%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET080-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 : 300s
% DateTime : Sat Jun 21 05:25:08 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 17 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 54 ( 26 ~; 22 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 13 ( 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(null_class_type,type,
null_class: $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(1,plain,
( ~ member(null_class,singleton(null_class))
<=> ~ member(null_class,singleton(null_class)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ member(null_class,singleton(null_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_in_its_singleton_1) ).
tff(3,plain,
~ member(null_class,singleton(null_class)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [X: $i] :
refl(( ( ~ member(X,universal_class)
| member(X,singleton(X)) )
<=> ( ~ member(X,universal_class)
| member(X,singleton(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
<=> ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
<=> ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_in_its_singleton) ).
tff(8,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( member(null_class,universal_class)
<=> member(null_class,universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
tff(13,plain,
member(null_class,universal_class),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(null_class,universal_class)
| member(null_class,singleton(null_class)) )
<=> ( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(null_class,universal_class)
| member(null_class,singleton(null_class)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(null_class,universal_class)
| member(null_class,singleton(null_class)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [X: $i] :
( ~ member(X,universal_class)
| member(X,singleton(X)) )
| ~ member(null_class,universal_class)
| member(null_class,singleton(null_class)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
$false,
inference(unit_resolution,[status(thm)],[16,13,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET080-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n013.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 : 300
% 0.13/0.34 % DateTime : Fri Jun 20 04:13:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------