%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET061-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n016.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 03:31:59 EDT 2022

% Result   : Unsatisfiable 0.17s 0.49s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   11 (   7 unt;   2 nHn;   7 RR)
%            Number of literals    :   16 (   4 equ;   7 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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   11 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(regularity1,axiom,
    ( X = null_class
    | member(regular(X),X) ) ).

cnf(special_classes_lemma,axiom,
    ~ member(Y,intersection(complement(X),X)) ).

cnf(prove_existence_of_null_class_1,negated_conjecture,
    member(z,null_class) ).

cnf(refute_0_0,plain,
    ~ member(regular(intersection(complement(X),X)),intersection(complement(X),X)),
    inference(subst,[],[special_classes_lemma:[bind(Y,$fot(regular(intersection(complement(X),X))))]]) ).

cnf(refute_0_1,plain,
    ( intersection(complement(X),X) = null_class
    | member(regular(intersection(complement(X),X)),intersection(complement(X),X)) ),
    inference(subst,[],[regularity1:[bind(X,$fot(intersection(complement(X),X)))]]) ).

cnf(refute_0_2,plain,
    intersection(complement(X),X) = null_class,
    inference(resolve,[$cnf( member(regular(intersection(complement(X),X)),intersection(complement(X),X)) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ( intersection(complement(X),X) != null_class
    | ~ member(Y,null_class)
    | member(Y,intersection(complement(X),X)) ),
    introduced(tautology,[equality,[$cnf( ~ member(Y,intersection(complement(X),X)) ),[1],$fot(null_class)]]) ).

cnf(refute_0_4,plain,
    ( ~ member(Y,null_class)
    | member(Y,intersection(complement(X),X)) ),
    inference(resolve,[$cnf( $equal(intersection(complement(X),X),null_class) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    ~ member(Y,null_class),
    inference(resolve,[$cnf( member(Y,intersection(complement(X),X)) )],[refute_0_4,special_classes_lemma]) ).

cnf(refute_0_6,plain,
    ~ member(z,null_class),
    inference(subst,[],[refute_0_5:[bind(Y,$fot(z))]]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( member(z,null_class) )],[prove_existence_of_null_class_1,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET061-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.32  % Computer : n016.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Sun Jul 10 16:37:41 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.13/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.49  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49  
% 0.17/0.49  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.17/0.49  
%------------------------------------------------------------------------------