%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU148+3 : 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 12:35:59 EDT 2023

% Result   : Theorem 0.14s 0.37s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   33 (   8 unt;   0 def)
%            Number of atoms       :   95 (  51 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  103 (  41   ~;  40   |;  15   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   47 (;  43   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] :
      ( B = singleton(A)
    <=> ! [C] :
          ( in(C,B)
        <=> C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : singleton(A) != empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [A,B] :
      ( subset(A,singleton(B))
    <=> ( A = empty_set
        | A = singleton(B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [A,B] :
      ( subset(singleton(A),singleton(B))
     => A = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [A,B] :
        ( subset(singleton(A),singleton(B))
       => A = B ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f13,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)],[f2]) ).

fof(f14,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)],[f13]) ).

fof(f15,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)],[f14]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | ~ in(X2,X0)
      | X2 = X1 ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | in(X2,X0)
      | X2 != X1 ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f21,plain,
    ! [X0] : singleton(X0) != empty_set,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f22,plain,
    ! [A,B] :
      ( ( ~ subset(A,singleton(B))
        | A = empty_set
        | A = singleton(B) )
      & ( subset(A,singleton(B))
        | ( A != empty_set
          & A != singleton(B) ) ) ),
    inference(NNF_transformation,[status(esa)],[f5]) ).

fof(f23,plain,
    ( ! [A,B] :
        ( ~ subset(A,singleton(B))
        | A = empty_set
        | A = singleton(B) )
    & ! [A,B] :
        ( subset(A,singleton(B))
        | ( A != empty_set
          & A != singleton(B) ) ) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ subset(X0,singleton(X1))
      | X0 = empty_set
      | X0 = singleton(X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f33,plain,
    ? [A,B] :
      ( subset(singleton(A),singleton(B))
      & A != B ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f34,plain,
    ( subset(singleton(sk0_3),singleton(sk0_4))
    & sk0_3 != sk0_4 ),
    inference(skolemization,[status(esa)],[f33]) ).

fof(f35,plain,
    subset(singleton(sk0_3),singleton(sk0_4)),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    sk0_3 != sk0_4,
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f16]) ).

fof(f38,plain,
    ! [X0] : in(X0,singleton(X0)),
    inference(destructive_equality_resolution,[status(esa)],[f17]) ).

fof(f50,plain,
    ( spl0_2
  <=> singleton(sk0_3) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f51,plain,
    ( singleton(sk0_3) = empty_set
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f50]) ).

fof(f53,plain,
    ( spl0_3
  <=> singleton(sk0_3) = singleton(sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f54,plain,
    ( singleton(sk0_3) = singleton(sk0_4)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f53]) ).

fof(f56,plain,
    ( singleton(sk0_3) = empty_set
    | singleton(sk0_3) = singleton(sk0_4) ),
    inference(resolution,[status(thm)],[f24,f35]) ).

fof(f57,plain,
    ( spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f56,f50,f53]) ).

fof(f58,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f51,f21]) ).

fof(f59,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f58]) ).

fof(f81,plain,
    ( in(sk0_4,singleton(sk0_3))
    | ~ spl0_3 ),
    inference(paramodulation,[status(thm)],[f54,f38]) ).

fof(f82,plain,
    ( sk0_4 = sk0_3
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f81,f37]) ).

fof(f83,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f82,f36]) ).

fof(f84,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f83]) ).

fof(f85,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f57,f59,f84]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n005.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 09:10:36 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.5.1
% 0.14/0.37  % Refutation found
% 0.14/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.59  % Elapsed time: 0.021571 seconds
% 0.21/0.59  % CPU time: 0.026218 seconds
% 0.21/0.59  % Memory used: 2.923 MB
%------------------------------------------------------------------------------