TSTP Solution File: NUM505+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM505+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 : n031.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 0.20s 0.64s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   60 (  13 unt;  20 typ;   0 def)
%            Number of atoms       :  152 (  48 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  181 (  69   ~;  77   |;  24   &)
%                                         (   2 <=>;   9  =>;   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   :   31 (   0 sgn;  20   !;   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(m__,conjecture,
    ( ~ sdtlseqdt0(xp,xk)
   => ( xk != xp
      & sdtlseqdt0(xk,xp) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

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

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

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

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

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

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

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,negated_conjecture,
    ~ ( ~ sdtlseqdt0(xp,xk)
     => ( xk != xp
        & sdtlseqdt0(xk,xp) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).

cnf(c_0_12,plain,
    ( aNaturalNumber0(X1)
    | X3 = sz00
    | X1 != sdtsldt0(X2,X3)
    | ~ doDivides0(X3,X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,negated_conjecture,
    ( ~ sdtlseqdt0(xp,xk)
    & ( xk = xp
      | ~ sdtlseqdt0(xk,xp) ) ),
    inference(fof_nnf,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X47,X48] :
      ( ( X48 != X47
        | sdtlseqdt0(X47,X48)
        | ~ aNaturalNumber0(X47)
        | ~ aNaturalNumber0(X48) )
      & ( sdtlseqdt0(X48,X47)
        | sdtlseqdt0(X47,X48)
        | ~ aNaturalNumber0(X47)
        | ~ aNaturalNumber0(X48) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).

cnf(c_0_15,plain,
    ( X1 = sz00
    | aNaturalNumber0(sdtsldt0(X2,X1))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_16,hypothesis,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_17,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_18,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

fof(c_0_19,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_20,negated_conjecture,
    ( xk = xp
    | ~ sdtlseqdt0(xk,xp) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,negated_conjecture,
    ~ sdtlseqdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_23,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_15,c_0_16]),c_0_17]),c_0_18])]) ).

cnf(c_0_24,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

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

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

cnf(c_0_27,negated_conjecture,
    ( xk = xp
    | ~ aNaturalNumber0(xk) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18])]),c_0_22]) ).

cnf(c_0_28,hypothesis,
    ( xp = sz00
    | aNaturalNumber0(xk) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).

cnf(c_0_29,negated_conjecture,
    ( xp = sz00
    | xk = xp ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_30,plain,
    ! [X41] :
      ( ~ aNaturalNumber0(X41)
      | sdtlseqdt0(X41,X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLERefl])]) ).

fof(c_0_31,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_32,negated_conjecture,
    ( xp = sz00
    | ~ sdtlseqdt0(xp,xp) ),
    inference(spm,[status(thm)],[c_0_22,c_0_29]) ).

cnf(c_0_33,plain,
    ( sdtlseqdt0(X1,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_34,plain,
    ( X1 != sz00
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_35,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_36,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_37,negated_conjecture,
    xp = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_18])]) ).

cnf(c_0_38,plain,
    ~ isPrime0(sz00),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_35])]) ).

cnf(c_0_39,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : NUM505+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n031.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 09:35:22 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.62  start to proof: theBenchmark
% 0.20/0.64  % Version  : CSE_E---1.5
% 0.20/0.64  % Problem  : theBenchmark.p
% 0.20/0.64  % Proof found
% 0.20/0.64  % SZS status Theorem for theBenchmark.p
% 0.20/0.64  % SZS output start Proof
% See solution above
% 0.20/0.65  % Total time : 0.020000 s
% 0.20/0.65  % SZS output end Proof
% 0.20/0.65  % Total time : 0.022000 s
%------------------------------------------------------------------------------