%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET062-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:25:02 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 26 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 59 ( 21 ~; 28 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 39 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(null_class_type,type,
null_class: $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(x_type,type,
x: $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(1,plain,
( ~ subclass(null_class,x)
<=> ~ subclass(null_class,x) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ subclass(null_class,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_null_class_is_subclass_1) ).
tff(3,plain,
~ subclass(null_class,x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
refl(( ( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
<=> ( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
<=> ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
<=> ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
^ [Y: $i,X: $i] :
rewrite(( ( member(not_subclass_element(X,Y),X)
| subclass(X,Y) )
<=> ( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Y: $i,X: $i] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Y: $i,X: $i] :
( member(not_subclass_element(X,Y),X)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
tff(10,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(null_class,x)
| member(not_subclass_element(null_class,x),null_class) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(null_class,x)
| member(not_subclass_element(null_class,x),null_class) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(null_class,x)
| member(not_subclass_element(null_class,x),null_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(null_class,x)
| member(not_subclass_element(null_class,x),null_class) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
member(not_subclass_element(null_class,x),null_class),
inference(unit_resolution,[status(thm)],[16,13,3]) ).
tff(18,plain,
^ [Z: $i] :
refl(( ~ member(Z,null_class)
<=> ~ member(Z,null_class) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Z: $i] : ~ member(Z,null_class)
<=> ! [Z: $i] : ~ member(Z,null_class) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Z: $i] : ~ member(Z,null_class)
<=> ! [Z: $i] : ~ member(Z,null_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [Z: $i] : ~ member(Z,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
tff(22,plain,
! [Z: $i] : ~ member(Z,null_class),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Z: $i] : ~ member(Z,null_class),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Z: $i] : ~ member(Z,null_class),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [Z: $i] : ~ member(Z,null_class)
| ~ member(not_subclass_element(null_class,x),null_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,24,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET062-7 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 : 300
% 0.12/0.33 % DateTime : Fri Jun 20 04:09:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% See solution above
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------