TSTP Solution File: NUM482+3 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : NUM482+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 : Tue Apr 30 20:34:52 EDT 2024

% Result   : Theorem 0.07s 0.27s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   32 (   8 unt;   0 def)
%            Number of atoms       :  151 (  56 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  179 (  60   ~;  54   |;  55   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   37 (  25   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [W0] :
      ( aNaturalNumber0(W0)
     => ( sdtasdt0(W0,sz10) = W0
        & W0 = sdtasdt0(sz10,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f38,hypothesis,
    aNaturalNumber0(xk),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f41,conjecture,
    ( ( ! [W0] :
          ( ( aNaturalNumber0(W0)
            & ( ? [W1] :
                  ( aNaturalNumber0(W1)
                  & xk = sdtasdt0(W0,W1) )
              | doDivides0(W0,xk) ) )
         => ( W0 = sz10
            | W0 = xk ) )
      & isPrime0(xk) )
   => ? [W0] :
        ( aNaturalNumber0(W0)
        & ( ? [W1] :
              ( aNaturalNumber0(W1)
              & xk = sdtasdt0(W0,W1) )
          | doDivides0(W0,xk) )
        & ( ( W0 != sz00
            & W0 != sz10
            & ! [W1] :
                ( ( aNaturalNumber0(W1)
                  & ? [W2] :
                      ( aNaturalNumber0(W2)
                      & W0 = sdtasdt0(W1,W2) )
                  & doDivides0(W1,W0) )
               => ( W1 = sz10
                  | W1 = W0 ) ) )
          | isPrime0(W0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f42,negated_conjecture,
    ~ ( ( ! [W0] :
            ( ( aNaturalNumber0(W0)
              & ( ? [W1] :
                    ( aNaturalNumber0(W1)
                    & xk = sdtasdt0(W0,W1) )
                | doDivides0(W0,xk) ) )
           => ( W0 = sz10
              | W0 = xk ) )
        & isPrime0(xk) )
     => ? [W0] :
          ( aNaturalNumber0(W0)
          & ( ? [W1] :
                ( aNaturalNumber0(W1)
                & xk = sdtasdt0(W0,W1) )
            | doDivides0(W0,xk) )
          & ( ( W0 != sz00
              & W0 != sz10
              & ! [W1] :
                  ( ( aNaturalNumber0(W1)
                    & ? [W2] :
                        ( aNaturalNumber0(W2)
                        & W0 = sdtasdt0(W1,W2) )
                    & doDivides0(W1,W0) )
                 => ( W1 = sz10
                    | W1 = W0 ) ) )
            | isPrime0(W0) ) ) ),
    inference(negated_conjecture,[status(cth)],[f41]) ).

fof(f47,plain,
    aNaturalNumber0(sz10),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f64,plain,
    ! [W0] :
      ( ~ aNaturalNumber0(W0)
      | ( sdtasdt0(W0,sz10) = W0
        & W0 = sdtasdt0(sz10,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtasdt0(X0,sz10) = X0 ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f156,plain,
    aNaturalNumber0(xk),
    inference(cnf_transformation,[status(esa)],[f38]) ).

fof(f170,plain,
    ( ! [W0] :
        ( ~ aNaturalNumber0(W0)
        | ( ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | xk != sdtasdt0(W0,W1) )
          & ~ doDivides0(W0,xk) )
        | W0 = sz10
        | W0 = xk )
    & isPrime0(xk)
    & ! [W0] :
        ( ~ aNaturalNumber0(W0)
        | ( ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | xk != sdtasdt0(W0,W1) )
          & ~ doDivides0(W0,xk) )
        | ( ( W0 = sz00
            | W0 = sz10
            | ? [W1] :
                ( aNaturalNumber0(W1)
                & ? [W2] :
                    ( aNaturalNumber0(W2)
                    & W0 = sdtasdt0(W1,W2) )
                & doDivides0(W1,W0)
                & W1 != sz10
                & W1 != W0 ) )
          & ~ isPrime0(W0) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f42]) ).

fof(f171,plain,
    ! [W0] :
      ( pd0_0(W0)
     => ( ! [W1] :
            ( ~ aNaturalNumber0(W1)
            | xk != sdtasdt0(W0,W1) )
        & ~ doDivides0(W0,xk) ) ),
    introduced(predicate_definition,[f170]) ).

fof(f172,plain,
    ( ! [W0] :
        ( ~ aNaturalNumber0(W0)
        | ( ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | xk != sdtasdt0(W0,W1) )
          & ~ doDivides0(W0,xk) )
        | W0 = sz10
        | W0 = xk )
    & isPrime0(xk)
    & ! [W0] :
        ( ~ aNaturalNumber0(W0)
        | pd0_0(W0)
        | ( ( W0 = sz00
            | W0 = sz10
            | ? [W1] :
                ( aNaturalNumber0(W1)
                & ? [W2] :
                    ( aNaturalNumber0(W2)
                    & W0 = sdtasdt0(W1,W2) )
                & doDivides0(W1,W0)
                & W1 != sz10
                & W1 != W0 ) )
          & ~ isPrime0(W0) ) ) ),
    inference(formula_renaming,[status(thm)],[f170,f171]) ).

fof(f173,plain,
    ( ! [W0] :
        ( ~ aNaturalNumber0(W0)
        | ( ! [W1] :
              ( ~ aNaturalNumber0(W1)
              | xk != sdtasdt0(W0,W1) )
          & ~ doDivides0(W0,xk) )
        | W0 = sz10
        | W0 = xk )
    & isPrime0(xk)
    & ! [W0] :
        ( ~ aNaturalNumber0(W0)
        | pd0_0(W0)
        | ( ( W0 = sz00
            | W0 = sz10
            | ( aNaturalNumber0(sk0_5(W0))
              & aNaturalNumber0(sk0_6(W0))
              & W0 = sdtasdt0(sk0_5(W0),sk0_6(W0))
              & doDivides0(sk0_5(W0),W0)
              & sk0_5(W0) != sz10
              & sk0_5(W0) != W0 ) )
          & ~ isPrime0(W0) ) ) ),
    inference(skolemization,[status(esa)],[f172]) ).

fof(f176,plain,
    isPrime0(xk),
    inference(cnf_transformation,[status(esa)],[f173]) ).

fof(f183,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | pd0_0(X0)
      | ~ isPrime0(X0) ),
    inference(cnf_transformation,[status(esa)],[f173]) ).

fof(f184,plain,
    ! [W0] :
      ( ~ pd0_0(W0)
      | ( ! [W1] :
            ( ~ aNaturalNumber0(W1)
            | xk != sdtasdt0(W0,W1) )
        & ~ doDivides0(W0,xk) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f171]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0)
      | ~ aNaturalNumber0(X1)
      | xk != sdtasdt0(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f184]) ).

fof(f218,plain,
    ( spl0_4
  <=> pd0_0(xk) ),
    introduced(split_symbol_definition) ).

fof(f219,plain,
    ( pd0_0(xk)
    | ~ spl0_4 ),
    inference(component_clause,[status(thm)],[f218]) ).

fof(f221,plain,
    ( spl0_5
  <=> isPrime0(xk) ),
    introduced(split_symbol_definition) ).

fof(f223,plain,
    ( ~ isPrime0(xk)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f221]) ).

fof(f224,plain,
    ( pd0_0(xk)
    | ~ isPrime0(xk) ),
    inference(resolution,[status(thm)],[f156,f183]) ).

fof(f225,plain,
    ( spl0_4
    | ~ spl0_5 ),
    inference(split_clause,[status(thm)],[f224,f218,f221]) ).

fof(f226,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f223,f176]) ).

fof(f227,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f226]) ).

fof(f230,plain,
    sdtasdt0(xk,sz10) = xk,
    inference(resolution,[status(thm)],[f65,f156]) ).

fof(f268,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | xk != sdtasdt0(xk,X0)
      | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f219,f185]) ).

fof(f271,plain,
    ( xk != sdtasdt0(xk,sz10)
    | ~ spl0_4 ),
    inference(resolution,[status(thm)],[f268,f47]) ).

fof(f272,plain,
    ( xk != xk
    | ~ spl0_4 ),
    inference(forward_demodulation,[status(thm)],[f230,f271]) ).

fof(f273,plain,
    ( $false
    | ~ spl0_4 ),
    inference(trivial_equality_resolution,[status(esa)],[f272]) ).

fof(f274,plain,
    ~ spl0_4,
    inference(contradiction_clause,[status(thm)],[f273]) ).

fof(f275,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f225,f227,f274]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : NUM482+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n026.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Mon Apr 29 20:55:48 EDT 2024
% 0.07/0.26  % CPUTime  : 
% 0.07/0.27  % Drodi V3.6.0
% 0.07/0.27  % Refutation found
% 0.07/0.27  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28  % Elapsed time: 0.014924 seconds
% 0.07/0.28  % CPU time: 0.025323 seconds
% 0.07/0.28  % Total memory used: 11.803 MB
% 0.07/0.28  % Net memory used: 11.787 MB
%------------------------------------------------------------------------------