%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU143+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 20:41:10 EDT 2024

% Result   : Theorem 0.11s 0.27s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   19 (   9 unt;   0 def)
%            Number of atoms       :   61 (  35 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   72 (  30   ~;  27   |;  12   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   42 (  37   !;   5   ?)

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

fof(f8,axiom,
    ! [A] :
      ( A = empty_set
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,conjecture,
    ! [A] : singleton(A) != empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f29,negated_conjecture,
    ~ ! [A] : singleton(A) != empty_set,
    inference(negated_conjecture,[status(cth)],[f28]) ).

fof(f78,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(f79,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)],[f78]) ).

fof(f80,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)],[f79]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | in(X2,X0)
      | X2 != X1 ),
    inference(cnf_transformation,[status(esa)],[f80]) ).

fof(f85,plain,
    ! [A] :
      ( ( A != empty_set
        | ! [B] : ~ in(B,A) )
      & ( A = empty_set
        | ? [B] : in(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

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

fof(f87,plain,
    ( ! [A] :
        ( A != empty_set
        | ! [B] : ~ in(B,A) )
    & ! [A] :
        ( A = empty_set
        | in(sk0_1(A),A) ) ),
    inference(skolemization,[status(esa)],[f86]) ).

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

fof(f155,plain,
    ? [A] : singleton(A) = empty_set,
    inference(pre_NNF_transformation,[status(esa)],[f29]) ).

fof(f156,plain,
    singleton(sk0_7) = empty_set,
    inference(skolemization,[status(esa)],[f155]) ).

fof(f157,plain,
    singleton(sk0_7) = empty_set,
    inference(cnf_transformation,[status(esa)],[f156]) ).

fof(f243,plain,
    ! [X0] : in(X0,singleton(X0)),
    inference(destructive_equality_resolution,[status(esa)],[f82]) ).

fof(f244,plain,
    ! [X0] : ~ in(X0,empty_set),
    inference(destructive_equality_resolution,[status(esa)],[f88]) ).

fof(f258,plain,
    in(sk0_7,empty_set),
    inference(paramodulation,[status(thm)],[f157,f243]) ).

fof(f259,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f258,f244]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : SEU143+2 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n007.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 19:43:47 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.11/0.27  % Drodi V3.6.0
% 0.11/0.27  % Refutation found
% 0.11/0.27  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.28  % Elapsed time: 0.014407 seconds
% 0.11/0.28  % CPU time: 0.020730 seconds
% 0.11/0.28  % Total memory used: 13.315 MB
% 0.11/0.28  % Net memory used: 13.300 MB
%------------------------------------------------------------------------------