%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM551+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 12:29:40 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (   7 unt;   0 def)
%            Number of atoms       :   63 (   6 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   57 (  23   ~;  15   |;  14   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   15 (;  11   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f62,hypothesis,
    ( aSet0(xS)
    & aSet0(xT)
    & xk != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f65,hypothesis,
    ( aSet0(xQ)
    & ! [W0] :
        ( aElementOf0(W0,xQ)
       => aElementOf0(W0,xS) )
    & aSubsetOf0(xQ,xS)
    & sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f67,hypothesis,
    ~ ( ~ ? [W0] : aElementOf0(W0,xQ)
      | xQ = slcrc0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f68,conjecture,
    ? [W0] :
      ( aElement0(W0)
      & aElementOf0(W0,xQ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f69,negated_conjecture,
    ~ ? [W0] :
        ( aElement0(W0)
        & aElementOf0(W0,xQ) ),
    inference(negated_conjecture,[status(cth)],[f68]) ).

fof(f76,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ! [W1] :
          ( ~ aElementOf0(W1,W0)
          | aElement0(W1) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ~ aSet0(X0)
      | ~ aElementOf0(X1,X0)
      | aElement0(X1) ),
    inference(cnf_transformation,[status(esa)],[f76]) ).

fof(f269,plain,
    aSet0(xS),
    inference(cnf_transformation,[status(esa)],[f62]) ).

fof(f303,plain,
    ( aSet0(xQ)
    & ! [W0] :
        ( ~ aElementOf0(W0,xQ)
        | aElementOf0(W0,xS) )
    & aSubsetOf0(xQ,xS)
    & sbrdtbr0(xQ) = xk
    & aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
    inference(pre_NNF_transformation,[status(esa)],[f65]) ).

fof(f305,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,xQ)
      | aElementOf0(X0,xS) ),
    inference(cnf_transformation,[status(esa)],[f303]) ).

fof(f312,plain,
    ( ? [W0] : aElementOf0(W0,xQ)
    & xQ != slcrc0 ),
    inference(pre_NNF_transformation,[status(esa)],[f67]) ).

fof(f313,plain,
    ( aElementOf0(sk0_15,xQ)
    & xQ != slcrc0 ),
    inference(skolemization,[status(esa)],[f312]) ).

fof(f314,plain,
    aElementOf0(sk0_15,xQ),
    inference(cnf_transformation,[status(esa)],[f313]) ).

fof(f316,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ~ aElementOf0(W0,xQ) ),
    inference(pre_NNF_transformation,[status(esa)],[f69]) ).

fof(f317,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ~ aElementOf0(X0,xQ) ),
    inference(cnf_transformation,[status(esa)],[f316]) ).

fof(f409,plain,
    ( spl0_11
  <=> aSet0(xS) ),
    introduced(split_symbol_definition) ).

fof(f411,plain,
    ( ~ aSet0(xS)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f409]) ).

fof(f417,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f411,f269]) ).

fof(f418,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f417]) ).

fof(f419,plain,
    aElementOf0(sk0_15,xS),
    inference(resolution,[status(thm)],[f314,f305]) ).

fof(f420,plain,
    ~ aElement0(sk0_15),
    inference(resolution,[status(thm)],[f314,f317]) ).

fof(f421,plain,
    ( spl0_13
  <=> aElement0(sk0_15) ),
    introduced(split_symbol_definition) ).

fof(f422,plain,
    ( aElement0(sk0_15)
    | ~ spl0_13 ),
    inference(component_clause,[status(thm)],[f421]) ).

fof(f426,plain,
    ( ~ aSet0(xS)
    | aElement0(sk0_15) ),
    inference(resolution,[status(thm)],[f419,f77]) ).

fof(f427,plain,
    ( ~ spl0_11
    | spl0_13 ),
    inference(split_clause,[status(thm)],[f426,f409,f421]) ).

fof(f451,plain,
    ( $false
    | ~ spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f422,f420]) ).

fof(f452,plain,
    ~ spl0_13,
    inference(contradiction_clause,[status(thm)],[f451]) ).

fof(f453,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f418,f427,f452]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM551+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Tue May 30 09:46:07 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.36  % Drodi V3.5.1
% 0.20/0.58  % Refutation found
% 0.20/0.58  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.58  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.58  % Elapsed time: 0.019191 seconds
% 0.20/0.58  % CPU time: 0.044609 seconds
% 0.20/0.58  % Memory used: 15.721 MB
%------------------------------------------------------------------------------