%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET254-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:25:32 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 102 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 370 ( 16 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 449 ( 197 ~; 209 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 273 ( 246 !; 0 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(x2_type,type,
x2: $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(restrict_type,type,
restrict: ( $i * $i * $i ) > $i ).
tff(z_type,type,
z: $i ).
tff(y_type,type,
y: $i ).
tff(x1_type,type,
x1: $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(1,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(2,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)],[1]) ).
tff(3,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(4,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(5,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
| ( intersection(cross_product(y,z),x2) = restrict(x2,y,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
intersection(cross_product(y,z),x2) = restrict(x2,y,z),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2))
<=> member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z)) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z))
<=> member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z))
<=> ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2)) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ subclass(restrict(x1,y,z),restrict(x2,y,z))
<=> ~ subclass(restrict(x1,y,z),restrict(x2,y,z)) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
~ subclass(restrict(x1,y,z),restrict(x2,y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_monotonicity_of_restriction1_2) ).
tff(15,plain,
~ subclass(restrict(x1,y,z),restrict(x2,y,z)),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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(20,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z))
| subclass(restrict(x1,y,z),restrict(x2,y,z)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z))
| subclass(restrict(x1,y,z),restrict(x2,y,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z))
| subclass(restrict(x1,y,z),restrict(x2,y,z)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z))
| subclass(restrict(x1,y,z),restrict(x2,y,z)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x2,y,z)),
inference(unit_resolution,[status(thm)],[25,22,15]) ).
tff(27,plain,
~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2)),
inference(modus_ponens,[status(thm)],[26,12]) ).
tff(28,plain,
( ~ ! [Y: $i,Xr: $i,X: $i] : ( intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y) )
| ( intersection(cross_product(y,z),x1) = restrict(x1,y,z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
intersection(cross_product(y,z),x1) = restrict(x1,y,z),
inference(unit_resolution,[status(thm)],[28,7]) ).
tff(30,plain,
( member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
<=> member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z)) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z))
<=> member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1)) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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(36,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)],[35]) ).
tff(37,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(38,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x1,y,z),restrict(x2,y,z))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z)) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x1,y,z),restrict(x2,y,z))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x1,y,z),restrict(x2,y,z))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x1,y,z),restrict(x2,y,z))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),restrict(x1,y,z)),
inference(unit_resolution,[status(thm)],[44,41,15]) ).
tff(46,plain,
member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1)),
inference(modus_ponens,[status(thm)],[45,31]) ).
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(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ) ),
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(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ),
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(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ),
inference(unit_resolution,[status(thm)],[56,53]) ).
tff(58,plain,
member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)),
inference(unit_resolution,[status(thm)],[57,46]) ).
tff(59,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
<=> ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
<=> ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) )
<=> ( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,Y)
| member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection3) ).
tff(65,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2))
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2))
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2))
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2))
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x2))
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),cross_product(y,z)) ),
inference(unit_resolution,[status(thm)],[71,68]) ).
tff(73,plain,
~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2),
inference(unit_resolution,[status(thm)],[72,58,27]) ).
tff(74,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',intersection2) ).
tff(78,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),intersection(cross_product(y,z),x1))
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1) ),
inference(unit_resolution,[status(thm)],[83,80]) ).
tff(85,plain,
member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1),
inference(unit_resolution,[status(thm)],[84,46]) ).
tff(86,plain,
( subclass(x1,x2)
<=> subclass(x1,x2) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
subclass(x1,x2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_monotonicity_of_restriction1_1) ).
tff(88,plain,
subclass(x1,x2),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [Y: $i,U: $i,X: $i] :
refl(( ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ subclass(X,Y)
| ~ member(U,X) )
<=> ( ~ member(U,X)
| ~ subclass(X,Y) ) )),
( ( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ( ~ member(U,X)
| ~ subclass(X,Y)
| member(U,Y) ) )),
rewrite(( ( ~ member(U,X)
| ~ subclass(X,Y)
| member(U,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
( ( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [Y: $i,U: $i,X: $i] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [Y: $i,U: $i,X: $i] :
( ~ subclass(X,Y)
| ~ member(U,X)
| member(U,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',subclass_members) ).
tff(95,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1)
| ~ subclass(x1,x2) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1)
| ~ subclass(x1,x2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1)
| ~ subclass(x1,x2) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x2)
| ~ member(not_subclass_element(restrict(x1,y,z),restrict(x2,y,z)),x1)
| ~ subclass(x1,x2) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,98,88,85,73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET254-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:39:11 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% See solution above
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------