%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET451-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:25:45 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 58 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 20 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 148 ( 55 ~; 72 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 129 ( 117 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(restrict_type,type,
restrict: ( $i * $i * $i ) > $i ).
tff(universal_class_type,type,
universal_class: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(element_relation_type,type,
element_relation: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(subset_relation_type,type,
subset_relation: $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(1,plain,
( ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation )
<=> ( intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subset_relation) ).
tff(3,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Y: $i,Xr: $i,X: $i] :
refl(( ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
<=> ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',restriction2) ).
tff(8,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
| ( intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))) = restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))) = restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class) = intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation)))),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)) = subset_relation,
inference(transitivity,[status(thm)],[14,3]) ).
tff(16,plain,
( member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)))
<=> member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation)
<=> member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( ~ subclass(subset_relation,cross_product(universal_class,universal_class))
<=> ~ subclass(subset_relation,cross_product(universal_class,universal_class)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ subclass(subset_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_relation_alternate_defn1_1) ).
tff(20,plain,
~ subclass(subset_relation,cross_product(universal_class,universal_class)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,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(27,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(subset_relation,cross_product(universal_class,universal_class))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(subset_relation,cross_product(universal_class,universal_class))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(subset_relation,cross_product(universal_class,universal_class))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(subset_relation,cross_product(universal_class,universal_class))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),subset_relation),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))),
inference(modus_ponens,[status(thm)],[34,17]) ).
tff(36,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
<=> ( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
tff(40,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))
| subclass(subset_relation,cross_product(universal_class,universal_class)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))
| subclass(subset_relation,cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))
| subclass(subset_relation,cross_product(universal_class,universal_class)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class))
| subclass(subset_relation,cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)),
inference(unit_resolution,[status(thm)],[45,42,20]) ).
tff(47,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection1) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class)))
| member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
~ member(not_subclass_element(subset_relation,cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),restrict(complement(compose(complement(element_relation),inverse(element_relation))),universal_class,universal_class))),
inference(unit_resolution,[status(thm)],[56,53,46]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET451-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 05:11:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------