%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET590+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 20:39:53 EDT 2024

% Result   : Theorem 0.11s 0.33s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   20 (   7 unt;   0 def)
%            Number of atoms       :   56 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   59 (  23   ~;  21   |;  11   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   53 (  49   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B,C,D] :
      ( member(D,difference(B,C))
    <=> ( member(D,B)
        & ~ member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,conjecture,
    ! [B,C] : subset(difference(B,C),B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f5,negated_conjecture,
    ~ ! [B,C] : subset(difference(B,C),B),
    inference(negated_conjecture,[status(cth)],[f4]) ).

fof(f6,plain,
    ! [B,C,D] :
      ( ( ~ member(D,difference(B,C))
        | ( member(D,B)
          & ~ member(D,C) ) )
      & ( member(D,difference(B,C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f7,plain,
    ( ! [B,C,D] :
        ( ~ member(D,difference(B,C))
        | ( member(D,B)
          & ~ member(D,C) ) )
    & ! [B,C,D] :
        ( member(D,difference(B,C))
        | ~ member(D,B)
        | member(D,C) ) ),
    inference(miniscoping,[status(esa)],[f6]) ).

fof(f8,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,difference(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f11,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f12,plain,
    ! [B,C] :
      ( ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
      & ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f11]) ).

fof(f13,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ? [D] :
            ( member(D,B)
            & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f12]) ).

fof(f14,plain,
    ( ! [B,C] :
        ( ~ subset(B,C)
        | ! [D] :
            ( ~ member(D,B)
            | member(D,C) ) )
    & ! [B,C] :
        ( subset(B,C)
        | ( member(sk0_0(C,B),B)
          & ~ member(sk0_0(C,B),C) ) ) ),
    inference(skolemization,[status(esa)],[f13]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f19,plain,
    ? [B,C] : ~ subset(difference(B,C),B),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f20,plain,
    ~ subset(difference(sk0_1,sk0_2),sk0_1),
    inference(skolemization,[status(esa)],[f19]) ).

fof(f21,plain,
    ~ subset(difference(sk0_1,sk0_2),sk0_1),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( subset(difference(X0,X1),X2)
      | member(sk0_0(X2,difference(X0,X1)),X0) ),
    inference(resolution,[status(thm)],[f16,f8]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( subset(difference(X0,X1),X0)
      | subset(difference(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f17,f23]) ).

fof(f59,plain,
    ! [X0,X1] : subset(difference(X0,X1),X0),
    inference(duplicate_literals_removal,[status(esa)],[f58]) ).

fof(f66,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f21,f59]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET590+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n014.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 21:22:04 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.6.0
% 0.11/0.33  % Refutation found
% 0.11/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.34  % Elapsed time: 0.015396 seconds
% 0.11/0.34  % CPU time: 0.037379 seconds
% 0.11/0.34  % Total memory used: 2.578 MB
% 0.11/0.34  % Net memory used: 2.566 MB
%------------------------------------------------------------------------------