%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU148+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%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  : 300s
% DateTime : Wed May 31 12:35:59 EDT 2023

% Result   : Theorem 0.23s 0.57s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   5 unt;   0 def)
%            Number of atoms       :   63 (  29 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   71 (  27   ~;  26   |;  13   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   41 (;  37   !;   4   ?)

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

fof(f31,lemma,
    ! [A,B] :
      ( subset(singleton(A),B)
    <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f66,conjecture,
    ! [A,B] :
      ( subset(singleton(A),singleton(B))
     => A = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f67,negated_conjecture,
    ~ ! [A,B] :
        ( subset(singleton(A),singleton(B))
       => A = B ),
    inference(negated_conjecture,[status(cth)],[f66]) ).

fof(f85,plain,
    ! [A,B] :
      ( ( B != singleton(A)
        | ! [C] :
            ( ( ~ in(C,B)
              | C = A )
            & ( in(C,B)
              | C != A ) ) )
      & ( B = singleton(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | C != A )
            & ( in(C,B)
              | C = A ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f86,plain,
    ( ! [A,B] :
        ( B != singleton(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | C = A )
          & ! [C] :
              ( in(C,B)
              | C != A ) ) )
    & ! [A,B] :
        ( B = singleton(A)
        | ? [C] :
            ( ( ~ in(C,B)
              | C != A )
            & ( in(C,B)
              | C = A ) ) ) ),
    inference(miniscoping,[status(esa)],[f85]) ).

fof(f87,plain,
    ( ! [A,B] :
        ( B != singleton(A)
        | ( ! [C] :
              ( ~ in(C,B)
              | C = A )
          & ! [C] :
              ( in(C,B)
              | C != A ) ) )
    & ! [A,B] :
        ( B = singleton(A)
        | ( ( ~ in(sk0_0(B,A),B)
            | sk0_0(B,A) != A )
          & ( in(sk0_0(B,A),B)
            | sk0_0(B,A) = A ) ) ) ),
    inference(skolemization,[status(esa)],[f86]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | ~ in(X2,X0)
      | X2 = X1 ),
    inference(cnf_transformation,[status(esa)],[f87]) ).

fof(f170,plain,
    ! [A,B] :
      ( ( ~ subset(singleton(A),B)
        | in(A,B) )
      & ( subset(singleton(A),B)
        | ~ in(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f31]) ).

fof(f171,plain,
    ( ! [A,B] :
        ( ~ subset(singleton(A),B)
        | in(A,B) )
    & ! [A,B] :
        ( subset(singleton(A),B)
        | ~ in(A,B) ) ),
    inference(miniscoping,[status(esa)],[f170]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( ~ subset(singleton(X0),X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f171]) ).

fof(f252,plain,
    ? [A,B] :
      ( subset(singleton(A),singleton(B))
      & A != B ),
    inference(pre_NNF_transformation,[status(esa)],[f67]) ).

fof(f253,plain,
    ( subset(singleton(sk0_13),singleton(sk0_14))
    & sk0_13 != sk0_14 ),
    inference(skolemization,[status(esa)],[f252]) ).

fof(f254,plain,
    subset(singleton(sk0_13),singleton(sk0_14)),
    inference(cnf_transformation,[status(esa)],[f253]) ).

fof(f255,plain,
    sk0_13 != sk0_14,
    inference(cnf_transformation,[status(esa)],[f253]) ).

fof(f271,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f88]) ).

fof(f301,plain,
    in(sk0_13,singleton(sk0_14)),
    inference(resolution,[status(thm)],[f172,f254]) ).

fof(f303,plain,
    sk0_13 = sk0_14,
    inference(resolution,[status(thm)],[f301,f271]) ).

fof(f304,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f303,f255]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU148+2 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 09:37:18 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.5.1
% 0.23/0.57  % Refutation found
% 0.23/0.57  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.57  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.57  % Elapsed time: 0.018892 seconds
% 0.23/0.57  % CPU time: 0.034487 seconds
% 0.23/0.57  % Memory used: 15.165 MB
%------------------------------------------------------------------------------