TSTP Solution File: NUM523+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM523+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 : n014.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 10:38:22 EDT 2023

% Result   : Theorem 0.20s 0.60s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   44 (  10 unt;  18 typ;   0 def)
%            Number of atoms       :   82 (   9 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :   96 (  40   ~;  36   |;  15   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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    :   13 (  13 usr;   5 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn;  15   !;   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,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk3_1: $i > $i ).

tff(decl_39,type,
    esk4_1: $i > $i ).

fof(mDefDiv,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & X2 = sdtasdt0(X1,X3) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).

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

fof(m__,conjecture,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m__3014,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).

fof(m__2987,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).

fof(mPDP,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( isPrime0(X3)
          & doDivides0(X3,sdtasdt0(X1,X2)) )
       => ( doDivides0(X3,X1)
          | doDivides0(X3,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPDP) ).

fof(m__3025,hypothesis,
    isPrime0(xp),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).

fof(c_0_7,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_8,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_9,plain,
    ( doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | X2 != sdtasdt0(X3,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_11,negated_conjecture,
    ~ ( doDivides0(xp,sdtasdt0(xn,xn))
      & doDivides0(xp,xn) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_12,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_9]),c_0_10]) ).

cnf(c_0_13,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(split_conjunct,[status(thm)],[m__3014]) ).

cnf(c_0_14,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

fof(c_0_15,negated_conjecture,
    ( ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ~ doDivides0(xp,xn) ),
    inference(fof_nnf,[status(thm)],[c_0_11]) ).

cnf(c_0_16,hypothesis,
    ( doDivides0(xp,sdtasdt0(xn,xn))
    | ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).

cnf(c_0_17,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

fof(c_0_18,plain,
    ! [X86,X87,X88] :
      ( ~ aNaturalNumber0(X86)
      | ~ aNaturalNumber0(X87)
      | ~ aNaturalNumber0(X88)
      | ~ isPrime0(X88)
      | ~ doDivides0(X88,sdtasdt0(X86,X87))
      | doDivides0(X88,X86)
      | doDivides0(X88,X87) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPDP])]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ doDivides0(xp,sdtasdt0(xn,xn))
    | ~ doDivides0(xp,xn) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_20,hypothesis,
    doDivides0(xp,sdtasdt0(xn,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_10]),c_0_17])]) ).

cnf(c_0_21,plain,
    ( doDivides0(X3,X1)
    | doDivides0(X3,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ isPrime0(X3)
    | ~ doDivides0(X3,sdtasdt0(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_22,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__3025]) ).

cnf(c_0_23,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

cnf(c_0_24,negated_conjecture,
    ~ doDivides0(xp,xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20])]) ).

cnf(c_0_25,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_22]),c_0_14]),c_0_23])]),c_0_24]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM523+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n014.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 12:49:48 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.60  % Version  : CSE_E---1.5
% 0.20/0.60  % Problem  : theBenchmark.p
% 0.20/0.60  % Proof found
% 0.20/0.60  % SZS status Theorem for theBenchmark.p
% 0.20/0.60  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.021000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.025000 s
%------------------------------------------------------------------------------