%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : NUM458+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 12:29:13 EDT 2023

% Result   : Theorem 0.14s 0.31s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   33 (  12 unt;   1 def)
%            Number of atoms       :   82 (  13 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   83 (  34   ~;  33   |;   9   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   21 (;  18   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f18,definition,
    ! [W0,W1] :
      ( ( aNaturalNumber0(W0)
        & aNaturalNumber0(W1) )
     => ( sdtlseqdt0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & sdtpldt0(W0,W2) = W1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,hypothesis,
    aNaturalNumber0(xm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,conjecture,
    sdtlseqdt0(xm,xm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,negated_conjecture,
    ~ sdtlseqdt0(xm,xm),
    inference(negated_conjecture,[status(cth)],[f21]) ).

fof(f26,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f37,plain,
    ! [W0] :
      ( ~ aNaturalNumber0(W0)
      | ( sdtpldt0(W0,sz00) = W0
        & W0 = sdtpldt0(sz00,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f38,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f64,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ( sdtlseqdt0(W0,W1)
      <=> ? [W2] :
            ( aNaturalNumber0(W2)
            & sdtpldt0(W0,W2) = W1 ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f65,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ( ( ~ sdtlseqdt0(W0,W1)
          | ? [W2] :
              ( aNaturalNumber0(W2)
              & sdtpldt0(W0,W2) = W1 ) )
        & ( sdtlseqdt0(W0,W1)
          | ! [W2] :
              ( ~ aNaturalNumber0(W2)
              | sdtpldt0(W0,W2) != W1 ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ! [W0,W1] :
      ( ~ aNaturalNumber0(W0)
      | ~ aNaturalNumber0(W1)
      | ( ( ~ sdtlseqdt0(W0,W1)
          | ( aNaturalNumber0(sk0_0(W1,W0))
            & sdtpldt0(W0,sk0_0(W1,W0)) = W1 ) )
        & ( sdtlseqdt0(W0,W1)
          | ! [W2] :
              ( ~ aNaturalNumber0(W2)
              | sdtpldt0(W0,W2) != W1 ) ) ) ),
    inference(skolemization,[status(esa)],[f65]) ).

fof(f69,plain,
    ! [X0,X1,X2] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(X1)
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | sdtpldt0(X0,X2) != X1 ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f76,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f77,plain,
    ~ sdtlseqdt0(xm,xm),
    inference(cnf_transformation,[status(esa)],[f22]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(sdtpldt0(X0,X1))
      | sdtlseqdt0(X0,sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1) ),
    inference(destructive_equality_resolution,[status(esa)],[f69]) ).

fof(f84,plain,
    sdtpldt0(xm,sz00) = xm,
    inference(resolution,[status(thm)],[f38,f76]) ).

fof(f85,plain,
    ( spl0_0
  <=> aNaturalNumber0(xm) ),
    introduced(split_symbol_definition) ).

fof(f87,plain,
    ( ~ aNaturalNumber0(xm)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f85]) ).

fof(f88,plain,
    ( spl0_1
  <=> sdtlseqdt0(xm,sdtpldt0(xm,sz00)) ),
    introduced(split_symbol_definition) ).

fof(f89,plain,
    ( sdtlseqdt0(xm,sdtpldt0(xm,sz00))
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f88]) ).

fof(f91,plain,
    ( spl0_2
  <=> aNaturalNumber0(sz00) ),
    introduced(split_symbol_definition) ).

fof(f93,plain,
    ( ~ aNaturalNumber0(sz00)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f91]) ).

fof(f94,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xm)
    | sdtlseqdt0(xm,sdtpldt0(xm,sz00))
    | ~ aNaturalNumber0(sz00) ),
    inference(paramodulation,[status(thm)],[f84,f78]) ).

fof(f95,plain,
    ( ~ spl0_0
    | spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f94,f85,f88,f91]) ).

fof(f96,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f93,f26]) ).

fof(f97,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f96]) ).

fof(f98,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f87,f76]) ).

fof(f99,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f98]) ).

fof(f100,plain,
    ( sdtlseqdt0(xm,xm)
    | ~ spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f84,f89]) ).

fof(f101,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f100,f77]) ).

fof(f102,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f101]) ).

fof(f103,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f95,f97,f99,f102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : NUM458+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n027.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue May 30 10:09:17 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.10/0.31  % Drodi V3.5.1
% 0.14/0.31  % Refutation found
% 0.14/0.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53  % Elapsed time: 0.012671 seconds
% 0.14/0.53  % CPU time: 0.011176 seconds
% 0.14/0.53  % Memory used: 2.920 MB
%------------------------------------------------------------------------------