%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET093-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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  : 600s
% DateTime : Tue Jul 19 03:32:31 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   6 unt;   0 nHn;   7 RR)
%            Number of literals    :   11 (   2 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :    1 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(singletons_are_sets,axiom,
    member(singleton(X),universal_class) ).

cnf(prove_corollary_2_to_singletons_are_sets_1,negated_conjecture,
    singleton(member_of(x)) = x ).

cnf(prove_corollary_2_to_singletons_are_sets_2,negated_conjecture,
    ~ member(x,universal_class) ).

cnf(refute_0_0,plain,
    member(singleton(member_of(x)),universal_class),
    inference(subst,[],[singletons_are_sets:[bind(X,$fot(member_of(x)))]]) ).

cnf(refute_0_1,plain,
    ( singleton(member_of(x)) != x
    | ~ member(singleton(member_of(x)),universal_class)
    | member(x,universal_class) ),
    introduced(tautology,[equality,[$cnf( member(singleton(member_of(x)),universal_class) ),[0],$fot(x)]]) ).

cnf(refute_0_2,plain,
    ( ~ member(singleton(member_of(x)),universal_class)
    | member(x,universal_class) ),
    inference(resolve,[$cnf( $equal(singleton(member_of(x)),x) )],[prove_corollary_2_to_singletons_are_sets_1,refute_0_1]) ).

cnf(refute_0_3,plain,
    member(x,universal_class),
    inference(resolve,[$cnf( member(singleton(member_of(x)),universal_class) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    $false,
    inference(resolve,[$cnf( member(x,universal_class) )],[refute_0_3,prove_corollary_2_to_singletons_are_sets_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET093-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n005.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  : 600
% 0.12/0.33  % DateTime : Mon Jul 11 02:04:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.42  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.42  
% 0.19/0.42  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42  
%------------------------------------------------------------------------------