%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM042-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:18:43 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 80 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 283 ( 13 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 329 ( 140 ~; 155 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 206 ( 186 !; 0 ?; 206 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(x_type,type,
x: $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(identity_relation_type,type,
identity_relation: $i ).
tff(restrict_type,type,
restrict: ( $i * $i * $i ) > $i ).
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(symmetrization_of_type,type,
symmetrization_of: $i > $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(irreflexive_type,type,
irreflexive: ( $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(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x) = restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x) = restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x))
<=> member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x)))) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))))
<=> member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ irreflexive(x,domain_of(symmetrization_of(x)))
<=> ~ irreflexive(x,domain_of(symmetrization_of(x))) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_2) ).
tff(14,plain,
~ irreflexive(x,domain_of(symmetrization_of(x))),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
<=> ( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',irreflexive2) ).
tff(19,plain,
! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
| ~ subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| irreflexive(x,domain_of(symmetrization_of(x))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
| ~ subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| irreflexive(x,domain_of(symmetrization_of(x))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ~ ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
| ~ subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| irreflexive(x,domain_of(symmetrization_of(x))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( ~ subclass(restrict(X,Y,Y),complement(identity_relation))
| irreflexive(X,Y) )
| ~ subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| irreflexive(x,domain_of(symmetrization_of(x))) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
~ subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,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)],[29]) ).
tff(31,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(32,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x)))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x)))),
inference(unit_resolution,[status(thm)],[38,35,25]) ).
tff(40,plain,
member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x)),
inference(modus_ponens,[status(thm)],[39,11]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(44,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(45,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),intersection(cross_product(domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),x))
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x) ),
inference(unit_resolution,[status(thm)],[50,47]) ).
tff(52,plain,
member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x),
inference(unit_resolution,[status(thm)],[51,40]) ).
tff(53,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(54,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)],[53]) ).
tff(55,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(56,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(57,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| subclass(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation)),
inference(unit_resolution,[status(thm)],[62,59,25]) ).
tff(64,plain,
( subclass(x,complement(identity_relation))
<=> subclass(x,complement(identity_relation)) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
subclass(x,complement(identity_relation)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_irreflexive_class_property4_1) ).
tff(66,plain,
subclass(x,complement(identity_relation)),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,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(68,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)],[67]) ).
tff(69,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(70,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(71,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)],[70]) ).
tff(72,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(73,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemize,[status(sab)],[74]) ).
tff(76,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[75,68]) ).
tff(77,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x)
| ~ subclass(x,complement(identity_relation)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x)
| ~ subclass(x,complement(identity_relation)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x)
| ~ subclass(x,complement(identity_relation)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),complement(identity_relation))
| ~ member(not_subclass_element(restrict(x,domain_of(symmetrization_of(x)),domain_of(symmetrization_of(x))),complement(identity_relation)),x)
| ~ subclass(x,complement(identity_relation)) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
$false,
inference(unit_resolution,[status(thm)],[79,76,66,63,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM042-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 00:03:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.49 % SZS status Unsatisfiable
% 0.20/0.49 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------