%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n021.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 : Mon Jul 18 12:24:59 EDT 2022

% Result   : Unsatisfiable 30.58s 30.74s
% Output   : CNFRefutation 30.58s
% 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    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 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(limit_ordinals,axiom,
    intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals ).

cnf(prove_limit_ordinals_are_ordinals_1,negated_conjecture,
    ~ subclass(limit_ordinals,ordinal_numbers) ).

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

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

cnf(refute_0_2,plain,
    ( ~ member(X_1051,intersection(complement(kind_1_ordinals),ordinal_numbers))
    | member(X_1051,ordinal_numbers) ),
    inference(subst,[],[intersection2:[bind(X,$fot(complement(kind_1_ordinals))),bind(Y,$fot(ordinal_numbers)),bind(Z,$fot(X_1051))]]) ).

cnf(refute_0_3,plain,
    ( intersection(complement(kind_1_ordinals),ordinal_numbers) != limit_ordinals
    | ~ member(X_1051,limit_ordinals)
    | member(X_1051,intersection(complement(kind_1_ordinals),ordinal_numbers)) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_1051,intersection(complement(kind_1_ordinals),ordinal_numbers)) ),[1],$fot(limit_ordinals)]]) ).

cnf(refute_0_4,plain,
    ( ~ member(X_1051,limit_ordinals)
    | member(X_1051,intersection(complement(kind_1_ordinals),ordinal_numbers)) ),
    inference(resolve,[$cnf( $equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals) )],[limit_ordinals,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ member(X_1051,limit_ordinals)
    | member(X_1051,ordinal_numbers) ),
    inference(resolve,[$cnf( member(X_1051,intersection(complement(kind_1_ordinals),ordinal_numbers)) )],[refute_0_4,refute_0_2]) ).

cnf(refute_0_6,plain,
    ( ~ member(not_subclass_element(limit_ordinals,Y),limit_ordinals)
    | member(not_subclass_element(limit_ordinals,Y),ordinal_numbers) ),
    inference(subst,[],[refute_0_5:[bind(X_1051,$fot(not_subclass_element(limit_ordinals,Y)))]]) ).

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

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

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

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( subclass(limit_ordinals,ordinal_numbers) )],[refute_0_9,prove_limit_ordinals_are_ordinals_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n021.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 : Wed Jul  6 05:31:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 30.58/30.74  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.58/30.74  
% 30.58/30.74  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 30.58/30.74  
%------------------------------------------------------------------------------