%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET004-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Tue Jul 19 03:30:56 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   14 (   4 unt;   4 nHn;  11 RR)
%            Number of literals    :   26 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   13 (   1 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(subsets_axiom1,axiom,
    ( subset(Subset,Superset)
    | member(member_of_1_not_of_2(Subset,Superset),Subset) ) ).

cnf(subsets_axiom2,axiom,
    ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
    | subset(Subset,Superset) ) ).

cnf(member_of_set1_is_member_of_union,axiom,
    ( ~ union(Set1,Set2,Union)
    | ~ member(Element,Set1)
    | member(Element,Union) ) ).

cnf(a_union_b_is_aUb,hypothesis,
    union(a,b,aUb) ).

cnf(prove_a_is_a_subset_of_aUb,negated_conjecture,
    ~ subset(a,aUb) ).

cnf(refute_0_0,plain,
    ( ~ member(member_of_1_not_of_2(a,aUb),aUb)
    | subset(a,aUb) ),
    inference(subst,[],[subsets_axiom2:[bind(Subset,$fot(a)),bind(Superset,$fot(aUb))]]) ).

cnf(refute_0_1,plain,
    ( member(member_of_1_not_of_2(a,Superset),a)
    | subset(a,Superset) ),
    inference(subst,[],[subsets_axiom1:[bind(Subset,$fot(a))]]) ).

cnf(refute_0_2,plain,
    ( ~ member(X_35,a)
    | ~ union(a,b,aUb)
    | member(X_35,aUb) ),
    inference(subst,[],[member_of_set1_is_member_of_union:[bind(Element,$fot(X_35)),bind(Set1,$fot(a)),bind(Set2,$fot(b)),bind(Union,$fot(aUb))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(X_35,a)
    | member(X_35,aUb) ),
    inference(resolve,[$cnf( union(a,b,aUb) )],[a_union_b_is_aUb,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(member_of_1_not_of_2(a,Superset),a)
    | member(member_of_1_not_of_2(a,Superset),aUb) ),
    inference(subst,[],[refute_0_3:[bind(X_35,$fot(member_of_1_not_of_2(a,Superset)))]]) ).

cnf(refute_0_5,plain,
    ( member(member_of_1_not_of_2(a,Superset),aUb)
    | subset(a,Superset) ),
    inference(resolve,[$cnf( member(member_of_1_not_of_2(a,Superset),a) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( member(member_of_1_not_of_2(a,aUb),aUb)
    | subset(a,aUb) ),
    inference(subst,[],[refute_0_5:[bind(Superset,$fot(aUb))]]) ).

cnf(refute_0_7,plain,
    subset(a,aUb),
    inference(resolve,[$cnf( member(member_of_1_not_of_2(a,aUb),aUb) )],[refute_0_6,refute_0_0]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( subset(a,aUb) )],[refute_0_7,prove_a_is_a_subset_of_aUb]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n021.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 08:56:37 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------