TSTP Solution File: SEU805^2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.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 03:43:52 EDT 2024

% Result   : Theorem 27.58s 5.64s
% Output   : Refutation 27.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   51 (  14 unt;  11 typ;   4 def)
%            Number of atoms       :  108 (  35 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  299 (  39   ~;  25   |;   9   &; 208   @)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   62 (   1   ^  48   !;  13   ?;  62   :)

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

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

thf(foundationAx_type,type,
    foundationAx: $o ).

thf(foundationAx_def,definition,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [B: $i] : ( in @ B @ A )
         => ? [B: $i] :
              ( ( in @ B @ A )
              & ~ ? [C: $i] :
                    ( ( in @ C @ B )
                    & ( in @ C @ A ) ) ) ) ) ) ).

thf(nonempty_type,type,
    nonempty: $i > $o ).

thf(nonempty_def,definition,
    ( nonempty
    = ( ^ [A: $i] : ( A != emptyset ) ) ) ).

thf(nonemptyE1_type,type,
    nonemptyE1: $o ).

thf(nonemptyE1_def,definition,
    ( nonemptyE1
    = ( ! [A: $i] :
          ( ( nonempty @ A )
         => ? [B: $i] : ( in @ B @ A ) ) ) ) ).

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf(disjointsetsI1_type,type,
    disjointsetsI1: $o ).

thf(disjointsetsI1_def,definition,
    ( disjointsetsI1
    = ( ! [A: $i,B: $i] :
          ( ~ ? [C: $i] :
                ( ( in @ C @ A )
                & ( in @ C @ B ) )
         => ( ( binintersect @ A @ B )
            = emptyset ) ) ) ) ).

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

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

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

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ( foundationAx
   => ( nonemptyE1
     => ( disjointsetsI1
       => ! [A: $i] :
            ( ( nonempty @ A )
           => ? [B: $i] :
                ( ( in @ B @ A )
                & ( ( binintersect @ B @ A )
                  = emptyset ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundation2) ).

thf(2,negated_conjecture,
    ~ ( foundationAx
     => ( nonemptyE1
       => ( disjointsetsI1
         => ! [A: $i] :
              ( ( nonempty @ A )
             => ? [B: $i] :
                  ( ( in @ B @ A )
                  & ( ( binintersect @ B @ A )
                    = emptyset ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

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

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk3 @ B @ A ) @ A )
      | ( ( binintersect @ A @ B )
        = emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ! [B: $i,A: $i] :
      ( ( ( binintersect @ A @ B )
        = emptyset )
      | ( in @ ( sk3 @ B @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[5]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ( ( binintersect @ A @ B )
        = emptyset )
      | ( in @ ( sk3 @ B @ A ) @ A ) ),
    inference(simp,[status(thm)],[11]) ).

thf(10,plain,
    ! [A: $i] :
      ( ( A = emptyset )
      | ( in @ ( sk2 @ A ) @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    ! [A: $i] :
      ( ( A = emptyset )
      | ( in @ ( sk2 @ A ) @ A ) ),
    inference(lifteq,[status(thm)],[10]) ).

thf(14,plain,
    ! [A: $i] :
      ( ( A = emptyset )
      | ( in @ ( sk2 @ A ) @ A ) ),
    inference(simp,[status(thm)],[13]) ).

thf(6,plain,
    sk4 != emptyset,
    inference(cnf,[status(esa)],[3]) ).

thf(15,plain,
    sk4 != emptyset,
    inference(lifteq,[status(thm)],[6]) ).

thf(30,plain,
    ! [A: $i] :
      ( ( in @ ( sk2 @ A ) @ A )
      | ( A != sk4 ) ),
    inference(paramod_ordered,[status(thm)],[14,15]) ).

thf(31,plain,
    in @ ( sk2 @ sk4 ) @ sk4,
    inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk4 ))]]) ).

thf(4,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ A )
      | ( in @ ( sk1 @ A ) @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(96,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ A ) @ A )
      | ( ( in @ ( sk2 @ sk4 ) @ sk4 )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[31,4]) ).

thf(97,plain,
    in @ ( sk1 @ sk4 ) @ sk4,
    inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 @ sk4 ))]]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk4 )
      | ( ( binintersect @ A @ sk4 )
       != emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(18,plain,
    ! [A: $i] :
      ( ( ( binintersect @ A @ sk4 )
       != emptyset )
      | ~ ( in @ A @ sk4 ) ),
    inference(lifteq,[status(thm)],[8]) ).

thf(19,plain,
    ! [A: $i] :
      ( ( ( binintersect @ A @ sk4 )
       != emptyset )
      | ~ ( in @ A @ sk4 ) ),
    inference(simp,[status(thm)],[18]) ).

thf(120,plain,
    ! [A: $i] :
      ( ( ( binintersect @ A @ sk4 )
       != emptyset )
      | ( ( in @ ( sk1 @ sk4 ) @ sk4 )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[97,19]) ).

thf(121,plain,
    ( ( binintersect @ ( sk1 @ sk4 ) @ sk4 )
   != emptyset ),
    inference(pattern_uni,[status(thm)],[120:[bind(A,$thf( sk1 @ sk4 ))]]) ).

thf(284,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk3 @ B @ A ) @ A )
      | ( ( binintersect @ A @ B )
       != ( binintersect @ ( sk1 @ sk4 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,121]) ).

thf(285,plain,
    in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ ( sk1 @ sk4 ),
    inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( sk4 ))]]) ).

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

thf(60,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( sk1 @ A ) )
      | ~ ( in @ C @ A )
      | ( ( in @ ( sk2 @ sk4 ) @ sk4 )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[31,7]) ).

thf(61,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( sk1 @ sk4 ) )
      | ~ ( in @ A @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 @ sk4 )),bind(C,$thf( C ))]]) ).

thf(82,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( sk1 @ sk4 ) )
      | ~ ( in @ A @ sk4 ) ),
    inference(simp,[status(thm)],[61]) ).

thf(2383,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk4 )
      | ( ( in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ ( sk1 @ sk4 ) )
       != ( in @ A @ ( sk1 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[285,82]) ).

thf(2384,plain,
    ~ ( in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ sk4 ),
    inference(pattern_uni,[status(thm)],[2383:[bind(A,$thf( sk3 @ sk4 @ ( sk1 @ sk4 ) ))]]) ).

thf(9,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk3 @ B @ A ) @ B )
      | ( ( binintersect @ A @ B )
        = emptyset ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(16,plain,
    ! [B: $i,A: $i] :
      ( ( ( binintersect @ A @ B )
        = emptyset )
      | ( in @ ( sk3 @ B @ A ) @ B ) ),
    inference(lifteq,[status(thm)],[9]) ).

thf(17,plain,
    ! [B: $i,A: $i] :
      ( ( ( binintersect @ A @ B )
        = emptyset )
      | ( in @ ( sk3 @ B @ A ) @ B ) ),
    inference(simp,[status(thm)],[16]) ).

thf(448,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk3 @ B @ A ) @ B )
      | ( ( binintersect @ A @ B )
       != ( binintersect @ ( sk1 @ sk4 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[17,121]) ).

thf(449,plain,
    in @ ( sk3 @ sk4 @ ( sk1 @ sk4 ) ) @ sk4,
    inference(pattern_uni,[status(thm)],[448:[bind(A,$thf( sk1 @ sk4 )),bind(B,$thf( sk4 ))]]) ).

thf(2921,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[2384,449]) ).

thf(2922,plain,
    $false,
    inference(simp,[status(thm)],[2921]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n015.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 18:16:09 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.89/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.08  % [INFO] 	 Parsing done (164ms). 
% 1.30/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.82/1.45  % [INFO] 	 nitpick registered as external prover. 
% 1.82/1.45  % [INFO] 	 Scanning for conjecture ... 
% 2.08/1.56  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.08/1.59  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.08/1.60  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.08/1.60  % [INFO] 	 Type checking passed. 
% 2.08/1.60  % [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 ... 
% 26.82/5.62  % [INFO] 	 Killing All external provers ... 
% 27.58/5.63  % Time passed: 5167ms (effective reasoning time: 4525ms)
% 27.58/5.63  % 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)>
% 27.58/5.63  % Axioms used in derivation (0): 
% 27.58/5.63  % No. of inferences in proof: 36
% 27.58/5.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5167 ms resp. 4525 ms w/o parsing
% 27.74/5.77  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.74/5.77  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------