(*Definition k_ind_step_ni (T : trans) (P : prop) (k: nat) : Prop := forall ss : sseq, ~(loop_free T ss 0 k /\ safety_nth_offset P ss 0 k /\ ~P ss.[k]).  Definition k_induction_post_ni (I : prop) (T : trans) (P : prop) (k: nat) : Prop := k_ind_step_ni T P k /\ safety_nth_ni I T P k. *)
Set SMT Solver "z3".
Set SMT Debug.

Axiom by_smt : forall P : Prop, P.