%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.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 20:40:36 EDT 2024

% Result   : Theorem 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (  10 unt;   0 def)
%            Number of atoms       :   82 (  36 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   81 (  32   ~;  31   |;  11   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   47 (  43   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : set_union2(A,B) = set_union2(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A,B] :
      ( B = singleton(A)
    <=> ! [C] :
          ( in(C,B)
        <=> C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B] :
      ( subset(set_union2(singleton(A),B),B)
     => in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,conjecture,
    ! [A,B] :
      ( set_union2(singleton(A),singleton(B)) = singleton(A)
     => A = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,negated_conjecture,
    ~ ! [A,B] :
        ( set_union2(singleton(A),singleton(B)) = singleton(A)
       => A = B ),
    inference(negated_conjecture,[status(cth)],[f11]) ).

fof(f15,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f16,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)],[f3]) ).

fof(f17,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)],[f16]) ).

fof(f18,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)],[f17]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( X0 != singleton(X1)
      | ~ in(X2,X0)
      | X2 = X1 ),
    inference(cnf_transformation,[status(esa)],[f18]) ).

fof(f31,plain,
    ! [A,B] :
      ( ~ subset(set_union2(singleton(A),B),B)
      | in(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ subset(set_union2(singleton(X0),X1),X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f37,plain,
    ! [A] : subset(A,A),
    inference(miniscoping,[status(esa)],[f10]) ).

fof(f38,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f39,plain,
    ? [A,B] :
      ( set_union2(singleton(A),singleton(B)) = singleton(A)
      & A != B ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f40,plain,
    ( set_union2(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3)
    & sk0_3 != sk0_4 ),
    inference(skolemization,[status(esa)],[f39]) ).

fof(f41,plain,
    set_union2(singleton(sk0_3),singleton(sk0_4)) = singleton(sk0_3),
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f42,plain,
    sk0_3 != sk0_4,
    inference(cnf_transformation,[status(esa)],[f40]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ in(X0,singleton(X1))
      | X0 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f19]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ~ subset(set_union2(X0,singleton(X1)),X0)
      | in(X1,X0) ),
    inference(paramodulation,[status(thm)],[f15,f32]) ).

fof(f71,plain,
    ( spl0_4
  <=> subset(singleton(sk0_3),singleton(sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f73,plain,
    ( ~ subset(singleton(sk0_3),singleton(sk0_3))
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f71]) ).

fof(f74,plain,
    ( spl0_5
  <=> in(sk0_4,singleton(sk0_3)) ),
    introduced(split_symbol_definition) ).

fof(f75,plain,
    ( in(sk0_4,singleton(sk0_3))
    | ~ spl0_5 ),
    inference(component_clause,[status(thm)],[f74]) ).

fof(f77,plain,
    ( ~ subset(singleton(sk0_3),singleton(sk0_3))
    | in(sk0_4,singleton(sk0_3)) ),
    inference(paramodulation,[status(thm)],[f41,f68]) ).

fof(f78,plain,
    ( ~ spl0_4
    | spl0_5 ),
    inference(split_clause,[status(thm)],[f77,f71,f74]) ).

fof(f82,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f73,f38]) ).

fof(f83,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f82]) ).

fof(f95,plain,
    ( sk0_4 = sk0_3
    | ~ spl0_5 ),
    inference(resolution,[status(thm)],[f75,f43]) ).

fof(f96,plain,
    ( $false
    | ~ spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f95,f42]) ).

fof(f97,plain,
    ~ spl0_5,
    inference(contradiction_clause,[status(thm)],[f96]) ).

fof(f98,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f78,f83,f97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n021.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Mon Apr 29 21:31:40 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.6.0
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35  % Elapsed time: 0.018545 seconds
% 0.11/0.35  % CPU time: 0.026494 seconds
% 0.11/0.35  % Total memory used: 12.756 MB
% 0.11/0.35  % Net memory used: 12.653 MB
%------------------------------------------------------------------------------