TSTP Solution File: NUM505+3 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM505+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 : n019.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 10:38:10 EDT 2023

% Result   : Theorem 0.18s 0.60s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   50 (   7 unt;  30 typ;   0 def)
%            Number of atoms       :   65 (  22 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :   72 (  27   ~;  23   |;  18   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   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    :   25 (  25 usr;  13 con; 0-3 aty)
%            Number of variables   :   16 (   0 sgn;   8   !;   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 ).

tff(decl_50,type,
    esk13_0: $i ).

tff(decl_51,type,
    esk14_0: $i ).

fof(m__,conjecture,
    ( ~ ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xp,X1) = xk )
        | sdtlseqdt0(xp,xk) )
   => ( xk != xp
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xk,X1) = xp )
        | sdtlseqdt0(xk,xp) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(m_AddZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).

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

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).

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

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(c_0_6,negated_conjecture,
    ~ ( ~ ( ? [X1] :
              ( aNaturalNumber0(X1)
              & sdtpldt0(xp,X1) = xk )
          | sdtlseqdt0(xp,xk) )
     => ( xk != xp
        & ( ? [X1] :
              ( aNaturalNumber0(X1)
              & sdtpldt0(xk,X1) = xp )
          | sdtlseqdt0(xk,xp) ) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_7,negated_conjecture,
    ! [X108,X109] :
      ( ( ~ aNaturalNumber0(X108)
        | sdtpldt0(xp,X108) != xk )
      & ~ sdtlseqdt0(xp,xk)
      & ( ~ aNaturalNumber0(X109)
        | sdtpldt0(xk,X109) != xp
        | xk = xp )
      & ( ~ sdtlseqdt0(xk,xp)
        | xk = xp ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).

fof(c_0_8,plain,
    ! [X15] :
      ( ( sdtpldt0(X15,sz00) = X15
        | ~ aNaturalNumber0(X15) )
      & ( X15 = sdtpldt0(sz00,X15)
        | ~ aNaturalNumber0(X15) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).

fof(c_0_9,plain,
    ! [X49,X50] :
      ( ( X50 != X49
        | sdtlseqdt0(X49,X50)
        | ~ aNaturalNumber0(X49)
        | ~ aNaturalNumber0(X50) )
      & ( sdtlseqdt0(X50,X49)
        | sdtlseqdt0(X49,X50)
        | ~ aNaturalNumber0(X49)
        | ~ aNaturalNumber0(X50) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).

cnf(c_0_10,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xp,X1) != xk ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_13,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_14,negated_conjecture,
    ( xk = xp
    | ~ sdtlseqdt0(xk,xp) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_15,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,hypothesis,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_17,negated_conjecture,
    xk != xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]) ).

cnf(c_0_18,negated_conjecture,
    ~ sdtlseqdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_13]),c_0_16])]),c_0_17]),c_0_18]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM505+3 : 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
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Aug 25 16:13:13 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.53  start to proof: theBenchmark
% 0.18/0.60  % Version  : CSE_E---1.5
% 0.18/0.60  % Problem  : theBenchmark.p
% 0.18/0.60  % Proof found
% 0.18/0.60  % SZS status Theorem for theBenchmark.p
% 0.18/0.60  % SZS output start Proof
% See solution above
% 0.18/0.60  % Total time : 0.061000 s
% 0.18/0.60  % SZS output end Proof
% 0.18/0.60  % Total time : 0.064000 s
%------------------------------------------------------------------------------