%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET045+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/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 14:32:29 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   16 (   7 unt;   3 typ;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   27 (  13   ~;   8   |;   4   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   22 (   3 sgn;  10   !;   4   ?;   0   :)

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

tff(decl_23,type,
    esk1_1: $i > $i ).

tff(decl_24,type,
    esk2_0: $i ).

fof(pel41_1,axiom,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( element(X3,X2)
    <=> ( element(X3,X1)
        & ~ element(X3,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel41_1) ).

fof(pel41,conjecture,
    ~ ? [X1] :
      ! [X3] : element(X3,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel41) ).

fof(c_0_2,plain,
    ! [X1] :
    ? [X2] :
    ! [X3] :
      ( element(X3,X2)
    <=> ( element(X3,X1)
        & ~ element(X3,X3) ) ),
    inference(fof_simplification,[status(thm)],[pel41_1]) ).

fof(c_0_3,negated_conjecture,
    ~ ~ ? [X1] :
        ! [X3] : element(X3,X1),
    inference(assume_negation,[status(cth)],[pel41]) ).

fof(c_0_4,plain,
    ! [X4,X6,X7] :
      ( ( element(X6,X4)
        | ~ element(X6,esk1_1(X4)) )
      & ( ~ element(X6,X6)
        | ~ element(X6,esk1_1(X4)) )
      & ( ~ element(X7,X4)
        | element(X7,X7)
        | element(X7,esk1_1(X4)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])]) ).

fof(c_0_5,negated_conjecture,
    ! [X9] : element(X9,esk2_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

cnf(c_0_6,plain,
    ( element(X1,X1)
    | element(X1,esk1_1(X2))
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_7,negated_conjecture,
    element(X1,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,plain,
    ( ~ element(X1,X1)
    | ~ element(X1,esk1_1(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_9,negated_conjecture,
    ( element(X1,esk1_1(esk2_0))
    | element(X1,X1) ),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,negated_conjecture,
    element(esk1_1(X1),esk1_1(esk2_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).

cnf(c_0_11,negated_conjecture,
    ~ element(esk1_1(X1),esk1_1(X1)),
    inference(spm,[status(thm)],[c_0_8,c_0_10]) ).

cnf(c_0_12,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_11,c_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET045+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox/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   : Sat Aug 26 11:01:07 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.59  % SZS status Theorem for theBenchmark.p
% 0.19/0.59  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.004000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.006000 s
%------------------------------------------------------------------------------