TSTP Solution File: NUM500+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM500+3 : 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 : n023.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 0.50s 0.63s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   46 (   5 unt;  28 typ;   0 def)
%            Number of atoms       :  146 (  71 equ)
%            Maximal formula atoms :   73 (   8 avg)
%            Number of connectives :  193 (  65   ~;  87   |;  38   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  19   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   9 con; 0-3 aty)
%            Number of variables   :   17 (   0 sgn;   6   !;   7   ?;   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,
    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 ).

tff(decl_41,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_42,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_43,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_44,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_45,type,
    esk9_0: $i ).

tff(decl_46,type,
    esk10_0: $i ).

tff(decl_47,type,
    esk11_0: $i ).

tff(decl_48,type,
    esk12_1: $i > $i ).

tff(decl_49,type,
    esk13_1: $i > $i ).

fof(m__,conjecture,
    ? [X1] :
      ( aNaturalNumber0(X1)
      & ( ? [X2] :
            ( aNaturalNumber0(X2)
            & xk = sdtasdt0(X1,X2) )
        | doDivides0(X1,xk) )
      & ( ( X1 != sz00
          & X1 != sz10
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & ? [X3] :
                    ( aNaturalNumber0(X3)
                    & X1 = sdtasdt0(X2,X3) )
                & doDivides0(X2,X1) )
             => ( X2 = sz10
                | X2 = X1 ) ) )
        | isPrime0(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

fof(m__2315,hypothesis,
    ~ ( xk = sz00
      | xk = sz10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

fof(c_0_4,negated_conjecture,
    ~ ? [X1] :
        ( aNaturalNumber0(X1)
        & ( ? [X2] :
              ( aNaturalNumber0(X2)
              & xk = sdtasdt0(X1,X2) )
          | doDivides0(X1,xk) )
        & ( ( X1 != sz00
            & X1 != sz10
            & ! [X2] :
                ( ( aNaturalNumber0(X2)
                  & ? [X3] :
                      ( aNaturalNumber0(X3)
                      & X1 = sdtasdt0(X2,X3) )
                  & doDivides0(X2,X1) )
               => ( X2 = sz10
                  | X2 = X1 ) ) )
          | isPrime0(X1) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_5,negated_conjecture,
    ! [X103,X104] :
      ( ( aNaturalNumber0(esk12_1(X103))
        | X103 = sz00
        | X103 = sz10
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( aNaturalNumber0(esk13_1(X103))
        | X103 = sz00
        | X103 = sz10
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( X103 = sdtasdt0(esk12_1(X103),esk13_1(X103))
        | X103 = sz00
        | X103 = sz10
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( doDivides0(esk12_1(X103),X103)
        | X103 = sz00
        | X103 = sz10
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( esk12_1(X103) != sz10
        | X103 = sz00
        | X103 = sz10
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( esk12_1(X103) != X103
        | X103 = sz00
        | X103 = sz10
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( ~ isPrime0(X103)
        | ~ aNaturalNumber0(X104)
        | xk != sdtasdt0(X103,X104)
        | ~ aNaturalNumber0(X103) )
      & ( aNaturalNumber0(esk12_1(X103))
        | X103 = sz00
        | X103 = sz10
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) )
      & ( aNaturalNumber0(esk13_1(X103))
        | X103 = sz00
        | X103 = sz10
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) )
      & ( X103 = sdtasdt0(esk12_1(X103),esk13_1(X103))
        | X103 = sz00
        | X103 = sz10
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) )
      & ( doDivides0(esk12_1(X103),X103)
        | X103 = sz00
        | X103 = sz10
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) )
      & ( esk12_1(X103) != sz10
        | X103 = sz00
        | X103 = sz10
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) )
      & ( esk12_1(X103) != X103
        | X103 = sz00
        | X103 = sz10
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) )
      & ( ~ isPrime0(X103)
        | ~ doDivides0(X103,xk)
        | ~ aNaturalNumber0(X103) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])]) ).

fof(c_0_6,plain,
    ! [X86] :
      ( ( aNaturalNumber0(esk4_1(X86))
        | ~ aNaturalNumber0(X86)
        | X86 = sz00
        | X86 = sz10 )
      & ( doDivides0(esk4_1(X86),X86)
        | ~ aNaturalNumber0(X86)
        | X86 = sz00
        | X86 = sz10 )
      & ( isPrime0(esk4_1(X86))
        | ~ aNaturalNumber0(X86)
        | X86 = sz00
        | X86 = sz10 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).

fof(c_0_7,hypothesis,
    ( xk != sz00
    & xk != sz10 ),
    inference(fof_nnf,[status(thm)],[m__2315]) ).

cnf(c_0_8,negated_conjecture,
    ( ~ isPrime0(X1)
    | ~ doDivides0(X1,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    ( doDivides0(esk4_1(X1),X1)
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,hypothesis,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_11,hypothesis,
    xk != sz00,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,hypothesis,
    xk != sz10,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,negated_conjecture,
    ( ~ isPrime0(esk4_1(xk))
    | ~ aNaturalNumber0(esk4_1(xk)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),c_0_11]),c_0_12]) ).

cnf(c_0_14,plain,
    ( aNaturalNumber0(esk4_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_15,negated_conjecture,
    ~ isPrime0(esk4_1(xk)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10])]),c_0_11]),c_0_12]) ).

cnf(c_0_16,plain,
    ( isPrime0(esk4_1(X1))
    | X1 = sz00
    | X1 = sz10
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_10])]),c_0_11]),c_0_12]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : NUM500+3 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Aug 25 14:44:27 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.50/0.58  start to proof: theBenchmark
% 0.50/0.63  % Version  : CSE_E---1.5
% 0.50/0.63  % Problem  : theBenchmark.p
% 0.50/0.63  % Proof found
% 0.50/0.63  % SZS status Theorem for theBenchmark.p
% 0.50/0.63  % SZS output start Proof
% See solution above
% 0.54/0.64  % Total time : 0.046000 s
% 0.54/0.64  % SZS output end Proof
% 0.54/0.64  % Total time : 0.050000 s
%------------------------------------------------------------------------------