Fixpoint fib n := match n with
| O => 1
| S m => match m with
| O => 1
| S o => fib o + fib m end end.
Ltac sleep n :=
try (assert (fib n = S (fib n)) by reflexivity).
(* Tune that depending on your PC *)
Let time := 18.
Ltac solve_P :=
match goal with |- P (S ?X) =>
sleep time; exact (P_triv Type _)
end.

Lemma test_fail x : P (S x) /\ P x /\ P (S x) /\ P (S x).