TSTP Solution File: NUM447+5 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:37:35 EDT 2023

% Result   : Theorem 6.66s 6.71s
% Output   : CNFRefutation 6.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  166 (  22 unt;  45 typ;   0 def)
%            Number of atoms       :  706 ( 173 equ)
%            Maximal formula atoms :  125 (   5 avg)
%            Number of connectives :  923 ( 338   ~; 405   |; 152   &)
%                                         (   4 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   47 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   63 (  36   >;  27   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :   35 (  35 usr;   9 con; 0-3 aty)
%            Number of variables   :  178 (   2 sgn;  65   !;  19   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aInteger0: $i > $o ).

tff(decl_23,type,
    sz00: $i ).

tff(decl_24,type,
    sz10: $i ).

tff(decl_25,type,
    smndt0: $i > $i ).

tff(decl_26,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_28,type,
    aDivisorOf0: ( $i * $i ) > $o ).

tff(decl_29,type,
    sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).

tff(decl_30,type,
    isPrime0: $i > $o ).

tff(decl_31,type,
    aSet0: $i > $o ).

tff(decl_32,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_33,type,
    aSubsetOf0: ( $i * $i ) > $o ).

tff(decl_34,type,
    isFinite0: $i > $o ).

tff(decl_35,type,
    cS1395: $i ).

tff(decl_36,type,
    sdtbsmnsldt0: ( $i * $i ) > $i ).

tff(decl_37,type,
    sdtslmnbsdt0: ( $i * $i ) > $i ).

tff(decl_38,type,
    sbsmnsldt0: $i > $i ).

tff(decl_39,type,
    stldt0: $i > $i ).

tff(decl_40,type,
    szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).

tff(decl_41,type,
    isOpen0: $i > $o ).

tff(decl_42,type,
    isClosed0: $i > $o ).

tff(decl_43,type,
    xS: $i ).

tff(decl_44,type,
    cS2043: $i ).

tff(decl_45,type,
    xn: $i ).

tff(decl_46,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk2_1: $i > $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk6_1: $i > $i ).

tff(decl_52,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk13_1: $i > $i ).

tff(decl_59,type,
    esk14_1: $i > $i ).

tff(decl_60,type,
    esk15_1: $i > $i ).

tff(decl_61,type,
    esk16_1: $i > $i ).

tff(decl_62,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_63,type,
    esk18_3: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk19_0: $i ).

tff(decl_65,type,
    esk20_0: $i ).

tff(decl_66,type,
    esk21_0: $i ).

fof(mAddZero,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).

fof(mAddNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtpldt0(X1,smndt0(X1)) = sz00
        & sz00 = sdtpldt0(smndt0(X1),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).

fof(mIntZero,axiom,
    aInteger0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).

fof(mIntNeg,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => aInteger0(smndt0(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).

fof(mArSeq,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => ! [X3] :
          ( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
        <=> ( aSet0(X3)
            & ! [X4] :
                ( aElementOf0(X4,X3)
              <=> ( aInteger0(X4)
                  & sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeq) ).

fof(m__2046,hypothesis,
    ( aSet0(xS)
    & ! [X1] :
        ( ( aElementOf0(X1,xS)
         => ? [X2] :
              ( aInteger0(X2)
              & X2 != sz00
              & isPrime0(X2)
              & aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
              & ! [X3] :
                  ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                   => ( aInteger0(X3)
                      & ? [X4] :
                          ( aInteger0(X4)
                          & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                      & aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                      & sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                  & ( ( aInteger0(X3)
                      & ( ? [X4] :
                            ( aInteger0(X4)
                            & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                        | aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                        | sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                   => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
              & szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
        & ( ? [X2] :
              ( aInteger0(X2)
              & X2 != sz00
              & isPrime0(X2)
              & ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                  & ! [X3] :
                      ( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
                       => ( aInteger0(X3)
                          & ? [X4] :
                              ( aInteger0(X4)
                              & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                          & aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                          & sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                      & ( ( aInteger0(X3)
                          & ( ? [X4] :
                                ( aInteger0(X4)
                                & sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
                            | aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
                            | sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
                       => aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
               => szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
         => aElementOf0(X1,xS) ) )
    & xS = cS2043 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).

fof(m__,conjecture,
    ( ( ( ? [X1] :
            ( aElementOf0(X1,xS)
            & aElementOf0(xn,X1) )
        & aElementOf0(xn,sbsmnsldt0(xS)) )
     => ? [X1] :
          ( ( ( aInteger0(X1)
              & X1 != sz00
              & ? [X2] :
                  ( aInteger0(X2)
                  & sdtasdt0(X1,X2) = xn ) )
            | aDivisorOf0(X1,xn) )
          & isPrime0(X1) ) )
    & ( ? [X1] :
          ( aInteger0(X1)
          & X1 != sz00
          & ? [X2] :
              ( aInteger0(X2)
              & sdtasdt0(X1,X2) = xn )
          & aDivisorOf0(X1,xn)
          & isPrime0(X1) )
     => ( ? [X1] :
            ( aElementOf0(X1,xS)
            & aElementOf0(xn,X1) )
        | aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mMulZero,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).

fof(mEquModRef,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & X2 != sz00 )
     => sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).

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

fof(mZeroDiv,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).

fof(mDivisor,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ! [X2] :
          ( aDivisorOf0(X2,X1)
        <=> ( aInteger0(X2)
            & X2 != sz00
            & ? [X3] :
                ( aInteger0(X3)
                & sdtasdt0(X2,X3) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).

fof(mEquMod,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3)
        & X3 != sz00 )
     => ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
      <=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).

fof(mDistrib,axiom,
    ! [X1,X2,X3] :
      ( ( aInteger0(X1)
        & aInteger0(X2)
        & aInteger0(X3) )
     => ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
        & sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).

fof(mMulOne,axiom,
    ! [X1] :
      ( aInteger0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).

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

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aInteger0(X1)
        & aInteger0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).

fof(c_0_17,plain,
    ! [X15] :
      ( ( sdtpldt0(X15,sz00) = X15
        | ~ aInteger0(X15) )
      & ( X15 = sdtpldt0(sz00,X15)
        | ~ aInteger0(X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).

fof(c_0_18,plain,
    ! [X16] :
      ( ( sdtpldt0(X16,smndt0(X16)) = sz00
        | ~ aInteger0(X16) )
      & ( sz00 = sdtpldt0(smndt0(X16),X16)
        | ~ aInteger0(X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).

cnf(c_0_19,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,plain,
    ( sz00 = sdtpldt0(smndt0(X1),X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_21,plain,
    aInteger0(sz00),
    inference(split_conjunct,[status(thm)],[mIntZero]) ).

fof(c_0_22,plain,
    ! [X5] :
      ( ~ aInteger0(X5)
      | aInteger0(smndt0(X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).

fof(c_0_23,plain,
    ! [X90,X91,X92,X93,X94,X95] :
      ( ( aSet0(X92)
        | X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 )
      & ( aInteger0(X93)
        | ~ aElementOf0(X93,X92)
        | X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(X93,X90,X91)
        | ~ aElementOf0(X93,X92)
        | X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 )
      & ( ~ aInteger0(X94)
        | ~ sdteqdtlpzmzozddtrp0(X94,X90,X91)
        | aElementOf0(X94,X92)
        | X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 )
      & ( ~ aElementOf0(esk11_3(X90,X91,X95),X95)
        | ~ aInteger0(esk11_3(X90,X91,X95))
        | ~ sdteqdtlpzmzozddtrp0(esk11_3(X90,X91,X95),X90,X91)
        | ~ aSet0(X95)
        | X95 = szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 )
      & ( aInteger0(esk11_3(X90,X91,X95))
        | aElementOf0(esk11_3(X90,X91,X95),X95)
        | ~ aSet0(X95)
        | X95 = szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 )
      & ( sdteqdtlpzmzozddtrp0(esk11_3(X90,X91,X95),X90,X91)
        | aElementOf0(esk11_3(X90,X91,X95),X95)
        | ~ aSet0(X95)
        | X95 = szAzrzSzezqlpdtcmdtrp0(X90,X91)
        | ~ aInteger0(X90)
        | ~ aInteger0(X91)
        | X91 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mArSeq])])])])])]) ).

fof(c_0_24,hypothesis,
    ! [X113,X115,X117,X118,X119,X120,X121,X123,X124] :
      ( aSet0(xS)
      & ( aInteger0(esk16_1(X113))
        | ~ aElementOf0(X113,xS) )
      & ( esk16_1(X113) != sz00
        | ~ aElementOf0(X113,xS) )
      & ( isPrime0(esk16_1(X113))
        | ~ aElementOf0(X113,xS) )
      & ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( aInteger0(X115)
        | ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( aInteger0(esk17_2(X113,X115))
        | ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( sdtasdt0(esk16_1(X113),esk17_2(X113,X115)) = sdtpldt0(X115,smndt0(sz00))
        | ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( aDivisorOf0(esk16_1(X113),sdtpldt0(X115,smndt0(sz00)))
        | ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( sdteqdtlpzmzozddtrp0(X115,sz00,esk16_1(X113))
        | ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( ~ aInteger0(X118)
        | sdtasdt0(esk16_1(X113),X118) != sdtpldt0(X117,smndt0(sz00))
        | ~ aInteger0(X117)
        | aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( ~ aDivisorOf0(esk16_1(X113),sdtpldt0(X117,smndt0(sz00)))
        | ~ aInteger0(X117)
        | aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( ~ sdteqdtlpzmzozddtrp0(X117,sz00,esk16_1(X113))
        | ~ aInteger0(X117)
        | aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
        | ~ aElementOf0(X113,xS) )
      & ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)) = X113
        | ~ aElementOf0(X113,xS) )
      & ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( aInteger0(X121)
        | ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( aInteger0(esk18_3(X119,X120,X121))
        | ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( sdtasdt0(X120,esk18_3(X119,X120,X121)) = sdtpldt0(X121,smndt0(sz00))
        | ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( aDivisorOf0(X120,sdtpldt0(X121,smndt0(sz00)))
        | ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( sdteqdtlpzmzozddtrp0(X121,sz00,X120)
        | ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( ~ aInteger0(X124)
        | sdtasdt0(X120,X124) != sdtpldt0(X123,smndt0(sz00))
        | ~ aInteger0(X123)
        | aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( ~ aDivisorOf0(X120,sdtpldt0(X123,smndt0(sz00)))
        | ~ aInteger0(X123)
        | aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( ~ sdteqdtlpzmzozddtrp0(X123,sz00,X120)
        | ~ aInteger0(X123)
        | aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & ( szAzrzSzezqlpdtcmdtrp0(sz00,X120) != X119
        | ~ aInteger0(X120)
        | X120 = sz00
        | ~ isPrime0(X120)
        | aElementOf0(X119,xS) )
      & xS = cS2043 ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2046])])])])])]) ).

cnf(c_0_25,plain,
    ( smndt0(sz00) = sz00
    | ~ aInteger0(smndt0(sz00)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).

cnf(c_0_26,plain,
    ( aInteger0(smndt0(X1))
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_27,plain,
    ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | X3 = sz00
    | ~ aElementOf0(X1,X4)
    | X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_28,hypothesis,
    ( aDivisorOf0(esk16_1(X1),sdtpldt0(X2,smndt0(sz00)))
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,plain,
    smndt0(sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_21])]) ).

cnf(c_0_30,plain,
    ( X1 = sz00
    | sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
    | ~ aInteger0(X1)
    | ~ aInteger0(X3) ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_31,hypothesis,
    ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_32,hypothesis,
    ( aInteger0(esk16_1(X1))
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_33,hypothesis,
    ( esk16_1(X1) != sz00
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_34,hypothesis,
    ( aInteger0(X1)
    | ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
    | ~ aElementOf0(X2,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_35,negated_conjecture,
    ~ ( ( ( ? [X1] :
              ( aElementOf0(X1,xS)
              & aElementOf0(xn,X1) )
          & aElementOf0(xn,sbsmnsldt0(xS)) )
       => ? [X1] :
            ( ( ( aInteger0(X1)
                & X1 != sz00
                & ? [X2] :
                    ( aInteger0(X2)
                    & sdtasdt0(X1,X2) = xn ) )
              | aDivisorOf0(X1,xn) )
            & isPrime0(X1) ) )
      & ( ? [X1] :
            ( aInteger0(X1)
            & X1 != sz00
            & ? [X2] :
                ( aInteger0(X2)
                & sdtasdt0(X1,X2) = xn )
            & aDivisorOf0(X1,xn)
            & isPrime0(X1) )
       => ( ? [X1] :
              ( aElementOf0(X1,xS)
              & aElementOf0(xn,X1) )
          | aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_36,hypothesis,
    ( aDivisorOf0(esk16_1(X1),sdtpldt0(X2,sz00))
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(rw,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_37,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
    | ~ sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2))
    | ~ aInteger0(X1)
    | ~ aElementOf0(X2,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_38,hypothesis,
    ( sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2))
    | ~ aElementOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21])]),c_0_32]),c_0_33]) ).

cnf(c_0_39,hypothesis,
    ( aInteger0(X1)
    | ~ aElementOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_31]) ).

cnf(c_0_40,hypothesis,
    ( X1 = sz00
    | aElementOf0(X2,xS)
    | szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X2
    | ~ aInteger0(X1)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_41,negated_conjecture,
    ! [X126,X127,X130] :
      ( ( aInteger0(esk20_0)
        | aElementOf0(esk19_0,xS) )
      & ( esk20_0 != sz00
        | aElementOf0(esk19_0,xS) )
      & ( aInteger0(esk21_0)
        | aElementOf0(esk19_0,xS) )
      & ( sdtasdt0(esk20_0,esk21_0) = xn
        | aElementOf0(esk19_0,xS) )
      & ( aDivisorOf0(esk20_0,xn)
        | aElementOf0(esk19_0,xS) )
      & ( isPrime0(esk20_0)
        | aElementOf0(esk19_0,xS) )
      & ( ~ aElementOf0(X130,xS)
        | ~ aElementOf0(xn,X130)
        | aElementOf0(esk19_0,xS) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | aElementOf0(esk19_0,xS) )
      & ( aInteger0(esk20_0)
        | aElementOf0(xn,esk19_0) )
      & ( esk20_0 != sz00
        | aElementOf0(xn,esk19_0) )
      & ( aInteger0(esk21_0)
        | aElementOf0(xn,esk19_0) )
      & ( sdtasdt0(esk20_0,esk21_0) = xn
        | aElementOf0(xn,esk19_0) )
      & ( aDivisorOf0(esk20_0,xn)
        | aElementOf0(xn,esk19_0) )
      & ( isPrime0(esk20_0)
        | aElementOf0(xn,esk19_0) )
      & ( ~ aElementOf0(X130,xS)
        | ~ aElementOf0(xn,X130)
        | aElementOf0(xn,esk19_0) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | aElementOf0(xn,esk19_0) )
      & ( aInteger0(esk20_0)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( esk20_0 != sz00
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( aInteger0(esk21_0)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( sdtasdt0(esk20_0,esk21_0) = xn
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( aDivisorOf0(esk20_0,xn)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( isPrime0(esk20_0)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( ~ aElementOf0(X130,xS)
        | ~ aElementOf0(xn,X130)
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | aElementOf0(xn,sbsmnsldt0(xS)) )
      & ( aInteger0(esk20_0)
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( esk20_0 != sz00
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( aInteger0(esk21_0)
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( sdtasdt0(esk20_0,esk21_0) = xn
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( aDivisorOf0(esk20_0,xn)
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( isPrime0(esk20_0)
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( ~ aElementOf0(X130,xS)
        | ~ aElementOf0(xn,X130)
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | ~ aInteger0(X126)
        | X126 = sz00
        | ~ aInteger0(X127)
        | sdtasdt0(X126,X127) != xn
        | ~ isPrime0(X126) )
      & ( aInteger0(esk20_0)
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( esk20_0 != sz00
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( aInteger0(esk21_0)
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( sdtasdt0(esk20_0,esk21_0) = xn
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( aDivisorOf0(esk20_0,xn)
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( isPrime0(esk20_0)
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( ~ aElementOf0(X130,xS)
        | ~ aElementOf0(xn,X130)
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) )
      & ( ~ aElementOf0(xn,sbsmnsldt0(xS))
        | ~ aDivisorOf0(X126,xn)
        | ~ isPrime0(X126) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])]) ).

cnf(c_0_42,hypothesis,
    ( aDivisorOf0(esk16_1(X1),X2)
    | ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_19]),c_0_34]) ).

cnf(c_0_43,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
    | ~ aElementOf0(X2,xS)
    | ~ aElementOf0(X1,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).

cnf(c_0_44,hypothesis,
    ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
    | ~ aInteger0(X1)
    | sdtasdt0(esk16_1(X2),X1) != sdtpldt0(X3,smndt0(sz00))
    | ~ aInteger0(X3)
    | ~ aElementOf0(X2,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_45,hypothesis,
    ( X1 = sz00
    | aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),xS)
    | ~ isPrime0(X1)
    | ~ aInteger0(X1) ),
    inference(er,[status(thm)],[c_0_40]) ).

cnf(c_0_46,hypothesis,
    ( isPrime0(esk16_1(X1))
    | ~ aElementOf0(X1,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_47,negated_conjecture,
    ( ~ aElementOf0(xn,sbsmnsldt0(xS))
    | ~ aDivisorOf0(X1,xn)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_48,hypothesis,
    ( aDivisorOf0(esk16_1(X1),X2)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(X2,X1) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    ( aElementOf0(xn,sbsmnsldt0(xS))
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_50,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
    | sdtasdt0(esk16_1(X2),X3) != sdtpldt0(X1,sz00)
    | ~ aElementOf0(X2,xS)
    | ~ aInteger0(X1)
    | ~ aInteger0(X3) ),
    inference(rw,[status(thm)],[c_0_44,c_0_29]) ).

cnf(c_0_51,hypothesis,
    ( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)),xS)
    | ~ aElementOf0(X1,xS) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32]),c_0_33]) ).

fof(c_0_52,plain,
    ! [X26] :
      ( ( sdtasdt0(X26,sz00) = sz00
        | ~ aInteger0(X26) )
      & ( sz00 = sdtasdt0(sz00,X26)
        | ~ aInteger0(X26) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).

fof(c_0_53,plain,
    ! [X38,X39] :
      ( ~ aInteger0(X38)
      | ~ aInteger0(X39)
      | X39 = sz00
      | sdteqdtlpzmzozddtrp0(X38,X38,X39) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).

cnf(c_0_54,negated_conjecture,
    ( ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46]),c_0_49]) ).

cnf(c_0_55,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))))
    | sdtasdt0(esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))),X3) != sdtpldt0(X1,sz00)
    | ~ aElementOf0(X2,xS)
    | ~ aInteger0(X1)
    | ~ aInteger0(X3) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_56,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_57,plain,
    ( X2 = sz00
    | sdteqdtlpzmzozddtrp0(X1,X1,X2)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_58,hypothesis,
    aInteger0(xn),
    inference(split_conjunct,[status(thm)],[m__2106]) ).

cnf(c_0_59,hypothesis,
    ( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
    | ~ aElementOf0(X1,xS) ),
    inference(spm,[status(thm)],[c_0_54,c_0_51]) ).

cnf(c_0_60,hypothesis,
    ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))))
    | sdtpldt0(X1,sz00) != sz00
    | ~ aElementOf0(X2,xS)
    | ~ aInteger0(esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_21])]) ).

fof(c_0_61,plain,
    ! [X28,X29] :
      ( ~ aInteger0(X28)
      | ~ aInteger0(X29)
      | sdtasdt0(X28,X29) != sz00
      | X28 = sz00
      | X29 = sz00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).

fof(c_0_62,plain,
    ! [X30,X31,X33,X34] :
      ( ( aInteger0(X31)
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( X31 != sz00
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( aInteger0(esk1_2(X30,X31))
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( sdtasdt0(X31,esk1_2(X30,X31)) = X30
        | ~ aDivisorOf0(X31,X30)
        | ~ aInteger0(X30) )
      & ( ~ aInteger0(X33)
        | X33 = sz00
        | ~ aInteger0(X34)
        | sdtasdt0(X33,X34) != X30
        | aDivisorOf0(X33,X30)
        | ~ aInteger0(X30) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivisor])])])])])]) ).

fof(c_0_63,plain,
    ! [X35,X36,X37] :
      ( ( ~ sdteqdtlpzmzozddtrp0(X35,X36,X37)
        | aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
        | ~ aInteger0(X35)
        | ~ aInteger0(X36)
        | ~ aInteger0(X37)
        | X37 = sz00 )
      & ( ~ aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
        | sdteqdtlpzmzozddtrp0(X35,X36,X37)
        | ~ aInteger0(X35)
        | ~ aInteger0(X36)
        | ~ aInteger0(X37)
        | X37 = sz00 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).

cnf(c_0_64,hypothesis,
    ( xn = sz00
    | sdteqdtlpzmzozddtrp0(X1,X1,xn)
    | ~ aInteger0(X1) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_65,hypothesis,
    ( sdtpldt0(xn,sz00) != sz00
    | ~ aElementOf0(X1,xS) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_58])]),c_0_32]),c_0_51]) ).

cnf(c_0_66,negated_conjecture,
    ( isPrime0(esk20_0)
    | aElementOf0(esk19_0,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_67,negated_conjecture,
    ( aInteger0(esk20_0)
    | aElementOf0(esk19_0,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_68,negated_conjecture,
    ( aElementOf0(esk19_0,xS)
    | esk20_0 != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_69,plain,
    ( X1 = sz00
    | X2 = sz00
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | sdtasdt0(X1,X2) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_70,plain,
    ( sdtasdt0(X1,esk1_2(X2,X1)) = X2
    | ~ aDivisorOf0(X1,X2)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_71,plain,
    ( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
    | X3 = sz00
    | ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_72,hypothesis,
    ( xn = sz00
    | sdteqdtlpzmzozddtrp0(sz00,sz00,xn) ),
    inference(spm,[status(thm)],[c_0_64,c_0_21]) ).

cnf(c_0_73,plain,
    sdtpldt0(sz00,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_21])]) ).

cnf(c_0_74,hypothesis,
    ( xn != sz00
    | ~ aElementOf0(X1,xS) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_19]),c_0_58])]) ).

cnf(c_0_75,negated_conjecture,
    ( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS)
    | aElementOf0(esk19_0,xS) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_66]),c_0_67]),c_0_68]) ).

cnf(c_0_76,plain,
    ( esk1_2(sz00,X1) = sz00
    | X1 = sz00
    | ~ aDivisorOf0(X1,sz00)
    | ~ aInteger0(esk1_2(sz00,X1))
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70])]),c_0_21])]) ).

cnf(c_0_77,plain,
    ( aInteger0(esk1_2(X1,X2))
    | ~ aDivisorOf0(X2,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_78,hypothesis,
    ( xn = sz00
    | aDivisorOf0(xn,sz00) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_29]),c_0_73]),c_0_58]),c_0_21])]) ).

cnf(c_0_79,negated_conjecture,
    xn != sz00,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_74]) ).

fof(c_0_80,plain,
    ! [X23,X24,X25] :
      ( ( sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25))
        | ~ aInteger0(X23)
        | ~ aInteger0(X24)
        | ~ aInteger0(X25) )
      & ( sdtasdt0(sdtpldt0(X23,X24),X25) = sdtpldt0(sdtasdt0(X23,X25),sdtasdt0(X24,X25))
        | ~ aInteger0(X23)
        | ~ aInteger0(X24)
        | ~ aInteger0(X25) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).

fof(c_0_81,plain,
    ! [X22] :
      ( ( sdtasdt0(X22,sz10) = X22
        | ~ aInteger0(X22) )
      & ( X22 = sdtasdt0(sz10,X22)
        | ~ aInteger0(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).

cnf(c_0_82,plain,
    ( esk1_2(sz00,X1) = sz00
    | X1 = sz00
    | ~ aDivisorOf0(X1,sz00)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_21])]) ).

cnf(c_0_83,hypothesis,
    aDivisorOf0(xn,sz00),
    inference(sr,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_84,plain,
    ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | ~ aInteger0(X1)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_85,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_81]) ).

cnf(c_0_86,plain,
    aInteger0(sz10),
    inference(split_conjunct,[status(thm)],[mIntOne]) ).

cnf(c_0_87,hypothesis,
    esk1_2(sz00,xn) = sz00,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_58])]),c_0_79]) ).

cnf(c_0_88,plain,
    ( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).

cnf(c_0_89,hypothesis,
    sdtasdt0(xn,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_87]),c_0_83]),c_0_21])]) ).

cnf(c_0_90,hypothesis,
    sdtasdt0(xn,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_21]),c_0_58])]) ).

cnf(c_0_91,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_92,hypothesis,
    sdtpldt0(sz00,xn) = sdtasdt0(xn,sz10),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_86])]) ).

cnf(c_0_93,plain,
    ( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).

fof(c_0_94,plain,
    ! [X13,X14] :
      ( ~ aInteger0(X13)
      | ~ aInteger0(X14)
      | sdtpldt0(X13,X14) = sdtpldt0(X14,X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_95,hypothesis,
    sdtasdt0(xn,sz10) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_58])]) ).

cnf(c_0_96,plain,
    ( sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | X1 = sz00
    | ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
    | ~ aInteger0(X2)
    | ~ aInteger0(X3)
    | ~ aInteger0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_97,hypothesis,
    sdtasdt0(xn,sdtpldt0(sz10,sz00)) = sdtpldt0(xn,sz00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_89]),c_0_21]),c_0_58])]) ).

cnf(c_0_98,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_94]) ).

cnf(c_0_99,hypothesis,
    sdtasdt0(xn,sdtpldt0(sz00,sz10)) = xn,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_92]),c_0_95]) ).

cnf(c_0_100,plain,
    ( X1 = sz00
    | sdteqdtlpzmzozddtrp0(X2,sz00,X1)
    | ~ aDivisorOf0(X1,sdtpldt0(X2,sz00))
    | ~ aInteger0(X2)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_29]),c_0_21])]) ).

cnf(c_0_101,hypothesis,
    sdtpldt0(xn,sz00) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_21]),c_0_86])]) ).

cnf(c_0_102,negated_conjecture,
    ( aElementOf0(xn,esk19_0)
    | esk20_0 != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_103,negated_conjecture,
    ( isPrime0(esk20_0)
    | aElementOf0(xn,esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_104,negated_conjecture,
    ( aInteger0(esk20_0)
    | aElementOf0(xn,esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_105,plain,
    ( aElementOf0(X1,X4)
    | X3 = sz00
    | ~ aInteger0(X1)
    | ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
    | X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
    | ~ aInteger0(X2)
    | ~ aInteger0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_106,hypothesis,
    ( X1 = sz00
    | sdteqdtlpzmzozddtrp0(xn,sz00,X1)
    | ~ aDivisorOf0(X1,xn)
    | ~ aInteger0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_58])]) ).

cnf(c_0_107,negated_conjecture,
    ( aDivisorOf0(esk20_0,xn)
    | aElementOf0(esk19_0,xS) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_108,negated_conjecture,
    esk20_0 != sz00,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_68]),c_0_102]) ).

cnf(c_0_109,negated_conjecture,
    ( aElementOf0(esk19_0,xS)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_110,negated_conjecture,
    ( aDivisorOf0(esk20_0,xn)
    | aElementOf0(xn,esk19_0) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_111,negated_conjecture,
    ( aElementOf0(xn,esk19_0)
    | ~ aElementOf0(X1,xS)
    | ~ aElementOf0(xn,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_112,negated_conjecture,
    ( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS)
    | aElementOf0(xn,esk19_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_103]),c_0_104]),c_0_102]) ).

cnf(c_0_113,plain,
    ( X1 = sz00
    | aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
    | ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
    | ~ aInteger0(X1)
    | ~ aInteger0(X3)
    | ~ aInteger0(X2) ),
    inference(er,[status(thm)],[c_0_105]) ).

cnf(c_0_114,negated_conjecture,
    ( aElementOf0(esk19_0,xS)
    | sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_67]) ).

cnf(c_0_115,negated_conjecture,
    ( aElementOf0(esk19_0,xS)
    | ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0)) ),
    inference(spm,[status(thm)],[c_0_109,c_0_75]) ).

cnf(c_0_116,negated_conjecture,
    ( aElementOf0(xn,esk19_0)
    | sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_110]),c_0_108]),c_0_104]) ).

cnf(c_0_117,negated_conjecture,
    ( aElementOf0(xn,esk19_0)
    | ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0)) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_118,negated_conjecture,
    aElementOf0(esk19_0,xS),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_21]),c_0_58])]),c_0_108]),c_0_67]),c_0_115]) ).

cnf(c_0_119,negated_conjecture,
    aElementOf0(xn,esk19_0),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_116]),c_0_21]),c_0_58])]),c_0_108]),c_0_104]),c_0_117]) ).

cnf(c_0_120,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_118]),c_0_119])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34  % CPULimit   : 300
% 0.19/0.34  % WCLimit    : 300
% 0.19/0.34  % DateTime   : Fri Aug 25 15:29:22 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 6.66/6.71  % Version  : CSE_E---1.5
% 6.66/6.71  % Problem  : theBenchmark.p
% 6.66/6.71  % Proof found
% 6.66/6.71  % SZS status Theorem for theBenchmark.p
% 6.66/6.71  % SZS output start Proof
% See solution above
% 6.66/6.72  % Total time : 6.151000 s
% 6.66/6.72  % SZS output end Proof
% 6.66/6.72  % Total time : 6.156000 s
%------------------------------------------------------------------------------