%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : TOP002-2 : TPTP v9.0.0. Released v1.0.0.
% 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 05:42:35 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 52 ( 21 ~; 23 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 33 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(element_of_set_type,type,
element_of_set: ( $i * $i ) > $o ).
tff(empty_set_type,type,
empty_set: $i ).
tff(f11_type,type,
f11: ( $i * $i ) > $i ).
tff(f_type,type,
f: $i ).
tff(element_of_collection_type,type,
element_of_collection: ( $i * $i ) > $o ).
tff(top_of_basis_type,type,
top_of_basis: $i > $i ).
tff(1,plain,
( ~ element_of_collection(empty_set,top_of_basis(f))
<=> ~ element_of_collection(empty_set,top_of_basis(f)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ element_of_collection(empty_set,top_of_basis(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1b_2) ).
tff(3,plain,
~ element_of_collection(empty_set,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/sandbox/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(empty_set,top_of_basis(f))
| element_of_set(f11(f,empty_set),empty_set) )
<=> ( ~ ! [Vf: $i,U: $i] :
( element_of_collection(U,top_of_basis(Vf))
| element_of_set(f11(Vf,U),U) )
| element_of_collection(empty_set,top_of_basis(f))
| element_of_set(f11(f,empty_set),empty_set) ) ),
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(empty_set,top_of_basis(f))
| element_of_set(f11(f,empty_set),empty_set) ),
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(empty_set,top_of_basis(f))
| element_of_set(f11(f,empty_set),empty_set) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
element_of_set(f11(f,empty_set),empty_set),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [X: $i] :
refl(( ~ element_of_set(X,empty_set)
<=> ~ element_of_set(X,empty_set) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] : ~ element_of_set(X,empty_set)
<=> ! [X: $i] : ~ element_of_set(X,empty_set) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] : ~ element_of_set(X,empty_set)
<=> ! [X: $i] : ~ element_of_set(X,empty_set) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [X: $i] : ~ element_of_set(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_6) ).
tff(19,plain,
! [X: $i] : ~ element_of_set(X,empty_set),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [X: $i] : ~ element_of_set(X,empty_set),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [X: $i] : ~ element_of_set(X,empty_set),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ~ ! [X: $i] : ~ element_of_set(X,empty_set)
| ~ element_of_set(f11(f,empty_set),empty_set) ),
inference(quant_inst,[status(thm)],[]) ).
tff(23,plain,
$false,
inference(unit_resolution,[status(thm)],[22,21,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : TOP002-2 : TPTP v9.0.0. Released v1.0.0.
% 0.08/0.13 % 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 13:52:08 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37 % SZS output start Proof
% See solution above
% 0.13/0.37 % E exiting
%------------------------------------------------------------------------------