 Scanning for conjecture ... 
% 2.06/1.55  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.13/1.58  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.13/1.58  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.13/1.59  % [INFO] 	 Type checking passed. 
% 2.13/1.59  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 13.17/4.01  % [INFO] 	 Killing All external provers ... 
% 13.17/4.01  % Time passed: 3559ms (effective reasoning time: 2922ms)
% 13.17/4.01  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.17/4.01  % Axioms used in derivation (0): 
% 13.17/4.01  % No. of inferences in proof: 27
% 13.17/4.01  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3559 ms resp. 2922 ms w/o parsing
% 13.17/4.07  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.17/4.07  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------