TSTP Solution File: NUM500+3 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 : Thu Aug 31 11:30:57 EDT 2023

% Result   : Theorem 7.26s 1.66s
% Output   : CNFRefutation 7.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   83 (  18 unt;   0 def)
%            Number of atoms       :  372 ( 177 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  432 ( 143   ~; 138   |; 137   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   7 con; 0-2 aty)
%            Number of variables   :   98 (   0 sgn;  50   !;  32   ?)

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

fof(f3,axiom,
    ( sz00 != sz10
    & aNaturalNumber0(sz10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).

fof(f11,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sz00 = sdtpldt0(X0,X1)
       => ( sz00 = X1
          & sz00 = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).

fof(f38,axiom,
    ! [X0] :
      ( ( sz10 != X0
        & sz00 != X0
        & aNaturalNumber0(X0) )
     => ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimDiv) ).

fof(f39,axiom,
    ( aNaturalNumber0(xp)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

fof(f41,axiom,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
    & isPrime0(xp)
    & ! [X0] :
        ( ( ( doDivides0(X0,xp)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xp
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xp = X0
          | sz10 = X0 ) )
    & sz10 != xp
    & sz00 != xp ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).

fof(f45,axiom,
    ( xk = sdtsldt0(sdtasdt0(xn,xm),xp)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & aNaturalNumber0(xk) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

fof(f47,axiom,
    ( sz10 != xk
    & sz00 != xk ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2327) ).

fof(f48,conjecture,
    ? [X0] :
      ( ( isPrime0(X0)
        | ( ! [X1] :
              ( ( doDivides0(X1,X0)
                & ? [X2] :
                    ( sdtasdt0(X1,X2) = X0
                    & aNaturalNumber0(X2) )
                & aNaturalNumber0(X1) )
             => ( X0 = X1
                | sz10 = X1 ) )
          & sz10 != X0
          & sz00 != X0 ) )
      & ( doDivides0(X0,xk)
        | ? [X1] :
            ( sdtasdt0(X0,X1) = xk
            & aNaturalNumber0(X1) ) )
      & aNaturalNumber0(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f49,negated_conjecture,
    ~ ? [X0] :
        ( ( isPrime0(X0)
          | ( ! [X1] :
                ( ( doDivides0(X1,X0)
                  & ? [X2] :
                      ( sdtasdt0(X1,X2) = X0
                      & aNaturalNumber0(X2) )
                  & aNaturalNumber0(X1) )
               => ( X0 = X1
                  | sz10 = X1 ) )
            & sz10 != X0
            & sz00 != X0 ) )
        & ( doDivides0(X0,xk)
          | ? [X1] :
              ( sdtasdt0(X0,X1) = xk
              & aNaturalNumber0(X1) ) )
        & aNaturalNumber0(X0) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f53,plain,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
    & isPrime0(xp)
    & ! [X1] :
        ( ( ( doDivides0(X1,xp)
            | ? [X2] :
                ( sdtasdt0(X1,X2) = xp
                & aNaturalNumber0(X2) ) )
          & aNaturalNumber0(X1) )
       => ( xp = X1
          | sz10 = X1 ) )
    & sz10 != xp
    & sz00 != xp ),
    inference(rectify,[],[f41]) ).

fof(f55,plain,
    ~ ? [X0] :
        ( ( isPrime0(X0)
          | ( ! [X1] :
                ( ( doDivides0(X1,X0)
                  & ? [X2] :
                      ( sdtasdt0(X1,X2) = X0
                      & aNaturalNumber0(X2) )
                  & aNaturalNumber0(X1) )
               => ( X0 = X1
                  | sz10 = X1 ) )
            & sz10 != X0
            & sz00 != X0 ) )
        & ( doDivides0(X0,xk)
          | ? [X3] :
              ( xk = sdtasdt0(X0,X3)
              & aNaturalNumber0(X3) ) )
        & aNaturalNumber0(X0) ),
    inference(rectify,[],[f49]) ).

fof(f64,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f69,plain,
    ! [X0] :
      ( ( sdtasdt0(sz10,X0) = X0
        & sdtasdt0(X0,sz10) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( sz00 = X1
        & sz00 = X0 )
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( sz00 = X1
        & sz00 = X0 )
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f77]) ).

fof(f118,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f119,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f118]) ).

fof(f122,plain,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
    & isPrime0(xp)
    & ! [X1] :
        ( xp = X1
        | sz10 = X1
        | ( ~ doDivides0(X1,xp)
          & ! [X2] :
              ( sdtasdt0(X1,X2) != xp
              | ~ aNaturalNumber0(X2) ) )
        | ~ aNaturalNumber0(X1) )
    & sz10 != xp
    & sz00 != xp ),
    inference(ennf_transformation,[],[f53]) ).

fof(f123,plain,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
    & isPrime0(xp)
    & ! [X1] :
        ( xp = X1
        | sz10 = X1
        | ( ~ doDivides0(X1,xp)
          & ! [X2] :
              ( sdtasdt0(X1,X2) != xp
              | ~ aNaturalNumber0(X2) ) )
        | ~ aNaturalNumber0(X1) )
    & sz10 != xp
    & sz00 != xp ),
    inference(flattening,[],[f122]) ).

fof(f127,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ( ~ doDivides0(X0,xk)
        & ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f55]) ).

fof(f128,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ( ~ doDivides0(X0,xk)
        & ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f127]) ).

fof(f132,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f133,plain,
    ! [X0] :
      ( sP2(X0)
      | ( ~ doDivides0(X0,xk)
        & ! [X3] :
            ( xk != sdtasdt0(X0,X3)
            | ~ aNaturalNumber0(X3) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(definition_folding,[],[f128,f132]) ).

fof(f151,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & doDivides0(X1,X0)
          & aNaturalNumber0(X1) )
     => ( isPrime0(sK6(X0))
        & doDivides0(sK6(X0),X0)
        & aNaturalNumber0(sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f152,plain,
    ! [X0] :
      ( ( isPrime0(sK6(X0))
        & doDivides0(sK6(X0),X0)
        & aNaturalNumber0(sK6(X0)) )
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f119,f151]) ).

fof(f165,plain,
    ( ? [X0] :
        ( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
   => ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK11)
      & aNaturalNumber0(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f166,plain,
    ( doDivides0(xp,sdtasdt0(xn,xm))
    & sdtasdt0(xn,xm) = sdtasdt0(xp,sK11)
    & aNaturalNumber0(sK11)
    & isPrime0(xp)
    & ! [X1] :
        ( xp = X1
        | sz10 = X1
        | ( ~ doDivides0(X1,xp)
          & ! [X2] :
              ( sdtasdt0(X1,X2) != xp
              | ~ aNaturalNumber0(X2) ) )
        | ~ aNaturalNumber0(X1) )
    & sz10 != xp
    & sz00 != xp ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f123,f165]) ).

fof(f170,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ? [X1] :
              ( X0 != X1
              & sz10 != X1
              & doDivides0(X1,X0)
              & ? [X2] :
                  ( sdtasdt0(X1,X2) = X0
                  & aNaturalNumber0(X2) )
              & aNaturalNumber0(X1) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f132]) ).

fof(f171,plain,
    ! [X0] :
      ( ? [X1] :
          ( X0 != X1
          & sz10 != X1
          & doDivides0(X1,X0)
          & ? [X2] :
              ( sdtasdt0(X1,X2) = X0
              & aNaturalNumber0(X2) )
          & aNaturalNumber0(X1) )
     => ( sK14(X0) != X0
        & sz10 != sK14(X0)
        & doDivides0(sK14(X0),X0)
        & ? [X2] :
            ( sdtasdt0(sK14(X0),X2) = X0
            & aNaturalNumber0(X2) )
        & aNaturalNumber0(sK14(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f172,plain,
    ! [X0] :
      ( ? [X2] :
          ( sdtasdt0(sK14(X0),X2) = X0
          & aNaturalNumber0(X2) )
     => ( sdtasdt0(sK14(X0),sK15(X0)) = X0
        & aNaturalNumber0(sK15(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ! [X0] :
      ( ( ~ isPrime0(X0)
        & ( ( sK14(X0) != X0
            & sz10 != sK14(X0)
            & doDivides0(sK14(X0),X0)
            & sdtasdt0(sK14(X0),sK15(X0)) = X0
            & aNaturalNumber0(sK15(X0))
            & aNaturalNumber0(sK14(X0)) )
          | sz10 = X0
          | sz00 = X0 ) )
      | ~ sP2(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f170,f172,f171]) ).

fof(f174,plain,
    ! [X0] :
      ( sP2(X0)
      | ( ~ doDivides0(X0,xk)
        & ! [X1] :
            ( sdtasdt0(X0,X1) != xk
            | ~ aNaturalNumber0(X1) ) )
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f133]) ).

fof(f175,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f176,plain,
    aNaturalNumber0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f182,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f187,plain,
    ! [X0] :
      ( sdtasdt0(sz10,X0) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( sz00 = X0
      | sz00 != sdtpldt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f240,plain,
    ! [X0] :
      ( aNaturalNumber0(sK6(X0))
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f241,plain,
    ! [X0] :
      ( doDivides0(sK6(X0),X0)
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f242,plain,
    ! [X0] :
      ( isPrime0(sK6(X0))
      | sz10 = X0
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f152]) ).

fof(f245,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f39]) ).

fof(f263,plain,
    sz10 != xp,
    inference(cnf_transformation,[],[f166]) ).

fof(f264,plain,
    ! [X2,X1] :
      ( xp = X1
      | sz10 = X1
      | sdtasdt0(X1,X2) != xp
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1) ),
    inference(cnf_transformation,[],[f166]) ).

fof(f282,plain,
    aNaturalNumber0(xk),
    inference(cnf_transformation,[],[f45]) ).

fof(f287,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f47]) ).

fof(f288,plain,
    sz10 != xk,
    inference(cnf_transformation,[],[f47]) ).

fof(f295,plain,
    ! [X0] :
      ( ~ isPrime0(X0)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f173]) ).

fof(f297,plain,
    ! [X0] :
      ( sP2(X0)
      | ~ doDivides0(X0,xk)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_49,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_51,plain,
    aNaturalNumber0(sz10),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_57,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f182]) ).

cnf(c_60,plain,
    ( ~ aNaturalNumber0(X0)
    | sdtasdt0(sz10,X0) = X0 ),
    inference(cnf_transformation,[],[f187]) ).

cnf(c_71,plain,
    ( sdtpldt0(X0,X1) != sz00
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz00 ),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_113,plain,
    ( ~ aNaturalNumber0(X0)
    | X0 = sz00
    | X0 = sz10
    | isPrime0(sK6(X0)) ),
    inference(cnf_transformation,[],[f242]) ).

cnf(c_114,plain,
    ( ~ aNaturalNumber0(X0)
    | X0 = sz00
    | X0 = sz10
    | doDivides0(sK6(X0),X0) ),
    inference(cnf_transformation,[],[f241]) ).

cnf(c_115,plain,
    ( ~ aNaturalNumber0(X0)
    | X0 = sz00
    | X0 = sz10
    | aNaturalNumber0(sK6(X0)) ),
    inference(cnf_transformation,[],[f240]) ).

cnf(c_116,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f245]) ).

cnf(c_140,plain,
    ( sdtasdt0(X0,X1) != xp
    | ~ aNaturalNumber0(X0)
    | ~ aNaturalNumber0(X1)
    | X0 = sz10
    | X0 = xp ),
    inference(cnf_transformation,[],[f264]) ).

cnf(c_141,plain,
    sz10 != xp,
    inference(cnf_transformation,[],[f263]) ).

cnf(c_157,plain,
    aNaturalNumber0(xk),
    inference(cnf_transformation,[],[f282]) ).

cnf(c_160,plain,
    sz10 != xk,
    inference(cnf_transformation,[],[f288]) ).

cnf(c_161,plain,
    sz00 != xk,
    inference(cnf_transformation,[],[f287]) ).

cnf(c_162,plain,
    ( ~ isPrime0(X0)
    | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f295]) ).

cnf(c_169,negated_conjecture,
    ( ~ doDivides0(X0,xk)
    | ~ aNaturalNumber0(X0)
    | sP2(X0) ),
    inference(cnf_transformation,[],[f297]) ).

cnf(c_180,plain,
    ( ~ aNaturalNumber0(sz00)
    | sdtpldt0(sz00,sz00) = sz00 ),
    inference(instantiation,[status(thm)],[c_57]) ).

cnf(c_213,plain,
    ( sdtpldt0(sz00,sz00) != sz00
    | ~ aNaturalNumber0(sz00)
    | sz00 = sz00 ),
    inference(instantiation,[status(thm)],[c_71]) ).

cnf(c_9999,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_11841,plain,
    sdtasdt0(sz10,xp) = xp,
    inference(superposition,[status(thm)],[c_116,c_60]) ).

cnf(c_12216,plain,
    ( sdtasdt0(sz10,xp) != xp
    | ~ aNaturalNumber0(sz10)
    | ~ aNaturalNumber0(xp)
    | sz10 = sz10
    | sz10 = xp ),
    inference(instantiation,[status(thm)],[c_140]) ).

cnf(c_12298,plain,
    ( sz10 != X0
    | xk != X0
    | sz10 = xk ),
    inference(instantiation,[status(thm)],[c_9999]) ).

cnf(c_12300,plain,
    ( sz00 != X0
    | xk != X0
    | sz00 = xk ),
    inference(instantiation,[status(thm)],[c_9999]) ).

cnf(c_12301,plain,
    ( sz00 != sz00
    | xk != sz00
    | sz00 = xk ),
    inference(instantiation,[status(thm)],[c_12300]) ).

cnf(c_13157,plain,
    ( ~ aNaturalNumber0(sK6(xk))
    | ~ aNaturalNumber0(xk)
    | sz00 = xk
    | sz10 = xk
    | sP2(sK6(xk)) ),
    inference(superposition,[status(thm)],[c_114,c_169]) ).

cnf(c_13158,plain,
    ( ~ aNaturalNumber0(sK6(xk))
    | sP2(sK6(xk)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_13157,c_160,c_161,c_157]) ).

cnf(c_13166,plain,
    ( ~ aNaturalNumber0(xk)
    | sz00 = xk
    | sz10 = xk
    | sP2(sK6(xk)) ),
    inference(superposition,[status(thm)],[c_115,c_13158]) ).

cnf(c_13167,plain,
    sP2(sK6(xk)),
    inference(forward_subsumption_resolution,[status(thm)],[c_13166,c_160,c_161,c_157]) ).

cnf(c_15453,plain,
    ( sz10 != sz10
    | xk != sz10
    | sz10 = xk ),
    inference(instantiation,[status(thm)],[c_12298]) ).

cnf(c_15492,plain,
    ( ~ aNaturalNumber0(xk)
    | xk = sz00
    | xk = sz10
    | isPrime0(sK6(xk)) ),
    inference(instantiation,[status(thm)],[c_113]) ).

cnf(c_24571,plain,
    ( ~ isPrime0(sK6(xk))
    | ~ sP2(sK6(xk)) ),
    inference(instantiation,[status(thm)],[c_162]) ).

cnf(c_24572,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_24571,c_15492,c_15453,c_13167,c_12301,c_12216,c_11841,c_213,c_180,c_141,c_160,c_161,c_49,c_51,c_116,c_157]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug 25 14:36:29 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.22/0.48  Running first-order theorem proving
% 0.22/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.26/1.66  % SZS status Started for theBenchmark.p
% 7.26/1.66  % SZS status Theorem for theBenchmark.p
% 7.26/1.66  
% 7.26/1.66  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 7.26/1.66  
% 7.26/1.66  ------  iProver source info
% 7.26/1.66  
% 7.26/1.66  git: date: 2023-05-31 18:12:56 +0000
% 7.26/1.66  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 7.26/1.66  git: non_committed_changes: false
% 7.26/1.66  git: last_make_outside_of_git: false
% 7.26/1.66  
% 7.26/1.66  ------ Parsing...
% 7.26/1.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 7.26/1.66  
% 7.26/1.66  ------ Preprocessing... sup_sim: 3  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 7.26/1.66  
% 7.26/1.66  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 7.26/1.66  
% 7.26/1.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 7.26/1.66  ------ Proving...
% 7.26/1.66  ------ Problem Properties 
% 7.26/1.66  
% 7.26/1.66  
% 7.26/1.66  clauses                                 115
% 7.26/1.66  conjectures                             2
% 7.26/1.66  EPR                                     37
% 7.26/1.66  Horn                                    71
% 7.26/1.66  unary                                   29
% 7.26/1.66  binary                                  14
% 7.26/1.66  lits                                    403
% 7.26/1.66  lits eq                                 126
% 7.26/1.66  fd_pure                                 0
% 7.26/1.66  fd_pseudo                               0
% 7.26/1.66  fd_cond                                 27
% 7.26/1.66  fd_pseudo_cond                          11
% 7.26/1.66  AC symbols                              0
% 7.26/1.66  
% 7.26/1.66  ------ Schedule dynamic 5 is on 
% 7.26/1.66  
% 7.26/1.66  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.26/1.66  
% 7.26/1.66  
% 7.26/1.66  ------ 
% 7.26/1.66  Current options:
% 7.26/1.66  ------ 
% 7.26/1.66  
% 7.26/1.66  
% 7.26/1.66  
% 7.26/1.66  
% 7.26/1.66  ------ Proving...
% 7.26/1.66  
% 7.26/1.66  
% 7.26/1.66  % SZS status Theorem for theBenchmark.p
% 7.26/1.66  
% 7.26/1.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.26/1.66  
% 7.26/1.67  
%------------------------------------------------------------------------------