%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:29:41 EDT 2023

% Result   : Theorem 0.15s 0.55s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   20 (   5 unt;   0 def)
%            Number of atoms       :   51 (  11 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   48 (  17   ~;  14   |;  12   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    5 (;   4   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f72,hypothesis,
    ( ! [W0] :
        ( aElementOf0(W0,xP)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xP,xS)
    & sbrdtbr0(xP) = xk ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f73,conjecture,
    ( ( ( ! [W0] :
            ( aElementOf0(W0,xP)
           => aElementOf0(W0,xS) )
        | aSubsetOf0(xP,xS) )
      & sbrdtbr0(xP) = xk )
    | aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f74,negated_conjecture,
    ~ ( ( ( ! [W0] :
              ( aElementOf0(W0,xP)
             => aElementOf0(W0,xS) )
          | aSubsetOf0(xP,xS) )
        & sbrdtbr0(xP) = xk )
      | aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    inference(negated_conjecture,[status(cth)],[f73]) ).

fof(f342,plain,
    ( ! [W0] :
        ( ~ aElementOf0(W0,xP)
        | aElementOf0(W0,xS) )
    & aSubsetOf0(xP,xS)
    & sbrdtbr0(xP) = xk ),
    inference(pre_NNF_transformation,[status(esa)],[f72]) ).

fof(f344,plain,
    aSubsetOf0(xP,xS),
    inference(cnf_transformation,[status(esa)],[f342]) ).

fof(f345,plain,
    sbrdtbr0(xP) = xk,
    inference(cnf_transformation,[status(esa)],[f342]) ).

fof(f346,plain,
    ( ( ( ? [W0] :
            ( aElementOf0(W0,xP)
            & ~ aElementOf0(W0,xS) )
        & ~ aSubsetOf0(xP,xS) )
      | sbrdtbr0(xP) != xk )
    & ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    inference(pre_NNF_transformation,[status(esa)],[f74]) ).

fof(f347,plain,
    ( ( ( aElementOf0(sk0_15,xP)
        & ~ aElementOf0(sk0_15,xS)
        & ~ aSubsetOf0(xP,xS) )
      | sbrdtbr0(xP) != xk )
    & ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
    inference(skolemization,[status(esa)],[f346]) ).

fof(f350,plain,
    ( ~ aSubsetOf0(xP,xS)
    | sbrdtbr0(xP) != xk ),
    inference(cnf_transformation,[status(esa)],[f347]) ).

fof(f361,plain,
    ( spl0_1
  <=> sbrdtbr0(xP) = xk ),
    introduced(split_symbol_definition) ).

fof(f363,plain,
    ( sbrdtbr0(xP) != xk
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f361]) ).

fof(f369,plain,
    ( spl0_3
  <=> aSubsetOf0(xP,xS) ),
    introduced(split_symbol_definition) ).

fof(f371,plain,
    ( ~ aSubsetOf0(xP,xS)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f369]) ).

fof(f372,plain,
    ( ~ spl0_3
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f350,f369,f361]) ).

fof(f513,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f371,f344]) ).

fof(f514,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f513]) ).

fof(f515,plain,
    ( xk != xk
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f345,f363]) ).

fof(f516,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f515]) ).

fof(f517,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f516]) ).

fof(f518,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f372,f514,f517]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n028.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue May 30 10:11:47 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.15/0.32  % Drodi V3.5.1
% 0.15/0.55  % Refutation found
% 0.15/0.55  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55  % Elapsed time: 0.018960 seconds
% 0.15/0.55  % CPU time: 0.018631 seconds
% 0.15/0.55  % Memory used: 4.039 MB
%------------------------------------------------------------------------------