%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET079-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 03:32:19 EDT 2022
% Result : Unsatisfiable 0.48s 0.68s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 16 ( 2 equ; 7 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; 3 con; 0-1 aty)
% Number of variables : 2 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_null_class,axiom,
~ member(Z,null_class) ).
cnf(set_in_its_singleton,axiom,
( ~ member(X,universal_class)
| member(X,singleton(X)) ) ).
cnf(prove_corollary_to_set_in_its_singleton_1,negated_conjecture,
member(x,universal_class) ).
cnf(prove_corollary_to_set_in_its_singleton_2,negated_conjecture,
singleton(x) = null_class ).
cnf(refute_0_0,plain,
( ~ member(x,universal_class)
| member(x,singleton(x)) ),
inference(subst,[],[set_in_its_singleton:[bind(X,$fot(x))]]) ).
cnf(refute_0_1,plain,
member(x,singleton(x)),
inference(resolve,[$cnf( member(x,universal_class) )],[prove_corollary_to_set_in_its_singleton_1,refute_0_0]) ).
cnf(refute_0_2,plain,
( singleton(x) != null_class
| ~ member(x,singleton(x))
| member(x,null_class) ),
introduced(tautology,[equality,[$cnf( member(x,singleton(x)) ),[1],$fot(null_class)]]) ).
cnf(refute_0_3,plain,
( ~ member(x,singleton(x))
| member(x,null_class) ),
inference(resolve,[$cnf( $equal(singleton(x),null_class) )],[prove_corollary_to_set_in_its_singleton_2,refute_0_2]) ).
cnf(refute_0_4,plain,
member(x,null_class),
inference(resolve,[$cnf( member(x,singleton(x)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
~ member(x,null_class),
inference(subst,[],[existence_of_null_class:[bind(Z,$fot(x))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( member(x,null_class) )],[refute_0_4,refute_0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET079-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.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 : Sat Jul 9 17:18:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.68
% 0.48/0.68 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.53/0.68
%------------------------------------------------------------------------------