%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU152+1 : 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 12:36:00 EDT 2023

% Result   : Theorem 0.13s 0.37s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   20 (   8 unt;   0 def)
%            Number of atoms       :   36 (  14 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   29 (  13   ~;   8   |;   4   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   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   :   28 (;  26   !;   2   ?)

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

fof(f6,conjecture,
    ! [A,B] :
      ( in(A,B)
     => set_union2(singleton(A),B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ~ ! [A,B] :
        ( in(A,B)
       => set_union2(singleton(A),B) = B ),
    inference(negated_conjecture,[status(cth)],[f6]) ).

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

fof(f10,axiom,
    ! [A,B] :
      ( subset(A,B)
     => set_union2(A,B) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f16,plain,
    ? [A,B] :
      ( in(A,B)
      & set_union2(singleton(A),B) != B ),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f17,plain,
    ( in(sk0_0,sk0_1)
    & set_union2(singleton(sk0_0),sk0_1) != sk0_1 ),
    inference(skolemization,[status(esa)],[f16]) ).

fof(f18,plain,
    in(sk0_0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f19,plain,
    set_union2(singleton(sk0_0),sk0_1) != sk0_1,
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f20,plain,
    ! [A,B] :
      ( ( ~ subset(singleton(A),B)
        | in(A,B) )
      & ( subset(singleton(A),B)
        | ~ in(A,B) ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

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

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

fof(f26,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | set_union2(A,B) = B ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_union2(X0,X1) = X1 ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f29,plain,
    set_union2(sk0_1,singleton(sk0_0)) != sk0_1,
    inference(paramodulation,[status(thm)],[f13,f19]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( set_union2(singleton(X0),X1) = X1
      | ~ in(X0,X1) ),
    inference(resolution,[status(thm)],[f27,f23]) ).

fof(f35,plain,
    set_union2(singleton(sk0_0),sk0_1) = sk0_1,
    inference(resolution,[status(thm)],[f33,f18]) ).

fof(f36,plain,
    set_union2(sk0_1,singleton(sk0_0)) = sk0_1,
    inference(forward_demodulation,[status(thm)],[f13,f35]) ).

fof(f37,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f36,f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU152+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n027.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 09:35:02 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37  % Elapsed time: 0.020383 seconds
% 0.13/0.37  % CPU time: 0.028724 seconds
% 0.13/0.37  % Memory used: 8.994 MB
%------------------------------------------------------------------------------