%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM049-1 : 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 05:18:44 AM UTC 2025
% Result : Unsatisfiable 9.77s 9.93s
% Output : Proof 9.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 61
% Syntax : Number of formulae : 144 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 507 ( 46 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 611 ( 269 ~; 281 |; 0 &)
% ( 61 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 21 ( 21 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 : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 355 ( 321 !; 0 ?; 355 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(identity_relation_type,type,
identity_relation: $i ).
tff(not_subclass_element_type,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(union_type,type,
union: ( $i * $i ) > $i ).
tff(symmetrization_of_type,type,
symmetrization_of: $i > $i ).
tff(x_type,type,
x: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(y_type,type,
y: $i ).
tff(complement_type,type,
complement: $i > $i ).
tff(intersection_type,type,
intersection: ( $i * $i ) > $i ).
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(connected_type,type,
connected: ( $i * $i ) > $o ).
tff(universal_class_type,type,
universal_class: $i ).
tff(unordered_pair_type,type,
unordered_pair: ( $i * $i ) > $i ).
tff(singleton_type,type,
singleton: $i > $i ).
tff(second_type,type,
second: $i > $i ).
tff(first_type,type,
first: $i > $i ).
tff(ordered_pair_type,type,
ordered_pair: ( $i * $i ) > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
<=> ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
<=> ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
<=> ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',union) ).
tff(5,plain,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Y: $i,X: $i] : ( complement(intersection(complement(X),complement(Y))) = union(X,Y) )
| ( complement(intersection(complement(identity_relation),complement(symmetrization_of(x)))) = union(identity_relation,symmetrization_of(x)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
complement(intersection(complement(identity_relation),complement(symmetrization_of(x)))) = union(identity_relation,symmetrization_of(x)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x)))))
<=> member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x))) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x)))
<=> member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x)))
<=> ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ connected(x,y)
<=> ~ connected(x,y) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
~ connected(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_connect_class_property4_2) ).
tff(15,plain,
~ connected(x,y),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
<=> ( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM004-0.ax',connected2) ).
tff(20,plain,
! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
| ~ subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| connected(x,y) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
| ~ subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| connected(x,y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
| ~ subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| connected(x,y) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X)))
| connected(X,Y) )
| ~ subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| connected(x,y) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))),
inference(unit_resolution,[status(thm)],[25,22,15]) ).
tff(27,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(28,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)],[27]) ).
tff(29,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(30,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(31,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x)))
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x)))
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x)))
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Y: $i,X: $i] :
( ~ member(not_subclass_element(X,Y),Y)
| subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x)))
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),union(identity_relation,symmetrization_of(x))),
inference(unit_resolution,[status(thm)],[36,33,26]) ).
tff(38,plain,
~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))),
inference(modus_ponens,[status(thm)],[37,12]) ).
tff(39,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(40,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)],[39]) ).
tff(41,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(42,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(43,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)],[42]) ).
tff(44,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(45,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y)) )
<=> ( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) )
| subclass(cross_product(y,y),union(identity_relation,symmetrization_of(x)))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y)),
inference(unit_resolution,[status(thm)],[51,48,26]) ).
tff(53,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
<=> ( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',cartesian_product4) ).
tff(57,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ( ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ( ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ( ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,cross_product(X,Y))
| ( ordered_pair(first(Z),second(Z)) = Z ) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ( ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),
inference(unit_resolution,[status(thm)],[62,59,52]) ).
tff(64,plain,
^ [Y: $i,X: $i] :
refl(( ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
<=> ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
tff(68,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [Y: $i,X: $i] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) )
| ( unordered_pair(singleton(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),unordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),singleton(second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))))) = ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
unordered_pair(singleton(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),unordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),singleton(second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))))) = ordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
unordered_pair(singleton(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),unordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),singleton(second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))))) = not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),
inference(transitivity,[status(thm)],[72,63]) ).
tff(74,plain,
( member(unordered_pair(singleton(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),unordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),singleton(second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))))),universal_class)
<=> member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
^ [Y: $i,X: $i] :
refl(( member(unordered_pair(X,Y),universal_class)
<=> member(unordered_pair(X,Y),universal_class) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class)
<=> ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class)
<=> ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,axiom,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).
tff(79,plain,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
( ~ ! [Y: $i,X: $i] : member(unordered_pair(X,Y),universal_class)
| member(unordered_pair(singleton(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),unordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),singleton(second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))))),universal_class) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
member(unordered_pair(singleton(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))),unordered_pair(first(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x)))),singleton(second(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))))))),universal_class),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class),
inference(modus_ponens,[status(thm)],[83,74]) ).
tff(85,plain,
^ [Z: $i,X: $i] :
refl(( ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
<=> ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
^ [Z: $i,X: $i] :
rewrite(( ( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) )
<=> ( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) )
<=> ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,universal_class)
| member(Z,complement(X))
| member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement2) ).
tff(91,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
( ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class)
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) )
<=> ( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class)
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class)
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [Z: $i,X: $i] :
( member(Z,X)
| ~ member(Z,universal_class)
| member(Z,complement(X)) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class)
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),universal_class)
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(intersection(complement(identity_relation),complement(symmetrization_of(x))))) ),
inference(unit_resolution,[status(thm)],[97,94]) ).
tff(99,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x)))),
inference(unit_resolution,[status(thm)],[98,84,38]) ).
tff(100,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(101,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)],[100]) ).
tff(102,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(103,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(104,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ member(Z,intersection(X,Y))
| member(Z,X) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),intersection(complement(identity_relation),complement(symmetrization_of(x))))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)),
inference(unit_resolution,[status(thm)],[109,106,99]) ).
tff(111,plain,
^ [Z: $i,X: $i] :
refl(( ( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ( ~ member(Z,X)
| ~ member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
^ [Z: $i,X: $i] :
rewrite(( ( ~ member(Z,complement(X))
| ~ member(Z,X) )
<=> ( ~ member(Z,X)
| ~ member(Z,complement(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [Z: $i,X: $i] :
( ~ member(Z,complement(X))
| ~ member(Z,X) )
<=> ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [Z: $i,X: $i] :
( ~ member(Z,complement(X))
| ~ member(Z,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',complement1) ).
tff(117,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) )
<=> ( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [Z: $i,X: $i] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),complement(identity_relation)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation),
inference(unit_resolution,[status(thm)],[123,120,110]) ).
tff(125,plain,
( subclass(cross_product(y,y),identity_relation)
<=> subclass(cross_product(y,y),identity_relation) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
subclass(cross_product(y,y),identity_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_connect_class_property4_1) ).
tff(127,plain,
subclass(cross_product(y,y),identity_relation),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,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(129,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)],[128]) ).
tff(130,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(131,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(132,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)],[131]) ).
tff(133,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(134,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemize,[status(sab)],[135]) ).
tff(137,plain,
! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(modus_ponens,[status(thm)],[136,129]) ).
tff(138,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ( member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ~ subclass(cross_product(y,y),identity_relation) )
<=> ( ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ~ subclass(cross_product(y,y),identity_relation) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation) ) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ~ subclass(cross_product(y,y),identity_relation) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation) ) ),
inference(transitivity,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| ~ subclass(cross_product(y,y),identity_relation) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) )
| ~ member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),cross_product(y,y))
| member(not_subclass_element(cross_product(y,y),union(identity_relation,symmetrization_of(x))),identity_relation)
| ~ subclass(cross_product(y,y),identity_relation) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
$false,
inference(unit_resolution,[status(thm)],[143,137,127,52,124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM049-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.07/0.13 % 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 00:03:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 9.77/9.93 % SZS status Unsatisfiable
% 9.77/9.93 % SZS output start Proof
% See solution above
% 9.77/10.00 % E exiting
%------------------------------------------------------------------------------