"search" is inconsistent on list of nominal constants

[MortenRhiger]

In version 2.0.4 of Abella, the search tactic seems inconsistent when working with lists of nominal constants (or my understanding of the underlying logic is terribly wrong). With

Kind t type.
Type f t -> o.

Abella (unexpectedly) proves this theorem with just an application of the search tactic:

Theorem bug : forall A, member A (f n1 :: nil) -> member A (f n2 :: nil).
search.

This results in inconsistencies. Indeed, we can (as expected) prove that no element can be a member of the two singleton lists mentioned above:

Theorem ok : forall A, member A (f n1 :: nil) -> member A (f n2 :: nil) -> false.
intros. case H1. case H2. case H3. case H2. case H3. case H3.

But then

Theorem proof_of_false : false.
assert member (f n1) (f n1 :: nil). apply bug to H1. apply ok to H1 H2.

[chaudhuri]

Thanks. The theorem bug should not be proved by search.

[MortenRhiger]

A similar error can actually be produced without lists and nominal constants: We have

Theorem bug2 : forall A, nabla x y, (A = f x) -> (A = f y).
search.

even though

Theorem nominals_differ : nabla x y, f x = f y -> false.
intros. case H1.

Again it's easy to establish a contradiction:

Theorem ok2 : forall A, nabla x y, (A = f x) -> (A = f y) -> false.
intros. case H1.

The problem seems to be the universally quantified A since neither of the following can be proved by searching:

Theorem not_provable1 : f n1 = f n2.
skip.         % cannot search here

Theorem not_provable2 : nabla x y, f x = f y.
intros. skip. % cannot search here