TSTP Solution File: NUM456+6 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM456+6 : 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 : n002.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 14:23:28 EDT 2024

% Result   : ContradictoryAxioms 0.22s 0.45s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   38 (   8 unt;   0 def)
%            Number of atoms       :  466 (  82 equ)
%            Maximal formula atoms :   32 (  12 avg)
%            Number of connectives :  586 ( 158   ~; 120   |; 282   &)
%                                         (  16 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   8 con; 0-2 aty)
%            Number of variables   :  108 (  76   !;  32   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1070,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1069]) ).

fof(f1069,plain,
    sz10 != sz10,
    inference(superposition,[],[f421,f1045]) ).

fof(f1045,plain,
    sz10 = sK40,
    inference(trivial_inequality_removal,[],[f1028]) ).

fof(f1028,plain,
    ( sK40 != sK40
    | sz10 = sK40 ),
    inference(superposition,[],[f422,f1023]) ).

fof(f1023,plain,
    ( smndt0(sz10) = sK40
    | sz10 = sK40 ),
    inference(resolution,[],[f564,f686]) ).

fof(f686,plain,
    aElementOf0(sK40,cS2076),
    inference(resolution,[],[f560,f420]) ).

fof(f420,plain,
    aElementOf0(sK40,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
    inference(cnf_transformation,[],[f228]) ).

fof(f228,plain,
    ( ~ aElementOf0(sK40,cS2200)
    & smndt0(sz10) != sK40
    & sz10 != sK40
    & aElementOf0(sK40,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sdteqdtlpzmzozddtrp0(sK40,sz10,xp)
    & aDivisorOf0(xp,sdtpldt0(sK40,smndt0(sz10)))
    & sdtpldt0(sK40,smndt0(sz10)) = sdtasdt0(xp,sK41)
    & aInteger0(sK41)
    & aInteger0(sK40) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f68,f227,f226]) ).

fof(f226,plain,
    ( ? [X0] :
        ( ~ aElementOf0(X0,cS2200)
        & smndt0(sz10) != X0
        & sz10 != X0
        & aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
        & sdteqdtlpzmzozddtrp0(X0,sz10,xp)
        & aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
        & ? [X1] :
            ( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
            & aInteger0(X1) )
        & aInteger0(X0) )
   => ( ~ aElementOf0(sK40,cS2200)
      & smndt0(sz10) != sK40
      & sz10 != sK40
      & aElementOf0(sK40,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
      & sdteqdtlpzmzozddtrp0(sK40,sz10,xp)
      & aDivisorOf0(xp,sdtpldt0(sK40,smndt0(sz10)))
      & ? [X1] :
          ( sdtasdt0(xp,X1) = sdtpldt0(sK40,smndt0(sz10))
          & aInteger0(X1) )
      & aInteger0(sK40) ) ),
    introduced(choice_axiom,[]) ).

fof(f227,plain,
    ( ? [X1] :
        ( sdtasdt0(xp,X1) = sdtpldt0(sK40,smndt0(sz10))
        & aInteger0(X1) )
   => ( sdtpldt0(sK40,smndt0(sz10)) = sdtasdt0(xp,sK41)
      & aInteger0(sK41) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ? [X0] :
      ( ~ aElementOf0(X0,cS2200)
      & smndt0(sz10) != X0
      & sz10 != X0
      & aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
      & sdteqdtlpzmzozddtrp0(X0,sz10,xp)
      & aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
      & ? [X1] :
          ( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
          & aInteger0(X1) )
      & aInteger0(X0) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ? [X0] :
      ( ~ aElementOf0(X0,cS2200)
      & smndt0(sz10) != X0
      & sz10 != X0
      & aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
      & sdteqdtlpzmzozddtrp0(X0,sz10,xp)
      & aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
      & ? [X1] :
          ( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
          & aInteger0(X1) )
      & aInteger0(X0) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,axiom,
    ? [X0] :
      ( ~ ( aElementOf0(X0,cS2200)
          | smndt0(sz10) = X0
          | sz10 = X0 )
      & aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
      & sdteqdtlpzmzozddtrp0(X0,sz10,xp)
      & aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
      & ? [X1] :
          ( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
          & aInteger0(X1) )
      & aInteger0(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).

fof(f560,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
      | aElementOf0(X0,cS2076) ),
    inference(backward_demodulation,[],[f348,f362]) ).

fof(f362,plain,
    stldt0(sbsmnsldt0(xS)) = cS2076,
    inference(cnf_transformation,[],[f196]) ).

fof(f196,plain,
    ( stldt0(sbsmnsldt0(xS)) = cS2076
    & ! [X0] :
        ( ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
          | ( smndt0(sz10) != X0
            & sz10 != X0 ) )
        & ( smndt0(sz10) = X0
          | sz10 = X0
          | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( aElementOf0(X2,sK33(X2))
            & aElementOf0(sK33(X2),xS)
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f194,f195]) ).

fof(f195,plain,
    ! [X2] :
      ( ? [X4] :
          ( aElementOf0(X2,X4)
          & aElementOf0(X4,xS) )
     => ( aElementOf0(X2,sK33(X2))
        & aElementOf0(sK33(X2),xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f194,plain,
    ( stldt0(sbsmnsldt0(xS)) = cS2076
    & ! [X0] :
        ( ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
          | ( smndt0(sz10) != X0
            & sz10 != X0 ) )
        & ( smndt0(sz10) = X0
          | sz10 = X0
          | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( ? [X4] :
                ( aElementOf0(X2,X4)
                & aElementOf0(X4,xS) )
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS)) ),
    inference(rectify,[],[f193]) ).

fof(f193,plain,
    ( stldt0(sbsmnsldt0(xS)) = cS2076
    & ! [X0] :
        ( ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
          | ( smndt0(sz10) != X0
            & sz10 != X0 ) )
        & ( smndt0(sz10) = X0
          | sz10 = X0
          | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( ? [X3] :
                ( aElementOf0(X2,X3)
                & aElementOf0(X3,xS) )
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS)) ),
    inference(flattening,[],[f192]) ).

fof(f192,plain,
    ( stldt0(sbsmnsldt0(xS)) = cS2076
    & ! [X0] :
        ( ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
          | ( smndt0(sz10) != X0
            & sz10 != X0 ) )
        & ( smndt0(sz10) = X0
          | sz10 = X0
          | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( ? [X3] :
                ( aElementOf0(X2,X3)
                & aElementOf0(X3,xS) )
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS)) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ( stldt0(sbsmnsldt0(xS)) = cS2076
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
      <=> ( smndt0(sz10) = X0
          | sz10 = X0 ) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
          & aInteger0(X1) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X2] :
        ( aElementOf0(X2,sbsmnsldt0(xS))
      <=> ( ? [X3] :
              ( aElementOf0(X2,X3)
              & aElementOf0(X3,xS) )
          & aInteger0(X2) ) )
    & aSet0(sbsmnsldt0(xS)) ),
    inference(rectify,[],[f43]) ).

fof(f43,axiom,
    ( stldt0(sbsmnsldt0(xS)) = cS2076
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
      <=> ( smndt0(sz10) = X0
          | sz10 = X0 ) )
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
          & aInteger0(X0) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,sbsmnsldt0(xS))
      <=> ( ? [X1] :
              ( aElementOf0(X0,X1)
              & aElementOf0(X1,xS) )
          & aInteger0(X0) ) )
    & aSet0(sbsmnsldt0(xS)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2079) ).

fof(f348,plain,
    ! [X0] :
      ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
      | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f191,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( aElementOf0(X2,sK32(X2))
            & aElementOf0(sK32(X2),xS)
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X5] :
        ( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X5,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X5,smndt0(sz10)))
            & ! [X6] :
                ( sdtasdt0(xp,X6) != sdtpldt0(X5,smndt0(sz10))
                | ~ aInteger0(X6) ) )
          | ~ aInteger0(X5) )
        & ( ( sdteqdtlpzmzozddtrp0(X5,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X5,smndt0(sz10)))
            & sP7(X5)
            & aInteger0(X5) )
          | ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f189,f190]) ).

fof(f190,plain,
    ! [X2] :
      ( ? [X4] :
          ( aElementOf0(X2,X4)
          & aElementOf0(X4,xS) )
     => ( aElementOf0(X2,sK32(X2))
        & aElementOf0(sK32(X2),xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f189,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( ? [X4] :
                ( aElementOf0(X2,X4)
                & aElementOf0(X4,xS) )
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X5] :
        ( ( aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X5,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X5,smndt0(sz10)))
            & ! [X6] :
                ( sdtasdt0(xp,X6) != sdtpldt0(X5,smndt0(sz10))
                | ~ aInteger0(X6) ) )
          | ~ aInteger0(X5) )
        & ( ( sdteqdtlpzmzozddtrp0(X5,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X5,smndt0(sz10)))
            & sP7(X5)
            & aInteger0(X5) )
          | ~ aElementOf0(X5,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(rectify,[],[f188]) ).

fof(f188,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( ? [X3] :
                ( aElementOf0(X2,X3)
                & aElementOf0(X3,xS) )
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X4] :
        ( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ! [X5] :
                ( sdtpldt0(X4,smndt0(sz10)) != sdtasdt0(xp,X5)
                | ~ aInteger0(X5) ) )
          | ~ aInteger0(X4) )
        & ( ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & sP7(X4)
            & aInteger0(X4) )
          | ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(flattening,[],[f187]) ).

fof(f187,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X1,sbsmnsldt0(xS))
          | ~ aInteger0(X1) )
        & ( ( ~ aElementOf0(X1,sbsmnsldt0(xS))
            & aInteger0(X1) )
          | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X2] :
        ( ( aElementOf0(X2,sbsmnsldt0(xS))
          | ! [X3] :
              ( ~ aElementOf0(X2,X3)
              | ~ aElementOf0(X3,xS) )
          | ~ aInteger0(X2) )
        & ( ( ? [X3] :
                ( aElementOf0(X2,X3)
                & aElementOf0(X3,xS) )
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X4] :
        ( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ! [X5] :
                ( sdtpldt0(X4,smndt0(sz10)) != sdtasdt0(xp,X5)
                | ~ aInteger0(X5) ) )
          | ~ aInteger0(X4) )
        & ( ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & sP7(X4)
            & aInteger0(X4) )
          | ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(nnf_transformation,[],[f134]) ).

fof(f134,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
          & aInteger0(X1) ) )
    & ! [X2] :
        ( aElementOf0(X2,sbsmnsldt0(xS))
      <=> ( ? [X3] :
              ( aElementOf0(X2,X3)
              & aElementOf0(X3,xS) )
          & aInteger0(X2) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X4] :
        ( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ! [X5] :
                ( sdtpldt0(X4,smndt0(sz10)) != sdtasdt0(xp,X5)
                | ~ aInteger0(X5) ) )
          | ~ aInteger0(X4) )
        & ( ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & sP7(X4)
            & aInteger0(X4) )
          | ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(definition_folding,[],[f64,f133]) ).

fof(f133,plain,
    ! [X4] :
      ( ? [X6] :
          ( sdtpldt0(X4,smndt0(sz10)) = sdtasdt0(xp,X6)
          & aInteger0(X6) )
      | ~ sP7(X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f64,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
          & aInteger0(X1) ) )
    & ! [X2] :
        ( aElementOf0(X2,sbsmnsldt0(xS))
      <=> ( ? [X3] :
              ( aElementOf0(X2,X3)
              & aElementOf0(X3,xS) )
          & aInteger0(X2) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X4] :
        ( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ! [X5] :
                ( sdtpldt0(X4,smndt0(sz10)) != sdtasdt0(xp,X5)
                | ~ aInteger0(X5) ) )
          | ~ aInteger0(X4) )
        & ( ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ? [X6] :
                ( sdtpldt0(X4,smndt0(sz10)) = sdtasdt0(xp,X6)
                & aInteger0(X6) )
            & aInteger0(X4) )
          | ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
        | ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
          & aInteger0(X1) ) )
    & ! [X2] :
        ( aElementOf0(X2,sbsmnsldt0(xS))
      <=> ( ? [X3] :
              ( aElementOf0(X2,X3)
              & aElementOf0(X3,xS) )
          & aInteger0(X2) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X4] :
        ( ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
          | ( ~ sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & ~ aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ! [X5] :
                ( sdtpldt0(X4,smndt0(sz10)) != sdtasdt0(xp,X5)
                | ~ aInteger0(X5) ) )
          | ~ aInteger0(X4) )
        & ( ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ? [X6] :
                ( sdtpldt0(X4,smndt0(sz10)) = sdtasdt0(xp,X6)
                & aInteger0(X6) )
            & aInteger0(X4) )
          | ~ aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
       => aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
    & ! [X1] :
        ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
          & aInteger0(X1) ) )
    & ! [X2] :
        ( aElementOf0(X2,sbsmnsldt0(xS))
      <=> ( ? [X3] :
              ( aElementOf0(X2,X3)
              & aElementOf0(X3,xS) )
          & aInteger0(X2) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X4] :
        ( ( ( ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
              | aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
              | ? [X5] :
                  ( sdtpldt0(X4,smndt0(sz10)) = sdtasdt0(xp,X5)
                  & aInteger0(X5) ) )
            & aInteger0(X4) )
         => aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
        & ( aElementOf0(X4,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
         => ( sdteqdtlpzmzozddtrp0(X4,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X4,smndt0(sz10)))
            & ? [X6] :
                ( sdtpldt0(X4,smndt0(sz10)) = sdtasdt0(xp,X6)
                & aInteger0(X6) )
            & aInteger0(X4) ) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    inference(rectify,[],[f46]) ).

fof(f46,axiom,
    ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
    & ! [X0] :
        ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
       => aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
    & ! [X0] :
        ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
          & aInteger0(X0) ) )
    & ! [X0] :
        ( aElementOf0(X0,sbsmnsldt0(xS))
      <=> ( ? [X1] :
              ( aElementOf0(X0,X1)
              & aElementOf0(X1,xS) )
          & aInteger0(X0) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X0] :
        ( ( ( ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
              | aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
              | ? [X1] :
                  ( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
                  & aInteger0(X1) ) )
            & aInteger0(X0) )
         => aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
        & ( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
         => ( sdteqdtlpzmzozddtrp0(X0,sz10,xp)
            & aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
            & ? [X1] :
                ( sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10))
                & aInteger0(X1) )
            & aInteger0(X0) ) ) )
    & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
    & sz00 != xp
    & aInteger0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2171) ).

fof(f564,plain,
    ! [X0] :
      ( ~ aElementOf0(X0,cS2076)
      | smndt0(sz10) = X0
      | sz10 = X0 ),
    inference(forward_demodulation,[],[f359,f362]) ).

fof(f359,plain,
    ! [X0] :
      ( smndt0(sz10) = X0
      | sz10 = X0
      | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ),
    inference(cnf_transformation,[],[f196]) ).

fof(f422,plain,
    smndt0(sz10) != sK40,
    inference(cnf_transformation,[],[f228]) ).

fof(f421,plain,
    sz10 != sK40,
    inference(cnf_transformation,[],[f228]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NUM456+6 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 00:17:25 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (3372)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (3374)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (3375)WARNING: value z3 for option sas not known
% 0.15/0.40  % (3373)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.40  % (3378)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)
% 0.15/0.40  % (3377)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)
% 0.15/0.40  % (3375)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)
% 0.15/0.40  % (3379)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)
% 0.15/0.40  % (3376)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.43  TRYING [1]
% 0.22/0.43  TRYING [2]
% 0.22/0.44  TRYING [1]
% 0.22/0.44  TRYING [2]
% 0.22/0.44  % (3378)First to succeed.
% 0.22/0.45  % (3378)Refutation found. Thanks to Tanya!
% 0.22/0.45  % SZS status ContradictoryAxioms for theBenchmark
% 0.22/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45  % (3378)------------------------------
% 0.22/0.45  % (3378)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45  % (3378)Termination reason: Refutation
% 0.22/0.45  
% 0.22/0.45  % (3378)Memory used [KB]: 1557
% 0.22/0.45  % (3378)Time elapsed: 0.051 s
% 0.22/0.45  % (3378)Instructions burned: 56 (million)
% 0.22/0.45  % (3378)------------------------------
% 0.22/0.45  % (3378)------------------------------
% 0.22/0.45  % (3372)Success in time 0.081 s
%------------------------------------------------------------------------------