TSTP Solution File: NUM481+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM481+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 10:37:57 EDT 2023

% Result   : Theorem 0.19s 0.62s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   82 (  14 unt;  19 typ;   0 def)
%            Number of atoms       :  413 ( 170 equ)
%            Maximal formula atoms :  128 (   6 avg)
%            Number of connectives :  557 ( 207   ~; 243   |;  84   &)
%                                         (   1 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   36 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  16   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :  107 (   0 sgn;  44   !;  13   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aNaturalNumber0: $i > $o ).

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

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

tff(decl_25,type,
    sdtpldt0: ( $i * $i ) > $i ).

tff(decl_26,type,
    sdtasdt0: ( $i * $i ) > $i ).

tff(decl_27,type,
    sdtlseqdt0: ( $i * $i ) > $o ).

tff(decl_28,type,
    sdtmndt0: ( $i * $i ) > $i ).

tff(decl_29,type,
    iLess0: ( $i * $i ) > $o ).

tff(decl_30,type,
    doDivides0: ( $i * $i ) > $o ).

tff(decl_31,type,
    sdtsldt0: ( $i * $i ) > $i ).

tff(decl_32,type,
    isPrime0: $i > $o ).

tff(decl_33,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk3_1: $i > $i ).

tff(decl_36,type,
    esk4_0: $i ).

tff(decl_37,type,
    esk5_1: $i > $i ).

tff(decl_38,type,
    esk6_1: $i > $i ).

tff(decl_39,type,
    esk7_1: $i > $i ).

tff(decl_40,type,
    esk8_1: $i > $i ).

fof(m__,conjecture,
    ! [X1] :
      ( ( aNaturalNumber0(X1)
        & X1 != sz00
        & X1 != sz10 )
     => ( ! [X2] :
            ( ( aNaturalNumber0(X2)
              & X2 != sz00
              & X2 != sz10 )
           => ( iLess0(X2,X1)
             => ? [X3] :
                  ( aNaturalNumber0(X3)
                  & ? [X4] :
                      ( aNaturalNumber0(X4)
                      & X2 = sdtasdt0(X3,X4) )
                  & doDivides0(X3,X2)
                  & X3 != sz00
                  & X3 != sz10
                  & ! [X4] :
                      ( ( aNaturalNumber0(X4)
                        & ( ? [X5] :
                              ( aNaturalNumber0(X5)
                              & X3 = sdtasdt0(X4,X5) )
                          | doDivides0(X4,X3) ) )
                     => ( X4 = sz10
                        | X4 = X3 ) )
                  & isPrime0(X3) ) ) )
       => ? [X2] :
            ( aNaturalNumber0(X2)
            & ( ? [X3] :
                  ( aNaturalNumber0(X3)
                  & X1 = sdtasdt0(X2,X3) )
              | doDivides0(X2,X1) )
            & ( ( X2 != sz00
                & X2 != sz10
                & ! [X3] :
                    ( ( aNaturalNumber0(X3)
                      & ? [X4] :
                          ( aNaturalNumber0(X4)
                          & X2 = sdtasdt0(X3,X4) )
                      & doDivides0(X3,X2) )
                   => ( X3 = sz10
                      | X3 = X2 ) ) )
              | isPrime0(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).

fof(m_MulUnit,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).

fof(mSortsC_01,axiom,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).

fof(mDivLE,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( doDivides0(X1,X2)
          & X2 != sz00 )
       => sdtlseqdt0(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).

fof(mIH_03,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != X2
          & sdtlseqdt0(X1,X2) )
       => iLess0(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).

fof(m_MulZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1] :
        ( ( aNaturalNumber0(X1)
          & X1 != sz00
          & X1 != sz10 )
       => ( ! [X2] :
              ( ( aNaturalNumber0(X2)
                & X2 != sz00
                & X2 != sz10 )
             => ( iLess0(X2,X1)
               => ? [X3] :
                    ( aNaturalNumber0(X3)
                    & ? [X4] :
                        ( aNaturalNumber0(X4)
                        & X2 = sdtasdt0(X3,X4) )
                    & doDivides0(X3,X2)
                    & X3 != sz00
                    & X3 != sz10
                    & ! [X4] :
                        ( ( aNaturalNumber0(X4)
                          & ( ? [X5] :
                                ( aNaturalNumber0(X5)
                                & X3 = sdtasdt0(X4,X5) )
                            | doDivides0(X4,X3) ) )
                       => ( X4 = sz10
                          | X4 = X3 ) )
                    & isPrime0(X3) ) ) )
         => ? [X2] :
              ( aNaturalNumber0(X2)
              & ( ? [X3] :
                    ( aNaturalNumber0(X3)
                    & X1 = sdtasdt0(X2,X3) )
                | doDivides0(X2,X1) )
              & ( ( X2 != sz00
                  & X2 != sz10
                  & ! [X3] :
                      ( ( aNaturalNumber0(X3)
                        & ? [X4] :
                            ( aNaturalNumber0(X4)
                            & X2 = sdtasdt0(X3,X4) )
                        & doDivides0(X3,X2) )
                     => ( X3 = sz10
                        | X3 = X2 ) ) )
                | isPrime0(X2) ) ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_11,negated_conjecture,
    ! [X87,X90,X91,X92,X93] :
      ( aNaturalNumber0(esk4_0)
      & esk4_0 != sz00
      & esk4_0 != sz10
      & ( aNaturalNumber0(esk5_1(X87))
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( aNaturalNumber0(esk6_1(X87))
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( X87 = sdtasdt0(esk5_1(X87),esk6_1(X87))
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( doDivides0(esk5_1(X87),X87)
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( esk5_1(X87) != sz00
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( esk5_1(X87) != sz10
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( ~ aNaturalNumber0(X91)
        | esk5_1(X87) != sdtasdt0(X90,X91)
        | ~ aNaturalNumber0(X90)
        | X90 = sz10
        | X90 = esk5_1(X87)
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( ~ doDivides0(X90,esk5_1(X87))
        | ~ aNaturalNumber0(X90)
        | X90 = sz10
        | X90 = esk5_1(X87)
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( isPrime0(esk5_1(X87))
        | ~ iLess0(X87,esk4_0)
        | ~ aNaturalNumber0(X87)
        | X87 = sz00
        | X87 = sz10 )
      & ( aNaturalNumber0(esk7_1(X92))
        | X92 = sz00
        | X92 = sz10
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( aNaturalNumber0(esk8_1(X92))
        | X92 = sz00
        | X92 = sz10
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( X92 = sdtasdt0(esk7_1(X92),esk8_1(X92))
        | X92 = sz00
        | X92 = sz10
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( doDivides0(esk7_1(X92),X92)
        | X92 = sz00
        | X92 = sz10
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( esk7_1(X92) != sz10
        | X92 = sz00
        | X92 = sz10
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( esk7_1(X92) != X92
        | X92 = sz00
        | X92 = sz10
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( ~ isPrime0(X92)
        | ~ aNaturalNumber0(X93)
        | esk4_0 != sdtasdt0(X92,X93)
        | ~ aNaturalNumber0(X92) )
      & ( aNaturalNumber0(esk7_1(X92))
        | X92 = sz00
        | X92 = sz10
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) )
      & ( aNaturalNumber0(esk8_1(X92))
        | X92 = sz00
        | X92 = sz10
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) )
      & ( X92 = sdtasdt0(esk7_1(X92),esk8_1(X92))
        | X92 = sz00
        | X92 = sz10
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) )
      & ( doDivides0(esk7_1(X92),X92)
        | X92 = sz00
        | X92 = sz10
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) )
      & ( esk7_1(X92) != sz10
        | X92 = sz00
        | X92 = sz10
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) )
      & ( esk7_1(X92) != X92
        | X92 = sz00
        | X92 = sz10
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) )
      & ( ~ isPrime0(X92)
        | ~ doDivides0(X92,esk4_0)
        | ~ aNaturalNumber0(X92) ) ),
    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_10])])])])]) ).

fof(c_0_12,plain,
    ! [X16,X17] :
      ( ~ aNaturalNumber0(X16)
      | ~ aNaturalNumber0(X17)
      | sdtasdt0(X16,X17) = sdtasdt0(X17,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ isPrime0(X1)
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_14,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_15,plain,
    ! [X18,X19,X20] :
      ( ~ aNaturalNumber0(X18)
      | ~ aNaturalNumber0(X19)
      | ~ aNaturalNumber0(X20)
      | sdtasdt0(sdtasdt0(X18,X19),X20) = sdtasdt0(X18,sdtasdt0(X19,X20)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

fof(c_0_16,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | aNaturalNumber0(sdtasdt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_17,negated_conjecture,
    ( sdtasdt0(X1,X2) != esk4_0
    | ~ isPrime0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_18,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( sdtasdt0(X1,sdtasdt0(X2,X3)) != esk4_0
    | ~ isPrime0(X3)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

fof(c_0_21,plain,
    ! [X62,X63,X65] :
      ( ( aNaturalNumber0(esk2_2(X62,X63))
        | ~ doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) )
      & ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
        | ~ doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) )
      & ( ~ aNaturalNumber0(X65)
        | X63 != sdtasdt0(X62,X65)
        | doDivides0(X62,X63)
        | ~ aNaturalNumber0(X62)
        | ~ aNaturalNumber0(X63) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).

cnf(c_0_22,negated_conjecture,
    ( sdtasdt0(X1,sdtasdt0(X2,X3)) != esk4_0
    | ~ isPrime0(X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_14]) ).

cnf(c_0_23,plain,
    ( X1 = sdtasdt0(X2,esk2_2(X2,X1))
    | ~ doDivides0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_24,plain,
    ( aNaturalNumber0(esk2_2(X1,X2))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_25,plain,
    ! [X21] :
      ( ( sdtasdt0(X21,sz10) = X21
        | ~ aNaturalNumber0(X21) )
      & ( X21 = sdtasdt0(sz10,X21)
        | ~ aNaturalNumber0(X21) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).

cnf(c_0_26,negated_conjecture,
    ( sdtasdt0(X1,X2) != esk4_0
    | ~ isPrime0(X3)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_27,negated_conjecture,
    ( X1 = sdtasdt0(esk7_1(X1),esk8_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_28,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_29,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_30,negated_conjecture,
    aNaturalNumber0(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_31,negated_conjecture,
    esk4_0 != sz00,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_32,negated_conjecture,
    esk4_0 != sz10,
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_33,negated_conjecture,
    ( aNaturalNumber0(esk8_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_34,negated_conjecture,
    ( aNaturalNumber0(esk7_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_35,negated_conjecture,
    ( sdtasdt0(X1,X2) != esk4_0
    | ~ isPrime0(X3)
    | ~ doDivides0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_14]) ).

cnf(c_0_36,negated_conjecture,
    sdtasdt0(esk7_1(esk4_0),esk8_1(esk4_0)) = esk4_0,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])])]),c_0_30])]),c_0_31]),c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    aNaturalNumber0(esk8_1(esk4_0)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_28]),c_0_29])])]),c_0_30])]),c_0_31]),c_0_32]) ).

cnf(c_0_38,negated_conjecture,
    aNaturalNumber0(esk7_1(esk4_0)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_29])])]),c_0_30])]),c_0_31]),c_0_32]) ).

cnf(c_0_39,negated_conjecture,
    ( X1 = sz00
    | X1 = sz10
    | esk7_1(X1) != sz10
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_40,negated_conjecture,
    ( ~ isPrime0(X1)
    | ~ doDivides0(X1,esk7_1(esk4_0))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]) ).

cnf(c_0_41,negated_conjecture,
    ( doDivides0(esk5_1(X1),X1)
    | X1 = sz00
    | X1 = sz10
    | ~ iLess0(X1,esk4_0)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_42,negated_conjecture,
    esk7_1(esk4_0) != sz10,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_28]),c_0_29])])]),c_0_30])]),c_0_31]),c_0_32]) ).

fof(c_0_43,plain,
    ! [X78,X79] :
      ( ~ aNaturalNumber0(X78)
      | ~ aNaturalNumber0(X79)
      | ~ doDivides0(X78,X79)
      | X79 = sz00
      | sdtlseqdt0(X78,X79) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivLE])]) ).

cnf(c_0_44,negated_conjecture,
    ( doDivides0(esk7_1(X1),X1)
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_45,negated_conjecture,
    ( esk7_1(esk4_0) = sz00
    | ~ isPrime0(esk5_1(esk7_1(esk4_0)))
    | ~ iLess0(esk7_1(esk4_0),esk4_0)
    | ~ aNaturalNumber0(esk5_1(esk7_1(esk4_0))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_38])]),c_0_42]) ).

cnf(c_0_46,negated_conjecture,
    ( isPrime0(esk5_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ iLess0(X1,esk4_0)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_47,plain,
    ! [X60,X61] :
      ( ~ aNaturalNumber0(X60)
      | ~ aNaturalNumber0(X61)
      | X60 = X61
      | ~ sdtlseqdt0(X60,X61)
      | iLess0(X60,X61) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).

cnf(c_0_48,plain,
    ( X2 = sz00
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_49,negated_conjecture,
    doDivides0(esk7_1(esk4_0),esk4_0),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_28]),c_0_29])])]),c_0_30])]),c_0_31]),c_0_32]) ).

cnf(c_0_50,negated_conjecture,
    ( X1 = sz00
    | X1 = sz10
    | esk7_1(X1) != X1
    | ~ aNaturalNumber0(X2)
    | esk4_0 != sdtasdt0(X1,X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_51,negated_conjecture,
    ( esk7_1(esk4_0) = sz00
    | ~ iLess0(esk7_1(esk4_0),esk4_0)
    | ~ aNaturalNumber0(esk5_1(esk7_1(esk4_0))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_38])]),c_0_42]) ).

cnf(c_0_52,plain,
    ( X1 = X2
    | iLess0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_53,negated_conjecture,
    sdtlseqdt0(esk7_1(esk4_0),esk4_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_30]),c_0_38])]),c_0_31]) ).

cnf(c_0_54,negated_conjecture,
    esk7_1(esk4_0) != esk4_0,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_29])])]),c_0_30])]),c_0_31]),c_0_32]) ).

cnf(c_0_55,negated_conjecture,
    ( aNaturalNumber0(esk5_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ iLess0(X1,esk4_0)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_56,negated_conjecture,
    ( esk7_1(esk4_0) = sz00
    | ~ aNaturalNumber0(esk5_1(esk7_1(esk4_0))) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_30]),c_0_38])]),c_0_54]) ).

cnf(c_0_57,negated_conjecture,
    ( X1 = esk4_0
    | X1 = sz10
    | X1 = sz00
    | aNaturalNumber0(esk5_1(X1))
    | ~ sdtlseqdt0(X1,esk4_0)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_52]),c_0_30])]) ).

fof(c_0_58,plain,
    ! [X22] :
      ( ( sdtasdt0(X22,sz00) = sz00
        | ~ aNaturalNumber0(X22) )
      & ( sz00 = sdtasdt0(sz00,X22)
        | ~ aNaturalNumber0(X22) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).

cnf(c_0_59,negated_conjecture,
    esk7_1(esk4_0) = sz00,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_53]),c_0_38])]),c_0_54]),c_0_42]) ).

cnf(c_0_60,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_61,negated_conjecture,
    sdtasdt0(sz00,esk8_1(esk4_0)) = esk4_0,
    inference(rw,[status(thm)],[c_0_36,c_0_59]) ).

cnf(c_0_62,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_37])]),c_0_31]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM481+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri Aug 25 08:10:17 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.62  % Version  : CSE_E---1.5
% 0.19/0.62  % Problem  : theBenchmark.p
% 0.19/0.62  % Proof found
% 0.19/0.62  % SZS status Theorem for theBenchmark.p
% 0.19/0.62  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.051000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.055000 s
%------------------------------------------------------------------------------