%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET078-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 03:32:18 EDT 2022

% Result   : Unsatisfiable 1.08s 1.27s
% Output   : CNFRefutation 1.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   9 unt;   0 nHn;   5 RR)
%            Number of literals    :   18 (   3 equ;   6 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;   3 con; 0-2 aty)
%            Number of variables   :   14 (   6 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(unordered_pair3,axiom,
    ( ~ member(Y,universal_class)
    | member(Y,unordered_pair(X,Y)) ) ).

cnf(unordered_pairs_in_universal,axiom,
    member(unordered_pair(X,Y),universal_class) ).

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

cnf(prove_corollary_1_to_singletons_are_sets_1,negated_conjecture,
    ~ member(singleton(y),unordered_pair(x,singleton(y))) ).

cnf(refute_0_0,plain,
    member(unordered_pair(X_11,X_11),universal_class),
    inference(subst,[],[unordered_pairs_in_universal:[bind(X,$fot(X_11)),bind(Y,$fot(X_11))]]) ).

cnf(refute_0_1,plain,
    unordered_pair(X_11,X_11) = singleton(X_11),
    inference(subst,[],[singleton_set:[bind(X,$fot(X_11))]]) ).

cnf(refute_0_2,plain,
    ( unordered_pair(X_11,X_11) != singleton(X_11)
    | ~ member(unordered_pair(X_11,X_11),universal_class)
    | member(singleton(X_11),universal_class) ),
    introduced(tautology,[equality,[$cnf( member(unordered_pair(X_11,X_11),universal_class) ),[0],$fot(singleton(X_11))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(unordered_pair(X_11,X_11),universal_class)
    | member(singleton(X_11),universal_class) ),
    inference(resolve,[$cnf( $equal(unordered_pair(X_11,X_11),singleton(X_11)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    member(singleton(X_11),universal_class),
    inference(resolve,[$cnf( member(unordered_pair(X_11,X_11),universal_class) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    ( ~ member(singleton(X_11),universal_class)
    | member(singleton(X_11),unordered_pair(X_110,singleton(X_11))) ),
    inference(subst,[],[unordered_pair3:[bind(X,$fot(X_110)),bind(Y,$fot(singleton(X_11)))]]) ).

cnf(refute_0_6,plain,
    member(singleton(X_11),unordered_pair(X_110,singleton(X_11))),
    inference(resolve,[$cnf( member(singleton(X_11),universal_class) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    member(singleton(y),unordered_pair(x,singleton(y))),
    inference(subst,[],[refute_0_6:[bind(X_11,$fot(y)),bind(X_110,$fot(x))]]) ).

cnf(refute_0_8,plain,
    $false,
    inference(resolve,[$cnf( member(singleton(y),unordered_pair(x,singleton(y))) )],[refute_0_7,prove_corollary_1_to_singletons_are_sets_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET078-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n005.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 22:31:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.08/1.27  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/1.27  
% 1.08/1.27  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.08/1.27  
%------------------------------------------------------------------------------