%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP004-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:42:36 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 2 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(element_of_collection_type,type,
element_of_collection: ( $i * $i ) > $o ).
tff(top_of_basis_type,type,
top_of_basis: $i > $i ).
tff(f_type,type,
f: $i ).
tff(intersection_of_sets_type,type,
intersection_of_sets: ( $i * $i ) > $i ).
tff(union_of_members_type,type,
union_of_members: $i > $i ).
tff(1,plain,
^ [V: $i,U: $i] :
refl(( ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
<=> ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
<=> ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
<=> ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1d_4) ).
tff(5,plain,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V: $i,U: $i] : ~ element_of_collection(intersection_of_sets(U,V),top_of_basis(f))
| ~ element_of_collection(intersection_of_sets(union_of_members(f),union_of_members(f)),top_of_basis(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
~ element_of_collection(intersection_of_sets(union_of_members(f),union_of_members(f)),top_of_basis(f)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [U: $i] :
refl(( element_of_collection(U,top_of_basis(f))
<=> element_of_collection(U,top_of_basis(f)) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [U: $i] : element_of_collection(U,top_of_basis(f))
<=> ! [U: $i] : element_of_collection(U,top_of_basis(f)) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [U: $i] : element_of_collection(U,top_of_basis(f))
<=> ! [U: $i] : element_of_collection(U,top_of_basis(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1d_2) ).
tff(14,plain,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [U: $i] : element_of_collection(U,top_of_basis(f)),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [U: $i] : element_of_collection(U,top_of_basis(f))
| element_of_collection(intersection_of_sets(union_of_members(f),union_of_members(f)),top_of_basis(f)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
$false,
inference(unit_resolution,[status(thm)],[17,16,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP004-2 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:52:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------