%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET184-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n018.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 03:33:24 EDT 2022

% Result   : Unsatisfiable 35.62s 35.80s
% Output   : CNFRefutation 35.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   16 (   4 unt;   4 nHn;  13 RR)
%            Number of literals    :   29 (   2 equ;  10 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   :   14 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(not_subclass_members1,axiom,
    ( member(not_subclass_element(X,Y),X)
    | subclass(X,Y) ) ).

cnf(not_subclass_members2,axiom,
    ( ~ member(not_subclass_element(X,Y),Y)
    | subclass(X,Y) ) ).

cnf(intersection2,axiom,
    ( ~ member(Z,intersection(X,Y))
    | member(Z,Y) ) ).

cnf(prove_subclass_property2_1,negated_conjecture,
    intersection(x,y) = x ).

cnf(prove_subclass_property2_2,negated_conjecture,
    ~ subclass(x,y) ).

cnf(refute_0_0,plain,
    ( ~ member(not_subclass_element(x,y),y)
    | subclass(x,y) ),
    inference(subst,[],[not_subclass_members2:[bind(X,$fot(x)),bind(Y,$fot(y))]]) ).

cnf(refute_0_1,plain,
    ( member(not_subclass_element(x,Y),x)
    | subclass(x,Y) ),
    inference(subst,[],[not_subclass_members1:[bind(X,$fot(x))]]) ).

cnf(refute_0_2,plain,
    ( ~ member(X_820,intersection(x,y))
    | member(X_820,y) ),
    inference(subst,[],[intersection2:[bind(X,$fot(x)),bind(Y,$fot(y)),bind(Z,$fot(X_820))]]) ).

cnf(refute_0_3,plain,
    ( intersection(x,y) != x
    | ~ member(X_820,x)
    | member(X_820,intersection(x,y)) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_820,intersection(x,y)) ),[1],$fot(x)]]) ).

cnf(refute_0_4,plain,
    ( ~ member(X_820,x)
    | member(X_820,intersection(x,y)) ),
    inference(resolve,[$cnf( $equal(intersection(x,y),x) )],[prove_subclass_property2_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ member(X_820,x)
    | member(X_820,y) ),
    inference(resolve,[$cnf( member(X_820,intersection(x,y)) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
    ( ~ member(not_subclass_element(x,Y),x)
    | member(not_subclass_element(x,Y),y) ),
    inference(subst,[],[refute_0_5:[bind(X_820,$fot(not_subclass_element(x,Y)))]]) ).

cnf(refute_0_7,plain,
    ( member(not_subclass_element(x,Y),y)
    | subclass(x,Y) ),
    inference(resolve,[$cnf( member(not_subclass_element(x,Y),x) )],[refute_0_1,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( member(not_subclass_element(x,y),y)
    | subclass(x,y) ),
    inference(subst,[],[refute_0_7:[bind(Y,$fot(y))]]) ).

cnf(refute_0_9,plain,
    subclass(x,y),
    inference(resolve,[$cnf( member(not_subclass_element(x,y),y) )],[refute_0_8,refute_0_0]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( subclass(x,y) )],[refute_0_9,prove_subclass_property2_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET184-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n018.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 : Sun Jul 10 03:39:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 35.62/35.80  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.62/35.80  
% 35.62/35.80  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 35.62/35.80  
%------------------------------------------------------------------------------