%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET077-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 03:32:17 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   10 (   8 unt;   0 nHn;   5 RR)
%            Number of literals    :   13 (   3 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    8 (   3 sgn)

% Comments : 
%------------------------------------------------------------------------------
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_singletons_are_sets_1,negated_conjecture,
    ~ member(singleton(x),universal_class) ).

cnf(refute_0_0,plain,
    member(unordered_pair(X_13,X_13),universal_class),
    inference(subst,[],[unordered_pairs_in_universal:[bind(X,$fot(X_13)),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_1,plain,
    unordered_pair(X_13,X_13) = singleton(X_13),
    inference(subst,[],[singleton_set:[bind(X,$fot(X_13))]]) ).

cnf(refute_0_2,plain,
    ( unordered_pair(X_13,X_13) != singleton(X_13)
    | ~ member(unordered_pair(X_13,X_13),universal_class)
    | member(singleton(X_13),universal_class) ),
    introduced(tautology,[equality,[$cnf( member(unordered_pair(X_13,X_13),universal_class) ),[0],$fot(singleton(X_13))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(unordered_pair(X_13,X_13),universal_class)
    | member(singleton(X_13),universal_class) ),
    inference(resolve,[$cnf( $equal(unordered_pair(X_13,X_13),singleton(X_13)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    member(singleton(X_13),universal_class),
    inference(resolve,[$cnf( member(unordered_pair(X_13,X_13),universal_class) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    member(singleton(x),universal_class),
    inference(subst,[],[refute_0_4:[bind(X_13,$fot(x))]]) ).

cnf(refute_0_6,plain,
    $false,
    inference(resolve,[$cnf( member(singleton(x),universal_class) )],[refute_0_5,prove_singletons_are_sets_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET077-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % 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
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 07:08:53 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.43  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.43  
% 0.20/0.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.43  
%------------------------------------------------------------------------------