TSTP Solution File: NUM496+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM496+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 : 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 10:38:04 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   61 (  14 unt;  19 typ;   0 def)
%            Number of atoms       :  136 (  24 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  163 (  69   ~;  67   |;  18   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   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   :   47 (   0 sgn;  23   !;   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(m__,conjecture,
    ( doDivides0(xp,xn)
    | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

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(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(mDivSum,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X1,X3) )
       => doDivides0(X1,sdtpldt0(X2,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivSum) ).

fof(m__2027,hypothesis,
    ( doDivides0(xp,xr)
    | doDivides0(xp,xm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2027) ).

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(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(c_0_11,negated_conjecture,
    ~ ( doDivides0(xp,xn)
      | doDivides0(xp,xm) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_12,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])])])]) ).

fof(c_0_13,negated_conjecture,
    ( ~ doDivides0(xp,xn)
    & ~ doDivides0(xp,xm) ),
    inference(fof_nnf,[status(thm)],[c_0_11]) ).

cnf(c_0_14,plain,
    ( aNaturalNumber0(X1)
    | X1 != sdtmndt0(X2,X3)
    | ~ sdtlseqdt0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_15,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_16,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_17,plain,
    ! [X70,X71,X72] :
      ( ~ aNaturalNumber0(X70)
      | ~ aNaturalNumber0(X71)
      | ~ aNaturalNumber0(X72)
      | ~ doDivides0(X70,X71)
      | ~ doDivides0(X70,X72)
      | doDivides0(X70,sdtpldt0(X71,X72)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).

cnf(c_0_18,hypothesis,
    ( doDivides0(xp,xr)
    | doDivides0(xp,xm) ),
    inference(split_conjunct,[status(thm)],[m__2027]) ).

cnf(c_0_19,negated_conjecture,
    ~ doDivides0(xp,xm),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( aNaturalNumber0(sdtmndt0(X1,X2))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_21,hypothesis,
    sdtlseqdt0(xp,xn),
    inference(split_conjunct,[status(thm)],[m__1870]) ).

cnf(c_0_22,hypothesis,
    xr = sdtmndt0(xn,xp),
    inference(split_conjunct,[status(thm)],[m__1883]) ).

cnf(c_0_23,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_24,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_25,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_26,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_27,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_28,plain,
    ( doDivides0(X1,sdtpldt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ doDivides0(X1,X2)
    | ~ doDivides0(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_29,hypothesis,
    doDivides0(xp,xr),
    inference(sr,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_30,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_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]) ).

cnf(c_0_31,plain,
    ( doDivides0(X1,sdtasdt0(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,
    ( sdtasdt0(X1,sz10) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_34,plain,
    ( sdtpldt0(X1,X2) = X3
    | X2 != sdtmndt0(X3,X1)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_35,hypothesis,
    ( doDivides0(xp,sdtpldt0(X1,xr))
    | ~ doDivides0(xp,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_23])]) ).

cnf(c_0_36,plain,
    ( doDivides0(X1,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).

cnf(c_0_37,plain,
    ( sdtpldt0(X1,sdtmndt0(X2,X1)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(er,[status(thm)],[c_0_34]) ).

cnf(c_0_38,hypothesis,
    doDivides0(xp,sdtpldt0(xp,xr)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23])]) ).

cnf(c_0_39,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_37,c_0_21]),c_0_22]),c_0_24]),c_0_23])]) ).

cnf(c_0_40,negated_conjecture,
    ~ doDivides0(xp,xn),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_41,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM496+1 : 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 17:04:09 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.62  % Total time : 0.032000 s
% 0.20/0.62  % SZS output end Proof
% 0.20/0.62  % Total time : 0.036000 s
%------------------------------------------------------------------------------