%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM458+2 : 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 : n002.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 10:37:41 EDT 2023

% Result   : Theorem 0.15s 0.52s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   21 (   5 unt;   9 typ;   0 def)
%            Number of atoms       :   25 (   9 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   22 (   9   ~;   7   |;   5   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   0 sgn;   3   !;   2   ?;   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,
    xm: $i ).

tff(decl_30,type,
    esk1_2: ( $i * $i ) > $i ).

fof(m__,conjecture,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xm,X1) = xm )
    | sdtlseqdt0(xm,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(m_AddZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).

fof(m__718,hypothesis,
    aNaturalNumber0(xm),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__718) ).

fof(c_0_4,negated_conjecture,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xm,X1) = xm )
      | sdtlseqdt0(xm,xm) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_5,negated_conjecture,
    ! [X41] :
      ( ( ~ aNaturalNumber0(X41)
        | sdtpldt0(xm,X41) != xm )
      & ~ sdtlseqdt0(xm,xm) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_6,plain,
    ! [X13] :
      ( ( sdtpldt0(X13,sz00) = X13
        | ~ aNaturalNumber0(X13) )
      & ( X13 = sdtpldt0(sz00,X13)
        | ~ aNaturalNumber0(X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).

cnf(c_0_7,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xm,X1) != xm ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_10,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__718]) ).

cnf(c_0_11,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : NUM458+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.11  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31  % Computer : n002.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Fri Aug 25 09:34:32 EDT 2023
% 0.11/0.31  % CPUTime  : 
% 0.15/0.50  start to proof: theBenchmark
% 0.15/0.52  % Version  : CSE_E---1.5
% 0.15/0.52  % Problem  : theBenchmark.p
% 0.15/0.52  % Proof found
% 0.15/0.52  % SZS status Theorem for theBenchmark.p
% 0.15/0.52  % SZS output start Proof
% See solution above
% 0.15/0.52  % Total time : 0.006000 s
% 0.15/0.52  % SZS output end Proof
% 0.15/0.52  % Total time : 0.008000 s
%------------------------------------------------------------------------------