TSTP Solution File: NUM448+5 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n004.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 02:49:20 EDT 2024

% Result   : Theorem 11.98s 2.67s
% Output   : CNFRefutation 11.98s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
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(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,conjecture,
    ( ! [X0] :
        ( aInteger0(X0)
       => ( ( ? [X1] :
                ( isPrime0(X1)
                & ( aDivisorOf0(X1,X0)
                  | ( ? [X2] :
                        ( sdtasdt0(X1,X2) = X0
                        & aInteger0(X2) )
                    & sz00 != X1
                    & aInteger0(X1) ) ) )
           => ( aElementOf0(X0,sbsmnsldt0(xS))
              & ? [X1] :
                  ( aElementOf0(X0,X1)
                  & aElementOf0(X1,xS) ) ) )
          & ( ( aElementOf0(X0,sbsmnsldt0(xS))
              | ? [X1] :
                  ( aElementOf0(X0,X1)
                  & aElementOf0(X1,xS) ) )
           => ? [X1] :
                ( isPrime0(X1)
                & aDivisorOf0(X1,X0)
                & ? [X2] :
                    ( sdtasdt0(X1,X2) = X0
                    & aInteger0(X2) )
                & sz00 != X1
                & aInteger0(X1) ) ) ) )
   => ( ( ! [X0] :
            ( aElementOf0(X0,sbsmnsldt0(xS))
          <=> ( ? [X1] :
                  ( aElementOf0(X0,X1)
                  & aElementOf0(X1,xS) )
              & aInteger0(X0) ) )
        & aSet0(sbsmnsldt0(xS)) )
     => ( ( ! [X0] :
              ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
            <=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
                & aInteger0(X0) ) )
          & aSet0(stldt0(sbsmnsldt0(xS))) )
       => ( stldt0(sbsmnsldt0(xS)) = cS2076
          | ! [X0] :
              ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
            <=> ( smndt0(sz10) = X0
                | sz10 = X0 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f44,negated_conjecture,
    ~ ( ! [X0] :
          ( aInteger0(X0)
         => ( ( ? [X1] :
                  ( isPrime0(X1)
                  & ( aDivisorOf0(X1,X0)
                    | ( ? [X2] :
                          ( sdtasdt0(X1,X2) = X0
                          & aInteger0(X2) )
                      & sz00 != X1
                      & aInteger0(X1) ) ) )
             => ( aElementOf0(X0,sbsmnsldt0(xS))
                & ? [X1] :
                    ( aElementOf0(X0,X1)
                    & aElementOf0(X1,xS) ) ) )
            & ( ( aElementOf0(X0,sbsmnsldt0(xS))
                | ? [X1] :
                    ( aElementOf0(X0,X1)
                    & aElementOf0(X1,xS) ) )
             => ? [X1] :
                  ( isPrime0(X1)
                  & aDivisorOf0(X1,X0)
                  & ? [X2] :
                      ( sdtasdt0(X1,X2) = X0
                      & aInteger0(X2) )
                  & sz00 != X1
                  & aInteger0(X1) ) ) ) )
     => ( ( ! [X0] :
              ( aElementOf0(X0,sbsmnsldt0(xS))
            <=> ( ? [X1] :
                    ( aElementOf0(X0,X1)
                    & aElementOf0(X1,xS) )
                & aInteger0(X0) ) )
          & aSet0(sbsmnsldt0(xS)) )
       => ( ( ! [X0] :
                ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
              <=> ( ~ aElementOf0(X0,sbsmnsldt0(xS))
                  & aInteger0(X0) ) )
            & aSet0(stldt0(sbsmnsldt0(xS))) )
         => ( stldt0(sbsmnsldt0(xS)) = cS2076
            | ! [X0] :
                ( aElementOf0(X0,stldt0(sbsmnsldt0(xS)))
              <=> ( smndt0(sz10) = X0
                  | sz10 = X0 ) ) ) ) ) ),
    inference(negated_conjecture,[],[f43]) ).

fof(f51,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(f52,plain,
    ~ ( ! [X0] :
          ( aInteger0(X0)
         => ( ( ? [X1] :
                  ( isPrime0(X1)
                  & ( aDivisorOf0(X1,X0)
                    | ( ? [X2] :
                          ( sdtasdt0(X1,X2) = X0
                          & aInteger0(X2) )
                      & sz00 != X1
                      & aInteger0(X1) ) ) )
             => ( aElementOf0(X0,sbsmnsldt0(xS))
                & ? [X3] :
                    ( aElementOf0(X0,X3)
                    & aElementOf0(X3,xS) ) ) )
            & ( ( aElementOf0(X0,sbsmnsldt0(xS))
                | ? [X4] :
                    ( aElementOf0(X0,X4)
                    & aElementOf0(X4,xS) ) )
             => ? [X5] :
                  ( isPrime0(X5)
                  & aDivisorOf0(X5,X0)
                  & ? [X6] :
                      ( sdtasdt0(X5,X6) = X0
                      & aInteger0(X6) )
                  & sz00 != X5
                  & aInteger0(X5) ) ) ) )
     => ( ( ! [X7] :
              ( aElementOf0(X7,sbsmnsldt0(xS))
            <=> ( ? [X8] :
                    ( aElementOf0(X7,X8)
                    & aElementOf0(X8,xS) )
                & aInteger0(X7) ) )
          & aSet0(sbsmnsldt0(xS)) )
       => ( ( ! [X9] :
                ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
              <=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
                  & aInteger0(X9) ) )
            & aSet0(stldt0(sbsmnsldt0(xS))) )
         => ( stldt0(sbsmnsldt0(xS)) = cS2076
            | ! [X10] :
                ( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
              <=> ( smndt0(sz10) = X10
                  | sz10 = X10 ) ) ) ) ) ),
    inference(rectify,[],[f44]) ).

fof(f54,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f87,plain,
    ! [X0] :
      ( ( ? [X1] :
            ( isPrime0(X1)
            & aDivisorOf0(X1,X0) )
      <=> ( smndt0(sz10) != X0
          & sz10 != X0 ) )
      | ~ aInteger0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f108,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,[],[f51]) ).

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(flattening,[],[f108]) ).

fof(f110,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ? [X10] :
        ( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
      <~> ( smndt0(sz10) = X10
          | sz10 = X10 ) )
    & ! [X9] :
        ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
          & aInteger0(X9) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X7] :
        ( aElementOf0(X7,sbsmnsldt0(xS))
      <=> ( ? [X8] :
              ( aElementOf0(X7,X8)
              & aElementOf0(X8,xS) )
          & aInteger0(X7) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X0] :
        ( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
              & ? [X3] :
                  ( aElementOf0(X0,X3)
                  & aElementOf0(X3,xS) ) )
            | ! [X1] :
                ( ~ isPrime0(X1)
                | ( ~ aDivisorOf0(X1,X0)
                  & ( ! [X2] :
                        ( sdtasdt0(X1,X2) != X0
                        | ~ aInteger0(X2) )
                    | sz00 = X1
                    | ~ aInteger0(X1) ) ) ) )
          & ( ? [X5] :
                ( isPrime0(X5)
                & aDivisorOf0(X5,X0)
                & ? [X6] :
                    ( sdtasdt0(X5,X6) = X0
                    & aInteger0(X6) )
                & sz00 != X5
                & aInteger0(X5) )
            | ( ~ aElementOf0(X0,sbsmnsldt0(xS))
              & ! [X4] :
                  ( ~ aElementOf0(X0,X4)
                  | ~ aElementOf0(X4,xS) ) ) ) )
        | ~ aInteger0(X0) ) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f111,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ? [X10] :
        ( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
      <~> ( smndt0(sz10) = X10
          | sz10 = X10 ) )
    & ! [X9] :
        ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
          & aInteger0(X9) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X7] :
        ( aElementOf0(X7,sbsmnsldt0(xS))
      <=> ( ? [X8] :
              ( aElementOf0(X7,X8)
              & aElementOf0(X8,xS) )
          & aInteger0(X7) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X0] :
        ( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
              & ? [X3] :
                  ( aElementOf0(X0,X3)
                  & aElementOf0(X3,xS) ) )
            | ! [X1] :
                ( ~ isPrime0(X1)
                | ( ~ aDivisorOf0(X1,X0)
                  & ( ! [X2] :
                        ( sdtasdt0(X1,X2) != X0
                        | ~ aInteger0(X2) )
                    | sz00 = X1
                    | ~ aInteger0(X1) ) ) ) )
          & ( ? [X5] :
                ( isPrime0(X5)
                & aDivisorOf0(X5,X0)
                & ? [X6] :
                    ( sdtasdt0(X5,X6) = X0
                    & aInteger0(X6) )
                & sz00 != X5
                & aInteger0(X5) )
            | ( ~ aElementOf0(X0,sbsmnsldt0(xS))
              & ! [X4] :
                  ( ~ aElementOf0(X0,X4)
                  | ~ aElementOf0(X4,xS) ) ) ) )
        | ~ aInteger0(X0) ) ),
    inference(flattening,[],[f110]) ).

fof(f121,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(f122,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(f123,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,[],[f109,f122,f121]) ).

fof(f124,plain,
    ! [X0] :
      ( ? [X5] :
          ( isPrime0(X5)
          & aDivisorOf0(X5,X0)
          & ? [X6] :
              ( sdtasdt0(X5,X6) = X0
              & aInteger0(X6) )
          & sz00 != X5
          & aInteger0(X5) )
      | ~ sP8(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

fof(f125,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ? [X10] :
        ( aElementOf0(X10,stldt0(sbsmnsldt0(xS)))
      <~> ( smndt0(sz10) = X10
          | sz10 = X10 ) )
    & ! [X9] :
        ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
      <=> ( ~ aElementOf0(X9,sbsmnsldt0(xS))
          & aInteger0(X9) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X7] :
        ( aElementOf0(X7,sbsmnsldt0(xS))
      <=> ( ? [X8] :
              ( aElementOf0(X7,X8)
              & aElementOf0(X8,xS) )
          & aInteger0(X7) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X0] :
        ( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
              & ? [X3] :
                  ( aElementOf0(X0,X3)
                  & aElementOf0(X3,xS) ) )
            | ! [X1] :
                ( ~ isPrime0(X1)
                | ( ~ aDivisorOf0(X1,X0)
                  & ( ! [X2] :
                        ( sdtasdt0(X1,X2) != X0
                        | ~ aInteger0(X2) )
                    | sz00 = X1
                    | ~ aInteger0(X1) ) ) ) )
          & ( sP8(X0)
            | ( ~ aElementOf0(X0,sbsmnsldt0(xS))
              & ! [X4] :
                  ( ~ aElementOf0(X0,X4)
                  | ~ aElementOf0(X4,xS) ) ) ) )
        | ~ aInteger0(X0) ) ),
    inference(definition_folding,[],[f111,f124]) ).

fof(f132,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,[],[f87]) ).

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(flattening,[],[f132]) ).

fof(f134,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,[],[f133]) ).

fof(f135,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aDivisorOf0(X1,X0) )
     => ( isPrime0(sK10(X0))
        & aDivisorOf0(sK10(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,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])],[f134,f135]) ).

fof(f191,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,[],[f123]) ).

fof(f192,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(f193,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])],[f191,f192]) ).

fof(f194,plain,
    ! [X0] :
      ( ? [X5] :
          ( isPrime0(X5)
          & aDivisorOf0(X5,X0)
          & ? [X6] :
              ( sdtasdt0(X5,X6) = X0
              & aInteger0(X6) )
          & sz00 != X5
          & aInteger0(X5) )
      | ~ sP8(X0) ),
    inference(nnf_transformation,[],[f124]) ).

fof(f195,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aDivisorOf0(X1,X0)
          & ? [X2] :
              ( sdtasdt0(X1,X2) = X0
              & aInteger0(X2) )
          & sz00 != X1
          & aInteger0(X1) )
      | ~ sP8(X0) ),
    inference(rectify,[],[f194]) ).

fof(f196,plain,
    ! [X0] :
      ( ? [X1] :
          ( isPrime0(X1)
          & aDivisorOf0(X1,X0)
          & ? [X2] :
              ( sdtasdt0(X1,X2) = X0
              & aInteger0(X2) )
          & sz00 != X1
          & aInteger0(X1) )
     => ( isPrime0(sK26(X0))
        & aDivisorOf0(sK26(X0),X0)
        & ? [X2] :
            ( sdtasdt0(sK26(X0),X2) = X0
            & aInteger0(X2) )
        & sz00 != sK26(X0)
        & aInteger0(sK26(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f197,plain,
    ! [X0] :
      ( ? [X2] :
          ( sdtasdt0(sK26(X0),X2) = X0
          & aInteger0(X2) )
     => ( sdtasdt0(sK26(X0),sK27(X0)) = X0
        & aInteger0(sK27(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f198,plain,
    ! [X0] :
      ( ( isPrime0(sK26(X0))
        & aDivisorOf0(sK26(X0),X0)
        & sdtasdt0(sK26(X0),sK27(X0)) = X0
        & aInteger0(sK27(X0))
        & sz00 != sK26(X0)
        & aInteger0(sK26(X0)) )
      | ~ sP8(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f195,f197,f196]) ).

fof(f199,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ? [X10] :
        ( ( ( smndt0(sz10) != X10
            & sz10 != X10 )
          | ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) )
        & ( smndt0(sz10) = X10
          | sz10 = X10
          | aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X9] :
        ( ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X9,sbsmnsldt0(xS))
          | ~ aInteger0(X9) )
        & ( ( ~ aElementOf0(X9,sbsmnsldt0(xS))
            & aInteger0(X9) )
          | ~ aElementOf0(X9,stldt0(sbsmnsldt0(xS))) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X7] :
        ( ( aElementOf0(X7,sbsmnsldt0(xS))
          | ! [X8] :
              ( ~ aElementOf0(X7,X8)
              | ~ aElementOf0(X8,xS) )
          | ~ aInteger0(X7) )
        & ( ( ? [X8] :
                ( aElementOf0(X7,X8)
                & aElementOf0(X8,xS) )
            & aInteger0(X7) )
          | ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X0] :
        ( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
              & ? [X3] :
                  ( aElementOf0(X0,X3)
                  & aElementOf0(X3,xS) ) )
            | ! [X1] :
                ( ~ isPrime0(X1)
                | ( ~ aDivisorOf0(X1,X0)
                  & ( ! [X2] :
                        ( sdtasdt0(X1,X2) != X0
                        | ~ aInteger0(X2) )
                    | sz00 = X1
                    | ~ aInteger0(X1) ) ) ) )
          & ( sP8(X0)
            | ( ~ aElementOf0(X0,sbsmnsldt0(xS))
              & ! [X4] :
                  ( ~ aElementOf0(X0,X4)
                  | ~ aElementOf0(X4,xS) ) ) ) )
        | ~ aInteger0(X0) ) ),
    inference(nnf_transformation,[],[f125]) ).

fof(f200,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ? [X10] :
        ( ( ( smndt0(sz10) != X10
            & sz10 != X10 )
          | ~ aElementOf0(X10,stldt0(sbsmnsldt0(xS))) )
        & ( smndt0(sz10) = X10
          | sz10 = X10
          | aElementOf0(X10,stldt0(sbsmnsldt0(xS))) ) )
    & ! [X9] :
        ( ( aElementOf0(X9,stldt0(sbsmnsldt0(xS)))
          | aElementOf0(X9,sbsmnsldt0(xS))
          | ~ aInteger0(X9) )
        & ( ( ~ aElementOf0(X9,sbsmnsldt0(xS))
            & aInteger0(X9) )
          | ~ aElementOf0(X9,stldt0(sbsmnsldt0(xS))) ) )
    & aSet0(stldt0(sbsmnsldt0(xS)))
    & ! [X7] :
        ( ( aElementOf0(X7,sbsmnsldt0(xS))
          | ! [X8] :
              ( ~ aElementOf0(X7,X8)
              | ~ aElementOf0(X8,xS) )
          | ~ aInteger0(X7) )
        & ( ( ? [X8] :
                ( aElementOf0(X7,X8)
                & aElementOf0(X8,xS) )
            & aInteger0(X7) )
          | ~ aElementOf0(X7,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X0] :
        ( ( ( ( aElementOf0(X0,sbsmnsldt0(xS))
              & ? [X3] :
                  ( aElementOf0(X0,X3)
                  & aElementOf0(X3,xS) ) )
            | ! [X1] :
                ( ~ isPrime0(X1)
                | ( ~ aDivisorOf0(X1,X0)
                  & ( ! [X2] :
                        ( sdtasdt0(X1,X2) != X0
                        | ~ aInteger0(X2) )
                    | sz00 = X1
                    | ~ aInteger0(X1) ) ) ) )
          & ( sP8(X0)
            | ( ~ aElementOf0(X0,sbsmnsldt0(xS))
              & ! [X4] :
                  ( ~ aElementOf0(X0,X4)
                  | ~ aElementOf0(X4,xS) ) ) ) )
        | ~ aInteger0(X0) ) ),
    inference(flattening,[],[f199]) ).

fof(f201,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ? [X0] :
        ( ( ( smndt0(sz10) != X0
            & sz10 != X0 )
          | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
        & ( 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))
    & ! [X5] :
        ( ( ( ( aElementOf0(X5,sbsmnsldt0(xS))
              & ? [X6] :
                  ( aElementOf0(X5,X6)
                  & aElementOf0(X6,xS) ) )
            | ! [X7] :
                ( ~ isPrime0(X7)
                | ( ~ aDivisorOf0(X7,X5)
                  & ( ! [X8] :
                        ( sdtasdt0(X7,X8) != X5
                        | ~ aInteger0(X8) )
                    | sz00 = X7
                    | ~ aInteger0(X7) ) ) ) )
          & ( sP8(X5)
            | ( ~ aElementOf0(X5,sbsmnsldt0(xS))
              & ! [X9] :
                  ( ~ aElementOf0(X5,X9)
                  | ~ aElementOf0(X9,xS) ) ) ) )
        | ~ aInteger0(X5) ) ),
    inference(rectify,[],[f200]) ).

fof(f202,plain,
    ( ? [X0] :
        ( ( ( smndt0(sz10) != X0
            & sz10 != X0 )
          | ~ aElementOf0(X0,stldt0(sbsmnsldt0(xS))) )
        & ( smndt0(sz10) = X0
          | sz10 = X0
          | aElementOf0(X0,stldt0(sbsmnsldt0(xS))) ) )
   => ( ( ( smndt0(sz10) != sK28
          & sz10 != sK28 )
        | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) )
      & ( smndt0(sz10) = sK28
        | sz10 = sK28
        | aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f203,plain,
    ! [X2] :
      ( ? [X4] :
          ( aElementOf0(X2,X4)
          & aElementOf0(X4,xS) )
     => ( aElementOf0(X2,sK29(X2))
        & aElementOf0(sK29(X2),xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f204,plain,
    ! [X5] :
      ( ? [X6] :
          ( aElementOf0(X5,X6)
          & aElementOf0(X6,xS) )
     => ( aElementOf0(X5,sK30(X5))
        & aElementOf0(sK30(X5),xS) ) ),
    introduced(choice_axiom,[]) ).

fof(f205,plain,
    ( stldt0(sbsmnsldt0(xS)) != cS2076
    & ( ( smndt0(sz10) != sK28
        & sz10 != sK28 )
      | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) )
    & ( smndt0(sz10) = sK28
      | sz10 = sK28
      | aElementOf0(sK28,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,sK29(X2))
            & aElementOf0(sK29(X2),xS)
            & aInteger0(X2) )
          | ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
    & aSet0(sbsmnsldt0(xS))
    & ! [X5] :
        ( ( ( ( aElementOf0(X5,sbsmnsldt0(xS))
              & aElementOf0(X5,sK30(X5))
              & aElementOf0(sK30(X5),xS) )
            | ! [X7] :
                ( ~ isPrime0(X7)
                | ( ~ aDivisorOf0(X7,X5)
                  & ( ! [X8] :
                        ( sdtasdt0(X7,X8) != X5
                        | ~ aInteger0(X8) )
                    | sz00 = X7
                    | ~ aInteger0(X7) ) ) ) )
          & ( sP8(X5)
            | ( ~ aElementOf0(X5,sbsmnsldt0(xS))
              & ! [X9] :
                  ( ~ aElementOf0(X5,X9)
                  | ~ aElementOf0(X9,xS) ) ) ) )
        | ~ aInteger0(X5) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30])],[f201,f204,f203,f202]) ).

fof(f207,plain,
    aInteger0(sz10),
    inference(cnf_transformation,[],[f3]) ).

fof(f208,plain,
    ! [X0] :
      ( aInteger0(smndt0(X0))
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f240,plain,
    ! [X2,X0] :
      ( sz10 != X0
      | ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f241,plain,
    ! [X2,X0] :
      ( smndt0(sz10) != X0
      | ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,X0)
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f242,plain,
    ! [X0] :
      ( aDivisorOf0(sK10(X0),X0)
      | smndt0(sz10) = X0
      | sz10 = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f243,plain,
    ! [X0] :
      ( isPrime0(sK10(X0))
      | smndt0(sz10) = X0
      | sz10 = X0
      | ~ aInteger0(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f338,plain,
    xS = cS2043,
    inference(cnf_transformation,[],[f193]) ).

fof(f343,plain,
    ! [X0] :
      ( aDivisorOf0(sK26(X0),X0)
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f344,plain,
    ! [X0] :
      ( isPrime0(sK26(X0))
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f198]) ).

fof(f346,plain,
    ! [X5] :
      ( sP8(X5)
      | ~ aElementOf0(X5,sbsmnsldt0(xS))
      | ~ aInteger0(X5) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f352,plain,
    ! [X7,X5] :
      ( aElementOf0(X5,sbsmnsldt0(xS))
      | ~ isPrime0(X7)
      | ~ aDivisorOf0(X7,X5)
      | ~ aInteger0(X5) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f354,plain,
    ! [X2] :
      ( aInteger0(X2)
      | ~ aElementOf0(X2,sbsmnsldt0(xS)) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f359,plain,
    ! [X1] :
      ( aInteger0(X1)
      | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f360,plain,
    ! [X1] :
      ( ~ aElementOf0(X1,sbsmnsldt0(xS))
      | ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f361,plain,
    ! [X1] :
      ( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
      | aElementOf0(X1,sbsmnsldt0(xS))
      | ~ aInteger0(X1) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f362,plain,
    ( smndt0(sz10) = sK28
    | sz10 = sK28
    | aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f363,plain,
    ( sz10 != sK28
    | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f364,plain,
    ( smndt0(sz10) != sK28
    | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(xS))) ),
    inference(cnf_transformation,[],[f205]) ).

fof(f377,plain,
    ( smndt0(sz10) != sK28
    | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
    inference(definition_unfolding,[],[f364,f338]) ).

fof(f378,plain,
    ( sz10 != sK28
    | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
    inference(definition_unfolding,[],[f363,f338]) ).

fof(f379,plain,
    ( smndt0(sz10) = sK28
    | sz10 = sK28
    | aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
    inference(definition_unfolding,[],[f362,f338]) ).

fof(f380,plain,
    ! [X1] :
      ( aElementOf0(X1,stldt0(sbsmnsldt0(cS2043)))
      | aElementOf0(X1,sbsmnsldt0(cS2043))
      | ~ aInteger0(X1) ),
    inference(definition_unfolding,[],[f361,f338,f338]) ).

fof(f381,plain,
    ! [X1] :
      ( ~ aElementOf0(X1,sbsmnsldt0(cS2043))
      | ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043))) ),
    inference(definition_unfolding,[],[f360,f338,f338]) ).

fof(f382,plain,
    ! [X1] :
      ( aInteger0(X1)
      | ~ aElementOf0(X1,stldt0(sbsmnsldt0(cS2043))) ),
    inference(definition_unfolding,[],[f359,f338]) ).

fof(f387,plain,
    ! [X2] :
      ( aInteger0(X2)
      | ~ aElementOf0(X2,sbsmnsldt0(cS2043)) ),
    inference(definition_unfolding,[],[f354,f338]) ).

fof(f389,plain,
    ! [X7,X5] :
      ( aElementOf0(X5,sbsmnsldt0(cS2043))
      | ~ isPrime0(X7)
      | ~ aDivisorOf0(X7,X5)
      | ~ aInteger0(X5) ),
    inference(definition_unfolding,[],[f352,f338]) ).

fof(f393,plain,
    ! [X5] :
      ( sP8(X5)
      | ~ aElementOf0(X5,sbsmnsldt0(cS2043))
      | ~ aInteger0(X5) ),
    inference(definition_unfolding,[],[f346,f338]) ).

fof(f397,plain,
    ! [X2] :
      ( ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,smndt0(sz10))
      | ~ aInteger0(smndt0(sz10)) ),
    inference(equality_resolution,[],[f241]) ).

fof(f398,plain,
    ! [X2] :
      ( ~ isPrime0(X2)
      | ~ aDivisorOf0(X2,sz10)
      | ~ aInteger0(sz10) ),
    inference(equality_resolution,[],[f240]) ).

cnf(c_50,plain,
    aInteger0(sz10),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_51,plain,
    ( ~ aInteger0(X0)
    | aInteger0(smndt0(X0)) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_83,plain,
    ( ~ aInteger0(X0)
    | smndt0(sz10) = X0
    | X0 = sz10
    | isPrime0(sK10(X0)) ),
    inference(cnf_transformation,[],[f243]) ).

cnf(c_84,plain,
    ( ~ aInteger0(X0)
    | smndt0(sz10) = X0
    | X0 = sz10
    | aDivisorOf0(sK10(X0),X0) ),
    inference(cnf_transformation,[],[f242]) ).

cnf(c_85,plain,
    ( ~ aDivisorOf0(X0,smndt0(sz10))
    | ~ aInteger0(smndt0(sz10))
    | ~ isPrime0(X0) ),
    inference(cnf_transformation,[],[f397]) ).

cnf(c_86,plain,
    ( ~ aDivisorOf0(X0,sz10)
    | ~ isPrime0(X0)
    | ~ aInteger0(sz10) ),
    inference(cnf_transformation,[],[f398]) ).

cnf(c_181,plain,
    ( ~ sP8(X0)
    | isPrime0(sK26(X0)) ),
    inference(cnf_transformation,[],[f344]) ).

cnf(c_182,plain,
    ( ~ sP8(X0)
    | aDivisorOf0(sK26(X0),X0) ),
    inference(cnf_transformation,[],[f343]) ).

cnf(c_188,negated_conjecture,
    ( smndt0(sz10) != sK28
    | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
    inference(cnf_transformation,[],[f377]) ).

cnf(c_189,negated_conjecture,
    ( sz10 != sK28
    | ~ aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
    inference(cnf_transformation,[],[f378]) ).

cnf(c_190,negated_conjecture,
    ( smndt0(sz10) = sK28
    | sz10 = sK28
    | aElementOf0(sK28,stldt0(sbsmnsldt0(cS2043))) ),
    inference(cnf_transformation,[],[f379]) ).

cnf(c_191,negated_conjecture,
    ( ~ aInteger0(X0)
    | aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
    | aElementOf0(X0,sbsmnsldt0(cS2043)) ),
    inference(cnf_transformation,[],[f380]) ).

cnf(c_192,negated_conjecture,
    ( ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
    | ~ aElementOf0(X0,sbsmnsldt0(cS2043)) ),
    inference(cnf_transformation,[],[f381]) ).

cnf(c_193,negated_conjecture,
    ( ~ aElementOf0(X0,stldt0(sbsmnsldt0(cS2043)))
    | aInteger0(X0) ),
    inference(cnf_transformation,[],[f382]) ).

cnf(c_198,negated_conjecture,
    ( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
    | aInteger0(X0) ),
    inference(cnf_transformation,[],[f387]) ).

cnf(c_200,negated_conjecture,
    ( ~ aDivisorOf0(X0,X1)
    | ~ aInteger0(X1)
    | ~ isPrime0(X0)
    | aElementOf0(X1,sbsmnsldt0(cS2043)) ),
    inference(cnf_transformation,[],[f389]) ).

cnf(c_206,negated_conjecture,
    ( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
    | ~ aInteger0(X0)
    | sP8(X0) ),
    inference(cnf_transformation,[],[f393]) ).

cnf(c_324,negated_conjecture,
    ( ~ aElementOf0(X0,sbsmnsldt0(cS2043))
    | sP8(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_206,c_198,c_206]) ).

cnf(c_327,plain,
    ( ~ isPrime0(X0)
    | ~ aDivisorOf0(X0,sz10) ),
    inference(global_subsumption_just,[status(thm)],[c_86,c_50,c_86]) ).

cnf(c_328,plain,
    ( ~ aDivisorOf0(X0,sz10)
    | ~ isPrime0(X0) ),
    inference(renaming,[status(thm)],[c_327]) ).

cnf(c_6827,plain,
    ( sK26(X0) != X1
    | X0 != sz10
    | ~ isPrime0(X1)
    | ~ sP8(X0) ),
    inference(resolution_lifted,[status(thm)],[c_328,c_182]) ).

cnf(c_6828,plain,
    ( ~ isPrime0(sK26(sz10))
    | ~ sP8(sz10) ),
    inference(unflattening,[status(thm)],[c_6827]) ).

cnf(c_6833,plain,
    ~ sP8(sz10),
    inference(forward_subsumption_resolution,[status(thm)],[c_6828,c_181]) ).

cnf(c_13694,plain,
    smndt0(sz10) = sP5_iProver_def,
    definition ).

cnf(c_13698,negated_conjecture,
    ( ~ aElementOf0(X0,sP3_iProver_def)
    | sP8(X0) ),
    inference(demodulation,[status(thm)],[c_324]) ).

cnf(c_13702,negated_conjecture,
    ( ~ aDivisorOf0(X0,X1)
    | ~ aInteger0(X1)
    | ~ isPrime0(X0)
    | aElementOf0(X1,sP3_iProver_def) ),
    inference(demodulation,[status(thm)],[c_200]) ).

cnf(c_13709,negated_conjecture,
    ( ~ aElementOf0(X0,sP4_iProver_def)
    | aInteger0(X0) ),
    inference(demodulation,[status(thm)],[c_193]) ).

cnf(c_13710,negated_conjecture,
    ( ~ aElementOf0(X0,sP3_iProver_def)
    | ~ aElementOf0(X0,sP4_iProver_def) ),
    inference(demodulation,[status(thm)],[c_192]) ).

cnf(c_13711,negated_conjecture,
    ( ~ aInteger0(X0)
    | aElementOf0(X0,sP3_iProver_def)
    | aElementOf0(X0,sP4_iProver_def) ),
    inference(demodulation,[status(thm)],[c_191]) ).

cnf(c_13712,negated_conjecture,
    ( sz10 = sK28
    | sP5_iProver_def = sK28
    | aElementOf0(sK28,sP4_iProver_def) ),
    inference(demodulation,[status(thm)],[c_190,c_13694]) ).

cnf(c_13713,negated_conjecture,
    ( sz10 != sK28
    | ~ aElementOf0(sK28,sP4_iProver_def) ),
    inference(demodulation,[status(thm)],[c_189]) ).

cnf(c_13714,negated_conjecture,
    ( sP5_iProver_def != sK28
    | ~ aElementOf0(sK28,sP4_iProver_def) ),
    inference(demodulation,[status(thm)],[c_188]) ).

cnf(c_16373,plain,
    ( ~ aInteger0(sz10)
    | aInteger0(sP5_iProver_def) ),
    inference(superposition,[status(thm)],[c_13694,c_51]) ).

cnf(c_16374,plain,
    aInteger0(sP5_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_16373,c_50]) ).

cnf(c_17598,plain,
    ( ~ aInteger0(sz10)
    | aInteger0(smndt0(sz10)) ),
    inference(instantiation,[status(thm)],[c_51]) ).

cnf(c_19081,plain,
    ( ~ isPrime0(sK26(sz10))
    | ~ sP8(sz10) ),
    inference(superposition,[status(thm)],[c_182,c_328]) ).

cnf(c_19714,plain,
    ( ~ aDivisorOf0(X0,smndt0(sz10))
    | ~ isPrime0(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_85,c_50,c_85,c_17598]) ).

cnf(c_19717,plain,
    ( ~ aDivisorOf0(X0,sP5_iProver_def)
    | ~ isPrime0(X0) ),
    inference(light_normalisation,[status(thm)],[c_19714,c_13694]) ).

cnf(c_19722,plain,
    ( ~ isPrime0(sK26(sP5_iProver_def))
    | ~ sP8(sP5_iProver_def) ),
    inference(superposition,[status(thm)],[c_182,c_19717]) ).

cnf(c_20585,plain,
    ~ sP8(sz10),
    inference(global_subsumption_just,[status(thm)],[c_19081,c_6833]) ).

cnf(c_21948,plain,
    ~ sP8(sP5_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_19722,c_181]) ).

cnf(c_23956,plain,
    ( ~ aInteger0(X0)
    | X0 = sz10
    | X0 = sP5_iProver_def
    | isPrime0(sK10(X0)) ),
    inference(light_normalisation,[status(thm)],[c_83,c_13694]) ).

cnf(c_26464,plain,
    ( ~ aInteger0(X0)
    | X0 = sz10
    | X0 = sP5_iProver_def
    | aDivisorOf0(sK10(X0),X0) ),
    inference(light_normalisation,[status(thm)],[c_84,c_13694]) ).

cnf(c_26477,plain,
    ( ~ isPrime0(sK10(X0))
    | ~ aInteger0(X0)
    | X0 = sz10
    | X0 = sP5_iProver_def
    | aElementOf0(X0,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_26464,c_13702]) ).

cnf(c_40375,plain,
    ( ~ aInteger0(X0)
    | X0 = sz10
    | X0 = sP5_iProver_def
    | aElementOf0(X0,sP3_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_26477,c_23956]) ).

cnf(c_40393,plain,
    ( ~ aElementOf0(X0,sP4_iProver_def)
    | ~ aInteger0(X0)
    | X0 = sz10
    | X0 = sP5_iProver_def ),
    inference(superposition,[status(thm)],[c_40375,c_13710]) ).

cnf(c_41052,plain,
    ( ~ aElementOf0(X0,sP4_iProver_def)
    | X0 = sz10
    | X0 = sP5_iProver_def ),
    inference(global_subsumption_just,[status(thm)],[c_40393,c_13709,c_40393]) ).

cnf(c_41079,plain,
    ( sz10 = sK28
    | sK28 = sP5_iProver_def ),
    inference(superposition,[status(thm)],[c_13712,c_41052]) ).

cnf(c_41402,plain,
    ( ~ aElementOf0(sK28,sP4_iProver_def)
    | sK28 = sP5_iProver_def ),
    inference(superposition,[status(thm)],[c_41079,c_13713]) ).

cnf(c_41411,plain,
    ( ~ aElementOf0(sz10,sP4_iProver_def)
    | sK28 = sP5_iProver_def ),
    inference(superposition,[status(thm)],[c_41079,c_41402]) ).

cnf(c_41985,plain,
    ( ~ aInteger0(sz10)
    | sK28 = sP5_iProver_def
    | aElementOf0(sz10,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_13711,c_41411]) ).

cnf(c_41986,plain,
    ( sK28 = sP5_iProver_def
    | aElementOf0(sz10,sP3_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41985,c_50]) ).

cnf(c_42026,plain,
    ( sK28 = sP5_iProver_def
    | sP8(sz10) ),
    inference(superposition,[status(thm)],[c_41986,c_13698]) ).

cnf(c_42027,plain,
    sK28 = sP5_iProver_def,
    inference(forward_subsumption_resolution,[status(thm)],[c_42026,c_20585]) ).

cnf(c_42029,plain,
    ( sP5_iProver_def != sP5_iProver_def
    | ~ aElementOf0(sP5_iProver_def,sP4_iProver_def) ),
    inference(demodulation,[status(thm)],[c_13714,c_42027]) ).

cnf(c_42033,plain,
    ~ aElementOf0(sP5_iProver_def,sP4_iProver_def),
    inference(equality_resolution_simp,[status(thm)],[c_42029]) ).

cnf(c_42034,plain,
    ( ~ aInteger0(sP5_iProver_def)
    | aElementOf0(sP5_iProver_def,sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_13711,c_42033]) ).

cnf(c_42035,plain,
    aElementOf0(sP5_iProver_def,sP3_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_42034,c_16374]) ).

cnf(c_43462,plain,
    sP8(sP5_iProver_def),
    inference(superposition,[status(thm)],[c_42035,c_13698]) ).

cnf(c_43463,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_43462,c_21948]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM448+5 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May  2 19:19:33 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  Running first-order theorem proving
% 0.18/0.46  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
% 11.98/2.67  % SZS status Started for theBenchmark.p
% 11.98/2.67  % SZS status Theorem for theBenchmark.p
% 11.98/2.67  
% 11.98/2.67  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 11.98/2.67  
% 11.98/2.67  ------  iProver source info
% 11.98/2.67  
% 11.98/2.67  git: date: 2024-05-02 19:28:25 +0000
% 11.98/2.67  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 11.98/2.67  git: non_committed_changes: false
% 11.98/2.67  
% 11.98/2.67  ------ Parsing...
% 11.98/2.67  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 11.98/2.67  
% 11.98/2.67  ------ 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 
% 11.98/2.67  
% 11.98/2.67  ------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 11.98/2.67  
% 11.98/2.67  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 11.98/2.67  ------ Proving...
% 11.98/2.67  ------ Problem Properties 
% 11.98/2.67  
% 11.98/2.67  
% 11.98/2.67  clauses                                 162
% 11.98/2.67  conjectures                             21
% 11.98/2.67  EPR                                     42
% 11.98/2.67  Horn                                    114
% 11.98/2.67  unary                                   9
% 11.98/2.67  binary                                  40
% 11.98/2.67  lits                                    558
% 11.98/2.67  lits eq                                 76
% 11.98/2.67  fd_pure                                 0
% 11.98/2.67  fd_pseudo                               0
% 11.98/2.67  fd_cond                                 24
% 11.98/2.67  fd_pseudo_cond                          9
% 11.98/2.67  AC symbols                              0
% 11.98/2.67  
% 11.98/2.67  ------ Schedule dynamic 5 is on 
% 11.98/2.67  
% 11.98/2.67  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 11.98/2.67  
% 11.98/2.67  
% 11.98/2.67  ------ 
% 11.98/2.67  Current options:
% 11.98/2.67  ------ 
% 11.98/2.67  
% 11.98/2.67  
% 11.98/2.67  
% 11.98/2.67  
% 11.98/2.67  ------ Proving...
% 11.98/2.67  
% 11.98/2.67  
% 11.98/2.67  % SZS status Theorem for theBenchmark.p
% 11.98/2.67  
% 11.98/2.67  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.98/2.67  
% 11.98/2.68  
%------------------------------------------------------------------------------