%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 12:29:22 EDT 2023

% Result   : Theorem 0.19s 0.38s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   35 (  14 unt;   1 def)
%            Number of atoms       :   88 (  23 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :   89 (  36   ~;  36   |;   9   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   18 (;  18   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f19,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
       => ! [W2] :
            ( W2 = sdtmndt0(W1,W0)
          <=> ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,hypothesis,
    sdtlseqdt0(xp,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f43,hypothesis,
    xr = sdtmndt0(xn,xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,conjecture,
    xn = sdtpldt0(xp,xr),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f46,negated_conjecture,
    xn != sdtpldt0(xp,xr),
    inference(negated_conjecture,[status(cth)],[f45]) ).

fof(f94,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ sdtlseqdt0(W0,W1)
      | ! [W2] :
          ( W2 = sdtmndt0(W1,W0)
        <=> ( aNaturalNumber0(W2)
            & sdtpldt0(W0,W2) = W1 ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f95,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ sdtlseqdt0(W0,W1)
      | ! [W2] :
          ( ( W2 != sdtmndt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) )
          & ( W2 = sdtmndt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | sdtpldt0(W0,W2) != W1 ) ) ),
    inference(NNF_transformation,[status(esa)],[f94]) ).

fof(f96,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ~ sdtlseqdt0(W0,W1)
      | ( ! [W2] :
            ( W2 != sdtmndt0(W1,W0)
            | ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) )
        & ! [W2] :
            ( W2 = sdtmndt0(W1,W0)
            | ~ aNaturalNumber0(W2)
            | sdtpldt0(W0,W2) != W1 ) ) ),
    inference(miniscoping,[status(esa)],[f95]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ sdtlseqdt0(X0,X1)
      | X2 != sdtmndt0(X1,X0)
      | sdtpldt0(X0,X2) = X1 ),
    inference(cnf_transformation,[status(esa)],[f96]) ).

fof(f165,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f167,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f172,plain,
    sdtlseqdt0(xp,xn),
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f173,plain,
    xr = sdtmndt0(xn,xp),
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f176,plain,
    xn != sdtpldt0(xp,xr),
    inference(cnf_transformation,[status(esa)],[f46]) ).

fof(f179,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | ~ sdtlseqdt0(X0,X1)
      | sdtpldt0(X0,sdtmndt0(X1,X0)) = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f98]) ).

fof(f277,plain,
    ( spl0_12
  <=> aNaturalNumber0(xp) ),
    introduced(split_symbol_definition) ).

fof(f279,plain,
    ( ~ aNaturalNumber0(xp)
    | spl0_12 ),
    inference(component_clause,[status(thm)],[f277]) ).

fof(f280,plain,
    ( spl0_13
  <=> aNaturalNumber0(xn) ),
    introduced(split_symbol_definition) ).

fof(f282,plain,
    ( ~ aNaturalNumber0(xn)
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f280]) ).

fof(f283,plain,
    ( spl0_14
  <=> sdtlseqdt0(xp,xn) ),
    introduced(split_symbol_definition) ).

fof(f285,plain,
    ( ~ sdtlseqdt0(xp,xn)
    | spl0_14 ),
    inference(component_clause,[status(thm)],[f283]) ).

fof(f291,plain,
    ( $false
    | spl0_14 ),
    inference(forward_subsumption_resolution,[status(thm)],[f285,f172]) ).

fof(f292,plain,
    spl0_14,
    inference(contradiction_clause,[status(thm)],[f291]) ).

fof(f293,plain,
    ( $false
    | spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f282,f165]) ).

fof(f294,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f293]) ).

fof(f295,plain,
    ( $false
    | spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f279,f167]) ).

fof(f296,plain,
    spl0_12,
    inference(contradiction_clause,[status(thm)],[f295]) ).

fof(f485,plain,
    ( spl0_41
  <=> sdtpldt0(xp,xr) = xn ),
    introduced(split_symbol_definition) ).

fof(f486,plain,
    ( sdtpldt0(xp,xr) = xn
    | ~ spl0_41 ),
    inference(component_clause,[status(thm)],[f485]) ).

fof(f488,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn)
    | ~ sdtlseqdt0(xp,xn)
    | sdtpldt0(xp,xr) = xn ),
    inference(paramodulation,[status(thm)],[f173,f179]) ).

fof(f489,plain,
    ( ~ spl0_12
    | ~ spl0_13
    | ~ spl0_14
    | spl0_41 ),
    inference(split_clause,[status(thm)],[f488,f277,f280,f283,f485]) ).

fof(f613,plain,
    ( $false
    | ~ spl0_41 ),
    inference(forward_subsumption_resolution,[status(thm)],[f486,f176]) ).

fof(f614,plain,
    ~ spl0_41,
    inference(contradiction_clause,[status(thm)],[f613]) ).

fof(f615,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f292,f294,f296,f489,f614]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33  % Computer : n005.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue May 30 09:57:36 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.19/0.38  % Refutation found
% 0.19/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.43  % Elapsed time: 0.077964 seconds
% 0.19/0.43  % CPU time: 0.090004 seconds
% 0.19/0.43  % Memory used: 7.877 MB
%------------------------------------------------------------------------------