TSTP Solution File: NUM504+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : 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 10:38:09 EDT 2023

% Result   : Theorem 0.67s 0.81s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   66 (  17 unt;  20 typ;   0 def)
%            Number of atoms       :  171 (  59 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  205 (  80   ~;  91   |;  24   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   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    :   15 (  15 usr;   7 con; 0-2 aty)
%            Number of variables   :   39 (   0 sgn;  22   !;   0   ?;   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,
    xk: $i ).

tff(decl_37,type,
    xr: $i ).

tff(decl_38,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_39,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk3_1: $i > $i ).

tff(decl_41,type,
    esk4_1: $i > $i ).

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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).

fof(mLEAsym,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).

fof(m__1860,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

fof(m__2306,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

fof(m__2414,hypothesis,
    ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
    & sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
    & sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
    & sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).

fof(mDefPrime,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( isPrime0(X1)
      <=> ( X1 != sz00
          & X1 != sz10
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & doDivides0(X2,X1) )
             => ( X2 = sz10
                | X2 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(c_0_10,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])])])]) ).

fof(c_0_11,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_12,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_13,plain,
    ( X1 = sdtasdt0(X2,X3)
    | X2 = sz00
    | X3 != sdtsldt0(X1,X2)
    | ~ doDivides0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,hypothesis,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_15,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_17,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_18,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_19,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,hypothesis,
    sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
    inference(split_conjunct,[status(thm)],[m__2414]) ).

cnf(c_0_21,hypothesis,
    sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
    inference(split_conjunct,[status(thm)],[m__2414]) ).

cnf(c_0_22,plain,
    ( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
    | X1 = sz00
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_23,hypothesis,
    doDivides0(xp,sdtasdt0(xm,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_24,hypothesis,
    sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_16]),c_0_17])]) ).

cnf(c_0_25,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_26,plain,
    ! [X6,X7] :
      ( ~ aNaturalNumber0(X6)
      | ~ aNaturalNumber0(X7)
      | aNaturalNumber0(sdtasdt0(X6,X7)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_27,plain,
    ( aNaturalNumber0(X1)
    | X3 = sz00
    | X1 != sdtsldt0(X2,X3)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_28,hypothesis,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(sdtasdt0(xn,xm))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_29,hypothesis,
    ( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
    | xp = sz00
    | ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).

cnf(c_0_30,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,plain,
    ( X1 = sz00
    | aNaturalNumber0(sdtsldt0(X2,X1))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_27]) ).

cnf(c_0_32,hypothesis,
    ( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xn))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_17]),c_0_16])]) ).

cnf(c_0_33,hypothesis,
    ( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
    | xp = sz00 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_16]),c_0_17])]) ).

cnf(c_0_34,hypothesis,
    sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
    inference(split_conjunct,[status(thm)],[m__2414]) ).

cnf(c_0_35,hypothesis,
    ( xp = sz00
    | aNaturalNumber0(xk)
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_18]),c_0_25])]) ).

cnf(c_0_36,hypothesis,
    ( xp = sz00
    | ~ aNaturalNumber0(sdtasdt0(xp,xk))
    | ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_37,hypothesis,
    ( xp = sz00
    | aNaturalNumber0(xk) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_17]),c_0_16])]) ).

fof(c_0_38,plain,
    ! [X81,X82] :
      ( ( X81 != sz00
        | ~ isPrime0(X81)
        | ~ aNaturalNumber0(X81) )
      & ( X81 != sz10
        | ~ isPrime0(X81)
        | ~ aNaturalNumber0(X81) )
      & ( ~ aNaturalNumber0(X82)
        | ~ doDivides0(X82,X81)
        | X82 = sz10
        | X82 = X81
        | ~ isPrime0(X81)
        | ~ aNaturalNumber0(X81) )
      & ( aNaturalNumber0(esk3_1(X81))
        | X81 = sz00
        | X81 = sz10
        | isPrime0(X81)
        | ~ aNaturalNumber0(X81) )
      & ( doDivides0(esk3_1(X81),X81)
        | X81 = sz00
        | X81 = sz10
        | isPrime0(X81)
        | ~ aNaturalNumber0(X81) )
      & ( esk3_1(X81) != sz10
        | X81 = sz00
        | X81 = sz10
        | isPrime0(X81)
        | ~ aNaturalNumber0(X81) )
      & ( esk3_1(X81) != X81
        | X81 = sz00
        | X81 = sz10
        | isPrime0(X81)
        | ~ aNaturalNumber0(X81) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).

cnf(c_0_39,hypothesis,
    ( xp = sz00
    | ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_25])]),c_0_37]) ).

cnf(c_0_40,plain,
    ( X1 != sz00
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_41,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_42,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_43,hypothesis,
    xp = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_17]),c_0_25])]) ).

cnf(c_0_44,plain,
    ~ isPrime0(sz00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41])]) ).

cnf(c_0_45,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/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 13:54:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.60  start to proof: theBenchmark
% 0.67/0.81  % Version  : CSE_E---1.5
% 0.67/0.81  % Problem  : theBenchmark.p
% 0.67/0.81  % Proof found
% 0.67/0.81  % SZS status Theorem for theBenchmark.p
% 0.67/0.81  % SZS output start Proof
% See solution above
% 0.67/0.81  % Total time : 0.202000 s
% 0.67/0.81  % SZS output end Proof
% 0.67/0.81  % Total time : 0.206000 s
%------------------------------------------------------------------------------