%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 12:35:39 EDT 2023

% Result   : Theorem 0.16s 0.55s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   15 (   7 unt;   0 def)
%            Number of atoms       :   27 (  14 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   27 (  15   ~;   5   |;   4   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    4 (   2 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   :   20 (;  18   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,conjecture,
    ! [A,B] :
      ( ~ in(A,B)
     => set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,negated_conjecture,
    ~ ! [A,B] :
        ( ~ in(A,B)
       => set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
    inference(negated_conjecture,[status(cth)],[f8]) ).

fof(f10,axiom,
    ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [A,B] :
      ( set_difference(A,singleton(B)) = A
    <=> ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,plain,
    ? [A,B] :
      ( ~ in(A,B)
      & set_difference(set_union2(B,singleton(A)),singleton(A)) != B ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f28,plain,
    ( ~ in(sk0_2,sk0_3)
    & set_difference(set_union2(sk0_3,singleton(sk0_2)),singleton(sk0_2)) != sk0_3 ),
    inference(skolemization,[status(esa)],[f27]) ).

fof(f29,plain,
    ~ in(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f30,plain,
    set_difference(set_union2(sk0_3,singleton(sk0_2)),singleton(sk0_2)) != sk0_3,
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f31,plain,
    ! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
    inference(cnf_transformation,[status(esa)],[f10]) ).

fof(f32,plain,
    ! [A,B] :
      ( ( set_difference(A,singleton(B)) != A
        | ~ in(B,A) )
      & ( set_difference(A,singleton(B)) = A
        | in(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f11]) ).

fof(f33,plain,
    ( ! [A,B] :
        ( set_difference(A,singleton(B)) != A
        | ~ in(B,A) )
    & ! [A,B] :
        ( set_difference(A,singleton(B)) = A
        | in(B,A) ) ),
    inference(miniscoping,[status(esa)],[f32]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( set_difference(X0,singleton(X1)) = X0
      | in(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f36,plain,
    set_difference(sk0_3,singleton(sk0_2)) != sk0_3,
    inference(backward_demodulation,[status(thm)],[f31,f30]) ).

fof(f40,plain,
    in(sk0_2,sk0_3),
    inference(resolution,[status(thm)],[f35,f36]) ).

fof(f41,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f40,f29]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : SET987+1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31  % Computer : n025.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Tue May 30 10:28:42 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.32  % Drodi V3.5.1
% 0.16/0.55  % Refutation found
% 0.16/0.55  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55  % Elapsed time: 0.013354 seconds
% 0.16/0.55  % CPU time: 0.011982 seconds
% 0.16/0.55  % Memory used: 3.588 MB
%------------------------------------------------------------------------------