%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM531+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 : 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 10:38:28 EDT 2023

% Result   : Theorem 0.53s 0.57s
% Output   : CNFRefutation 0.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   23 (   8 unt;   8 typ;   0 def)
%            Number of atoms       :   32 (   4 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   31 (  14   ~;   4   |;   9   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   6   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :    9 (   0 sgn;   6   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    aSet0: $i > $o ).

tff(decl_23,type,
    aElement0: $i > $o ).

tff(decl_24,type,
    aElementOf0: ( $i * $i ) > $o ).

tff(decl_25,type,
    isFinite0: $i > $o ).

tff(decl_26,type,
    slcrc0: $i ).

tff(decl_27,type,
    isCountable0: $i > $o ).

tff(decl_28,type,
    esk1_1: $i > $i ).

tff(decl_29,type,
    esk2_0: $i ).

fof(m__,conjecture,
    ! [X1] :
      ( ( aSet0(X1)
        & isCountable0(X1) )
     => ~ ( ~ ? [X2] : aElementOf0(X2,X1)
          & X1 = slcrc0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(mCountNFin,axiom,
    ! [X1] :
      ( ( aSet0(X1)
        & isCountable0(X1) )
     => ~ isFinite0(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).

fof(mEmpFin,axiom,
    isFinite0(slcrc0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEmpFin) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1] :
        ( ( aSet0(X1)
          & isCountable0(X1) )
       => ~ ( ~ ? [X2] : aElementOf0(X2,X1)
            & X1 = slcrc0 ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

fof(c_0_4,plain,
    ! [X1] :
      ( ( aSet0(X1)
        & isCountable0(X1) )
     => ~ isFinite0(X1) ),
    inference(fof_simplification,[status(thm)],[mCountNFin]) ).

fof(c_0_5,negated_conjecture,
    ! [X11] :
      ( aSet0(esk2_0)
      & isCountable0(esk2_0)
      & ~ aElementOf0(X11,esk2_0)
      & esk2_0 = slcrc0 ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])]) ).

fof(c_0_6,plain,
    ! [X9] :
      ( ~ aSet0(X9)
      | ~ isCountable0(X9)
      | ~ isFinite0(X9) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).

cnf(c_0_7,negated_conjecture,
    isCountable0(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    esk2_0 = slcrc0,
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    aSet0(esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( ~ aSet0(X1)
    | ~ isCountable0(X1)
    | ~ isFinite0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    isCountable0(slcrc0),
    inference(rw,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_12,plain,
    isFinite0(slcrc0),
    inference(split_conjunct,[status(thm)],[mEmpFin]) ).

cnf(c_0_13,negated_conjecture,
    aSet0(slcrc0),
    inference(rw,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_14,negated_conjecture,
    $false,
    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])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM531+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n023.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 15:04:12 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.20/0.55  start to proof: theBenchmark
% 0.53/0.57  % Version  : CSE_E---1.5
% 0.53/0.57  % Problem  : theBenchmark.p
% 0.53/0.57  % Proof found
% 0.53/0.57  % SZS status Theorem for theBenchmark.p
% 0.53/0.57  % SZS output start Proof
% See solution above
% 0.53/0.57  % Total time : 0.006000 s
% 0.53/0.57  % SZS output end Proof
% 0.53/0.57  % Total time : 0.008000 s
%------------------------------------------------------------------------------