TSTP Solution File: NUM471+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM471+2 : 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 : n023.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 10:37:48 EDT 2023

% Result   : Theorem 0.53s 0.97s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   89 (  23 unt;  19 typ;   0 def)
%            Number of atoms       :  289 (  92 equ)
%            Maximal formula atoms :   28 (   4 avg)
%            Number of connectives :  359 ( 140   ~; 147   |;  53   &)
%                                         (   3 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   9 con; 0-2 aty)
%            Number of variables   :   89 (   0 sgn;  47   !;   6   ?;   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,
    xl: $i ).

tff(decl_33,type,
    xm: $i ).

tff(decl_34,type,
    xn: $i ).

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

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

tff(decl_37,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk3_0: $i ).

tff(decl_40,type,
    esk4_0: $i ).

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

fof(mMulCanc,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 != sz00
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
                | sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
             => X2 = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).

fof(m__1324_04,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & xm = sdtasdt0(xl,X1) )
    & doDivides0(xl,xm)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
    & doDivides0(xl,sdtpldt0(xm,xn)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).

fof(mDefQuot,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( X3 = sdtsldt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & X2 = sdtasdt0(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).

fof(m__,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xp,X1) = xq )
    | sdtlseqdt0(xp,xq) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(mDefLE,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & sdtpldt0(X1,X3) = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).

fof(mSortsB,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).

fof(m__1360,hypothesis,
    ( aNaturalNumber0(xp)
    & xm = sdtasdt0(xl,xp)
    & xp = sdtsldt0(xm,xl) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).

fof(m__1324,hypothesis,
    ( aNaturalNumber0(xl)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).

fof(m__1347,hypothesis,
    xl != sz00,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).

fof(m__1379,hypothesis,
    ( aNaturalNumber0(xq)
    & sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
    & xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).

fof(m_AddZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).

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

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

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

fof(mMonMul,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( X1 != sz00
          & X2 != X3
          & sdtlseqdt0(X2,X3) )
       => ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
          & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
          & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).

fof(c_0_17,plain,
    ! [X60,X61,X63] :
      ( ( aNaturalNumber0(esk2_2(X60,X61))
        | ~ doDivides0(X60,X61)
        | ~ aNaturalNumber0(X60)
        | ~ aNaturalNumber0(X61) )
      & ( X61 = sdtasdt0(X60,esk2_2(X60,X61))
        | ~ doDivides0(X60,X61)
        | ~ aNaturalNumber0(X60)
        | ~ aNaturalNumber0(X61) )
      & ( ~ aNaturalNumber0(X63)
        | X61 != sdtasdt0(X60,X63)
        | doDivides0(X60,X61)
        | ~ aNaturalNumber0(X60)
        | ~ aNaturalNumber0(X61) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).

fof(c_0_18,plain,
    ! [X6,X7] :
      ( ~ aNaturalNumber0(X6)
      | ~ aNaturalNumber0(X7)
      | aNaturalNumber0(sdtasdt0(X6,X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

fof(c_0_19,plain,
    ! [X27,X28,X29] :
      ( ( sdtasdt0(X27,X28) != sdtasdt0(X27,X29)
        | X28 = X29
        | ~ aNaturalNumber0(X28)
        | ~ aNaturalNumber0(X29)
        | X27 = sz00
        | ~ aNaturalNumber0(X27) )
      & ( sdtasdt0(X28,X27) != sdtasdt0(X29,X27)
        | X28 = X29
        | ~ aNaturalNumber0(X28)
        | ~ aNaturalNumber0(X29)
        | X27 = sz00
        | ~ aNaturalNumber0(X27) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).

fof(c_0_20,hypothesis,
    ( aNaturalNumber0(esk3_0)
    & xm = sdtasdt0(xl,esk3_0)
    & doDivides0(xl,xm)
    & aNaturalNumber0(esk4_0)
    & sdtpldt0(xm,xn) = sdtasdt0(xl,esk4_0)
    & doDivides0(xl,sdtpldt0(xm,xn)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__1324_04])]) ).

fof(c_0_21,plain,
    ! [X64,X65,X66] :
      ( ( aNaturalNumber0(X66)
        | X66 != sdtsldt0(X65,X64)
        | X64 = sz00
        | ~ doDivides0(X64,X65)
        | ~ aNaturalNumber0(X64)
        | ~ aNaturalNumber0(X65) )
      & ( X65 = sdtasdt0(X64,X66)
        | X66 != sdtsldt0(X65,X64)
        | X64 = sz00
        | ~ doDivides0(X64,X65)
        | ~ aNaturalNumber0(X64)
        | ~ aNaturalNumber0(X65) )
      & ( ~ aNaturalNumber0(X66)
        | X65 != sdtasdt0(X64,X66)
        | X66 = sdtsldt0(X65,X64)
        | X64 = sz00
        | ~ doDivides0(X64,X65)
        | ~ aNaturalNumber0(X64)
        | ~ aNaturalNumber0(X65) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).

cnf(c_0_22,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_24,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xp,X1) = xq )
      | sdtlseqdt0(xp,xq) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_25,plain,
    ! [X34,X35,X37] :
      ( ( aNaturalNumber0(esk1_2(X34,X35))
        | ~ sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) )
      & ( sdtpldt0(X34,esk1_2(X34,X35)) = X35
        | ~ sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) )
      & ( ~ aNaturalNumber0(X37)
        | sdtpldt0(X34,X37) != X35
        | sdtlseqdt0(X34,X35)
        | ~ aNaturalNumber0(X34)
        | ~ aNaturalNumber0(X35) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).

fof(c_0_26,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | aNaturalNumber0(sdtpldt0(X4,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

cnf(c_0_27,plain,
    ( X2 = X3
    | X1 = sz00
    | sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,hypothesis,
    xm = sdtasdt0(xl,xp),
    inference(split_conjunct,[status(thm)],[m__1360]) ).

cnf(c_0_29,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1360]) ).

cnf(c_0_30,hypothesis,
    aNaturalNumber0(xl),
    inference(split_conjunct,[status(thm)],[m__1324]) ).

cnf(c_0_31,hypothesis,
    xl != sz00,
    inference(split_conjunct,[status(thm)],[m__1347]) ).

cnf(c_0_32,hypothesis,
    sdtpldt0(xm,xn) = sdtasdt0(xl,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_33,hypothesis,
    sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
    inference(split_conjunct,[status(thm)],[m__1379]) ).

cnf(c_0_34,plain,
    ( X1 = sdtsldt0(X2,X3)
    | X3 = sz00
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_35,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_22]),c_0_23]) ).

cnf(c_0_36,hypothesis,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    inference(split_conjunct,[status(thm)],[m__1379]) ).

fof(c_0_37,negated_conjecture,
    ! [X75] :
      ( ( ~ aNaturalNumber0(X75)
        | sdtpldt0(xp,X75) != xq )
      & ~ sdtlseqdt0(xp,xq) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])]) ).

fof(c_0_38,plain,
    ! [X13] :
      ( ( sdtpldt0(X13,sz00) = X13
        | ~ aNaturalNumber0(X13) )
      & ( X13 = sdtpldt0(sz00,X13)
        | ~ aNaturalNumber0(X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).

fof(c_0_39,plain,
    ! [X42,X43] :
      ( ~ aNaturalNumber0(X42)
      | ~ aNaturalNumber0(X43)
      | ~ sdtlseqdt0(X42,X43)
      | ~ sdtlseqdt0(X43,X42)
      | X42 = X43 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).

cnf(c_0_40,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_41,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_42,hypothesis,
    ( X1 = xp
    | sdtasdt0(xl,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[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]) ).

cnf(c_0_43,hypothesis,
    sdtasdt0(xl,esk4_0) = sdtasdt0(xl,xq),
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_44,hypothesis,
    aNaturalNumber0(esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_45,plain,
    ( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
    | X1 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_23]),c_0_35]) ).

cnf(c_0_46,hypothesis,
    sdtsldt0(sdtasdt0(xl,xq),xl) = xq,
    inference(rw,[status(thm)],[c_0_36,c_0_33]) ).

cnf(c_0_47,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xp,X1) != xq ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_48,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_49,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

fof(c_0_50,plain,
    ! [X47,X48] :
      ( ( X48 != X47
        | sdtlseqdt0(X47,X48)
        | ~ aNaturalNumber0(X47)
        | ~ aNaturalNumber0(X48) )
      & ( sdtlseqdt0(X48,X47)
        | sdtlseqdt0(X47,X48)
        | ~ aNaturalNumber0(X47)
        | ~ aNaturalNumber0(X48) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).

cnf(c_0_51,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_52,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41]) ).

cnf(c_0_53,hypothesis,
    ( esk4_0 = xp
    | sdtasdt0(xl,xq) != xm ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44])]) ).

cnf(c_0_54,hypothesis,
    esk4_0 = xq,
    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_45,c_0_43]),c_0_46]),c_0_30]),c_0_44])]),c_0_31]) ).

cnf(c_0_55,negated_conjecture,
    xq != xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_29])]) ).

fof(c_0_56,plain,
    ! [X52,X53,X54] :
      ( ( sdtasdt0(X52,X53) != sdtasdt0(X52,X54)
        | X52 = sz00
        | X53 = X54
        | ~ sdtlseqdt0(X53,X54)
        | ~ aNaturalNumber0(X52)
        | ~ aNaturalNumber0(X53)
        | ~ aNaturalNumber0(X54) )
      & ( sdtlseqdt0(sdtasdt0(X52,X53),sdtasdt0(X52,X54))
        | X52 = sz00
        | X53 = X54
        | ~ sdtlseqdt0(X53,X54)
        | ~ aNaturalNumber0(X52)
        | ~ aNaturalNumber0(X53)
        | ~ aNaturalNumber0(X54) )
      & ( sdtasdt0(X53,X52) != sdtasdt0(X54,X52)
        | X52 = sz00
        | X53 = X54
        | ~ sdtlseqdt0(X53,X54)
        | ~ aNaturalNumber0(X52)
        | ~ aNaturalNumber0(X53)
        | ~ aNaturalNumber0(X54) )
      & ( sdtlseqdt0(sdtasdt0(X53,X52),sdtasdt0(X54,X52))
        | X52 = sz00
        | X53 = X54
        | ~ sdtlseqdt0(X53,X54)
        | ~ aNaturalNumber0(X52)
        | ~ aNaturalNumber0(X53)
        | ~ aNaturalNumber0(X54) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).

cnf(c_0_57,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_58,hypothesis,
    aNaturalNumber0(xq),
    inference(split_conjunct,[status(thm)],[m__1379]) ).

cnf(c_0_59,plain,
    ( sdtpldt0(X1,X2) = X1
    | ~ sdtlseqdt0(sdtpldt0(X1,X2),X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_41]) ).

cnf(c_0_60,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1324]) ).

cnf(c_0_61,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1324]) ).

cnf(c_0_62,hypothesis,
    sdtasdt0(xl,xq) != xm,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).

cnf(c_0_63,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | X1 = sz00
    | X2 = X3
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_64,hypothesis,
    ( sdtlseqdt0(X1,xq)
    | sdtlseqdt0(xq,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_65,negated_conjecture,
    ~ sdtlseqdt0(xp,xq),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_66,hypothesis,
    ~ sdtlseqdt0(sdtasdt0(xl,xq),xm),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_33]),c_0_60]),c_0_61])]),c_0_62]) ).

cnf(c_0_67,hypothesis,
    ( X1 = xp
    | sdtlseqdt0(sdtasdt0(xl,X1),xm)
    | ~ sdtlseqdt0(X1,xp)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_28]),c_0_29]),c_0_30])]),c_0_31]) ).

cnf(c_0_68,hypothesis,
    sdtlseqdt0(xq,xp),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_29]),c_0_65]) ).

cnf(c_0_69,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),c_0_58])]),c_0_55]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : NUM471+2 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n023.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Fri Aug 25 08:36:57 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.51/0.55  start to proof: theBenchmark
% 0.53/0.97  % Version  : CSE_E---1.5
% 0.53/0.97  % Problem  : theBenchmark.p
% 0.53/0.97  % Proof found
% 0.53/0.97  % SZS status Theorem for theBenchmark.p
% 0.53/0.97  % SZS output start Proof
% See solution above
% 0.53/0.97  % Total time : 0.400000 s
% 0.53/0.97  % SZS output end Proof
% 0.53/0.97  % Total time : 0.404000 s
%------------------------------------------------------------------------------