| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Z3 4.7.1 | Z3 4.8.10 |
| Deter | 0.00 | 0.01 | --- | --- |
| Total | 0.01 | 0.03 | 0.08 | 0.03 |
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Z3 4.7.1 | Z3 4.8.10 |
| Numof_no_add | 0.14 | Timeout (1s) | 0.02 | 0.02 |
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Z3 4.7.1 |
| VC for bint | 0.00 | --- | --- |
| VC for low_bint | 0.00 | --- | --- |
| TotalStrictOrder.Trans | 0.00 | --- | --- |
| TotalStrictOrder.Asymm | 0.00 | --- | --- |
| TotalStrictOrder.Trichotomy | 0.00 | --- | --- |
| VC for of_int | 0.00 | --- | --- |
| of_int_quasi_inj | --- | 0.02 | 0.02 |
| of_intK | 0.00 | --- | --- |
| VC for numof_bint | 0.00 | --- | --- |
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Z3 4.7.1 |
| TOOB.Deter | 0.01 | --- | --- |
| TOOB.Total | --- | 0.02 | 0.04 |
| TOOB.Injec | 0.01 | --- | --- |
| TOOB.Surjec | 0.11 | --- | --- |
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Coq 8.12.2 | Z3 4.7.1 | Z3 4.8.10 | ||||||||
| ex_rel_permut | Timeout (5s) | 0.07 | 0.52 | Timeout (5s) | Timeout (5s) | ||||||||
| inline_goal | |||||||||||||
| ex_rel_permut.0 | --- | --- | --- | --- | --- | ||||||||
| split_all_full | |||||||||||||
| ex_rel_permut.0.0 | Timeout (30s) | 0.09 | --- | --- | Timeout (30s) | ||||||||
| Proposition2 | Timeout (5s) | 0.08 | --- | Timeout (5s) | Timeout (5s) | ||||||||
| inline_goal | |||||||||||||
| Proposition2.0 | --- | --- | --- | --- | --- | ||||||||
| split_all_full | |||||||||||||
| Proposition2.0.0 | --- | 0.18 | --- | Timeout (1s) | --- | ||||||||
| inline_goal | |||||||||||||
| Proposition2.0.0.0 | --- | 0.05 | --- | Timeout (1s) | --- | ||||||||
| inline_goal | |||||||||||||
| Proposition2.0.0.0.0 | Timeout (5s) | 0.06 | --- | Timeout (1s) | Timeout (5s) | ||||||||
| inline_goal | |||||||||||||
| Proposition2.0.0.0.0.0 | Timeout (30s) | 0.07 | --- | --- | Timeout (30s) | ||||||||
| destruct ex_rel_permut | |||||||||||||
| Proposition2.0 | --- | --- | --- | --- | --- | ||||||||
| exists rel_permut | |||||||||||||
| Proposition2.0.0 | --- | --- | --- | --- | --- | ||||||||
| split_goal_full | |||||||||||||
| Proposition2.0.0.0 | --- | --- | --- | --- | --- | ||||||||
| unfold bijective | |||||||||||||
| Proposition2.0.0.0.0 | --- | --- | --- | --- | --- | ||||||||
| split_goal_full | |||||||||||||
| Proposition2.0.0.0.0.0 | 0.00 | --- | --- | --- | --- | ||||||||
| Proposition2.0.0.0.0.1 | Timeout (1s) | 0.08 | --- | Timeout (1s) | Timeout (1s) | ||||||||
| inline_goal | |||||||||||||
| Proposition2.0.0.0.0.1.0 | Timeout (1s) | 0.06 | --- | --- | Timeout (1s) | ||||||||
| intros j | |||||||||||||
| Proposition2.0.0.0.0.1.0.0 | Timeout (1s) | 0.07 | --- | Timeout (1s) | Timeout (1s) | ||||||||
| cut (exists x:a. rel x (bint2a j)) | |||||||||||||
| Proposition2.0.0.0.0.1.0.0.0 | 1.43 | 0.09 | --- | 0.03 | 0.04 | ||||||||
| asserted formula | Timeout (1s) | 0.07 | --- | Timeout (1s) | Timeout (1s) | ||||||||
| apply Surjec2 | |||||||||||||
| Proposition2.0.0.1 | Timeout (5s) | 0.09 | --- | Timeout (1s) | --- | ||||||||
| inline_goal | |||||||||||||
| Proposition2.0.0.1.0 | Timeout (5s) | --- | --- | --- | --- | ||||||||
| exists a2bint | |||||||||||||
| Proposition2.0.0.1.0.0 | 0.02 | 0.11 | --- | Timeout (1s) | --- | ||||||||
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 |
| VC for arrow | 0.00 | --- |
| Trans | 0.01 | --- |
| Asymm | 0.01 | --- |
| Trichotomy | --- | 0.03 |
| Source_inj | --- | 0.02 |
| Obligations | Alt-Ergo 2.4.0 |
| TOTO.Trans | 0.01 |
| TOTO.Asymm | 0.01 |
| TOTO.Trichotomy | 0.01 |
| TOTO.V.Trans | 0.01 |
| TOTO.V.Asymm | 0.01 |
| TOTO.V.Trichotomy | 0.01 |
| Obligations | Alt-Ergo 2.4.0 |
| Strict | 0.00 |
| Obligations | Alt-Ergo 2.4.0 |
| Trans | 0.01 |
| Asymm | 0.01 |
| Trichotomy | 0.01 |
| Obligations | Alt-Ergo 2.4.0 |
| Trans | 0.01 |
| Asymm | 0.01 |
| Trichotomy | 0.01 |
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Coq 8.12.2 | Z3 4.7.1 | Z3 4.8.10 | ||||||||
| irrefl | 0.01 | --- | --- | --- | --- | ||||||||
| VC for lt_int | 0.01 | --- | --- | --- | --- | ||||||||
| numof_max | Timeout (1s) | Timeout (1s) | --- | Timeout (1s) | Timeout (1s) | ||||||||
| split_vc | |||||||||||||
| numof_max.0 | Timeout (1s) | Timeout (1s) | --- | Timeout (1s) | Timeout (1s) | ||||||||
| intros lt,A,a | |||||||||||||
| numof_max.0 | Timeout (1s) | Timeout (1s) | --- | Timeout (1s) | Timeout (1s) | ||||||||
| rewrite Numof_no_add with (to_int a) | |||||||||||||
| numof_max.0.0 | 0.02 | --- | --- | --- | --- | ||||||||
| rewrite premises | 0.01 | --- | --- | --- | --- | ||||||||
| rewrite premises | 0.01 | --- | --- | --- | --- | ||||||||
| lt_map_bij_sto | 0.02 | --- | --- | --- | --- | ||||||||
| VC for rank | 0.06 | 0.04 | --- | 0.03 | --- | ||||||||
| rank_lt_inj | Timeout (1s) | Timeout (1s) | 0.43 | Timeout (1s) | Timeout (1s) | ||||||||
| split_vc | |||||||||||||
| rank_lt_inj.0 | Timeout (5s) | Timeout (5s) | --- | --- | Timeout (5s) | ||||||||
| inline_goal | |||||||||||||
| rank_lt_inj.0.0 | --- | --- | --- | --- | --- | ||||||||
| split_all_full | |||||||||||||
| rank_lt_inj.0.0.0 | Timeout (1s) | Timeout (1s) | --- | --- | Timeout (1s) | ||||||||
| split_vc | |||||||||||||
| rank_lt_inj.0.0.0.0 | Timeout (30s) | Timeout (30s) | --- | --- | Timeout (30s) | ||||||||
| VC for max | 0.03 | 0.07 | --- | --- | --- | ||||||||
| max_is_max | 0.14 | Timeout (1s) | --- | 0.06 | --- | ||||||||
| VC for succ | 0.43 | --- | --- | --- | --- | ||||||||
| VC for min | 0.04 | 0.07 | --- | --- | --- | ||||||||
| VC for unrank | 0.01 | 0.05 | --- | 0.03 | --- | ||||||||
| rank_ltK | Timeout (1s) | Timeout (1s) | --- | Timeout (1s) | Timeout (1s) | ||||||||
| split_vc | |||||||||||||
| rank_ltK.0 | Timeout (5s) | Timeout (1s) | --- | Timeout (1s) | --- | ||||||||
| unrank_ltK | 0.01 | Timeout (1s) | --- | 0.09 | --- | ||||||||
| intros lt, H, i | |||||||||||||
| unrank_ltK.0 | --- | --- | --- | --- | --- | ||||||||
| assert (injective ((fun (y0:bint -> bint -> bool) (y1:bint) -> rank y0 y1) @ lt)) | |||||||||||||
| asserted formula | --- | --- | --- | --- | --- | ||||||||
| apply rank_lt_inj | |||||||||||||
| apply premises | --- | --- | --- | --- | --- | ||||||||
| apply H | |||||||||||||
| unrank_ltK.0.1 | --- | --- | --- | --- | --- | ||||||||
| unfold injective in h | |||||||||||||
| unrank_ltK.0.1.0 | --- | --- | --- | --- | --- | ||||||||
| apply h | |||||||||||||
| apply premises | 0.01 | --- | --- | --- | --- | ||||||||
| lt_mapK | Timeout (5s) | Timeout (1s) | --- | 0.09 | 0.21 | ||||||||
| Proposition1 | Timeout (5s) | Timeout (1s) | --- | Timeout (1s) | Timeout (5s) | ||||||||
| split_vc | |||||||||||||
| Proposition1.0 | --- | Timeout (5s) | --- | Timeout (5s) | --- | ||||||||
| inline_goal | |||||||||||||
| Proposition1.0.0 | --- | --- | --- | --- | --- | ||||||||
| split_all_full | |||||||||||||
| Proposition1.0.0.0 | --- | Timeout (5s) | --- | Timeout (5s) | --- | ||||||||
| inline_goal | |||||||||||||
| Proposition1.0.0.0.0 | Timeout (5s) | Timeout (5s) | --- | Timeout (30s) | Timeout (5s) | ||||||||
| inline_goal | |||||||||||||
| Proposition1.0.0.0.0.0 | Timeout (30s) | Timeout (30s) | --- | --- | Timeout (30s) | ||||||||
| intros lt, T | |||||||||||||
| Proposition1.0 | --- | --- | --- | --- | --- | ||||||||
| exists (rank lt) | |||||||||||||
| Proposition1.0.0 | Timeout (5s) | Timeout (1s) | --- | Timeout (1s) | --- | ||||||||
| split_goal_full | |||||||||||||
| Proposition1.0.0.0 | --- | --- | --- | --- | --- | ||||||||
| unfold bijective | |||||||||||||
| Proposition1.0.0.0.0 | --- | --- | --- | --- | --- | ||||||||
| split_goal_full | |||||||||||||
| Proposition1.0.0.0.0.0 | 0.01 | --- | --- | --- | --- | ||||||||
| Proposition1.0.0.0.0.1 | --- | --- | --- | --- | --- | ||||||||
| unfold surjective | |||||||||||||
| Proposition1.0.0.0.0.1.0 | --- | --- | --- | --- | --- | ||||||||
| intros j | |||||||||||||
| Proposition1.0.0.0.0.1.0.0 | --- | --- | --- | --- | --- | ||||||||
| exists (unrank lt j) | |||||||||||||
| Proposition1.0.0.0.0.1.0.0.0 | 0.00 | --- | --- | --- | --- | ||||||||
| Proposition1.0.0.1 | 0.01 | --- | --- | --- | --- | ||||||||
| Obligations | Alt-Ergo 2.4.0 | CVC4 1.6 | Z3 4.7.1 | |||||
| VC for array_sto | 0.04 | --- | --- | |||||
| VC for rank_cancel | 0.02 | 0.10 | 0.04 | |||||
| VC for rank_cancel_array | 0.01 | --- | --- | |||||
| VC for rank_cancel_test | Timeout (1s) | Timeout (1s) | Timeout (1s) | |||||
| split_vc | ||||||||
| precondition | Timeout (1s) | Timeout (1s) | Timeout (1s) | |||||
| split_vc | ||||||||
| precondition | Timeout (5s) | Timeout (5s) | Timeout (5s) | |||||
| inline_goal | ||||||||
| precondition | --- | --- | --- | |||||
| split_all_full | ||||||||
| precondition | Timeout (5s) | Timeout (30s) | Timeout (30s) | |||||
| precondition | Timeout (5s) | Timeout (5s) | Timeout (5s) | |||||
| inline_goal | ||||||||
| precondition | --- | --- | --- | |||||
| split_all_full | ||||||||
| VC for rank_cancel_test | Timeout (5s) | Timeout (5s) | Timeout (5s) | |||||
| inline_goal | ||||||||
| VC for rank_cancel_test | Timeout (5s) | Timeout (30s) | Timeout (30s) | |||||
| VC for rank_cancel_test | Timeout (5s) | Timeout (5s) | Timeout (5s) | |||||
| inline_goal | ||||||||
| VC for rank_cancel_test | Timeout (5s) | Timeout (30s) | Timeout (30s) | |||||