%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET093-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:32:31 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : CNFRefutation 0.19s
% 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 : 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 : 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_corollary_2_to_singletons_are_sets_1,negated_conjecture,
singleton(member_of(x)) = x ).
cnf(prove_corollary_2_to_singletons_are_sets_2,negated_conjecture,
~ member(x,universal_class) ).
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(member_of(x)),universal_class),
inference(subst,[],[refute_0_4:[bind(X_11,$fot(member_of(x)))]]) ).
cnf(refute_0_6,plain,
( singleton(member_of(x)) != x
| ~ member(singleton(member_of(x)),universal_class)
| member(x,universal_class) ),
introduced(tautology,[equality,[$cnf( member(singleton(member_of(x)),universal_class) ),[0],$fot(x)]]) ).
cnf(refute_0_7,plain,
( ~ member(singleton(member_of(x)),universal_class)
| member(x,universal_class) ),
inference(resolve,[$cnf( $equal(singleton(member_of(x)),x) )],[prove_corollary_2_to_singletons_are_sets_1,refute_0_6]) ).
cnf(refute_0_8,plain,
member(x,universal_class),
inference(resolve,[$cnf( member(singleton(member_of(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_2_to_singletons_are_sets_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET093-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.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 15:32:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.42
% 0.19/0.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------