TSTP Solution File: NUM463+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM463+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 : n029.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 10:37:44 EDT 2023

% Result   : Theorem 0.77s 0.87s
% Output   : CNFRefutation 0.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   97 (  12 unt;  10 typ;   0 def)
%            Number of atoms       :  319 ( 110 equ)
%            Maximal formula atoms :   28 (   3 avg)
%            Number of connectives :  410 ( 178   ~; 174   |;  40   &)
%                                         (   1 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  117 (   0 sgn;  46   !;   3   ?;   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,
    xm: $i ).

tff(decl_30,type,
    xn: $i ).

tff(decl_31,type,
    esk1_2: ( $i * $i ) > $i ).

fof(mZeroAdd,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtpldt0(X1,X2) = sz00
       => ( X1 = sz00
          & X2 = sz00 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).

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

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

fof(m__,conjecture,
    ( xm != sz00
   => ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
      | sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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

fof(m__987,hypothesis,
    ( aNaturalNumber0(xm)
    & aNaturalNumber0(xn) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).

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(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(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(mLENTr,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 = sz00
        | X1 = sz10
        | ( sz10 != X1
          & sdtlseqdt0(sz10,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).

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(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(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_16,plain,
    ! [X30,X31] :
      ( ( X30 = sz00
        | sdtpldt0(X30,X31) != sz00
        | ~ aNaturalNumber0(X30)
        | ~ aNaturalNumber0(X31) )
      & ( X31 = sz00
        | sdtpldt0(X30,X31) != sz00
        | ~ aNaturalNumber0(X30)
        | ~ aNaturalNumber0(X31) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).

fof(c_0_17,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])])])])]) ).

cnf(c_0_18,plain,
    ( X1 = sz00
    | sdtpldt0(X2,X1) != sz00
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,plain,
    ( sdtpldt0(X1,esk1_2(X1,X2)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_20,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

fof(c_0_21,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_22,negated_conjecture,
    ~ ( xm != sz00
     => ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xn,X1) = sdtasdt0(xn,xm) )
        | sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_23,plain,
    ( esk1_2(X1,sz00) = sz00
    | ~ sdtlseqdt0(X1,sz00)
    | ~ aNaturalNumber0(esk1_2(X1,sz00))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19])]),c_0_20])]) ).

cnf(c_0_24,plain,
    ( aNaturalNumber0(esk1_2(X1,X2))
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_26,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

fof(c_0_27,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_28,negated_conjecture,
    ! [X56] :
      ( xm != sz00
      & ( ~ aNaturalNumber0(X56)
        | sdtpldt0(xn,X56) != sdtasdt0(xn,xm) )
      & ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).

fof(c_0_29,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | sdtpldt0(X8,X9) = sdtpldt0(X9,X8) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).

cnf(c_0_30,plain,
    ( esk1_2(X1,sz00) = sz00
    | ~ sdtlseqdt0(X1,sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20])]) ).

cnf(c_0_31,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26]) ).

cnf(c_0_32,plain,
    ( X1 = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xn,X1) != sdtasdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_34,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__987]) ).

fof(c_0_36,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_37,plain,
    ( sdtpldt0(X1,sz00) = sz00
    | ~ sdtlseqdt0(X1,sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30]),c_0_20])]) ).

cnf(c_0_38,plain,
    ( sdtlseqdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]) ).

cnf(c_0_39,negated_conjecture,
    ( sdtpldt0(X1,xn) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).

cnf(c_0_40,plain,
    ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_36]) ).

cnf(c_0_41,plain,
    sdtpldt0(sz00,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_20])]) ).

cnf(c_0_42,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(X2,xn)) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35])]),c_0_26]) ).

cnf(c_0_43,plain,
    ( sdtpldt0(sz00,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_20])]) ).

cnf(c_0_44,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

fof(c_0_45,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_46,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(X3,xn))) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_40]),c_0_35])]),c_0_26]) ).

cnf(c_0_47,plain,
    ( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_34]),c_0_20])]) ).

cnf(c_0_48,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_40]),c_0_20])]),c_0_26]) ).

cnf(c_0_49,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(xn,X2)) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_34]),c_0_35])]) ).

fof(c_0_50,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])]) ).

fof(c_0_51,plain,
    ! [X55] :
      ( ( sz10 != X55
        | X55 = sz00
        | X55 = sz10
        | ~ aNaturalNumber0(X55) )
      & ( sdtlseqdt0(sz10,X55)
        | X55 = sz00
        | X55 = sz10
        | ~ aNaturalNumber0(X55) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLENTr])])]) ).

cnf(c_0_52,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_53,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__987]) ).

cnf(c_0_54,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(xn,X3))) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_34]),c_0_35])]) ).

cnf(c_0_55,plain,
    ( sdtpldt0(sz00,X1) = sdtpldt0(X1,sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_20])]) ).

cnf(c_0_56,negated_conjecture,
    ( sdtpldt0(sdtpldt0(xn,X1),X2) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtpldt0(xn,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[c_0_49,c_0_34]) ).

fof(c_0_57,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])])]) ).

fof(c_0_58,plain,
    ! [X19] :
      ( ( sdtasdt0(X19,sz10) = X19
        | ~ aNaturalNumber0(X19) )
      & ( X19 = sdtasdt0(sz10,X19)
        | ~ aNaturalNumber0(X19) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).

cnf(c_0_59,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,plain,
    ( sdtlseqdt0(sz10,X1)
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_61,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_62,hypothesis,
    ( sdtlseqdt0(X1,xm)
    | sdtlseqdt0(xm,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_63,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(X2,sdtpldt0(sz00,xn))) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_20]),c_0_35])]) ).

cnf(c_0_64,plain,
    ( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_40]),c_0_26]) ).

cnf(c_0_65,negated_conjecture,
    ( sdtpldt0(xn,sdtpldt0(X1,X2)) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtpldt0(xn,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_35])]) ).

cnf(c_0_66,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_57]) ).

cnf(c_0_67,plain,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_58]) ).

cnf(c_0_68,plain,
    ( X1 = sz00
    | X1 = sz10
    | ~ sdtlseqdt0(X1,sz10)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).

cnf(c_0_69,hypothesis,
    ( sdtlseqdt0(xm,sz10)
    | sdtlseqdt0(sz10,xm) ),
    inference(spm,[status(thm)],[c_0_62,c_0_61]) ).

cnf(c_0_70,negated_conjecture,
    xm != sz00,
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_71,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(sz00,sdtpldt0(xn,X2))) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_35]),c_0_20])]) ).

cnf(c_0_72,negated_conjecture,
    ( sdtasdt0(xn,xm) != sdtpldt0(xn,sz00)
    | ~ aNaturalNumber0(sdtpldt0(xn,sz00)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_41]),c_0_20])]) ).

cnf(c_0_73,negated_conjecture,
    ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_74,plain,
    ( sz10 = X1
    | X2 = sz00
    | sdtlseqdt0(X2,sdtasdt0(X2,X1))
    | ~ sdtlseqdt0(sz10,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_61])]) ).

cnf(c_0_75,hypothesis,
    ( xm = sz10
    | sdtlseqdt0(sz10,xm) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_53])]),c_0_70]) ).

cnf(c_0_76,negated_conjecture,
    ( sdtpldt0(X1,sdtpldt0(sz00,sdtpldt0(sz00,xn))) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_55]),c_0_20]),c_0_35])]) ).

cnf(c_0_77,negated_conjecture,
    sdtasdt0(xn,xm) != xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_44]),c_0_35])]) ).

cnf(c_0_78,negated_conjecture,
    ( xn = sz00
    | xm = sz10 ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_53]),c_0_35])]),c_0_75]) ).

cnf(c_0_79,negated_conjecture,
    ( sdtpldt0(sdtpldt0(sz00,sdtpldt0(sz00,xn)),X1) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtpldt0(sz00,sdtpldt0(sz00,xn)))
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_76,c_0_34]) ).

cnf(c_0_80,negated_conjecture,
    ( xn = sz00
    | sdtasdt0(xn,sz10) != xn ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_81,negated_conjecture,
    ( sdtpldt0(sz00,sdtpldt0(sz00,sdtpldt0(sz00,xn))) != sdtasdt0(xn,xm)
    | ~ aNaturalNumber0(sdtpldt0(sz00,sdtpldt0(sz00,xn))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_55]),c_0_20])]) ).

cnf(c_0_82,negated_conjecture,
    xn = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_67]),c_0_35])]) ).

fof(c_0_83,plain,
    ! [X20] :
      ( ( sdtasdt0(X20,sz00) = sz00
        | ~ aNaturalNumber0(X20) )
      & ( sz00 = sdtasdt0(sz00,X20)
        | ~ aNaturalNumber0(X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).

cnf(c_0_84,negated_conjecture,
    sdtasdt0(sz00,xm) != sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_41]),c_0_41]),c_0_41]),c_0_82]),c_0_82]),c_0_41]),c_0_41]),c_0_20])]) ).

cnf(c_0_85,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_83]) ).

cnf(c_0_86,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_53])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM463+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 13:44:39 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.77/0.87  % Version  : CSE_E---1.5
% 0.77/0.87  % Problem  : theBenchmark.p
% 0.77/0.87  % Proof found
% 0.77/0.87  % SZS status Theorem for theBenchmark.p
% 0.77/0.87  % SZS output start Proof
% See solution above
% 0.77/0.88  % Total time : 0.283000 s
% 0.77/0.88  % SZS output end Proof
% 0.77/0.88  % Total time : 0.287000 s
%------------------------------------------------------------------------------