%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM550+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n010.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 12:29:39 EDT 2023

% Result   : Theorem 0.14s 0.32s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   24 (  10 unt;   1 def)
%            Number of atoms       :   60 (  31 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   62 (  26   ~;  18   |;  13   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-1 aty)
%            Number of variables   :   19 (;  16   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5,definition,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( aSet0(W0)
        & ~ ? [W1] : aElementOf0(W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ( sbrdtbr0(W0) = sz00
      <=> W0 = slcrc0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f66,hypothesis,
    ( aSet0(xQ)
    & isFinite0(xQ)
    & sbrdtbr0(xQ) = xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f67,conjecture,
    xQ != slcrc0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f68,negated_conjecture,
    ~ ( xQ != slcrc0 ),
    inference(negated_conjecture,[status(cth)],[f67]) ).

fof(f79,plain,
    ! [W0] :
      ( W0 = slcrc0
    <=> ( aSet0(W0)
        & ! [W1] : ~ aElementOf0(W1,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f80,plain,
    ! [W0] :
      ( ( W0 != slcrc0
        | ( aSet0(W0)
          & ! [W1] : ~ aElementOf0(W1,W0) ) )
      & ( W0 = slcrc0
        | ~ aSet0(W0)
        | ? [W1] : aElementOf0(W1,W0) ) ),
    inference(NNF_transformation,[status(esa)],[f79]) ).

fof(f81,plain,
    ( ! [W0] :
        ( W0 != slcrc0
        | ( aSet0(W0)
          & ! [W1] : ~ aElementOf0(W1,W0) ) )
    & ! [W0] :
        ( W0 = slcrc0
        | ~ aSet0(W0)
        | ? [W1] : aElementOf0(W1,W0) ) ),
    inference(miniscoping,[status(esa)],[f80]) ).

fof(f82,plain,
    ( ! [W0] :
        ( W0 != slcrc0
        | ( aSet0(W0)
          & ! [W1] : ~ aElementOf0(W1,W0) ) )
    & ! [W0] :
        ( W0 = slcrc0
        | ~ aSet0(W0)
        | aElementOf0(sk0_0(W0),W0) ) ),
    inference(skolemization,[status(esa)],[f81]) ).

fof(f83,plain,
    ! [X0] :
      ( X0 != slcrc0
      | aSet0(X0) ),
    inference(cnf_transformation,[status(esa)],[f82]) ).

fof(f189,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ( sbrdtbr0(W0) = sz00
      <=> W0 = slcrc0 ) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f190,plain,
    ! [W0] :
      ( ~ aSet0(W0)
      | ( ( sbrdtbr0(W0) != sz00
          | W0 = slcrc0 )
        & ( sbrdtbr0(W0) = sz00
          | W0 != slcrc0 ) ) ),
    inference(NNF_transformation,[status(esa)],[f189]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ aSet0(X0)
      | sbrdtbr0(X0) = sz00
      | X0 != slcrc0 ),
    inference(cnf_transformation,[status(esa)],[f190]) ).

fof(f270,plain,
    xk != sz00,
    inference(cnf_transformation,[status(esa)],[f62]) ).

fof(f277,plain,
    sbrdtbr0(xQ) = xk,
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f278,plain,
    xQ = slcrc0,
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f285,plain,
    aSet0(slcrc0),
    inference(destructive_equality_resolution,[status(esa)],[f83]) ).

fof(f297,plain,
    ( ~ aSet0(slcrc0)
    | sbrdtbr0(slcrc0) = sz00 ),
    inference(destructive_equality_resolution,[status(esa)],[f192]) ).

fof(f315,plain,
    sbrdtbr0(slcrc0) = xk,
    inference(forward_demodulation,[status(thm)],[f278,f277]) ).

fof(f399,plain,
    ( ~ aSet0(slcrc0)
    | xk = sz00 ),
    inference(forward_demodulation,[status(thm)],[f315,f297]) ).

fof(f400,plain,
    xk = sz00,
    inference(forward_subsumption_resolution,[status(thm)],[f399,f285]) ).

fof(f407,plain,
    sz00 != sz00,
    inference(backward_demodulation,[status(thm)],[f400,f270]) ).

fof(f408,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f407]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : NUM550+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n010.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 09:41:52 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.5.1
% 0.14/0.32  % Refutation found
% 0.14/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.54  % Elapsed time: 0.018039 seconds
% 0.14/0.54  % CPU time: 0.015991 seconds
% 0.14/0.54  % Memory used: 3.916 MB
%------------------------------------------------------------------------------