TSTP Solution File: TOP005-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Fri Sep 30 01:55:48 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 69
% Syntax : Number of formulae : 143 ( 28 unt; 11 typ; 0 def)
% Number of atoms : 816 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1170 ( 543 ~; 547 |; 0 &)
% ( 80 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 57 ( 57 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 9 >; 8 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 420 ( 378 !; 0 ?; 420 :)
% Comments :
%------------------------------------------------------------------------------
tff(element_of_collection_type,type,
element_of_collection: ( $i * $i ) > $o ).
tff(f_type,type,
f: $i ).
tff(f10_type,type,
f10: ( $i * $i * $i ) > $i ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(union_of_members_type,type,
union_of_members: $i > $i ).
tff(g_type,type,
g: $i ).
tff(f1_type,type,
f1: ( $i * $i ) > $i ).
tff(top_of_basis_type,type,
top_of_basis: $i > $i ).
tff(element_of_set_type,type,
element_of_set: ( $i * $i ) > $o ).
tff(subset_collections_type,type,
subset_collections: ( $i * $i ) > $o ).
tff(subset_sets_type,type,
subset_sets: ( $i * $i ) > $o ).
tff(1,plain,
( ~ element_of_collection(union_of_members(g),top_of_basis(f))
<=> ~ element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).
tff(3,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Vf: $i,U: $i] :
refl(
( ( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
<=> ( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
<=> ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
<=> ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
tff(8,plain,
! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),union_of_members(g)) )
<=> ( ~ ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),union_of_members(g)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
element_of_set(f11(f,union_of_members(g)),union_of_members(g)),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [Vf: $i,U: $i] :
refl(
( ( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
<=> ( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
<=> ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
<=> ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).
tff(19,plain,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_collection(f1(g,f11(f,union_of_members(g))),g) )
<=> ( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_collection(f1(g,f11(f,union_of_members(g))),g) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_collection(f1(g,f11(f,union_of_members(g))),g) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_collection(f1(Vf,U),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_collection(f1(g,f11(f,union_of_members(g))),g) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
element_of_collection(f1(g,f11(f,union_of_members(g))),g),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
( subset_collections(g,top_of_basis(f))
<=> subset_collections(g,top_of_basis(f)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
subset_collections(g,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).
tff(28,plain,
subset_collections(g,top_of_basis(f)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [Y: $i,U: $i,X: $i] :
refl(
( ( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
<=> ( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [Y: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X) )
<=> ( ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) )),
( ( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X)
| element_of_collection(U,Y) )
<=> ( ~ element_of_collection(U,X)
| ~ subset_collections(X,Y)
| element_of_collection(U,Y) ) )),
rewrite(
( ( ~ element_of_collection(U,X)
| ~ subset_collections(X,Y)
| element_of_collection(U,Y) )
<=> ( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) )),
( ( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X)
| element_of_collection(U,Y) )
<=> ( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [Y: $i,U: $i,X: $i] :
( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X)
| element_of_collection(U,Y) )
<=> ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [Y: $i,U: $i,X: $i] :
( ~ subset_collections(X,Y)
| ~ element_of_collection(U,X)
| element_of_collection(U,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).
tff(35,plain,
! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ subset_collections(g,top_of_basis(f)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ subset_collections(g,top_of_basis(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| ~ subset_collections(g,top_of_basis(f)) )
<=> ( ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ subset_collections(g,top_of_basis(f)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| ~ subset_collections(g,top_of_basis(f)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ subset_collections(g,top_of_basis(f)) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| ~ subset_collections(g,top_of_basis(f)) )
<=> ( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ subset_collections(g,top_of_basis(f)) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| ~ subset_collections(g,top_of_basis(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [Y: $i,U: $i,X: $i] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| ~ subset_collections(g,top_of_basis(f)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)),
inference(unit_resolution,[status(thm)],[44,38,28,25]) ).
tff(46,plain,
^ [Vf: $i,U: $i] :
refl(
( ( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
<=> ( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
<=> ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
<=> ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).
tff(50,plain,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) )
<=> ( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
( ~ ! [Vf: $i,U: $i] :
( ~ element_of_set(U,union_of_members(Vf))
| element_of_set(U,f1(Vf,U)) )
| ~ element_of_set(f11(f,union_of_members(g)),union_of_members(g))
| element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))),
inference(unit_resolution,[status(thm)],[55,52,14]) ).
tff(57,plain,
^ [Vf: $i,U: $i,X: $i] :
refl(
( ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
^ [Vf: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) )),
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) )),
rewrite(
( ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) )),
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) )
<=> ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_collection(f10(Vf,U,X),Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_38) ).
tff(63,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) )
<=> ( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_collection(f10(Vf,U,X),Vf) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f),
inference(unit_resolution,[status(thm)],[69,66,56,45]) ).
tff(71,plain,
^ [Vf: $i,U: $i,X: $i] :
refl(
( ( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
<=> ( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
<=> ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
<=> ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [Vf: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) )),
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_set(X,f10(Vf,U,X)) ) )),
rewrite(
( ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| element_of_set(X,f10(Vf,U,X)) )
<=> ( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) )),
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) )
<=> ( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) )
<=> ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| element_of_set(X,f10(Vf,U,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_37) ).
tff(77,plain,
! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) )
<=> ( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) )
<=> ( ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) )
<=> ( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) )
<=> ( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [Vf: $i,U: $i,X: $i] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))),
inference(unit_resolution,[status(thm)],[86,80,56,45]) ).
tff(88,plain,
^ [Vf: $i,U: $i,X: $i] :
refl(
( ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
<=> ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
<=> ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
^ [Vf: $i,U: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ) )),
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| subset_sets(f10(Vf,U,X),U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) )),
rewrite(
( ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) )),
( ( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| subset_sets(f10(Vf,U,X),U) )
<=> ( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| subset_sets(f10(Vf,U,X),U) )
<=> ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(X,U)
| subset_sets(f10(Vf,U,X),U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).
tff(94,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) )
<=> ( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [Vf: $i,U: $i,X: $i] :
( ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf))
| subset_sets(f10(Vf,U,X),U) )
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f))
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))),
inference(unit_resolution,[status(thm)],[100,97,56,45]) ).
tff(102,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
<=> ( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z) )
<=> ( ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y) ) )),
( ( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z)) )
<=> ( ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y)
| subset_sets(X,union_of_members(Z)) ) )),
rewrite(
( ( ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y)
| subset_sets(X,union_of_members(Z)) )
<=> ( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ) )),
( ( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z)) )
<=> ( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ subset_sets(X,Y)
| ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).
tff(108,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ element_of_collection(Y,Z)
| subset_sets(X,union_of_members(Z))
| ~ subset_sets(X,Y) )
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),g)
| subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)),
inference(unit_resolution,[status(thm)],[114,111,25,101]) ).
tff(116,plain,
^ [Vf: $i,Uu11: $i,U: $i] :
refl(
( ( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
<=> ( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) )),
inference(bind,[status(th)],]) ).
tff(117,plain,
( ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
<=> ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
<=> ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
^ [Vf: $i,Uu11: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11) )
<=> ( ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) )),
( ( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf) )
<=> ( ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf))
| ~ element_of_collection(Uu11,Vf) ) )),
rewrite(
( ( ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf))
| ~ element_of_collection(Uu11,Vf) )
<=> ( ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) )),
( ( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf) )
<=> ( ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) )),
( ( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf)
| ~ subset_sets(Uu11,U) )
<=> ( ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf))
| ~ subset_sets(Uu11,U) ) )),
rewrite(
( ( ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf))
| ~ subset_sets(Uu11,U) )
<=> ( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) )),
( ( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf)
| ~ subset_sets(Uu11,U) )
<=> ( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [Vf: $i,Uu11: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf)
| ~ subset_sets(Uu11,U) )
<=> ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [Vf: $i,Uu11: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| ~ element_of_set(f11(Vf,U),Uu11)
| ~ element_of_collection(Uu11,Vf)
| ~ subset_sets(Uu11,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).
tff(122,plain,
! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) )
<=> ( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(f)) )
<=> ( element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
( ( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(f)) )
<=> ( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(f)) )
<=> ( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [Vf: $i,Uu11: $i,U: $i] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) )
| element_of_collection(union_of_members(g),top_of_basis(f))
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
$false,
inference(unit_resolution,[status(thm)],[131,125,3,115,87,70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.14 % Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.36 % Computer : n028.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Aug 29 09:24:32 EDT 2022
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.37 Usage: tptp [options] [-file:]file
% 0.12/0.37 -h, -? prints this message.
% 0.12/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.37 -m, -model generate model.
% 0.12/0.37 -p, -proof generate proof.
% 0.12/0.37 -c, -core generate unsat core of named formulas.
% 0.12/0.37 -st, -statistics display statistics.
% 0.12/0.37 -t:timeout set timeout (in second).
% 0.12/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.37 -<param>:<value> configuration parameter and value.
% 0.12/0.37 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------