TSTP Solution File: NUM447+5 by iProver---3.9

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%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 : Fri May  3 02:49:19 EDT 2024

% Result   : Theorem 62.68s 9.28s
% Output   : CNFRefutation 62.68s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).

fof(f3,axiom,
    aInteger0(sz10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).

fof(f4,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => aInteger0(smndt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aInteger0(X1)
        & aInteger0(X0) )
     => aInteger0(sdtasdt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).

fof(f9,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(f10,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).

fof(f16,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        & smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).

fof(f25,axiom,
    ! [X0] :
      ( aInteger0(X0)
     => ( ? [X1] :
            ( isPrime0(X1)
            & aDivisorOf0(X1,X0) )
      <=> ( smndt0(sz10) != X0
          & sz10 != X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimeDivisor) ).

fof(f42,axiom,
    ( xS = cS2043
    & ! [X0] :
        ( ( ? [X1] :
              ( ( ( ! [X2] :
                      ( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                            | aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                            | ? [X3] :
                                ( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
                                & aInteger0(X3) ) )
                          & aInteger0(X2) )
                       => aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
                      & ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
                       => ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                          & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                          & ? [X3] :
                              ( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
                              & aInteger0(X3) )
                          & aInteger0(X2) ) ) )
                  & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
               => szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
              & isPrime0(X1)
              & sz00 != X1
              & aInteger0(X1) )
         => aElementOf0(X0,xS) )
        & ( aElementOf0(X0,xS)
         => ? [X1] :
              ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
              & ! [X2] :
                  ( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                        | aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                        | ? [X3] :
                            ( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
                            & aInteger0(X3) ) )
                      & aInteger0(X2) )
                   => aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
                  & ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
                   => ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                      & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                      & ? [X3] :
                          ( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
                          & aInteger0(X3) )
                      & aInteger0(X2) ) ) )
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
              & isPrime0(X1)
              & sz00 != X1
              & aInteger0(X1) ) ) )
    & aSet0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).

fof(f43,axiom,
    aInteger0(xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2106) ).

fof(f44,conjecture,
    ( ( ? [X0] :
          ( isPrime0(X0)
          & aDivisorOf0(X0,xn)
          & ? [X1] :
              ( sdtasdt0(X0,X1) = xn
              & aInteger0(X1) )
          & sz00 != X0
          & aInteger0(X0) )
     => ( aElementOf0(xn,sbsmnsldt0(xS))
        | ? [X0] :
            ( aElementOf0(xn,X0)
            & aElementOf0(X0,xS) ) ) )
    & ( ( aElementOf0(xn,sbsmnsldt0(xS))
        & ? [X0] :
            ( aElementOf0(xn,X0)
            & aElementOf0(X0,xS) ) )
     => ? [X0] :
          ( isPrime0(X0)
          & ( aDivisorOf0(X0,xn)
            | ( ? [X1] :
                  ( sdtasdt0(X0,X1) = xn
                  & aInteger0(X1) )
              & sz00 != X0
              & aInteger0(X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f45,negated_conjecture,
    ~ ( ( ? [X0] :
            ( isPrime0(X0)
            & aDivisorOf0(X0,xn)
            & ? [X1] :
                ( sdtasdt0(X0,X1) = xn
                & aInteger0(X1) )
            & sz00 != X0
            & aInteger0(X0) )
       => ( aElementOf0(xn,sbsmnsldt0(xS))
          | ? [X0] :
              ( aElementOf0(xn,X0)
              & aElementOf0(X0,xS) ) ) )
      & ( ( aElementOf0(xn,sbsmnsldt0(xS))
          & ? [X0] :
              ( aElementOf0(xn,X0)
              & aElementOf0(X0,xS) ) )
       => ? [X0] :
            ( isPrime0(X0)
            & ( aDivisorOf0(X0,xn)
              | ( ? [X1] :
                    ( sdtasdt0(X0,X1) = xn
                    & aInteger0(X1) )
                & sz00 != X0
                & aInteger0(X0) ) ) ) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f52,plain,
    ( xS = cS2043
    & ! [X0] :
        ( ( ? [X1] :
              ( ( ( ! [X2] :
                      ( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                            | aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                            | ? [X3] :
                                ( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
                                & aInteger0(X3) ) )
                          & aInteger0(X2) )
                       => aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
                      & ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
                       => ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                          & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                          & ? [X4] :
                              ( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
                              & aInteger0(X4) )
                          & aInteger0(X2) ) ) )
                  & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
               => szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
              & isPrime0(X1)
              & sz00 != X1
              & aInteger0(X1) )
         => aElementOf0(X0,xS) )
        & ( aElementOf0(X0,xS)
         => ? [X5] :
              ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
              & ! [X6] :
                  ( ( ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
                        | aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
                        | ? [X7] :
                            ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X7)
                            & aInteger0(X7) ) )
                      & aInteger0(X6) )
                   => aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
                  & ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
                   => ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
                      & aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
                      & ? [X8] :
                          ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
                          & aInteger0(X8) )
                      & aInteger0(X6) ) ) )
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
              & isPrime0(X5)
              & sz00 != X5
              & aInteger0(X5) ) ) )
    & aSet0(xS) ),
    inference(rectify,[],[f42]) ).

fof(f53,plain,
    ~ ( ( ? [X0] :
            ( isPrime0(X0)
            & aDivisorOf0(X0,xn)
            & ? [X1] :
                ( sdtasdt0(X0,X1) = xn
                & aInteger0(X1) )
            & sz00 != X0
            & aInteger0(X0) )
       => ( aElementOf0(xn,sbsmnsldt0(xS))
          | ? [X2] :
              ( aElementOf0(xn,X2)
              & aElementOf0(X2,xS) ) ) )
      & ( ( aElementOf0(xn,sbsmnsldt0(xS))
          & ? [X3] :
              ( aElementOf0(xn,X3)
              & aElementOf0(X3,xS) ) )
       => ? [X4] :
            ( isPrime0(X4)
            & ( aDivisorOf0(X4,xn)
              | ( ? [X5] :
                    ( xn = sdtasdt0(X4,X5)
                    & aInteger0(X5) )
                & sz00 != X4
                & aInteger0(X4) ) ) ) ) ),
    inference(rectify,[],[f45]) ).

fof(f55,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( aInteger0(sdtasdt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( aInteger0(sdtasdt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f58]) ).

fof(f64,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f65,plain,
    ! [X0] :
      ( ( sz00 = sdtpldt0(smndt0(X0),X0)
        & sz00 = sdtpldt0(X0,smndt0(X0)) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f74,plain,
    ! [X0] :
      ( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
        & smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f88,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( isPrime0(X1)
            & aDivisorOf0(X1,X0) )
      <=> ( smndt0(sz10) != X0
          & sz10 != X0 ) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f109,plain,
    ( xS = cS2043
    & ! [X0] :
        ( ( aElementOf0(X0,xS)
          | ! [X1] :
              ( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
                & ! [X2] :
                    ( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
                      | ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                        & ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                        & ! [X3] :
                            ( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
                            | ~ aInteger0(X3) ) )
                      | ~ aInteger0(X2) )
                    & ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                        & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                        & ? [X4] :
                            ( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
                            & aInteger0(X4) )
                        & aInteger0(X2) )
                      | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
                & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
              | ~ isPrime0(X1)
              | sz00 = X1
              | ~ aInteger0(X1) ) )
        & ( ? [X5] :
              ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
              & ! [X6] :
                  ( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
                    | ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
                      & ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
                      & ! [X7] :
                          ( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
                          | ~ aInteger0(X7) ) )
                    | ~ aInteger0(X6) )
                  & ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
                      & aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
                      & ? [X8] :
                          ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
                          & aInteger0(X8) )
                      & aInteger0(X6) )
                    | ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
              & isPrime0(X5)
              & sz00 != X5
              & aInteger0(X5) )
          | ~ aElementOf0(X0,xS) ) )
    & aSet0(xS) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f110,plain,
    ( xS = cS2043
    & ! [X0] :
        ( ( aElementOf0(X0,xS)
          | ! [X1] :
              ( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
                & ! [X2] :
                    ( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
                      | ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                        & ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                        & ! [X3] :
                            ( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
                            | ~ aInteger0(X3) ) )
                      | ~ aInteger0(X2) )
                    & ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
                        & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
                        & ? [X4] :
                            ( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
                            & aInteger0(X4) )
                        & aInteger0(X2) )
                      | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
                & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
              | ~ isPrime0(X1)
              | sz00 = X1
              | ~ aInteger0(X1) ) )
        & ( ? [X5] :
              ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
              & ! [X6] :
                  ( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
                    | ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
                      & ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
                      & ! [X7] :
                          ( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
                          | ~ aInteger0(X7) ) )
                    | ~ aInteger0(X6) )
                  & ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
                      & aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
                      & ? [X8] :
                          ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
                          & aInteger0(X8) )
                      & aInteger0(X6) )
                    | ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
              & isPrime0(X5)
              & sz00 != X5
              & aInteger0(X5) )
          | ~ aElementOf0(X0,xS) ) )
    & aSet0(xS) ),
    inference(flattening,[],[f109]) ).

fof(f111,plain,
    ( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
      & ! [X2] :
          ( ~ aElementOf0(xn,X2)
          | ~ aElementOf0(X2,xS) )
      & ? [X0] :
          ( isPrime0(X0)
          & aDivisorOf0(X0,xn)
          & ? [X1] :
              ( sdtasdt0(X0,X1) = xn
              & aInteger0(X1) )
          & sz00 != X0
          & aInteger0(X0) ) )
    | ( ! [X4] :
          ( ~ isPrime0(X4)
          | ( ~ aDivisorOf0(X4,xn)
            & ( ! [X5] :
                  ( xn != sdtasdt0(X4,X5)
                  | ~ aInteger0(X5) )
              | sz00 = X4
              | ~ aInteger0(X4) ) ) )
      & aElementOf0(xn,sbsmnsldt0(xS))
      & ? [X3] :
          ( aElementOf0(xn,X3)
          & aElementOf0(X3,xS) ) ) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f112,plain,
    ( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
      & ! [X2] :
          ( ~ aElementOf0(xn,X2)
          | ~ aElementOf0(X2,xS) )
      & ? [X0] :
          ( isPrime0(X0)
          & aDivisorOf0(X0,xn)
          & ? [X1] :
              ( sdtasdt0(X0,X1) = xn
              & aInteger0(X1) )
          & sz00 != X0
          & aInteger0(X0) ) )
    | ( ! [X4] :
          ( ~ isPrime0(X4)
          | ( ~ aDivisorOf0(X4,xn)
            & ( ! [X5] :
                  ( xn != sdtasdt0(X4,X5)
                  | ~ aInteger0(X5) )
              | sz00 = X4
              | ~ aInteger0(X4) ) ) )
      & aElementOf0(xn,sbsmnsldt0(xS))
      & ? [X3] :
          ( aElementOf0(xn,X3)
          & aElementOf0(X3,xS) ) ) ),
    inference(flattening,[],[f111]) ).

fof(f119,plain,
    ! [X0,X2] :
      ( sP4(X0,X2)
    <=> ( ! [X3] :
            ( aElementOf0(X3,X2)
          <=> ( ? [X4] :
                  ( aElementOf0(X3,X4)
                  & aElementOf0(X4,X0) )
              & aInteger0(X3) ) )
        & aSet0(X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

fof(f122,plain,
    ! [X5] :
      ( ! [X6] :
          ( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
            | ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
              & ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
              & ! [X7] :
                  ( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
                  | ~ aInteger0(X7) ) )
            | ~ aInteger0(X6) )
          & ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
              & aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
              & ? [X8] :
                  ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
                  & aInteger0(X8) )
              & aInteger0(X6) )
            | ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
      | ~ sP6(X5) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

fof(f123,plain,
    ! [X1] :
      ( ! [X2] :
          ( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
            | ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
              & ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
              & ! [X3] :
                  ( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
                  | ~ aInteger0(X3) ) )
            | ~ aInteger0(X2) )
          & ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
              & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
              & ? [X4] :
                  ( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
                  & aInteger0(X4) )
              & aInteger0(X2) )
            | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
      | ~ sP7(X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

fof(f124,plain,
    ( xS = cS2043
    & ! [X0] :
        ( ( aElementOf0(X0,xS)
          | ! [X1] :
              ( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
                & sP7(X1)
                & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
              | ~ isPrime0(X1)
              | sz00 = X1
              | ~ aInteger0(X1) ) )
        & ( ? [X5] :
              ( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
              & sP6(X5)
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
              & isPrime0(X5)
              & sz00 != X5
              & aInteger0(X5) )
          | ~ aElementOf0(X0,xS) ) )
    & aSet0(xS) ),
    inference(definition_folding,[],[f110,f123,f122]) ).

fof(f125,plain,
    ( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
      & ! [X2] :
          ( ~ aElementOf0(xn,X2)
          | ~ aElementOf0(X2,xS) )
      & ? [X0] :
          ( isPrime0(X0)
          & aDivisorOf0(X0,xn)
          & ? [X1] :
              ( sdtasdt0(X0,X1) = xn
              & aInteger0(X1) )
          & sz00 != X0
          & aInteger0(X0) ) )
    | ~ sP8 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f126,plain,
    ( sP8
    | ( ! [X4] :
          ( ~ isPrime0(X4)
          | ( ~ aDivisorOf0(X4,xn)
            & ( ! [X5] :
                  ( xn != sdtasdt0(X4,X5)
                  | ~ aInteger0(X5) )
              | sz00 = X4
              | ~ aInteger0(X4) ) ) )
      & aElementOf0(xn,sbsmnsldt0(xS))
      & ? [X3] :
          ( aElementOf0(xn,X3)
          & aElementOf0(X3,xS) ) ) ),
    inference(definition_folding,[],[f112,f125]) ).

fof(f133,plain,
    ! [X0] :
      ( ( ( ? [X1] :
              ( isPrime0(X1)
              & aDivisorOf0(X1,X0) )
          | smndt0(sz10) = X0
          | sz10 = X0 )
        & ( ( smndt0(sz10) != X0
            & sz10 != X0 )
          | ! [X1] :
              ( ~ isPrime0(X1)
              | ~ aDivisorOf0(X1,X0) ) ) )
      | ~ aInteger0(X0) ),
    inference(nnf_transformation,[],[f88]) ).

fof(f134,plain,
    ! [X0] :
      ( ( ( ? [X1] :
              ( isPrime0(X1)
              & aDivisorOf0(X1,X0) )
          | smndt0(sz10) = X0
          | sz10 = X0 )
        & ( ( smndt0(sz10) != X0
            & sz10 != X0 )
          | ! [X1] :
              ( ~ isPrime0(X1)
              | ~ aDivisorOf0(X1,X0) ) ) )
      | ~ aInteger0(X0) ),
    inference(flattening,[],[f133]) ).

fof(f135,plain,
    ! [X0] :
      ( ( ( ? [X1] :
              ( isPrime0(X1)
              & aDivisorOf0(X1,X0) )
          | smndt0(sz10) = X0
          | sz10 = X0 )
        & ( ( smndt0(sz10) != X0
            & sz10 != X0 )
          | ! [X2] :
              ( ~ isPrime0(X2)
              | ~ aDivisorOf0(X2,X0) ) ) )
      | ~ aInteger0(X0) ),
    inference(rectify,[],[f134]) ).

fof(f136,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aDivisorOf0(X1,X0) )
     => ( isPrime0(sK10(X0))
        & aDivisorOf0(sK10(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ! [X0] :
      ( ( ( ( isPrime0(sK10(X0))
            & aDivisorOf0(sK10(X0),X0) )
          | smndt0(sz10) = X0
          | sz10 = X0 )
        & ( ( smndt0(sz10) != X0
            & sz10 != X0 )
          | ! [X2] :
              ( ~ isPrime0(X2)
              | ~ aDivisorOf0(X2,X0) ) ) )
      | ~ aInteger0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f135,f136]) ).

fof(f157,plain,
    ! [X0,X2] :
      ( ( sP4(X0,X2)
        | ? [X3] :
            ( ( ! [X4] :
                  ( ~ aElementOf0(X3,X4)
                  | ~ aElementOf0(X4,X0) )
              | ~ aInteger0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( ? [X4] :
                    ( aElementOf0(X3,X4)
                    & aElementOf0(X4,X0) )
                & aInteger0(X3) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | ! [X4] :
                    ( ~ aElementOf0(X3,X4)
                    | ~ aElementOf0(X4,X0) )
                | ~ aInteger0(X3) )
              & ( ( ? [X4] :
                      ( aElementOf0(X3,X4)
                      & aElementOf0(X4,X0) )
                  & aInteger0(X3) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP4(X0,X2) ) ),
    inference(nnf_transformation,[],[f119]) ).

fof(f158,plain,
    ! [X0,X2] :
      ( ( sP4(X0,X2)
        | ? [X3] :
            ( ( ! [X4] :
                  ( ~ aElementOf0(X3,X4)
                  | ~ aElementOf0(X4,X0) )
              | ~ aInteger0(X3)
              | ~ aElementOf0(X3,X2) )
            & ( ( ? [X4] :
                    ( aElementOf0(X3,X4)
                    & aElementOf0(X4,X0) )
                & aInteger0(X3) )
              | aElementOf0(X3,X2) ) )
        | ~ aSet0(X2) )
      & ( ( ! [X3] :
              ( ( aElementOf0(X3,X2)
                | ! [X4] :
                    ( ~ aElementOf0(X3,X4)
                    | ~ aElementOf0(X4,X0) )
                | ~ aInteger0(X3) )
              & ( ( ? [X4] :
                      ( aElementOf0(X3,X4)
                      & aElementOf0(X4,X0) )
                  & aInteger0(X3) )
                | ~ aElementOf0(X3,X2) ) )
          & aSet0(X2) )
        | ~ sP4(X0,X2) ) ),
    inference(flattening,[],[f157]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ( sP4(X0,X1)
        | ? [X2] :
            ( ( ! [X3] :
                  ( ~ aElementOf0(X2,X3)
                  | ~ aElementOf0(X3,X0) )
              | ~ aInteger0(X2)
              | ~ aElementOf0(X2,X1) )
            & ( ( ? [X4] :
                    ( aElementOf0(X2,X4)
                    & aElementOf0(X4,X0) )
                & aInteger0(X2) )
              | aElementOf0(X2,X1) ) )
        | ~ aSet0(X1) )
      & ( ( ! [X5] :
              ( ( aElementOf0(X5,X1)
                | ! [X6] :
                    ( ~ aElementOf0(X5,X6)
                    | ~ aElementOf0(X6,X0) )
                | ~ aInteger0(X5) )
              & ( ( ? [X7] :
                      ( aElementOf0(X5,X7)
                      & aElementOf0(X7,X0) )
                  & aInteger0(X5) )
                | ~ aElementOf0(X5,X1) ) )
          & aSet0(X1) )
        | ~ sP4(X0,X1) ) ),
    inference(rectify,[],[f158]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] :
                ( ~ aElementOf0(X2,X3)
                | ~ aElementOf0(X3,X0) )
            | ~ aInteger0(X2)
            | ~ aElementOf0(X2,X1) )
          & ( ( ? [X4] :
                  ( aElementOf0(X2,X4)
                  & aElementOf0(X4,X0) )
              & aInteger0(X2) )
            | aElementOf0(X2,X1) ) )
     => ( ( ! [X3] :
              ( ~ aElementOf0(sK14(X0,X1),X3)
              | ~ aElementOf0(X3,X0) )
          | ~ aInteger0(sK14(X0,X1))
          | ~ aElementOf0(sK14(X0,X1),X1) )
        & ( ( ? [X4] :
                ( aElementOf0(sK14(X0,X1),X4)
                & aElementOf0(X4,X0) )
            & aInteger0(sK14(X0,X1)) )
          | aElementOf0(sK14(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( aElementOf0(sK14(X0,X1),X4)
          & aElementOf0(X4,X0) )
     => ( aElementOf0(sK14(X0,X1),sK15(X0,X1))
        & aElementOf0(sK15(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f162,plain,
    ! [X0,X5] :
      ( ? [X7] :
          ( aElementOf0(X5,X7)
          & aElementOf0(X7,X0) )
     => ( aElementOf0(X5,sK16(X0,X5))
        & aElementOf0(sK16(X0,X5),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ( sP4(X0,X1)
        | ( ( ! [X3] :
                ( ~ aElementOf0(sK14(X0,X1),X3)
                | ~ aElementOf0(X3,X0) )
            | ~ aInteger0(sK14(X0,X1))
            | ~ aElementOf0(sK14(X0,X1),X1) )
          & ( ( aElementOf0(sK14(X0,X1),sK15(X0,X1))
              & aElementOf0(sK15(X0,X1),X0)
              & aInteger0(sK14(X0,X1)) )
            | aElementOf0(sK14(X0,X1),X1) ) )
        | ~ aSet0(X1) )
      & ( ( ! [X5] :
              ( ( aElementOf0(X5,X1)
                | ! [X6] :
                    ( ~ aElementOf0(X5,X6)
                    | ~ aElementOf0(X6,X0) )
                | ~ aInteger0(X5) )
              & ( ( aElementOf0(X5,sK16(X0,X5))
                  & aElementOf0(sK16(X0,X5),X0)
                  & aInteger0(X5) )
                | ~ aElementOf0(X5,X1) ) )
          & aSet0(X1) )
        | ~ sP4(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f159,f162,f161,f160]) ).

fof(f184,plain,
    ! [X1] :
      ( ! [X2] :
          ( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
            | ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
              & ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
              & ! [X3] :
                  ( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
                  | ~ aInteger0(X3) ) )
            | ~ aInteger0(X2) )
          & ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
              & aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
              & ? [X4] :
                  ( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
                  & aInteger0(X4) )
              & aInteger0(X2) )
            | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
      | ~ sP7(X1) ),
    inference(nnf_transformation,[],[f123]) ).

fof(f185,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
            | ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & ! [X2] :
                  ( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
                  | ~ aInteger0(X2) ) )
            | ~ aInteger0(X1) )
          & ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & ? [X3] :
                  ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
                  & aInteger0(X3) )
              & aInteger0(X1) )
            | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
      | ~ sP7(X0) ),
    inference(rectify,[],[f184]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
          & aInteger0(X3) )
     => ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK23(X0,X1))
        & aInteger0(sK23(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f187,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
            | ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & ! [X2] :
                  ( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
                  | ~ aInteger0(X2) ) )
            | ~ aInteger0(X1) )
          & ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK23(X0,X1))
              & aInteger0(sK23(X0,X1))
              & aInteger0(X1) )
            | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
      | ~ sP7(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f185,f186]) ).

fof(f188,plain,
    ! [X5] :
      ( ! [X6] :
          ( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
            | ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
              & ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
              & ! [X7] :
                  ( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
                  | ~ aInteger0(X7) ) )
            | ~ aInteger0(X6) )
          & ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
              & aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
              & ? [X8] :
                  ( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
                  & aInteger0(X8) )
              & aInteger0(X6) )
            | ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
      | ~ sP6(X5) ),
    inference(nnf_transformation,[],[f122]) ).

fof(f189,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
            | ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & ! [X2] :
                  ( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
                  | ~ aInteger0(X2) ) )
            | ~ aInteger0(X1) )
          & ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & ? [X3] :
                  ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
                  & aInteger0(X3) )
              & aInteger0(X1) )
            | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
      | ~ sP6(X0) ),
    inference(rectify,[],[f188]) ).

fof(f190,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
          & aInteger0(X3) )
     => ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK24(X0,X1))
        & aInteger0(sK24(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f191,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
            | ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & ! [X2] :
                  ( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
                  | ~ aInteger0(X2) ) )
            | ~ aInteger0(X1) )
          & ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
              & aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
              & sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK24(X0,X1))
              & aInteger0(sK24(X0,X1))
              & aInteger0(X1) )
            | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
      | ~ sP6(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f189,f190]) ).

fof(f192,plain,
    ( xS = cS2043
    & ! [X0] :
        ( ( aElementOf0(X0,xS)
          | ! [X1] :
              ( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
                & sP7(X1)
                & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
              | ~ isPrime0(X1)
              | sz00 = X1
              | ~ aInteger0(X1) ) )
        & ( ? [X2] :
              ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X0
              & sP6(X2)
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
              & isPrime0(X2)
              & sz00 != X2
              & aInteger0(X2) )
          | ~ aElementOf0(X0,xS) ) )
    & aSet0(xS) ),
    inference(rectify,[],[f124]) ).

fof(f193,plain,
    ! [X0] :
      ( ? [X2] :
          ( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X0
          & sP6(X2)
          & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
          & isPrime0(X2)
          & sz00 != X2
          & aInteger0(X2) )
     => ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
        & sP6(sK25(X0))
        & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)))
        & isPrime0(sK25(X0))
        & sz00 != sK25(X0)
        & aInteger0(sK25(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f194,plain,
    ( xS = cS2043
    & ! [X0] :
        ( ( aElementOf0(X0,xS)
          | ! [X1] :
              ( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
                & sP7(X1)
                & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
              | ~ isPrime0(X1)
              | sz00 = X1
              | ~ aInteger0(X1) ) )
        & ( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
            & sP6(sK25(X0))
            & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)))
            & isPrime0(sK25(X0))
            & sz00 != sK25(X0)
            & aInteger0(sK25(X0)) )
          | ~ aElementOf0(X0,xS) ) )
    & aSet0(xS) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f192,f193]) ).

fof(f195,plain,
    ( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
      & ! [X2] :
          ( ~ aElementOf0(xn,X2)
          | ~ aElementOf0(X2,xS) )
      & ? [X0] :
          ( isPrime0(X0)
          & aDivisorOf0(X0,xn)
          & ? [X1] :
              ( sdtasdt0(X0,X1) = xn
              & aInteger0(X1) )
          & sz00 != X0
          & aInteger0(X0) ) )
    | ~ sP8 ),
    inference(nnf_transformation,[],[f125]) ).

fof(f196,plain,
    ( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
      & ! [X0] :
          ( ~ aElementOf0(xn,X0)
          | ~ aElementOf0(X0,xS) )
      & ? [X1] :
          ( isPrime0(X1)
          & aDivisorOf0(X1,xn)
          & ? [X2] :
              ( sdtasdt0(X1,X2) = xn
              & aInteger0(X2) )
          & sz00 != X1
          & aInteger0(X1) ) )
    | ~ sP8 ),
    inference(rectify,[],[f195]) ).

fof(f197,plain,
    ( ? [X1] :
        ( isPrime0(X1)
        & aDivisorOf0(X1,xn)
        & ? [X2] :
            ( sdtasdt0(X1,X2) = xn
            & aInteger0(X2) )
        & sz00 != X1
        & aInteger0(X1) )
   => ( isPrime0(sK26)
      & aDivisorOf0(sK26,xn)
      & ? [X2] :
          ( xn = sdtasdt0(sK26,X2)
          & aInteger0(X2) )
      & sz00 != sK26
      & aInteger0(sK26) ) ),
    introduced(choice_axiom,[]) ).

fof(f198,plain,
    ( ? [X2] :
        ( xn = sdtasdt0(sK26,X2)
        & aInteger0(X2) )
   => ( xn = sdtasdt0(sK26,sK27)
      & aInteger0(sK27) ) ),
    introduced(choice_axiom,[]) ).

fof(f199,plain,
    ( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
      & ! [X0] :
          ( ~ aElementOf0(xn,X0)
          | ~ aElementOf0(X0,xS) )
      & isPrime0(sK26)
      & aDivisorOf0(sK26,xn)
      & xn = sdtasdt0(sK26,sK27)
      & aInteger0(sK27)
      & sz00 != sK26
      & aInteger0(sK26) )
    | ~ sP8 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f196,f198,f197]) ).

fof(f200,plain,
    ( sP8
    | ( ! [X0] :
          ( ~ isPrime0(X0)
          | ( ~ aDivisorOf0(X0,xn)
            & ( ! [X1] :
                  ( sdtasdt0(X0,X1) != xn
                  | ~ aInteger0(X1) )
              | sz00 = X0
              | ~ aInteger0(X0) ) ) )
      & aElementOf0(xn,sbsmnsldt0(xS))
      & ? [X2] :
          ( aElementOf0(xn,X2)
          & aElementOf0(X2,xS) ) ) ),
    inference(rectify,[],[f126]) ).

fof(f201,plain,
    ( ? [X2] :
        ( aElementOf0(xn,X2)
        & aElementOf0(X2,xS) )
   => ( aElementOf0(xn,sK28)
      & aElementOf0(sK28,xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f202,plain,
    ( sP8
    | ( ! [X0] :
          ( ~ isPrime0(X0)
          | ( ~ aDivisorOf0(X0,xn)
            & ( ! [X1] :
                  ( sdtasdt0(X0,X1) != xn
                  | ~ aInteger0(X1) )
              | sz00 = X0
              | ~ aInteger0(X0) ) ) )
      & aElementOf0(xn,sbsmnsldt0(xS))
      & aElementOf0(xn,sK28)
      & aElementOf0(sK28,xS) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f200,f201]) ).

fof(f203,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f204,plain,
    aInteger0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f205,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( aInteger0(sdtasdt0(X0,X1))
      | ~ aInteger0(X1)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f210,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f211,plain,
    ! [X0] :
      ( sdtpldt0(sz00,X0) = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f212,plain,
    ! [X0] :
      ( sz00 = sdtpldt0(X0,smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f223,plain,
    ! [X0] :
      ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f237,plain,
    ! [X2,X0] :
      ( sz10 != X0
      | ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f238,plain,
    ! [X2,X0] :
      ( smndt0(sz10) != X0
      | ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f239,plain,
    ! [X0] :
      ( aDivisorOf0(sK10(X0),X0)
      | smndt0(sz10) = X0
      | sz10 = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f240,plain,
    ! [X0] :
      ( isPrime0(sK10(X0))
      | smndt0(sz10) = X0
      | sz10 = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f137]) ).

fof(f273,plain,
    ! [X0,X1,X5] :
      ( aElementOf0(sK16(X0,X5),X0)
      | ~ aElementOf0(X5,X1)
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f163]) ).

fof(f275,plain,
    ! [X0,X1,X6,X5] :
      ( aElementOf0(X5,X1)
      | ~ aElementOf0(X5,X6)
      | ~ aElementOf0(X6,X0)
      | ~ aInteger0(X5)
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f163]) ).

fof(f312,plain,
    ! [X0,X1] :
      ( aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
      | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
      | ~ sP7(X0) ),
    inference(cnf_transformation,[],[f187]) ).

fof(f314,plain,
    ! [X2,X0,X1] :
      ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
      | sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
      | ~ aInteger0(X2)
      | ~ aInteger0(X1)
      | ~ sP7(X0) ),
    inference(cnf_transformation,[],[f187]) ).

fof(f317,plain,
    ! [X0,X1] :
      ( aInteger0(X1)
      | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f320,plain,
    ! [X0,X1] :
      ( aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
      | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
      | ~ sP6(X0) ),
    inference(cnf_transformation,[],[f191]) ).

fof(f326,plain,
    ! [X0] :
      ( aInteger0(sK25(X0))
      | ~ aElementOf0(X0,xS) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f327,plain,
    ! [X0] :
      ( sz00 != sK25(X0)
      | ~ aElementOf0(X0,xS) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f328,plain,
    ! [X0] :
      ( isPrime0(sK25(X0))
      | ~ aElementOf0(X0,xS) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f330,plain,
    ! [X0] :
      ( sP6(sK25(X0))
      | ~ aElementOf0(X0,xS) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f331,plain,
    ! [X0] :
      ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
      | ~ aElementOf0(X0,xS) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f332,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,xS)
      | aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f333,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,xS)
      | sP7(X1)
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f334,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,xS)
      | szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(cnf_transformation,[],[f194]) ).

fof(f335,plain,
    xS = cS2043,
    inference(cnf_transformation,[],[f194]) ).

fof(f336,plain,
    aInteger0(xn),
    inference(cnf_transformation,[],[f43]) ).

fof(f337,plain,
    ( aInteger0(sK26)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f338,plain,
    ( sz00 != sK26
    | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f339,plain,
    ( aInteger0(sK27)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f340,plain,
    ( xn = sdtasdt0(sK26,sK27)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f341,plain,
    ( aDivisorOf0(sK26,xn)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f342,plain,
    ( isPrime0(sK26)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f343,plain,
    ! [X0] :
      ( ~ aElementOf0(xn,X0)
      | ~ aElementOf0(X0,xS)
      | ~ sP8 ),
    inference(cnf_transformation,[],[f199]) ).

fof(f345,plain,
    ( sP8
    | aElementOf0(sK28,xS) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f346,plain,
    ( sP8
    | aElementOf0(xn,sK28) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f347,plain,
    ( sP8
    | aElementOf0(xn,sbsmnsldt0(xS)) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f348,plain,
    ! [X0,X1] :
      ( sP8
      | ~ isPrime0(X0)
      | sdtasdt0(X0,X1) != xn
      | ~ aInteger0(X1)
      | sz00 = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f349,plain,
    ! [X0] :
      ( sP8
      | ~ isPrime0(X0)
      | ~ aDivisorOf0(X0,xn) ),
    inference(cnf_transformation,[],[f202]) ).

fof(f350,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,cS2043)
      | szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(definition_unfolding,[],[f334,f335]) ).

fof(f351,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,cS2043)
      | sP7(X1)
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(definition_unfolding,[],[f333,f335]) ).

fof(f352,plain,
    ! [X0,X1] :
      ( aElementOf0(X0,cS2043)
      | aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(definition_unfolding,[],[f332,f335]) ).

fof(f353,plain,
    ! [X0] :
      ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
      | ~ aElementOf0(X0,cS2043) ),
    inference(definition_unfolding,[],[f331,f335]) ).

fof(f354,plain,
    ! [X0] :
      ( sP6(sK25(X0))
      | ~ aElementOf0(X0,cS2043) ),
    inference(definition_unfolding,[],[f330,f335]) ).

fof(f356,plain,
    ! [X0] :
      ( isPrime0(sK25(X0))
      | ~ aElementOf0(X0,cS2043) ),
    inference(definition_unfolding,[],[f328,f335]) ).

fof(f357,plain,
    ! [X0] :
      ( sz00 != sK25(X0)
      | ~ aElementOf0(X0,cS2043) ),
    inference(definition_unfolding,[],[f327,f335]) ).

fof(f358,plain,
    ! [X0] :
      ( aInteger0(sK25(X0))
      | ~ aElementOf0(X0,cS2043) ),
    inference(definition_unfolding,[],[f326,f335]) ).

fof(f361,plain,
    ! [X0] :
      ( ~ aElementOf0(xn,X0)
      | ~ aElementOf0(X0,cS2043)
      | ~ sP8 ),
    inference(definition_unfolding,[],[f343,f335]) ).

fof(f362,plain,
    ( sP8
    | aElementOf0(xn,sbsmnsldt0(cS2043)) ),
    inference(definition_unfolding,[],[f347,f335]) ).

fof(f363,plain,
    ( sP8
    | aElementOf0(sK28,cS2043) ),
    inference(definition_unfolding,[],[f345,f335]) ).

fof(f366,plain,
    ! [X2] :
      ( ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,smndt0(sz10))
      | ~ aInteger0(smndt0(sz10)) ),
    inference(equality_resolution,[],[f238]) ).

fof(f367,plain,
    ! [X2] :
      ( ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,sz10)
      | ~ aInteger0(sz10) ),
    inference(equality_resolution,[],[f237]) ).

fof(f379,plain,
    ! [X1] :
      ( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),cS2043)
      | ~ isPrime0(X1)
      | sz00 = X1
      | ~ aInteger0(X1) ),
    inference(equality_resolution,[],[f350]) ).

cnf(c_49,plain,
    aInteger0(sz00),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_50,plain,
    aInteger0(sz10),
    inference(cnf_transformation,[],[f204]) ).

cnf(c_51,plain,
    ( ~ aInteger0(X0)
    | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_53,plain,
    ( ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | aInteger0(sdtasdt0(X0,X1)) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_56,plain,
    ( ~ aInteger0(X0)
    | sdtpldt0(sz00,X0) = X0 ),
    inference(cnf_transformation,[],[f211]) ).

cnf(c_57,plain,
    ( ~ aInteger0(X0)
    | sdtpldt0(X0,sz00) = X0 ),
    inference(cnf_transformation,[],[f210]) ).

cnf(c_59,plain,
    ( ~ aInteger0(X0)
    | sdtpldt0(X0,smndt0(X0)) = sz00 ),
    inference(cnf_transformation,[],[f212]) ).

cnf(c_68,plain,
    ( ~ aInteger0(X0)
    | sdtasdt0(X0,smndt0(sz10)) = smndt0(X0) ),
    inference(cnf_transformation,[],[f223]) ).

cnf(c_83,plain,
    ( ~ aInteger0(X0)
    | smndt0(sz10) = X0
    | X0 = sz10
    | isPrime0(sK10(X0)) ),
    inference(cnf_transformation,[],[f240]) ).

cnf(c_84,plain,
    ( ~ aInteger0(X0)
    | smndt0(sz10) = X0
    | X0 = sz10
    | aDivisorOf0(sK10(X0),X0) ),
    inference(cnf_transformation,[],[f239]) ).

cnf(c_85,plain,
    ( ~ aDivisorOf0(X0,smndt0(sz10))
    | ~ aInteger0(smndt0(sz10))
    | ~ isPrime0(X0) ),
    inference(cnf_transformation,[],[f366]) ).

cnf(c_86,plain,
    ( ~ aDivisorOf0(X0,sz10)
    | ~ isPrime0(X0)
    | ~ aInteger0(sz10) ),
    inference(cnf_transformation,[],[f367]) ).

cnf(c_121,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aElementOf0(X1,X2)
    | ~ sP4(X2,X3)
    | ~ aInteger0(X0)
    | aElementOf0(X0,X3) ),
    inference(cnf_transformation,[],[f275]) ).

cnf(c_123,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ sP4(X2,X1)
    | aElementOf0(sK16(X2,X0),X2) ),
    inference(cnf_transformation,[],[f273]) ).

cnf(c_157,plain,
    ( sdtpldt0(X0,smndt0(sz00)) != sdtasdt0(X1,X2)
    | ~ aInteger0(X0)
    | ~ aInteger0(X2)
    | ~ sP7(X1)
    | aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
    inference(cnf_transformation,[],[f314]) ).

cnf(c_159,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
    | ~ sP7(X1)
    | aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00))) ),
    inference(cnf_transformation,[],[f312]) ).

cnf(c_167,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
    | ~ sP6(X1)
    | aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00))) ),
    inference(cnf_transformation,[],[f320]) ).

cnf(c_170,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
    | ~ sP6(X1)
    | aInteger0(X0) ),
    inference(cnf_transformation,[],[f317]) ).

cnf(c_171,plain,
    ( ~ aInteger0(X0)
    | ~ isPrime0(X0)
    | X0 = sz00
    | aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS2043) ),
    inference(cnf_transformation,[],[f379]) ).

cnf(c_172,plain,
    ( ~ aInteger0(X0)
    | ~ isPrime0(X0)
    | X0 = sz00
    | aElementOf0(X1,cS2043)
    | sP7(X0) ),
    inference(cnf_transformation,[],[f351]) ).

cnf(c_173,plain,
    ( ~ aInteger0(X0)
    | ~ isPrime0(X0)
    | X0 = sz00
    | aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X0))
    | aElementOf0(X1,cS2043) ),
    inference(cnf_transformation,[],[f352]) ).

cnf(c_174,plain,
    ( ~ aElementOf0(X0,cS2043)
    | szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0 ),
    inference(cnf_transformation,[],[f353]) ).

cnf(c_175,plain,
    ( ~ aElementOf0(X0,cS2043)
    | sP6(sK25(X0)) ),
    inference(cnf_transformation,[],[f354]) ).

cnf(c_177,plain,
    ( ~ aElementOf0(X0,cS2043)
    | isPrime0(sK25(X0)) ),
    inference(cnf_transformation,[],[f356]) ).

cnf(c_178,plain,
    ( sK25(X0) != sz00
    | ~ aElementOf0(X0,cS2043) ),
    inference(cnf_transformation,[],[f357]) ).

cnf(c_179,plain,
    ( ~ aElementOf0(X0,cS2043)
    | aInteger0(sK25(X0)) ),
    inference(cnf_transformation,[],[f358]) ).

cnf(c_181,plain,
    aInteger0(xn),
    inference(cnf_transformation,[],[f336]) ).

cnf(c_183,plain,
    ( ~ aElementOf0(X0,cS2043)
    | ~ aElementOf0(xn,X0)
    | ~ sP8 ),
    inference(cnf_transformation,[],[f361]) ).

cnf(c_184,plain,
    ( ~ sP8
    | isPrime0(sK26) ),
    inference(cnf_transformation,[],[f342]) ).

cnf(c_185,plain,
    ( ~ sP8
    | aDivisorOf0(sK26,xn) ),
    inference(cnf_transformation,[],[f341]) ).

cnf(c_186,plain,
    ( ~ sP8
    | sdtasdt0(sK26,sK27) = xn ),
    inference(cnf_transformation,[],[f340]) ).

cnf(c_187,plain,
    ( ~ sP8
    | aInteger0(sK27) ),
    inference(cnf_transformation,[],[f339]) ).

cnf(c_188,plain,
    ( sz00 != sK26
    | ~ sP8 ),
    inference(cnf_transformation,[],[f338]) ).

cnf(c_189,plain,
    ( ~ sP8
    | aInteger0(sK26) ),
    inference(cnf_transformation,[],[f337]) ).

cnf(c_190,negated_conjecture,
    ( ~ aDivisorOf0(X0,xn)
    | ~ isPrime0(X0)
    | sP8 ),
    inference(cnf_transformation,[],[f349]) ).

cnf(c_191,negated_conjecture,
    ( sdtasdt0(X0,X1) != xn
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ isPrime0(X0)
    | X0 = sz00
    | sP8 ),
    inference(cnf_transformation,[],[f348]) ).

cnf(c_192,negated_conjecture,
    ( aElementOf0(xn,sbsmnsldt0(cS2043))
    | sP8 ),
    inference(cnf_transformation,[],[f362]) ).

cnf(c_193,negated_conjecture,
    ( aElementOf0(xn,sK28)
    | sP8 ),
    inference(cnf_transformation,[],[f346]) ).

cnf(c_194,negated_conjecture,
    ( aElementOf0(sK28,cS2043)
    | sP8 ),
    inference(cnf_transformation,[],[f363]) ).

cnf(c_196,plain,
    ( ~ aInteger0(sz00)
    | aInteger0(smndt0(sz00)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_333,plain,
    ( ~ isPrime0(X0)
    | ~ aDivisorOf0(X0,sz10) ),
    inference(prop_impl_just,[status(thm)],[c_50,c_86]) ).

cnf(c_334,plain,
    ( ~ aDivisorOf0(X0,sz10)
    | ~ isPrime0(X0) ),
    inference(renaming,[status(thm)],[c_333]) ).

cnf(c_359,plain,
    ( ~ aElementOf0(X0,cS2043)
    | sP6(sK25(X0)) ),
    inference(prop_impl_just,[status(thm)],[c_175]) ).

cnf(c_373,plain,
    ( ~ sP8
    | aDivisorOf0(sK26,xn) ),
    inference(prop_impl_just,[status(thm)],[c_185]) ).

cnf(c_2881,plain,
    ( sK25(X0) != X1
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
    | ~ aElementOf0(X0,cS2043)
    | aInteger0(X2) ),
    inference(resolution_lifted,[status(thm)],[c_170,c_359]) ).

cnf(c_2882,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
    | ~ aElementOf0(X1,cS2043)
    | aInteger0(X0) ),
    inference(unflattening,[status(thm)],[c_2881]) ).

cnf(c_2916,plain,
    ( sK25(X0) != X1
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
    | ~ aElementOf0(X0,cS2043)
    | aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00))) ),
    inference(resolution_lifted,[status(thm)],[c_167,c_359]) ).

cnf(c_2917,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
    | ~ aElementOf0(X1,cS2043)
    | aDivisorOf0(sK25(X1),sdtpldt0(X0,smndt0(sz00))) ),
    inference(unflattening,[status(thm)],[c_2916]) ).

cnf(c_6778,plain,
    ( smndt0(sz10) != xn
    | X0 != sK26
    | ~ aInteger0(smndt0(sz10))
    | ~ isPrime0(X0)
    | ~ sP8 ),
    inference(resolution_lifted,[status(thm)],[c_85,c_373]) ).

cnf(c_6779,plain,
    ( smndt0(sz10) != xn
    | ~ aInteger0(smndt0(sz10))
    | ~ isPrime0(sK26)
    | ~ sP8 ),
    inference(unflattening,[status(thm)],[c_6778]) ).

cnf(c_6780,plain,
    ( ~ aInteger0(smndt0(sz10))
    | smndt0(sz10) != xn
    | ~ sP8 ),
    inference(global_subsumption_just,[status(thm)],[c_6779,c_184,c_6779]) ).

cnf(c_6781,plain,
    ( smndt0(sz10) != xn
    | ~ aInteger0(smndt0(sz10))
    | ~ sP8 ),
    inference(renaming,[status(thm)],[c_6780]) ).

cnf(c_6825,plain,
    ( X0 != sK26
    | sz10 != xn
    | ~ isPrime0(X0)
    | ~ sP8 ),
    inference(resolution_lifted,[status(thm)],[c_334,c_373]) ).

cnf(c_6826,plain,
    ( sz10 != xn
    | ~ isPrime0(sK26)
    | ~ sP8 ),
    inference(unflattening,[status(thm)],[c_6825]) ).

cnf(c_6827,plain,
    ( sz10 != xn
    | ~ sP8 ),
    inference(global_subsumption_just,[status(thm)],[c_6826,c_184,c_6826]) ).

cnf(c_13763,plain,
    ( aElementOf0(X0,cS2043)
    | ~ sP0_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_def])],[c_173]) ).

cnf(c_13766,plain,
    ( sP7(X0)
    | ~ isPrime0(X0)
    | ~ aInteger0(X0)
    | X0 = sz00
    | ~ sP2_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_172]) ).

cnf(c_13767,plain,
    ( sP0_iProver_def
    | sP2_iProver_def ),
    inference(splitting,[splitting(split),new_symbols(definition,[])],[c_172]) ).

cnf(c_13768,plain,
    sbsmnsldt0(cS2043) = sP3_iProver_def,
    definition ).

cnf(c_13769,negated_conjecture,
    ( aElementOf0(sK28,cS2043)
    | sP8 ),
    inference(demodulation,[status(thm)],[c_194]) ).

cnf(c_13770,negated_conjecture,
    ( aElementOf0(xn,sK28)
    | sP8 ),
    inference(demodulation,[status(thm)],[c_193]) ).

cnf(c_13771,negated_conjecture,
    ( aElementOf0(xn,sP3_iProver_def)
    | sP8 ),
    inference(demodulation,[status(thm)],[c_192,c_13768]) ).

cnf(c_13772,negated_conjecture,
    ( sdtasdt0(X0,X1) != xn
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ isPrime0(X0)
    | X0 = sz00
    | sP8 ),
    inference(demodulation,[status(thm)],[c_191]) ).

cnf(c_13773,negated_conjecture,
    ( ~ aDivisorOf0(X0,xn)
    | ~ isPrime0(X0)
    | sP8 ),
    inference(demodulation,[status(thm)],[c_190]) ).

cnf(c_16229,plain,
    ( ~ sP0_iProver_def
    | isPrime0(sK25(X0)) ),
    inference(superposition,[status(thm)],[c_13763,c_177]) ).

cnf(c_16230,plain,
    ( isPrime0(sK25(sK28))
    | sP8 ),
    inference(superposition,[status(thm)],[c_13769,c_177]) ).

cnf(c_16241,plain,
    ( aInteger0(sK25(sK28))
    | sP8 ),
    inference(superposition,[status(thm)],[c_13769,c_179]) ).

cnf(c_16329,plain,
    sdtpldt0(xn,sz00) = xn,
    inference(superposition,[status(thm)],[c_181,c_57]) ).

cnf(c_16889,plain,
    sdtpldt0(sz00,smndt0(sz00)) = sz00,
    inference(superposition,[status(thm)],[c_49,c_59]) ).

cnf(c_17128,plain,
    ( ~ aInteger0(sz10)
    | aInteger0(smndt0(sz10)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_17268,plain,
    ( ~ aInteger0(sK25(X0))
    | ~ isPrime0(sK25(X0))
    | ~ sP2_iProver_def
    | sK25(X0) = sz00
    | sP7(sK25(X0)) ),
    inference(instantiation,[status(thm)],[c_13766]) ).

cnf(c_17294,plain,
    ( ~ aElementOf0(xn,X0)
    | ~ sP8
    | ~ sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_13763,c_183]) ).

cnf(c_17321,plain,
    sdtasdt0(sz00,smndt0(sz10)) = smndt0(sz00),
    inference(superposition,[status(thm)],[c_49,c_68]) ).

cnf(c_18174,plain,
    ( ~ sP0_iProver_def
    | szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0 ),
    inference(superposition,[status(thm)],[c_13763,c_174]) ).

cnf(c_18175,plain,
    ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
    | sP8 ),
    inference(superposition,[status(thm)],[c_13769,c_174]) ).

cnf(c_18326,plain,
    ( ~ sP8
    | ~ sP0_iProver_def ),
    inference(superposition,[status(thm)],[c_13763,c_17294]) ).

cnf(c_18579,plain,
    ( ~ sP4(X0,sK28)
    | aElementOf0(sK16(X0,xn),X0)
    | sP8 ),
    inference(superposition,[status(thm)],[c_13770,c_123]) ).

cnf(c_18698,plain,
    ( ~ aInteger0(smndt0(sz10))
    | ~ aInteger0(sz00)
    | aInteger0(smndt0(sz00)) ),
    inference(superposition,[status(thm)],[c_17321,c_53]) ).

cnf(c_18701,plain,
    ( ~ aInteger0(smndt0(sz10))
    | aInteger0(smndt0(sz00)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_18698,c_49]) ).

cnf(c_18704,plain,
    aInteger0(smndt0(sz00)),
    inference(global_subsumption_just,[status(thm)],[c_18701,c_49,c_196]) ).

cnf(c_18715,plain,
    sdtpldt0(sz00,smndt0(sz00)) = smndt0(sz00),
    inference(superposition,[status(thm)],[c_18704,c_56]) ).

cnf(c_18716,plain,
    smndt0(sz00) = sz00,
    inference(light_normalisation,[status(thm)],[c_18715,c_16889]) ).

cnf(c_23389,plain,
    ( sK25(sK28) != sz00
    | ~ aElementOf0(sK28,cS2043) ),
    inference(instantiation,[status(thm)],[c_178]) ).

cnf(c_23515,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
    | ~ sP7(X1)
    | aDivisorOf0(X1,sdtpldt0(X0,sz00)) ),
    inference(light_normalisation,[status(thm)],[c_159,c_18716]) ).

cnf(c_23799,plain,
    ( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
    | ~ aInteger0(X0)
    | ~ isPrime0(X0)
    | ~ sP8
    | X0 = sz00 ),
    inference(superposition,[status(thm)],[c_171,c_183]) ).

cnf(c_23936,plain,
    ( ~ isPrime0(sK10(xn))
    | ~ aInteger0(xn)
    | smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(superposition,[status(thm)],[c_84,c_13773]) ).

cnf(c_23941,plain,
    ( ~ isPrime0(sK10(xn))
    | smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23936,c_181]) ).

cnf(c_24432,plain,
    ( ~ aInteger0(xn)
    | smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(superposition,[status(thm)],[c_83,c_23941]) ).

cnf(c_24433,plain,
    ( smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_24432,c_181]) ).

cnf(c_26277,plain,
    ( ~ aInteger0(sK25(sK28))
    | ~ isPrime0(sK25(sK28))
    | ~ sP2_iProver_def
    | sK25(sK28) = sz00
    | sP7(sK25(sK28)) ),
    inference(instantiation,[status(thm)],[c_17268]) ).

cnf(c_27107,plain,
    ( ~ aInteger0(sK16(X0,xn))
    | ~ aElementOf0(X0,X1)
    | ~ sP4(X1,X2)
    | ~ sP4(X0,sK28)
    | aElementOf0(sK16(X0,xn),X2)
    | sP8 ),
    inference(superposition,[status(thm)],[c_18579,c_121]) ).

cnf(c_30872,plain,
    ( ~ aInteger0(sK16(xn,xn))
    | ~ sP4(sP3_iProver_def,X0)
    | ~ sP4(xn,sK28)
    | aElementOf0(sK16(xn,xn),X0)
    | sP8 ),
    inference(superposition,[status(thm)],[c_13771,c_27107]) ).

cnf(c_32903,plain,
    ( ~ aInteger0(sK16(xn,xn))
    | ~ aElementOf0(X0,X1)
    | ~ sP4(X1,X2)
    | ~ sP4(sP3_iProver_def,X0)
    | ~ sP4(xn,sK28)
    | aElementOf0(sK16(xn,xn),X2)
    | sP8 ),
    inference(superposition,[status(thm)],[c_30872,c_121]) ).

cnf(c_40341,plain,
    ( sdtasdt0(X0,X1) != sdtpldt0(X2,sz00)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ sP7(X0)
    | aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
    inference(light_normalisation,[status(thm)],[c_157,c_18716]) ).

cnf(c_40391,plain,
    ( sdtasdt0(X0,X1) != xn
    | ~ aInteger0(X1)
    | ~ sP7(X0)
    | ~ aInteger0(xn)
    | aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
    inference(superposition,[status(thm)],[c_16329,c_40341]) ).

cnf(c_40397,plain,
    ( sdtasdt0(X0,X1) != xn
    | ~ aInteger0(X1)
    | ~ sP7(X0)
    | aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_40391,c_181]) ).

cnf(c_88656,plain,
    ( X0 = sz00
    | ~ isPrime0(X0)
    | ~ aInteger0(X1)
    | ~ aInteger0(X0)
    | sdtasdt0(X0,X1) != xn ),
    inference(global_subsumption_just,[status(thm)],[c_13772,c_191,c_13766,c_13767,c_18326,c_23799,c_40397]) ).

cnf(c_88657,negated_conjecture,
    ( sdtasdt0(X0,X1) != xn
    | ~ aInteger0(X0)
    | ~ aInteger0(X1)
    | ~ isPrime0(X0)
    | X0 = sz00 ),
    inference(renaming,[status(thm)],[c_88656]) ).

cnf(c_97341,plain,
    ( ~ isPrime0(sK10(xn))
    | ~ aInteger0(xn)
    | smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(superposition,[status(thm)],[c_84,c_13773]) ).

cnf(c_97346,plain,
    ( ~ isPrime0(sK10(xn))
    | smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(forward_subsumption_resolution,[status(thm)],[c_97341,c_181]) ).

cnf(c_101066,plain,
    ( smndt0(sz10) = xn
    | sz10 = xn
    | sP8 ),
    inference(global_subsumption_just,[status(thm)],[c_97346,c_24433]) ).

cnf(c_101080,plain,
    ( sdtasdt0(sK26,sK27) = xn
    | smndt0(sz10) = xn
    | sz10 = xn ),
    inference(superposition,[status(thm)],[c_101066,c_186]) ).

cnf(c_111184,plain,
    ( ~ aInteger0(sK16(xn,xn))
    | ~ sP4(sP3_iProver_def,X0)
    | ~ sP4(xn,sK28)
    | ~ sP4(sP3_iProver_def,xn)
    | aElementOf0(sK16(xn,xn),X0)
    | sP8 ),
    inference(superposition,[status(thm)],[c_13771,c_32903]) ).

cnf(c_112209,plain,
    ( ~ aInteger0(sK26)
    | ~ aInteger0(sK27)
    | ~ isPrime0(sK26)
    | smndt0(sz10) = xn
    | sz00 = sK26
    | sz10 = xn ),
    inference(superposition,[status(thm)],[c_101080,c_88657]) ).

cnf(c_112301,plain,
    ( aElementOf0(sK16(xn,xn),X0)
    | ~ aInteger0(sK16(xn,xn))
    | ~ sP4(sP3_iProver_def,X0)
    | ~ sP4(xn,sK28) ),
    inference(global_subsumption_just,[status(thm)],[c_111184,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17128,c_30872,c_112209]) ).

cnf(c_112302,plain,
    ( ~ aInteger0(sK16(xn,xn))
    | ~ sP4(sP3_iProver_def,X0)
    | ~ sP4(xn,sK28)
    | aElementOf0(sK16(xn,xn),X0) ),
    inference(renaming,[status(thm)],[c_112301]) ).

cnf(c_112335,plain,
    ( ~ aElementOf0(xn,sK16(xn,xn))
    | ~ aInteger0(sK16(xn,xn))
    | ~ sP4(xn,sK28)
    | ~ sP4(sP3_iProver_def,cS2043)
    | ~ sP8 ),
    inference(superposition,[status(thm)],[c_112302,c_183]) ).

cnf(c_112972,plain,
    ~ sP8,
    inference(global_subsumption_just,[status(thm)],[c_112335,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17128,c_112209]) ).

cnf(c_113228,plain,
    szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28,
    inference(backward_subsumption_resolution,[status(thm)],[c_18175,c_112972]) ).

cnf(c_113241,plain,
    isPrime0(sK25(sK28)),
    inference(backward_subsumption_resolution,[status(thm)],[c_16230,c_112972]) ).

cnf(c_113244,plain,
    aElementOf0(xn,sK28),
    inference(backward_subsumption_resolution,[status(thm)],[c_13770,c_112972]) ).

cnf(c_113246,plain,
    ( ~ aDivisorOf0(X0,xn)
    | ~ isPrime0(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_13773,c_112972]) ).

cnf(c_114599,plain,
    ( ~ aElementOf0(X0,sK28)
    | ~ sP7(sK25(sK28))
    | aDivisorOf0(sK25(sK28),sdtpldt0(X0,sz00)) ),
    inference(superposition,[status(thm)],[c_113228,c_23515]) ).

cnf(c_181478,plain,
    ( ~ aElementOf0(xn,sK28)
    | ~ sP7(sK25(sK28))
    | aDivisorOf0(sK25(sK28),xn) ),
    inference(superposition,[status(thm)],[c_16329,c_114599]) ).

cnf(c_181498,plain,
    ( ~ sP7(sK25(sK28))
    | aDivisorOf0(sK25(sK28),xn) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_181478,c_113244]) ).

cnf(c_181557,plain,
    ( ~ isPrime0(sK25(sK28))
    | ~ sP7(sK25(sK28)) ),
    inference(superposition,[status(thm)],[c_181498,c_113246]) ).

cnf(c_181558,plain,
    ~ sP7(sK25(sK28)),
    inference(forward_subsumption_resolution,[status(thm)],[c_181557,c_113241]) ).

cnf(c_191077,plain,
    ~ sP2_iProver_def,
    inference(global_subsumption_just,[status(thm)],[c_13766,c_50,c_194,c_189,c_187,c_184,c_188,c_6781,c_6827,c_16230,c_16241,c_17128,c_23389,c_26277,c_112209,c_181558]) ).

cnf(c_191079,plain,
    sP0_iProver_def,
    inference(backward_subsumption_resolution,[status(thm)],[c_13767,c_191077]) ).

cnf(c_191104,plain,
    szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0,
    inference(backward_subsumption_resolution,[status(thm)],[c_18174,c_191079]) ).

cnf(c_191117,plain,
    isPrime0(sK25(X0)),
    inference(backward_subsumption_resolution,[status(thm)],[c_16229,c_191079]) ).

cnf(c_191118,plain,
    aElementOf0(X0,cS2043),
    inference(backward_subsumption_resolution,[status(thm)],[c_13763,c_191079]) ).

cnf(c_191157,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aElementOf0(X1,cS2043)
    | aInteger0(X0) ),
    inference(demodulation,[status(thm)],[c_2882,c_191104]) ).

cnf(c_191165,plain,
    ( ~ aElementOf0(X0,X1)
    | aInteger0(X0) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_191157,c_191118]) ).

cnf(c_191984,plain,
    aInteger0(X0),
    inference(superposition,[status(thm)],[c_191118,c_191165]) ).

cnf(c_192194,plain,
    sdtpldt0(X0,sz00) = X0,
    inference(backward_subsumption_resolution,[status(thm)],[c_57,c_191984]) ).

cnf(c_241696,plain,
    ( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
    | ~ aElementOf0(X1,cS2043)
    | aDivisorOf0(sK25(X1),X0) ),
    inference(light_normalisation,[status(thm)],[c_2917,c_18716,c_192194]) ).

cnf(c_241697,plain,
    ( ~ aElementOf0(X0,X1)
    | ~ aElementOf0(X1,cS2043)
    | aDivisorOf0(sK25(X1),X0) ),
    inference(demodulation,[status(thm)],[c_241696,c_191104]) ).

cnf(c_241698,plain,
    ( ~ aElementOf0(X0,X1)
    | aDivisorOf0(sK25(X1),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_241697,c_191118]) ).

cnf(c_241707,plain,
    ( ~ isPrime0(sK25(X0))
    | ~ aElementOf0(xn,X0) ),
    inference(superposition,[status(thm)],[c_241698,c_113246]) ).

cnf(c_241710,plain,
    ~ aElementOf0(xn,X0),
    inference(forward_subsumption_resolution,[status(thm)],[c_241707,c_191117]) ).

cnf(c_241721,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_113244,c_241710]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : run_iprover %s %d THM
% 0.13/0.35  % Computer : n031.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May  2 20:16:46 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 62.68/9.28  % SZS status Started for theBenchmark.p
% 62.68/9.28  % SZS status Theorem for theBenchmark.p
% 62.68/9.28  
% 62.68/9.28  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 62.68/9.28  
% 62.68/9.28  ------  iProver source info
% 62.68/9.28  
% 62.68/9.28  git: date: 2024-05-02 19:28:25 +0000
% 62.68/9.28  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 62.68/9.28  git: non_committed_changes: false
% 62.68/9.28  
% 62.68/9.28  ------ Parsing...
% 62.68/9.28  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 62.68/9.28  
% 62.68/9.28  ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 62.68/9.28  
% 62.68/9.28  ------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 62.68/9.28  
% 62.68/9.28  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 62.68/9.28  ------ Proving...
% 62.68/9.28  ------ Problem Properties 
% 62.68/9.28  
% 62.68/9.28  
% 62.68/9.28  clauses                                 147
% 62.68/9.28  conjectures                             5
% 62.68/9.28  EPR                                     39
% 62.68/9.28  Horn                                    100
% 62.68/9.28  unary                                   5
% 62.68/9.28  binary                                  36
% 62.68/9.28  lits                                    517
% 62.68/9.28  lits eq                                 68
% 62.68/9.28  fd_pure                                 0
% 62.68/9.28  fd_pseudo                               0
% 62.68/9.28  fd_cond                                 22
% 62.68/9.28  fd_pseudo_cond                          9
% 62.68/9.28  AC symbols                              0
% 62.68/9.28  
% 62.68/9.28  ------ Schedule dynamic 5 is on 
% 62.68/9.28  
% 62.68/9.28  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 62.68/9.28  
% 62.68/9.28  
% 62.68/9.28  ------ 
% 62.68/9.28  Current options:
% 62.68/9.28  ------ 
% 62.68/9.28  
% 62.68/9.28  
% 62.68/9.28  
% 62.68/9.28  
% 62.68/9.28  ------ Proving...
% 62.68/9.28  
% 62.68/9.28  
% 62.68/9.28  % SZS status Theorem for theBenchmark.p
% 62.68/9.28  
% 62.68/9.28  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.68/9.28  
% 62.68/9.28  
%------------------------------------------------------------------------------