TSTP Solution File: SET095+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 Apr 30 20:39:05 EDT 2024

% Result   : Theorem 0.14s 0.34s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (   9 unt;   0 def)
%            Number of atoms       :  119 (  28 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  123 (  46   ~;  48   |;  20   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   76 (  72   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( X = Y
    <=> ( subclass(X,Y)
        & subclass(Y,X) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( U = X
          | U = Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : singleton(X) = unordered_pair(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    ! [X,Y] :
      ( member(X,Y)
     => subclass(singleton(X),Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ ! [X,Y] :
        ( member(X,Y)
       => subclass(singleton(X),Y) ),
    inference(negated_conjecture,[status(cth)],[f44]) ).

fof(f46,plain,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( ~ member(U,X)
          | member(U,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f47,plain,
    ! [X,Y] :
      ( ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
      & ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ( member(sk0_0(Y,X),X)
          & ~ member(sk0_0(Y,X),Y) ) ) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f54,plain,
    ! [X,Y] :
      ( ( X != Y
        | ( subclass(X,Y)
          & subclass(Y,X) ) )
      & ( X = Y
        | ~ subclass(X,Y)
        | ~ subclass(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f55,plain,
    ( ! [X,Y] :
        ( X != Y
        | ( subclass(X,Y)
          & subclass(Y,X) ) )
    & ! [X,Y] :
        ( X = Y
        | ~ subclass(X,Y)
        | ~ subclass(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f54]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f59,plain,
    ! [U,X,Y] :
      ( ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
      & ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f60,plain,
    ( ! [U,X,Y] :
        ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
    & ! [U,X,Y] :
        ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(miniscoping,[status(esa)],[f59]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f66,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f191,plain,
    ? [X,Y] :
      ( member(X,Y)
      & ~ subclass(singleton(X),Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f192,plain,
    ( member(sk0_7,sk0_8)
    & ~ subclass(singleton(sk0_7),sk0_8) ),
    inference(skolemization,[status(esa)],[f191]) ).

fof(f193,plain,
    member(sk0_7,sk0_8),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f194,plain,
    ~ subclass(singleton(sk0_7),sk0_8),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f195,plain,
    ! [X0] : subclass(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f56]) ).

fof(f237,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | X0 = X2
      | ~ subclass(X3,unordered_pair(X1,X2))
      | ~ member(X0,X3) ),
    inference(resolution,[status(thm)],[f62,f50]) ).

fof(f255,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | X0 = X1
      | ~ subclass(X2,singleton(X1))
      | ~ member(X0,X2) ),
    inference(paramodulation,[status(thm)],[f66,f237]) ).

fof(f256,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ subclass(X2,singleton(X1))
      | ~ member(X0,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f255]) ).

fof(f258,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(X0,singleton(X1)) ),
    inference(resolution,[status(thm)],[f256,f195]) ).

fof(f260,plain,
    ! [X0,X1] :
      ( sk0_0(X0,singleton(X1)) = X1
      | subclass(singleton(X1),X0) ),
    inference(resolution,[status(thm)],[f258,f51]) ).

fof(f271,plain,
    sk0_0(sk0_8,singleton(sk0_7)) = sk0_7,
    inference(resolution,[status(thm)],[f260,f194]) ).

fof(f279,plain,
    ( spl0_4
  <=> subclass(singleton(sk0_7),sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f280,plain,
    ( subclass(singleton(sk0_7),sk0_8)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f279]) ).

fof(f287,plain,
    ( spl0_6
  <=> member(sk0_7,sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f289,plain,
    ( ~ member(sk0_7,sk0_8)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f287]) ).

fof(f290,plain,
    ( subclass(singleton(sk0_7),sk0_8)
    | ~ member(sk0_7,sk0_8) ),
    inference(paramodulation,[status(thm)],[f271,f52]) ).

fof(f291,plain,
    ( spl0_4
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f290,f279,f287]) ).

fof(f297,plain,
    ( $false
    | ~ spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f280,f194]) ).

fof(f298,plain,
    ~ spl0_4,
    inference(contradiction_clause,[status(thm)],[f297]) ).

fof(f299,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f289,f193]) ).

fof(f300,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f299]) ).

fof(f301,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f291,f298,f300]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.08/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33  % Computer : n016.cluster.edu
% 0.09/0.33  % Model    : x86_64 x86_64
% 0.09/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33  % Memory   : 8042.1875MB
% 0.09/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33  % CPULimit : 300
% 0.09/0.33  % WCLimit  : 300
% 0.09/0.33  % DateTime : Mon Apr 29 22:14:40 EDT 2024
% 0.09/0.33  % CPUTime  : 
% 0.09/0.34  % Drodi V3.6.0
% 0.14/0.34  % Refutation found
% 0.14/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.36  % Elapsed time: 0.020084 seconds
% 0.14/0.36  % CPU time: 0.032113 seconds
% 0.14/0.36  % Total memory used: 13.598 MB
% 0.14/0.36  % Net memory used: 13.573 MB
%------------------------------------------------------------------------------