%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET094-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n027.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 03:32:32 EDT 2022

% Result   : Unsatisfiable 152.70s 152.87s
% Output   : CNFRefutation 152.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   22 (   9 unt;   1 nHn;  19 RR)
%            Number of literals    :   39 (  23 equ;  18 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 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   :   22 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(unordered_pair_member,axiom,
    ( ~ member(U,unordered_pair(X,Y))
    | U = X
    | U = Y ) ).

cnf(singleton_set,axiom,
    unordered_pair(X,X) = singleton(X) ).

cnf(prove_property_of_singletons1_1,negated_conjecture,
    singleton(member_of(x)) = x ).

cnf(prove_property_of_singletons1_2,negated_conjecture,
    member(y,x) ).

cnf(prove_property_of_singletons1_3,negated_conjecture,
    member_of(x) != y ).

cnf(refute_0_0,plain,
    ( ~ member(X_2405,unordered_pair(X_2407,X_2407))
    | X_2405 = X_2407 ),
    inference(subst,[],[unordered_pair_member:[bind(U,$fot(X_2405)),bind(X,$fot(X_2407)),bind(Y,$fot(X_2407))]]) ).

cnf(refute_0_1,plain,
    unordered_pair(X_2407,X_2407) = singleton(X_2407),
    inference(subst,[],[singleton_set:[bind(X,$fot(X_2407))]]) ).

cnf(refute_0_2,plain,
    ( unordered_pair(X_2407,X_2407) != singleton(X_2407)
    | ~ member(X_2405,singleton(X_2407))
    | member(X_2405,unordered_pair(X_2407,X_2407)) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_2405,unordered_pair(X_2407,X_2407)) ),[1],$fot(singleton(X_2407))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(X_2405,singleton(X_2407))
    | member(X_2405,unordered_pair(X_2407,X_2407)) ),
    inference(resolve,[$cnf( $equal(unordered_pair(X_2407,X_2407),singleton(X_2407)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ member(X_2405,singleton(X_2407))
    | X_2405 = X_2407 ),
    inference(resolve,[$cnf( member(X_2405,unordered_pair(X_2407,X_2407)) )],[refute_0_3,refute_0_0]) ).

cnf(refute_0_5,plain,
    ( ~ member(X_2411,singleton(member_of(x)))
    | X_2411 = member_of(x) ),
    inference(subst,[],[refute_0_4:[bind(X_2405,$fot(X_2411)),bind(X_2407,$fot(member_of(x)))]]) ).

cnf(refute_0_6,plain,
    ( singleton(member_of(x)) != x
    | ~ member(X_2411,x)
    | member(X_2411,singleton(member_of(x))) ),
    introduced(tautology,[equality,[$cnf( ~ member(X_2411,singleton(member_of(x))) ),[1],$fot(x)]]) ).

cnf(refute_0_7,plain,
    ( ~ member(X_2411,x)
    | member(X_2411,singleton(member_of(x))) ),
    inference(resolve,[$cnf( $equal(singleton(member_of(x)),x) )],[prove_property_of_singletons1_1,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ member(X_2411,x)
    | X_2411 = member_of(x) ),
    inference(resolve,[$cnf( member(X_2411,singleton(member_of(x))) )],[refute_0_7,refute_0_5]) ).

cnf(refute_0_9,plain,
    ( ~ member(y,x)
    | y = member_of(x) ),
    inference(subst,[],[refute_0_8:[bind(X_2411,$fot(y))]]) ).

cnf(refute_0_10,plain,
    y = member_of(x),
    inference(resolve,[$cnf( member(y,x) )],[prove_property_of_singletons1_2,refute_0_9]) ).

cnf(refute_0_11,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_13,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( y != member_of(x)
    | member_of(x) = y ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(y)),bind(Y0,$fot(member_of(x)))]]) ).

cnf(refute_0_15,plain,
    y != member_of(x),
    inference(resolve,[$cnf( $equal(member_of(x),y) )],[refute_0_14,prove_property_of_singletons1_3]) ).

cnf(refute_0_16,plain,
    $false,
    inference(resolve,[$cnf( $equal(y,member_of(x)) )],[refute_0_10,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET094-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n027.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 07:25:02 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 152.70/152.87  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 152.70/152.87  
% 152.70/152.87  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 152.70/152.87  
%------------------------------------------------------------------------------