TSTP Solution File: NUM476+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM476+1 : 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 : n006.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 08:30:48 EDT 2024

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  110 (  20 unt;   0 def)
%            Number of atoms       :  432 ( 163 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  515 ( 193   ~; 214   |;  82   &)
%                                         (   9 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  127 ( 103   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6644,plain,
    $false,
    inference(resolution,[],[f5921,f3185]) ).

fof(f3185,plain,
    ~ doDivides0(sz00,xn),
    inference(backward_demodulation,[],[f121,f3182]) ).

fof(f3182,plain,
    sz00 = xl,
    inference(resolution,[],[f3181,f122]) ).

fof(f122,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).

fof(f3181,plain,
    ( ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(resolution,[],[f3180,f124]) ).

fof(f124,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f34]) ).

fof(f3180,plain,
    ( ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(resolution,[],[f3179,f123]) ).

fof(f123,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f34]) ).

fof(f3179,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xn)
    | sz00 = xl ),
    inference(duplicate_literal_removal,[],[f3178]) ).

fof(f3178,plain,
    ( ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sz00 = xl
    | sz00 = xl
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[],[f3175,f1127]) ).

fof(f1127,plain,
    ( aNaturalNumber0(sK2)
    | sz00 = xl
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[],[f1121,f125]) ).

fof(f125,plain,
    doDivides0(xl,xm),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).

fof(f1121,plain,
    ( ~ doDivides0(xl,xm)
    | aNaturalNumber0(sK2)
    | sz00 = xl
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(duplicate_literal_removal,[],[f1118]) ).

fof(f1118,plain,
    ( aNaturalNumber0(sK2)
    | ~ doDivides0(xl,xm)
    | sz00 = xl
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(superposition,[],[f188,f117]) ).

fof(f117,plain,
    ( sdtsldt0(xm,xl) = sK2
    | sz00 = xl ),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    ( ~ doDivides0(xl,xn)
    & ( ( sP0(sK2,sK3)
        & sdtlseqdt0(sK2,sK3)
        & sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
        & sdtsldt0(xm,xl) = sK2 )
      | sz00 = xl ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f95,f100,f99]) ).

fof(f99,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( sP0(X0,X1)
            & sdtlseqdt0(X0,X1)
            & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
        & sdtsldt0(xm,xl) = X0 )
   => ( ? [X1] :
          ( sP0(sK2,X1)
          & sdtlseqdt0(sK2,X1)
          & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
      & sdtsldt0(xm,xl) = sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ( ? [X1] :
        ( sP0(sK2,X1)
        & sdtlseqdt0(sK2,X1)
        & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
   => ( sP0(sK2,sK3)
      & sdtlseqdt0(sK2,sK3)
      & sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ) ),
    introduced(choice_axiom,[]) ).

fof(f95,plain,
    ( ~ doDivides0(xl,xn)
    & ( ? [X0] :
          ( ? [X1] :
              ( sP0(X0,X1)
              & sdtlseqdt0(X0,X1)
              & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
          & sdtsldt0(xm,xl) = X0 )
      | sz00 = xl ) ),
    inference(definition_folding,[],[f41,f94]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( xn = sdtasdt0(xl,X2)
          & sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
          & sdtmndt0(X1,X0) = X2 )
      | ~ sP0(X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f41,plain,
    ( ~ doDivides0(xl,xn)
    & ( ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( xn = sdtasdt0(xl,X2)
                  & sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
                  & sdtmndt0(X1,X0) = X2 )
              & sdtlseqdt0(X0,X1)
              & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
          & sdtsldt0(xm,xl) = X0 )
      | sz00 = xl ) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ( ( sz00 != xl
       => ? [X0] :
            ( ? [X1] :
                ( ? [X2] :
                    ( xn = sdtasdt0(xl,X2)
                    & sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
                    & sdtmndt0(X1,X0) = X2 )
                & sdtlseqdt0(X0,X1)
                & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
            & sdtsldt0(xm,xl) = X0 ) )
     => doDivides0(xl,xn) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ( ( sz00 != xl
     => ? [X0] :
          ( ? [X1] :
              ( ? [X2] :
                  ( xn = sdtasdt0(xl,X2)
                  & sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
                  & sdtmndt0(X1,X0) = X2 )
              & sdtlseqdt0(X0,X1)
              & sdtsldt0(sdtpldt0(xm,xn),xl) = X1 )
          & sdtsldt0(xm,xl) = X0 ) )
   => doDivides0(xl,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f188,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtsldt0(X1,X0))
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f158]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtsldt0(X1,X0) = X2
            | sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtsldt0(X1,X0) != X2 ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtsldt0(X1,X0) = X2
            | sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtsldt0(X1,X0) != X2 ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtsldt0(X1,X0) = X2
        <=> ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtsldt0(X1,X0) = X2
        <=> ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( doDivides0(X0,X1)
          & sz00 != X0 )
       => ! [X2] :
            ( sdtsldt0(X1,X0) = X2
          <=> ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).

fof(f3175,plain,
    ( ~ aNaturalNumber0(sK2)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sz00 = xl ),
    inference(duplicate_literal_removal,[],[f3115]) ).

fof(f3115,plain,
    ( sz00 = xl
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn)
    | sz00 = xl
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sK2) ),
    inference(resolution,[],[f3112,f925]) ).

fof(f925,plain,
    ( ~ aNaturalNumber0(sK3)
    | sz00 = xl
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(sK2) ),
    inference(duplicate_literal_removal,[],[f922]) ).

fof(f922,plain,
    ( ~ aNaturalNumber0(xl)
    | sz00 = xl
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sK3)
    | ~ aNaturalNumber0(sK2)
    | sz00 = xl ),
    inference(resolution,[],[f921,f119]) ).

fof(f119,plain,
    ( sdtlseqdt0(sK2,sK3)
    | sz00 = xl ),
    inference(cnf_transformation,[],[f101]) ).

fof(f921,plain,
    ( ~ sdtlseqdt0(sK2,sK3)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(sK3)
    | ~ aNaturalNumber0(sK2) ),
    inference(resolution,[],[f920,f185]) ).

fof(f185,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtmndt0(X1,X0))
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f148]) ).

fof(f148,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
       => ! [X2] :
            ( sdtmndt0(X1,X0) = X2
          <=> ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).

fof(f920,plain,
    ( ~ aNaturalNumber0(sdtmndt0(sK3,sK2))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(duplicate_literal_removal,[],[f919]) ).

fof(f919,plain,
    ( ~ aNaturalNumber0(sdtmndt0(sK3,sK2))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl
    | sz00 = xl ),
    inference(superposition,[],[f916,f262]) ).

fof(f262,plain,
    ( sdtmndt0(sK3,sK2) = sK1(sK2,sK3)
    | sz00 = xl ),
    inference(resolution,[],[f114,f120]) ).

fof(f120,plain,
    ( sP0(sK2,sK3)
    | sz00 = xl ),
    inference(cnf_transformation,[],[f101]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | sdtmndt0(X1,X0) = sK1(X0,X1) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ( xn = sdtasdt0(xl,sK1(X0,X1))
        & sdtpldt0(sdtasdt0(xl,X0),xn) = sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,sK1(X0,X1)))
        & sdtmndt0(X1,X0) = sK1(X0,X1) )
      | ~ sP0(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f96,f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( xn = sdtasdt0(xl,X2)
          & sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
          & sdtmndt0(X1,X0) = X2 )
     => ( xn = sdtasdt0(xl,sK1(X0,X1))
        & sdtpldt0(sdtasdt0(xl,X0),xn) = sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,sK1(X0,X1)))
        & sdtmndt0(X1,X0) = sK1(X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( xn = sdtasdt0(xl,X2)
          & sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
          & sdtmndt0(X1,X0) = X2 )
      | ~ sP0(X0,X1) ),
    inference(nnf_transformation,[],[f94]) ).

fof(f916,plain,
    ( ~ aNaturalNumber0(sK1(sK2,sK3))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(resolution,[],[f811,f121]) ).

fof(f811,plain,
    ( doDivides0(xl,xn)
    | ~ aNaturalNumber0(sK1(sK2,sK3))
    | ~ aNaturalNumber0(xn)
    | ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(superposition,[],[f189,f263]) ).

fof(f263,plain,
    ( xn = sdtasdt0(xl,sK1(sK2,sK3))
    | sz00 = xl ),
    inference(resolution,[],[f116,f120]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ~ sP0(X0,X1)
      | xn = sdtasdt0(xl,sK1(X0,X1)) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f189,plain,
    ! [X2,X0] :
      ( doDivides0(X0,sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f164]) ).

fof(f164,plain,
    ! [X2,X0,X1] :
      ( doDivides0(X0,X1)
      | sdtasdt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( ( doDivides0(X0,X1)
          | ! [X2] :
              ( sdtasdt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtasdt0(X0,sK4(X0,X1)) = X1
            & aNaturalNumber0(sK4(X0,X1)) )
          | ~ doDivides0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f107,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtasdt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtasdt0(X0,sK4(X0,X1)) = X1
        & aNaturalNumber0(sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,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,[],[f106]) ).

fof(f106,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,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ( doDivides0(X0,X1)
      <=> ? [X2] :
            ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f74]) ).

fof(f74,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/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

fof(f3112,plain,
    ( aNaturalNumber0(sK3)
    | sz00 = xl
    | ~ aNaturalNumber0(xl)
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xn) ),
    inference(resolution,[],[f3092,f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).

fof(f3092,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | sz00 = xl
    | aNaturalNumber0(sK3)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[],[f1120,f317]) ).

fof(f317,plain,
    doDivides0(xl,sdtpldt0(xn,xm)),
    inference(backward_demodulation,[],[f126,f315]) ).

fof(f315,plain,
    sdtpldt0(xm,xn) = sdtpldt0(xn,xm),
    inference(resolution,[],[f273,f124]) ).

fof(f273,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtpldt0(X0,xm) = sdtpldt0(xm,X0) ),
    inference(resolution,[],[f143,f123]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(f126,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f35]) ).

fof(f1120,plain,
    ( ~ doDivides0(xl,sdtpldt0(xn,xm))
    | aNaturalNumber0(sK3)
    | sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xl) ),
    inference(duplicate_literal_removal,[],[f1119]) ).

fof(f1119,plain,
    ( aNaturalNumber0(sK3)
    | ~ doDivides0(xl,sdtpldt0(xn,xm))
    | sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(xl)
    | sz00 = xl ),
    inference(superposition,[],[f188,f318]) ).

fof(f318,plain,
    ( sK3 = sdtsldt0(sdtpldt0(xn,xm),xl)
    | sz00 = xl ),
    inference(backward_demodulation,[],[f118,f315]) ).

fof(f118,plain,
    ( sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
    | sz00 = xl ),
    inference(cnf_transformation,[],[f101]) ).

fof(f121,plain,
    ~ doDivides0(xl,xn),
    inference(cnf_transformation,[],[f101]) ).

fof(f5921,plain,
    doDivides0(sz00,xn),
    inference(forward_demodulation,[],[f5372,f206]) ).

fof(f206,plain,
    xn = sdtpldt0(xn,sz00),
    inference(resolution,[],[f133,f124]) ).

fof(f133,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).

fof(f5372,plain,
    doDivides0(sz00,sdtpldt0(xn,sz00)),
    inference(backward_demodulation,[],[f3201,f5220]) ).

fof(f5220,plain,
    sz00 = xm,
    inference(resolution,[],[f5219,f127]) ).

fof(f127,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(f5219,plain,
    ( ~ aNaturalNumber0(sz00)
    | sz00 = xm ),
    inference(resolution,[],[f5217,f123]) ).

fof(f5217,plain,
    ( ~ aNaturalNumber0(xm)
    | sz00 = xm
    | ~ aNaturalNumber0(sz00) ),
    inference(forward_demodulation,[],[f5193,f3728]) ).

fof(f3728,plain,
    xm = sdtasdt0(sz00,sK4(sz00,xm)),
    inference(resolution,[],[f3727,f127]) ).

fof(f3727,plain,
    ( ~ aNaturalNumber0(sz00)
    | xm = sdtasdt0(sz00,sK4(sz00,xm)) ),
    inference(resolution,[],[f3443,f123]) ).

fof(f3443,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz00)
    | xm = sdtasdt0(sz00,sK4(sz00,xm)) ),
    inference(forward_demodulation,[],[f3253,f3182]) ).

fof(f3253,plain,
    ( ~ aNaturalNumber0(sz00)
    | xm = sdtasdt0(xl,sK4(xl,xm))
    | ~ aNaturalNumber0(xm) ),
    inference(backward_demodulation,[],[f886,f3182]) ).

fof(f886,plain,
    ( xm = sdtasdt0(xl,sK4(xl,xm))
    | ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(xl) ),
    inference(resolution,[],[f163,f125]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ doDivides0(X0,X1)
      | sdtasdt0(X0,sK4(X0,X1)) = X1
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f5193,plain,
    ( ~ aNaturalNumber0(xm)
    | ~ aNaturalNumber0(sz00)
    | sz00 = sdtasdt0(sz00,sK4(sz00,xm)) ),
    inference(resolution,[],[f321,f3187]) ).

fof(f3187,plain,
    doDivides0(sz00,xm),
    inference(backward_demodulation,[],[f125,f3182]) ).

fof(f321,plain,
    ! [X0,X1] :
      ( ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0)
      | sz00 = sdtasdt0(sz00,sK4(X0,X1)) ),
    inference(resolution,[],[f162,f132]) ).

fof(f132,plain,
    ! [X0] :
      ( ~ aNaturalNumber0(X0)
      | sz00 = sdtasdt0(sz00,X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0] :
      ( ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 = sdtasdt0(sz00,X0)
        & sz00 = sdtasdt0(X0,sz00) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).

fof(f162,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sK4(X0,X1))
      | ~ doDivides0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f109]) ).

fof(f3201,plain,
    doDivides0(sz00,sdtpldt0(xn,xm)),
    inference(backward_demodulation,[],[f317,f3182]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : NUM476+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri May  3 14:11:53 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.35  % (9050)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36  % (9051)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (9055)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)
% 0.14/0.37  % (9057)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)
% 0.14/0.37  TRYING [1]
% 0.14/0.37  TRYING [2]
% 0.14/0.37  % (9056)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)
% 0.14/0.37  TRYING [3]
% 0.14/0.38  % (9054)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  TRYING [1]
% 0.14/0.38  % (9053)WARNING: value z3 for option sas not known
% 0.14/0.38  TRYING [2]
% 0.14/0.38  % (9053)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)
% 0.14/0.38  TRYING [3]
% 0.14/0.38  % (9052)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40  TRYING [4]
% 0.20/0.40  TRYING [4]
% 0.20/0.47  TRYING [5]
% 0.20/0.47  TRYING [1]
% 0.20/0.47  TRYING [2]
% 0.20/0.47  TRYING [3]
% 0.20/0.47  TRYING [5]
% 0.20/0.47  TRYING [4]
% 0.20/0.52  TRYING [5]
% 0.20/0.54  % (9056)First to succeed.
% 0.20/0.55  % (9056)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9050"
% 0.20/0.55  % (9056)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (9056)------------------------------
% 0.20/0.55  % (9056)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.55  % (9056)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (9056)Memory used [KB]: 3660
% 0.20/0.55  % (9056)Time elapsed: 0.178 s
% 0.20/0.55  % (9056)Instructions burned: 469 (million)
% 0.20/0.55  % (9050)Success in time 0.201 s
%------------------------------------------------------------------------------