%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET095-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 03:32:34 EDT 2022

% Result   : Unsatisfiable 2.35s 2.53s
% Output   : CNFRefutation 2.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  10 RR)
%            Number of literals    :   20 (   3 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   13 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(singleton_set,axiom,
    unordered_pair(X,X) = singleton(X) ).

cnf(unordered_pair_is_subset,axiom,
    ( ~ member(X,Z)
    | ~ member(Y,Z)
    | subclass(unordered_pair(X,Y),Z) ) ).

cnf(prove_property_of_singletons2_1,negated_conjecture,
    member(x,y) ).

cnf(prove_property_of_singletons2_2,negated_conjecture,
    ~ subclass(singleton(x),y) ).

cnf(refute_0_0,plain,
    ( ~ member(Y,Z)
    | subclass(unordered_pair(Y,Y),Z) ),
    inference(subst,[],[unordered_pair_is_subset:[bind(X,$fot(Y))]]) ).

cnf(refute_0_1,plain,
    unordered_pair(Y,Y) = singleton(Y),
    inference(subst,[],[singleton_set:[bind(X,$fot(Y))]]) ).

cnf(refute_0_2,plain,
    ( unordered_pair(Y,Y) != singleton(Y)
    | ~ subclass(unordered_pair(Y,Y),Z)
    | subclass(singleton(Y),Z) ),
    introduced(tautology,[equality,[$cnf( subclass(unordered_pair(Y,Y),Z) ),[0],$fot(singleton(Y))]]) ).

cnf(refute_0_3,plain,
    ( ~ subclass(unordered_pair(Y,Y),Z)
    | subclass(singleton(Y),Z) ),
    inference(resolve,[$cnf( $equal(unordered_pair(Y,Y),singleton(Y)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(Y,Z)
    | subclass(singleton(Y),Z) ),
    inference(resolve,[$cnf( subclass(unordered_pair(Y,Y),Z) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ member(x,y)
    | subclass(singleton(x),y) ),
    inference(subst,[],[refute_0_4:[bind(Y,$fot(x)),bind(Z,$fot(y))]]) ).

cnf(refute_0_6,plain,
    subclass(singleton(x),y),
    inference(resolve,[$cnf( member(x,y) )],[prove_property_of_singletons2_1,refute_0_5]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( subclass(singleton(x),y) )],[refute_0_6,prove_property_of_singletons2_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET095-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n007.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  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 05:03:31 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.35/2.53  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.35/2.53  
% 2.35/2.53  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.35/2.53  
%------------------------------------------------------------------------------