TSTP Solution File: NUM518+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 : Sun May  5 08:35:18 EDT 2024

% Result   : Theorem 6.63s 1.26s
% Output   : Refutation 6.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   73 (  15 unt;   0 def)
%            Number of atoms       :  316 (  88 equ)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  369 ( 126   ~; 118   |; 111   &)
%                                         (   3 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;  11 con; 0-2 aty)
%            Number of variables   :   85 (  54   !;  31   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16465,plain,
    $false,
    inference(resolution,[],[f16464,f240]) ).

fof(f240,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f39]) ).

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

fof(f16464,plain,
    ~ aNaturalNumber0(xn),
    inference(resolution,[],[f16462,f242]) ).

fof(f242,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f39]) ).

fof(f16462,plain,
    ( ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[],[f16458,f231]) ).

fof(f231,plain,
    aNaturalNumber0(xr),
    inference(cnf_transformation,[],[f158]) ).

fof(f158,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & xk = sdtasdt0(xr,sK9)
    & aNaturalNumber0(sK9)
    & aNaturalNumber0(xr) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f70,f157]) ).

fof(f157,plain,
    ( ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
   => ( xk = sdtasdt0(xr,sK9)
      & aNaturalNumber0(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(flattening,[],[f69]) ).

fof(f69,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( xr = X0
        | sz10 = X0
        | ( ~ doDivides0(X0,xr)
          & ! [X1] :
              ( sdtasdt0(X0,X1) != xr
              | ~ aNaturalNumber0(X1) ) )
        | ~ aNaturalNumber0(X0) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(ennf_transformation,[],[f59]) ).

fof(f59,plain,
    ( isPrime0(xr)
    & ! [X0] :
        ( ( ( doDivides0(X0,xr)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xr
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xr = X0
          | sz10 = X0 ) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X2] :
        ( xk = sdtasdt0(xr,X2)
        & aNaturalNumber0(X2) )
    & aNaturalNumber0(xr) ),
    inference(rectify,[],[f48]) ).

fof(f48,axiom,
    ( isPrime0(xr)
    & ! [X0] :
        ( ( ( doDivides0(X0,xr)
            | ? [X1] :
                ( sdtasdt0(X0,X1) = xr
                & aNaturalNumber0(X1) ) )
          & aNaturalNumber0(X0) )
       => ( xr = X0
          | sz10 = X0 ) )
    & sz10 != xr
    & sz00 != xr
    & doDivides0(xr,xk)
    & ? [X0] :
        ( xk = sdtasdt0(xr,X0)
        & aNaturalNumber0(X0) )
    & aNaturalNumber0(xr) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).

fof(f16458,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[],[f16457,f815]) ).

fof(f815,plain,
    aNaturalNumber0(sdtasdt0(xp,sK19)),
    inference(backward_demodulation,[],[f265,f814]) ).

fof(f814,plain,
    sdtsldt0(xn,xr) = sdtasdt0(xp,sK19),
    inference(resolution,[],[f580,f409]) ).

fof(f409,plain,
    sP1,
    inference(resolution,[],[f294,f227]) ).

fof(f227,plain,
    ~ doDivides0(xp,xm),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ( ~ doDivides0(xp,xm)
    & ! [X0] :
        ( xm != sdtasdt0(xp,X0)
        | ~ aNaturalNumber0(X0) )
    & ~ doDivides0(xp,xn)
    & ! [X1] :
        ( xn != sdtasdt0(xp,X1)
        | ~ aNaturalNumber0(X1) ) ),
    inference(ennf_transformation,[],[f58]) ).

fof(f58,plain,
    ~ ( doDivides0(xp,xm)
      | ? [X0] :
          ( xm = sdtasdt0(xp,X0)
          & aNaturalNumber0(X0) )
      | doDivides0(xp,xn)
      | ? [X1] :
          ( xn = sdtasdt0(xp,X1)
          & aNaturalNumber0(X1) ) ),
    inference(rectify,[],[f57]) ).

fof(f57,negated_conjecture,
    ~ ( doDivides0(xp,xm)
      | ? [X0] :
          ( xm = sdtasdt0(xp,X0)
          & aNaturalNumber0(X0) )
      | doDivides0(xp,xn)
      | ? [X0] :
          ( xn = sdtasdt0(xp,X0)
          & aNaturalNumber0(X0) ) ),
    inference(negated_conjecture,[],[f56]) ).

fof(f56,conjecture,
    ( doDivides0(xp,xm)
    | ? [X0] :
        ( xm = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
    | doDivides0(xp,xn)
    | ? [X0] :
        ( xn = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f294,plain,
    ( doDivides0(xp,xm)
    | sP1 ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ( ( doDivides0(xp,xm)
      & xm = sdtasdt0(xp,sK20)
      & aNaturalNumber0(sK20) )
    | sP1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f146,f180]) ).

fof(f180,plain,
    ( ? [X0] :
        ( xm = sdtasdt0(xp,X0)
        & aNaturalNumber0(X0) )
   => ( xm = sdtasdt0(xp,sK20)
      & aNaturalNumber0(sK20) ) ),
    introduced(choice_axiom,[]) ).

fof(f146,plain,
    ( ( doDivides0(xp,xm)
      & ? [X0] :
          ( xm = sdtasdt0(xp,X0)
          & aNaturalNumber0(X0) ) )
    | sP1 ),
    inference(definition_folding,[],[f63,f145,f144]) ).

fof(f144,plain,
    ( ? [X1] :
        ( sdtsldt0(xn,xr) = sdtasdt0(xp,X1)
        & aNaturalNumber0(X1) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f145,plain,
    ( ( doDivides0(xp,sdtsldt0(xn,xr))
      & sP0
      & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
      & aNaturalNumber0(sdtsldt0(xn,xr)) )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f63,plain,
    ( ( doDivides0(xp,xm)
      & ? [X0] :
          ( xm = sdtasdt0(xp,X0)
          & aNaturalNumber0(X0) ) )
    | ( doDivides0(xp,sdtsldt0(xn,xr))
      & ? [X1] :
          ( sdtsldt0(xn,xr) = sdtasdt0(xp,X1)
          & aNaturalNumber0(X1) )
      & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
      & aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
    inference(rectify,[],[f55]) ).

fof(f55,axiom,
    ( ( doDivides0(xp,xm)
      & ? [X0] :
          ( xm = sdtasdt0(xp,X0)
          & aNaturalNumber0(X0) ) )
    | ( doDivides0(xp,sdtsldt0(xn,xr))
      & ? [X0] :
          ( sdtasdt0(xp,X0) = sdtsldt0(xn,xr)
          & aNaturalNumber0(X0) )
      & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
      & aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).

fof(f580,plain,
    ( ~ sP1
    | sdtsldt0(xn,xr) = sdtasdt0(xp,sK19) ),
    inference(resolution,[],[f291,f288]) ).

fof(f288,plain,
    ( sP0
    | ~ sP1 ),
    inference(cnf_transformation,[],[f175]) ).

fof(f175,plain,
    ( ( doDivides0(xp,sdtsldt0(xn,xr))
      & sP0
      & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
      & aNaturalNumber0(sdtsldt0(xn,xr)) )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f145]) ).

fof(f291,plain,
    ( ~ sP0
    | sdtsldt0(xn,xr) = sdtasdt0(xp,sK19) ),
    inference(cnf_transformation,[],[f179]) ).

fof(f179,plain,
    ( ( sdtsldt0(xn,xr) = sdtasdt0(xp,sK19)
      & aNaturalNumber0(sK19) )
    | ~ sP0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f177,f178]) ).

fof(f178,plain,
    ( ? [X0] :
        ( sdtasdt0(xp,X0) = sdtsldt0(xn,xr)
        & aNaturalNumber0(X0) )
   => ( sdtsldt0(xn,xr) = sdtasdt0(xp,sK19)
      & aNaturalNumber0(sK19) ) ),
    introduced(choice_axiom,[]) ).

fof(f177,plain,
    ( ? [X0] :
        ( sdtasdt0(xp,X0) = sdtsldt0(xn,xr)
        & aNaturalNumber0(X0) )
    | ~ sP0 ),
    inference(rectify,[],[f176]) ).

fof(f176,plain,
    ( ? [X1] :
        ( sdtsldt0(xn,xr) = sdtasdt0(xp,X1)
        & aNaturalNumber0(X1) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f144]) ).

fof(f265,plain,
    aNaturalNumber0(sdtsldt0(xn,xr)),
    inference(cnf_transformation,[],[f167]) ).

fof(f167,plain,
    ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
    & sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK14)
    & aNaturalNumber0(sK14)
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & aNaturalNumber0(sdtsldt0(xn,xr)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f54,f166]) ).

fof(f166,plain,
    ( ? [X0] :
        ( sdtasdt0(xp,X0) = sdtasdt0(sdtsldt0(xn,xr),xm)
        & aNaturalNumber0(X0) )
   => ( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK14)
      & aNaturalNumber0(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,axiom,
    ( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
    & ? [X0] :
        ( sdtasdt0(xp,X0) = sdtasdt0(sdtsldt0(xn,xr),xm)
        & aNaturalNumber0(X0) )
    & xn = sdtasdt0(xr,sdtsldt0(xn,xr))
    & aNaturalNumber0(sdtsldt0(xn,xr)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2529) ).

fof(f16457,plain,
    ( ~ aNaturalNumber0(sdtasdt0(xp,sK19))
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[],[f16449,f409]) ).

fof(f16449,plain,
    ( ~ sP1
    | ~ aNaturalNumber0(sdtasdt0(xp,sK19))
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[],[f4093,f820]) ).

fof(f820,plain,
    ( doDivides0(xp,sdtasdt0(xp,sK19))
    | ~ sP1 ),
    inference(backward_demodulation,[],[f289,f814]) ).

fof(f289,plain,
    ( doDivides0(xp,sdtsldt0(xn,xr))
    | ~ sP1 ),
    inference(cnf_transformation,[],[f175]) ).

fof(f4093,plain,
    ( ~ doDivides0(xp,sdtasdt0(xp,sK19))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtasdt0(xp,sK19))
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xp) ),
    inference(duplicate_literal_removal,[],[f4088]) ).

fof(f4088,plain,
    ( ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtasdt0(xp,sK19))
    | ~ doDivides0(xp,sdtasdt0(xp,sK19))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtasdt0(xp,sK19))
    | ~ aNaturalNumber0(xp) ),
    inference(resolution,[],[f2054,f2795]) ).

fof(f2795,plain,
    ! [X0] :
      ( ~ doDivides0(xp,X0)
      | ~ doDivides0(X0,xn)
      | ~ aNaturalNumber0(xn)
      | ~ aNaturalNumber0(X0)
      | ~ aNaturalNumber0(xp) ),
    inference(resolution,[],[f390,f225]) ).

fof(f225,plain,
    ~ doDivides0(xp,xn),
    inference(cnf_transformation,[],[f68]) ).

fof(f390,plain,
    ! [X2,X0,X1] :
      ( doDivides0(X0,X2)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f137,plain,
    ! [X0,X1,X2] :
      ( doDivides0(X0,X2)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f136]) ).

fof(f136,plain,
    ! [X0,X1,X2] :
      ( doDivides0(X0,X2)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X0,X1) )
       => doDivides0(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).

fof(f2054,plain,
    ( doDivides0(sdtasdt0(xp,sK19),xn)
    | ~ aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sdtasdt0(xp,sK19)) ),
    inference(superposition,[],[f406,f1113]) ).

fof(f1113,plain,
    xn = sdtasdt0(sdtasdt0(xp,sK19),xr),
    inference(forward_demodulation,[],[f1089,f816]) ).

fof(f816,plain,
    xn = sdtasdt0(xr,sdtasdt0(xp,sK19)),
    inference(backward_demodulation,[],[f266,f814]) ).

fof(f266,plain,
    xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
    inference(cnf_transformation,[],[f167]) ).

fof(f1089,plain,
    sdtasdt0(xr,sdtasdt0(xp,sK19)) = sdtasdt0(sdtasdt0(xp,sK19),xr),
    inference(resolution,[],[f978,f231]) ).

fof(f978,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtasdt0(X0,sdtasdt0(xp,sK19)) = sdtasdt0(sdtasdt0(xp,sK19),X0) ),
    inference(resolution,[],[f354,f815]) ).

fof(f354,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

fof(f406,plain,
    ! [X2,X0] :
      ( doDivides0(X0,sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f380]) ).

fof(f380,plain,
    ! [X2,X0,X1] :
      ( doDivides0(X0,X1)
      | sdtasdt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f223]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtasdt0(X0,sK30(X0,X1)) = X1
            & aNaturalNumber0(sK30(X0,X1)) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f221,f222]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtasdt0(X0,sK30(X0,X1)) = X1
        & aNaturalNumber0(sK30(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X3] :
              ( sdtasdt0(X0,X3) = X1
              & aNaturalNumber0(X3) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f220]) ).

fof(f220,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X2] :
              ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem    : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n008.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 15:01:37 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  % (32403)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34  % (32406)WARNING: value z3 for option sas not known
% 0.11/0.34  % (32409)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.34  % (32410)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.34  % (32407)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34  % (32405)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34  % (32404)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34  % (32408)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.34  % (32406)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.35  Detected minimum model sizes of [4]
% 0.11/0.35  Detected maximum model sizes of [max]
% 0.11/0.35  TRYING [4]
% 0.11/0.37  Detected minimum model sizes of [4]
% 0.11/0.37  Detected maximum model sizes of [max]
% 0.16/0.38  TRYING [4]
% 0.16/0.47  TRYING [5]
% 2.54/0.71  TRYING [5]
% 3.11/0.79  TRYING [6]
% 6.46/1.26  % (32409)First to succeed.
% 6.63/1.26  % (32409)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-32403"
% 6.63/1.26  % (32409)Refutation found. Thanks to Tanya!
% 6.63/1.26  % SZS status Theorem for theBenchmark
% 6.63/1.26  % SZS output start Proof for theBenchmark
% See solution above
% 6.63/1.27  % (32409)------------------------------
% 6.63/1.27  % (32409)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.63/1.27  % (32409)Termination reason: Refutation
% 6.63/1.27  
% 6.63/1.27  % (32409)Memory used [KB]: 15878
% 6.63/1.27  % (32409)Time elapsed: 0.926 s
% 6.63/1.27  % (32409)Instructions burned: 1913 (million)
% 6.63/1.27  % (32403)Success in time 0.922 s
%------------------------------------------------------------------------------