TSTP Solution File: NUM501+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM501+3 : 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 10:38:07 EDT 2023

% Result   : Theorem 0.74s 0.89s
% Output   : CNFRefutation 0.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   56 (   6 unt;  28 typ;   0 def)
%            Number of atoms       :   94 (  33 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  107 (  41   ~;  34   |;  28   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   34 (  17   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  11 con; 0-3 aty)
%            Number of variables   :   37 (   0 sgn;  18   !;   4   ?;   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 ).

tff(decl_42,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    esk9_0: $i ).

tff(decl_47,type,
    esk10_0: $i ).

tff(decl_48,type,
    esk11_0: $i ).

tff(decl_49,type,
    esk12_0: $i ).

fof(m__,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
    | doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).

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__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xk = sdtasdt0(xr,X1) )
    & doDivides0(xr,xk)
    & xr != sz00
    & xr != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xr = sdtasdt0(X1,X2) )
            | doDivides0(X1,xr) ) )
       => ( X1 = sz10
          | X1 = xr ) )
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).

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

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

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

fof(c_0_7,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
      | doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_8,negated_conjecture,
    ! [X106] :
      ( ( ~ aNaturalNumber0(X106)
        | sdtasdt0(xn,xm) != sdtasdt0(xr,X106) )
      & ~ doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

cnf(c_0_9,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtasdt0(xn,xm) != sdtasdt0(xr,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_10,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

fof(c_0_11,plain,
    ! [X16,X17] :
      ( ~ aNaturalNumber0(X16)
      | ~ aNaturalNumber0(X17)
      | sdtasdt0(X16,X17) = sdtasdt0(X17,X16) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

fof(c_0_12,hypothesis,
    ! [X104,X105] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk12_0)
      & xk = sdtasdt0(xr,esk12_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X105)
        | xr != sdtasdt0(X104,X105)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & ( ~ doDivides0(X104,xr)
        | ~ aNaturalNumber0(X104)
        | X104 = sz10
        | X104 = xr )
      & isPrime0(xr) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).

cnf(c_0_13,negated_conjecture,
    ( sdtasdt0(xr,X1) != sdtasdt0(xp,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X18,X19,X20] :
      ( ~ aNaturalNumber0(X18)
      | ~ aNaturalNumber0(X19)
      | ~ aNaturalNumber0(X20)
      | sdtasdt0(sdtasdt0(X18,X19),X20) = sdtasdt0(X18,sdtasdt0(X19,X20)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).

fof(c_0_17,plain,
    ! [X8,X9] :
      ( ~ aNaturalNumber0(X8)
      | ~ aNaturalNumber0(X9)
      | aNaturalNumber0(sdtasdt0(X8,X9)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_18,negated_conjecture,
    ( sdtasdt0(X1,xr) != sdtasdt0(xp,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_19,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ( sdtasdt0(X1,sdtasdt0(X2,xr)) != sdtasdt0(xp,xk)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]),c_0_20]) ).

cnf(c_0_22,negated_conjecture,
    ( sdtasdt0(X1,sdtasdt0(xr,X2)) != sdtasdt0(xp,xk)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_15])]) ).

cnf(c_0_23,hypothesis,
    xk = sdtasdt0(xr,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_24,hypothesis,
    aNaturalNumber0(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_25,hypothesis,
    ( sdtasdt0(X1,xk) != sdtasdt0(xp,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_26,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_27,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_25]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM501+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n001.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 18:21:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.74/0.89  % Version  : CSE_E---1.5
% 0.74/0.89  % Problem  : theBenchmark.p
% 0.74/0.89  % Proof found
% 0.74/0.89  % SZS status Theorem for theBenchmark.p
% 0.74/0.89  % SZS output start Proof
% See solution above
% 0.74/0.89  % Total time : 0.293000 s
% 0.74/0.89  % SZS output end Proof
% 0.74/0.89  % Total time : 0.298000 s
%------------------------------------------------------------------------------