%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET090-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 03:32:28 EDT 2022

% Result   : Unsatisfiable 6.65s 6.85s
% Output   : CNFRefutation 6.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   18 (   8 unt;   0 nHn;  18 RR)
%            Number of literals    :   29 (   8 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   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   :    5 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(set_in_its_singleton,axiom,
    ( ~ member(X,universal_class)
    | member(X,singleton(X)) ) ).

cnf(only_member_in_singleton,axiom,
    ( ~ member(Y,singleton(X))
    | Y = X ) ).

cnf(member_exists1,axiom,
    ( ~ member(Y,universal_class)
    | member(member_of(singleton(Y)),universal_class) ) ).

cnf(member_exists2,axiom,
    ( ~ member(Y,universal_class)
    | singleton(member_of(singleton(Y))) = singleton(Y) ) ).

cnf(prove_member_of_singleton_is_unique_1,negated_conjecture,
    member(u,universal_class) ).

cnf(prove_member_of_singleton_is_unique_2,negated_conjecture,
    member_of(singleton(u)) != u ).

cnf(refute_0_0,plain,
    ( ~ member(member_of(singleton(u)),singleton(u))
    | member_of(singleton(u)) = u ),
    inference(subst,[],[only_member_in_singleton:[bind(X,$fot(u)),bind(Y,$fot(member_of(singleton(u))))]]) ).

cnf(refute_0_1,plain,
    ( ~ member(member_of(singleton(u)),universal_class)
    | member(member_of(singleton(u)),singleton(member_of(singleton(u)))) ),
    inference(subst,[],[set_in_its_singleton:[bind(X,$fot(member_of(singleton(u))))]]) ).

cnf(refute_0_2,plain,
    ( ~ member(u,universal_class)
    | member(member_of(singleton(u)),universal_class) ),
    inference(subst,[],[member_exists1:[bind(Y,$fot(u))]]) ).

cnf(refute_0_3,plain,
    member(member_of(singleton(u)),universal_class),
    inference(resolve,[$cnf( member(u,universal_class) )],[prove_member_of_singleton_is_unique_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    member(member_of(singleton(u)),singleton(member_of(singleton(u)))),
    inference(resolve,[$cnf( member(member_of(singleton(u)),universal_class) )],[refute_0_3,refute_0_1]) ).

cnf(refute_0_5,plain,
    ( ~ member(u,universal_class)
    | singleton(member_of(singleton(u))) = singleton(u) ),
    inference(subst,[],[member_exists2:[bind(Y,$fot(u))]]) ).

cnf(refute_0_6,plain,
    singleton(member_of(singleton(u))) = singleton(u),
    inference(resolve,[$cnf( member(u,universal_class) )],[prove_member_of_singleton_is_unique_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( singleton(member_of(singleton(u))) != singleton(u)
    | ~ member(member_of(singleton(u)),singleton(member_of(singleton(u))))
    | member(member_of(singleton(u)),singleton(u)) ),
    introduced(tautology,[equality,[$cnf( member(member_of(singleton(u)),singleton(member_of(singleton(u)))) ),[1],$fot(singleton(u))]]) ).

cnf(refute_0_8,plain,
    ( ~ member(member_of(singleton(u)),singleton(member_of(singleton(u))))
    | member(member_of(singleton(u)),singleton(u)) ),
    inference(resolve,[$cnf( $equal(singleton(member_of(singleton(u))),singleton(u)) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    member(member_of(singleton(u)),singleton(u)),
    inference(resolve,[$cnf( member(member_of(singleton(u)),singleton(member_of(singleton(u)))) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    member_of(singleton(u)) = u,
    inference(resolve,[$cnf( member(member_of(singleton(u)),singleton(u)) )],[refute_0_9,refute_0_0]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( $equal(member_of(singleton(u)),u) )],[refute_0_10,prove_member_of_singleton_is_unique_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : SET090-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.09/0.15  % Command  : metis --show proof --show saturation %s
% 0.15/0.37  % Computer : n017.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Sun Jul 10 09:06:17 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.65/6.85  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.65/6.85  
% 6.65/6.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.65/6.85  
%------------------------------------------------------------------------------