%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET001-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 03:30:53 EDT 2022

% Result   : Unsatisfiable 0.19s 0.35s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   6 unt;   0 nHn;  12 RR)
%            Number of literals    :   20 (   0 equ;   9 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    7 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(membership_in_subsets,axiom,
    ( ~ member(Element,Subset)
    | ~ subset(Subset,Superset)
    | member(Element,Superset) ) ).

cnf(set_equal_sets_are_subsets1,axiom,
    ( ~ equal_sets(Subset,Superset)
    | subset(Subset,Superset) ) ).

cnf(b_equals_bb,hypothesis,
    equal_sets(b,bb) ).

cnf(element_of_b,hypothesis,
    member(element_of_b,b) ).

cnf(prove_element_of_bb,negated_conjecture,
    ~ member(element_of_b,bb) ).

cnf(refute_0_0,plain,
    ( ~ equal_sets(b,bb)
    | subset(b,bb) ),
    inference(subst,[],[set_equal_sets_are_subsets1:[bind(Subset,$fot(b)),bind(Superset,$fot(bb))]]) ).

cnf(refute_0_1,plain,
    subset(b,bb),
    inference(resolve,[$cnf( equal_sets(b,bb) )],[b_equals_bb,refute_0_0]) ).

cnf(refute_0_2,plain,
    ( ~ member(X_13,b)
    | ~ subset(b,bb)
    | member(X_13,bb) ),
    inference(subst,[],[membership_in_subsets:[bind(Element,$fot(X_13)),bind(Subset,$fot(b)),bind(Superset,$fot(bb))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(X_13,b)
    | member(X_13,bb) ),
    inference(resolve,[$cnf( subset(b,bb) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(element_of_b,b)
    | member(element_of_b,bb) ),
    inference(subst,[],[refute_0_3:[bind(X_13,$fot(element_of_b))]]) ).

cnf(refute_0_5,plain,
    member(element_of_b,bb),
    inference(resolve,[$cnf( member(element_of_b,b) )],[element_of_b,refute_0_4]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( member(element_of_b,bb) )],[refute_0_5,prove_element_of_bb]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET001-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n008.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
% 0.19/0.34  % WCLimit  : 600
% 0.19/0.34  % DateTime : Mon Jul 11 02:50:08 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.35  
% 0.19/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.35  
%------------------------------------------------------------------------------