%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 12:34:14 EDT 2023

% Result   : Theorem 0.10s 0.33s
% Output   : CNFRefutation 0.10s
% 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 :   58 (  22   ~;  22   |;  10   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   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,union(B,C))
    <=> ( member(D,B)
        | member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f6,conjecture,
    ! [B,C] : subset(B,union(B,C)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,negated_conjecture,
    ~ ! [B,C] : subset(B,union(B,C)),
    inference(negated_conjecture,[status(cth)],[f6]) ).

fof(f8,plain,
    ! [B,C,D] :
      ( ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
      & ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f9,plain,
    ( ! [B,C,D] :
        ( ~ member(D,union(B,C))
        | member(D,B)
        | member(D,C) )
    & ! [B,C,D] :
        ( member(D,union(B,C))
        | ( ~ member(D,B)
          & ~ member(D,C) ) ) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( member(X0,union(X1,X2))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f13,plain,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( ~ member(D,B)
          | member(D,C) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f14,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)],[f13]) ).

fof(f15,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)],[f14]) ).

fof(f16,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)],[f15]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f29,plain,
    ? [B,C] : ~ subset(B,union(B,C)),
    inference(pre_NNF_transformation,[status(esa)],[f7]) ).

fof(f30,plain,
    ~ subset(sk0_2,union(sk0_2,sk0_3)),
    inference(skolemization,[status(esa)],[f29]) ).

fof(f31,plain,
    ~ subset(sk0_2,union(sk0_2,sk0_3)),
    inference(cnf_transformation,[status(esa)],[f30]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( subset(X0,X1)
      | member(sk0_0(X1,X0),union(X0,X2)) ),
    inference(resolution,[status(thm)],[f18,f11]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( subset(X0,union(X0,X1))
      | subset(X0,union(X0,X1)) ),
    inference(resolution,[status(thm)],[f19,f37]) ).

fof(f109,plain,
    ! [X0,X1] : subset(X0,union(X0,X1)),
    inference(duplicate_literals_removal,[status(esa)],[f108]) ).

fof(f116,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[f31,f109]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET194+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n018.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 10:24:25 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.5.1
% 0.10/0.33  % Refutation found
% 0.10/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.55  % Elapsed time: 0.014835 seconds
% 0.16/0.55  % CPU time: 0.014989 seconds
% 0.16/0.55  % Memory used: 3.643 MB
%------------------------------------------------------------------------------