TSTP Solution File: SET925+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 : Wed May 31 12:35:33 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (   1 unt;   0 def)
%            Number of atoms       :   58 (  20 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   56 (  23   ~;  23   |;   4   &)
%                                         (   5 <=>;   0  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   20 (;  16   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,conjecture,
    ! [A,B] :
      ( set_difference(singleton(A),B) = empty_set
    <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ~ ! [A,B] :
        ( set_difference(singleton(A),B) = empty_set
      <=> in(A,B) ),
    inference(negated_conjecture,[status(cth)],[f5]) ).

fof(f7,axiom,
    ! [A,B] :
      ( set_difference(singleton(A),B) = empty_set
    <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,plain,
    ? [A,B] :
      ( set_difference(singleton(A),B) = empty_set
    <~> in(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f16,plain,
    ? [A,B] :
      ( ( set_difference(singleton(A),B) = empty_set
        | in(A,B) )
      & ( set_difference(singleton(A),B) != empty_set
        | ~ in(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ( ( set_difference(singleton(sk0_2),sk0_3) = empty_set
      | in(sk0_2,sk0_3) )
    & ( set_difference(singleton(sk0_2),sk0_3) != empty_set
      | ~ in(sk0_2,sk0_3) ) ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f18,plain,
    ( set_difference(singleton(sk0_2),sk0_3) = empty_set
    | in(sk0_2,sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    ( set_difference(singleton(sk0_2),sk0_3) != empty_set
    | ~ in(sk0_2,sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [A,B] :
      ( ( set_difference(singleton(A),B) != empty_set
        | in(A,B) )
      & ( set_difference(singleton(A),B) = empty_set
        | ~ in(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f21,plain,
    ( ! [A,B] :
        ( set_difference(singleton(A),B) != empty_set
        | in(A,B) )
    & ! [A,B] :
        ( set_difference(singleton(A),B) = empty_set
        | ~ in(A,B) ) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( set_difference(singleton(X0),X1) != empty_set
      | in(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( set_difference(singleton(X0),X1) = empty_set
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f24,plain,
    ( spl0_0
  <=> set_difference(singleton(sk0_2),sk0_3) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f25,plain,
    ( set_difference(singleton(sk0_2),sk0_3) = empty_set
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f24]) ).

fof(f26,plain,
    ( set_difference(singleton(sk0_2),sk0_3) != empty_set
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f24]) ).

fof(f27,plain,
    ( spl0_1
  <=> in(sk0_2,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f28,plain,
    ( in(sk0_2,sk0_3)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f27]) ).

fof(f30,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f18,f24,f27]) ).

fof(f31,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f19,f24,f27]) ).

fof(f32,plain,
    ( set_difference(singleton(sk0_2),sk0_3) = empty_set
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f28,f23]) ).

fof(f34,plain,
    ( $false
    | spl0_0
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f32,f26]) ).

fof(f35,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f34]) ).

fof(f36,plain,
    ( in(sk0_2,sk0_3)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f25,f22]) ).

fof(f37,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f36,f27,f24]) ).

fof(f43,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f30,f31,f35,f37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET925+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 10:18:21 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.20/0.58  % Refutation found
% 0.20/0.58  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58  % Elapsed time: 0.017377 seconds
% 0.20/0.58  % CPU time: 0.018644 seconds
% 0.20/0.58  % Memory used: 2.859 MB
%------------------------------------------------------------------------------