%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SET117-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 03:32:51 EDT 2022

% Result   : Unsatisfiable 0.45s 0.60s
% Output   : CNFRefutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   14 (  10 unt;   0 nHn;   9 RR)
%            Number of literals    :   20 (   5 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-2 aty)
%            Number of variables   :   14 (   5 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(unordered_pairs_in_universal,axiom,
    member(unordered_pair(X,Y),universal_class) ).

cnf(ordered_pair,axiom,
    unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ).

cnf(prove_corollary_1_to_ordered_pairs_are_sets_1,negated_conjecture,
    ordered_pair(first(x),second(x)) = x ).

cnf(prove_corollary_1_to_ordered_pairs_are_sets_2,negated_conjecture,
    ~ member(x,universal_class) ).

cnf(refute_0_0,plain,
    member(unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))),universal_class),
    inference(subst,[],[unordered_pairs_in_universal:[bind(X,$fot(singleton(X_70))),bind(Y,$fot(unordered_pair(X_70,singleton(X_71))))]]) ).

cnf(refute_0_1,plain,
    unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))) = ordered_pair(X_70,X_71),
    inference(subst,[],[ordered_pair:[bind(X,$fot(X_70)),bind(Y,$fot(X_71))]]) ).

cnf(refute_0_2,plain,
    ( unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))) != ordered_pair(X_70,X_71)
    | ~ member(unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))),universal_class)
    | member(ordered_pair(X_70,X_71),universal_class) ),
    introduced(tautology,[equality,[$cnf( member(unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))),universal_class) ),[0],$fot(ordered_pair(X_70,X_71))]]) ).

cnf(refute_0_3,plain,
    ( ~ member(unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))),universal_class)
    | member(ordered_pair(X_70,X_71),universal_class) ),
    inference(resolve,[$cnf( $equal(unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))),ordered_pair(X_70,X_71)) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    member(ordered_pair(X_70,X_71),universal_class),
    inference(resolve,[$cnf( member(unordered_pair(singleton(X_70),unordered_pair(X_70,singleton(X_71))),universal_class) )],[refute_0_0,refute_0_3]) ).

cnf(refute_0_5,plain,
    member(ordered_pair(first(x),second(x)),universal_class),
    inference(subst,[],[refute_0_4:[bind(X_70,$fot(first(x))),bind(X_71,$fot(second(x)))]]) ).

cnf(refute_0_6,plain,
    ( ordered_pair(first(x),second(x)) != x
    | ~ member(ordered_pair(first(x),second(x)),universal_class)
    | member(x,universal_class) ),
    introduced(tautology,[equality,[$cnf( member(ordered_pair(first(x),second(x)),universal_class) ),[0],$fot(x)]]) ).

cnf(refute_0_7,plain,
    ( ~ member(ordered_pair(first(x),second(x)),universal_class)
    | member(x,universal_class) ),
    inference(resolve,[$cnf( $equal(ordered_pair(first(x),second(x)),x) )],[prove_corollary_1_to_ordered_pairs_are_sets_1,refute_0_6]) ).

cnf(refute_0_8,plain,
    member(x,universal_class),
    inference(resolve,[$cnf( member(ordered_pair(first(x),second(x)),universal_class) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    $false,
    inference(resolve,[$cnf( member(x,universal_class) )],[refute_0_8,prove_corollary_1_to_ordered_pairs_are_sets_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET117-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n029.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jul 11 10:50:02 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.45/0.60  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.45/0.60  
% 0.45/0.60  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.45/0.60  
%------------------------------------------------------------------------------