TSTP Solution File: NUM493+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM493+1 : 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 : n001.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 10:38:03 EDT 2023

% Result   : Theorem 3.28s 3.37s
% Output   : CNFRefutation 3.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   39
% Syntax   : Number of formulae    :  119 (  37 unt;  19 typ;   0 def)
%            Number of atoms       :  333 (  84 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  408 ( 175   ~; 172   |;  39   &)
%                                         (   2 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  13   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :  120 (   0 sgn;  59   !;   1   ?;   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,
    xn: $i ).

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

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

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

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

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

tff(decl_39,type,
    esk3_1: $i > $i ).

tff(decl_40,type,
    esk4_1: $i > $i ).

fof(mDefDiff,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
       => ! [X3] :
            ( X3 = sdtmndt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & sdtpldt0(X1,X3) = X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).

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

fof(m__1870,hypothesis,
    sdtlseqdt0(xp,xn),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).

fof(m__1883,hypothesis,
    xr = sdtmndt0(xn,xp),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).

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

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

fof(m__,conjecture,
    ( doDivides0(xp,xr)
    | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__1894,hypothesis,
    ( xr != xn
    & sdtlseqdt0(xr,xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).

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

fof(m__1799,hypothesis,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( isPrime0(X3)
          & doDivides0(X3,sdtasdt0(X1,X2)) )
       => ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
         => ( doDivides0(X3,X1)
            | doDivides0(X3,X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).

fof(m__1913,hypothesis,
    doDivides0(xp,sdtasdt0(xr,xm)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1913) ).

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(m__1860,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).

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

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

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

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

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(c_0_20,plain,
    ! [X38,X39,X40] :
      ( ( aNaturalNumber0(X40)
        | X40 != sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) )
      & ( sdtpldt0(X38,X40) = X39
        | X40 != sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) )
      & ( ~ aNaturalNumber0(X40)
        | sdtpldt0(X38,X40) != X39
        | X40 = sdtmndt0(X39,X38)
        | ~ sdtlseqdt0(X38,X39)
        | ~ aNaturalNumber0(X38)
        | ~ aNaturalNumber0(X39) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiff])])])]) ).

cnf(c_0_21,plain,
    ( sdtpldt0(X1,X2) = X3
    | X2 != sdtmndt0(X3,X1)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_22,plain,
    ( aNaturalNumber0(X1)
    | X1 != sdtmndt0(X2,X3)
    | ~ sdtlseqdt0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_23,plain,
    ! [X24,X25,X26] :
      ( ( sdtpldt0(X24,X25) != sdtpldt0(X24,X26)
        | X25 = X26
        | ~ aNaturalNumber0(X24)
        | ~ aNaturalNumber0(X25)
        | ~ aNaturalNumber0(X26) )
      & ( sdtpldt0(X25,X24) != sdtpldt0(X26,X24)
        | X25 = X26
        | ~ aNaturalNumber0(X24)
        | ~ aNaturalNumber0(X25)
        | ~ aNaturalNumber0(X26) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).

cnf(c_0_24,plain,
    ( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_25,hypothesis,
    sdtlseqdt0(xp,xn),
    inference(split_conjunct,[status(thm)],[m__1870]) ).

cnf(c_0_26,hypothesis,
    xr = sdtmndt0(xn,xp),
    inference(split_conjunct,[status(thm)],[m__1883]) ).

cnf(c_0_27,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_28,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_29,plain,
    ( aNaturalNumber0(sdtmndt0(X1,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_22]) ).

cnf(c_0_30,plain,
    ( X1 = X3
    | sdtpldt0(X1,X2) != sdtpldt0(X3,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_31,hypothesis,
    sdtpldt0(xp,xr) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),c_0_28])]) ).

cnf(c_0_32,hypothesis,
    aNaturalNumber0(xr),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_26]),c_0_28]),c_0_27])]) ).

fof(c_0_33,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

fof(c_0_34,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_35,plain,
    ! [X14,X15] :
      ( ~ aNaturalNumber0(X14)
      | ~ aNaturalNumber0(X15)
      | sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

fof(c_0_36,negated_conjecture,
    ~ ( doDivides0(xp,xr)
      | doDivides0(xp,xm) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_37,hypothesis,
    ( X1 = xp
    | sdtpldt0(X1,xr) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_32])]) ).

cnf(c_0_38,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_39,plain,
    ( sdtpldt0(X1,esk1_2(X1,X2)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_40,hypothesis,
    sdtlseqdt0(xr,xn),
    inference(split_conjunct,[status(thm)],[m__1894]) ).

cnf(c_0_41,plain,
    ( aNaturalNumber0(esk1_2(X1,X2))
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_42,plain,
    ! [X49,X50,X51] :
      ( ( sdtpldt0(X51,X49) != sdtpldt0(X51,X50)
        | ~ aNaturalNumber0(X51)
        | X49 = X50
        | ~ sdtlseqdt0(X49,X50)
        | ~ aNaturalNumber0(X49)
        | ~ aNaturalNumber0(X50) )
      & ( sdtlseqdt0(sdtpldt0(X51,X49),sdtpldt0(X51,X50))
        | ~ aNaturalNumber0(X51)
        | X49 = X50
        | ~ sdtlseqdt0(X49,X50)
        | ~ aNaturalNumber0(X49)
        | ~ aNaturalNumber0(X50) )
      & ( sdtpldt0(X49,X51) != sdtpldt0(X50,X51)
        | ~ aNaturalNumber0(X51)
        | X49 = X50
        | ~ sdtlseqdt0(X49,X50)
        | ~ aNaturalNumber0(X49)
        | ~ aNaturalNumber0(X50) )
      & ( sdtlseqdt0(sdtpldt0(X49,X51),sdtpldt0(X50,X51))
        | ~ aNaturalNumber0(X51)
        | X49 = X50
        | ~ sdtlseqdt0(X49,X50)
        | ~ aNaturalNumber0(X49)
        | ~ aNaturalNumber0(X50) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).

fof(c_0_43,hypothesis,
    ! [X86,X87,X88] :
      ( ~ aNaturalNumber0(X86)
      | ~ aNaturalNumber0(X87)
      | ~ aNaturalNumber0(X88)
      | ~ isPrime0(X88)
      | ~ doDivides0(X88,sdtasdt0(X86,X87))
      | ~ iLess0(sdtpldt0(sdtpldt0(X86,X87),X88),sdtpldt0(sdtpldt0(xn,xm),xp))
      | doDivides0(X88,X86)
      | doDivides0(X88,X87) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).

cnf(c_0_44,hypothesis,
    doDivides0(xp,sdtasdt0(xr,xm)),
    inference(split_conjunct,[status(thm)],[m__1913]) ).

cnf(c_0_45,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_46,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_47,negated_conjecture,
    ( ~ doDivides0(xp,xr)
    & ~ doDivides0(xp,xm) ),
    inference(fof_nnf,[status(thm)],[c_0_36]) ).

cnf(c_0_48,hypothesis,
    ( X1 = xp
    | sdtpldt0(xr,X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_32])]) ).

cnf(c_0_49,hypothesis,
    sdtpldt0(xr,esk1_2(xr,xn)) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_27]),c_0_32])]) ).

cnf(c_0_50,hypothesis,
    aNaturalNumber0(esk1_2(xr,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_40]),c_0_27])]),c_0_32])]) ).

cnf(c_0_51,plain,
    ( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
    | X2 = X3
    | ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_52,hypothesis,
    xr != xn,
    inference(split_conjunct,[status(thm)],[m__1894]) ).

fof(c_0_53,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])])]) ).

cnf(c_0_54,hypothesis,
    ( doDivides0(X3,X1)
    | doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ isPrime0(X3)
    | ~ doDivides0(X3,sdtasdt0(X1,X2))
    | ~ iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_55,hypothesis,
    doDivides0(xp,sdtasdt0(xm,xr)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_32]),c_0_46])]) ).

cnf(c_0_56,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_57,negated_conjecture,
    ~ doDivides0(xp,xr),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_58,negated_conjecture,
    ~ doDivides0(xp,xm),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

fof(c_0_59,plain,
    ! [X10,X11,X12] :
      ( ~ aNaturalNumber0(X10)
      | ~ aNaturalNumber0(X11)
      | ~ aNaturalNumber0(X12)
      | sdtpldt0(sdtpldt0(X10,X11),X12) = sdtpldt0(X10,sdtpldt0(X11,X12)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).

cnf(c_0_60,hypothesis,
    esk1_2(xr,xn) = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).

fof(c_0_61,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | aNaturalNumber0(sdtpldt0(X4,X5)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

fof(c_0_62,plain,
    ! [X44,X45,X46] :
      ( ~ aNaturalNumber0(X44)
      | ~ aNaturalNumber0(X45)
      | ~ aNaturalNumber0(X46)
      | ~ sdtlseqdt0(X44,X45)
      | ~ sdtlseqdt0(X45,X46)
      | sdtlseqdt0(X44,X46) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).

cnf(c_0_63,hypothesis,
    ( sdtlseqdt0(sdtpldt0(X1,xr),sdtpldt0(X1,xn))
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40]),c_0_27]),c_0_32])]),c_0_52]) ).

cnf(c_0_64,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_65,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_66,hypothesis,
    ~ iLess0(sdtpldt0(sdtpldt0(xm,xr),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[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_54,c_0_55]),c_0_56]),c_0_28]),c_0_32]),c_0_46])]),c_0_57]),c_0_58]) ).

cnf(c_0_67,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_68,hypothesis,
    sdtpldt0(xr,xp) = xn,
    inference(rw,[status(thm)],[c_0_49,c_0_60]) ).

fof(c_0_69,plain,
    ! [X58,X59] :
      ( ~ aNaturalNumber0(X58)
      | ~ aNaturalNumber0(X59)
      | X58 = X59
      | ~ sdtlseqdt0(X58,X59)
      | iLess0(X58,X59) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).

cnf(c_0_70,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_71,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_72,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_73,hypothesis,
    sdtlseqdt0(sdtpldt0(sz00,xr),xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]),c_0_27])]) ).

cnf(c_0_74,hypothesis,
    ~ iLess0(sdtpldt0(xm,xn),sdtpldt0(sdtpldt0(xn,xm),xp)),
    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_66,c_0_67]),c_0_68]),c_0_28]),c_0_32]),c_0_46])]) ).

cnf(c_0_75,plain,
    ( X1 = X2
    | iLess0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_76,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_70]),c_0_71]) ).

cnf(c_0_77,hypothesis,
    ( sdtlseqdt0(X1,xn)
    | ~ sdtlseqdt0(X1,sdtpldt0(sz00,xr))
    | ~ aNaturalNumber0(sdtpldt0(sz00,xr))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_27])]) ).

cnf(c_0_78,hypothesis,
    ~ iLess0(sdtpldt0(xn,xm),sdtpldt0(sdtpldt0(xn,xm),xp)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_38]),c_0_27]),c_0_46])]) ).

cnf(c_0_79,plain,
    ( sdtpldt0(X1,X2) = X1
    | iLess0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_71]) ).

cnf(c_0_80,hypothesis,
    ( sdtlseqdt0(X1,xn)
    | ~ sdtlseqdt0(X1,xr)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_64]),c_0_32])]) ).

cnf(c_0_81,plain,
    ( sdtlseqdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_64]),c_0_65])]) ).

cnf(c_0_82,plain,
    ( X2 = X3
    | sdtpldt0(X1,X2) != sdtpldt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_83,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_84,hypothesis,
    ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm)
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_28])]) ).

cnf(c_0_85,hypothesis,
    sdtlseqdt0(sz00,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_65]),c_0_32])]) ).

cnf(c_0_86,hypothesis,
    ( xr = X1
    | sdtpldt0(xp,X1) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_31]),c_0_32]),c_0_28])]) ).

cnf(c_0_87,hypothesis,
    ( sdtpldt0(xp,sdtpldt0(xr,X1)) = sdtpldt0(xn,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_31]),c_0_32]),c_0_28])]) ).

cnf(c_0_88,plain,
    ( X1 = sz00
    | sdtpldt0(X2,X1) != X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_65])]) ).

cnf(c_0_89,hypothesis,
    sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(xn,xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_71]),c_0_46]),c_0_27])]) ).

cnf(c_0_90,hypothesis,
    sdtpldt0(sz00,esk1_2(sz00,xn)) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_85]),c_0_27]),c_0_65])]) ).

cnf(c_0_91,hypothesis,
    aNaturalNumber0(esk1_2(sz00,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_85]),c_0_27]),c_0_65])]) ).

cnf(c_0_92,hypothesis,
    ( xr = X1
    | sdtpldt0(X1,xp) != xn
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_38]),c_0_28])]) ).

cnf(c_0_93,hypothesis,
    sdtpldt0(xn,xp) = sdtpldt0(xp,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_68]),c_0_28])]) ).

cnf(c_0_94,hypothesis,
    ( xp = sz00
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_28])]) ).

cnf(c_0_95,hypothesis,
    esk1_2(sz00,xn) = xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_90]),c_0_91])]) ).

cnf(c_0_96,hypothesis,
    sdtpldt0(xp,xn) != xn,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_27])]),c_0_52]) ).

cnf(c_0_97,hypothesis,
    xp = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_71]),c_0_46]),c_0_27])]) ).

cnf(c_0_98,hypothesis,
    sdtpldt0(sz00,xn) = xn,
    inference(rw,[status(thm)],[c_0_90,c_0_95]) ).

cnf(c_0_99,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97]),c_0_98])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM493+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33  % Computer : n001.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri Aug 25 18:23:28 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 3.28/3.37  % Version  : CSE_E---1.5
% 3.28/3.37  % Problem  : theBenchmark.p
% 3.28/3.37  % Proof found
% 3.28/3.37  % SZS status Theorem for theBenchmark.p
% 3.28/3.37  % SZS output start Proof
% See solution above
% 3.28/3.38  % Total time : 2.806000 s
% 3.28/3.38  % SZS output end Proof
% 3.28/3.38  % Total time : 2.810000 s
%------------------------------------------------------------------------------