%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n024.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 14:34:45 EDT 2023

% Result   : Theorem 0.20s 0.58s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   19 (   8 unt;   8 typ;   0 def)
%            Number of atoms       :   16 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   11 (   6   ~;   3   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   11 (   1 sgn;   8   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    empty_set: $i ).

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

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

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

tff(decl_26,type,
    empty: $i > $o ).

tff(decl_27,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk2_1: $i > $i ).

tff(decl_29,type,
    esk3_0: $i ).

fof(prove_no_difference_with_empty_set,conjecture,
    ! [X1] : difference(empty_set,X1) = empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_no_difference_with_empty_set) ).

fof(difference_empty_set,axiom,
    ! [X1,X2] :
      ( difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_empty_set) ).

fof(empty_set_subset,axiom,
    ! [X1] : subset(empty_set,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_subset) ).

fof(c_0_3,negated_conjecture,
    ~ ! [X1] : difference(empty_set,X1) = empty_set,
    inference(assume_negation,[status(cth)],[prove_no_difference_with_empty_set]) ).

fof(c_0_4,negated_conjecture,
    difference(empty_set,esk3_0) != empty_set,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).

fof(c_0_5,plain,
    ! [X5,X6] :
      ( ( difference(X5,X6) != empty_set
        | subset(X5,X6) )
      & ( ~ subset(X5,X6)
        | difference(X5,X6) = empty_set ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[difference_empty_set])]) ).

fof(c_0_6,plain,
    ! [X4] : subset(empty_set,X4),
    inference(variable_rename,[status(thm)],[empty_set_subset]) ).

cnf(c_0_7,negated_conjecture,
    difference(empty_set,esk3_0) != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

cnf(c_0_8,plain,
    ( difference(X1,X2) = empty_set
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,plain,
    subset(empty_set,X1),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET604+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sat Aug 26 12:34:39 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.58  % Version  : CSE_E---1.5
% 0.20/0.58  % Problem  : theBenchmark.p
% 0.20/0.58  % Proof found
% 0.20/0.58  % SZS status Theorem for theBenchmark.p
% 0.20/0.58  % SZS output start Proof
% See solution above
% 0.20/0.58  % Total time : 0.007000 s
% 0.20/0.58  % SZS output end Proof
% 0.20/0.58  % Total time : 0.009000 s
%------------------------------------------------------------------------------