init: 3.316sec
norm: 3.664sec
prop: 0.04sec
nb of constant: 1076
nb of subterms: 0
nb_prop: 10521
Property of 1 constant: 
23: (!V1, (!V0, ((V1 = V0) = ((C0 V1) = (C0 V0)))))
  'none/Rep_real_inject' 'none/Rep_unit_inject' 'none/natural.simps_1' 'none/nat_of_nibble_eq_iff' 'none/STR_inject\'' 'none/int_of_integer_inject' 'none/arctan_eq_iff' 'none/Suc_Rep_inject\'' 'none/real_sqrt_eq_iff' 'none/Rep_rat_inject' 'none/rel_simps_23' 'none/rel_simps_20' 'none/num.simps_2' 'none/num.simps_1' 'none/Rep_int_inject' 'none/old.nat.inject' 'none/explode_inject' 'none/nat_of_natural_inject' 'none/quotient_of_inject_eq' 'none/nat_of_char_eq_iff' 'none/Rep_Nat_inject' 'none/nat.simps_1' 'none/complex_cnj_cancel_iff'
9: (!V3, (!V0, (!V2, (!V1, ((V3 = V0) = ((((C0 V2) V1) V3) = (((C0 V2) V1) V0)))))))
  'none/sum.simps_2' 'none/sum.simps_1' 'none/same_append_eq' 'none/conversep_inject' 'none/converse_inject' 'none/Rep_prod_inject' 'none/Rep_sum_inject' 'none/old.sum.inject_2' 'none/old.sum.inject_1'
6: (!V2, (!V0, (!V1, ((V2 = V0) = (((C0 V1) V2) = ((C0 V1) V0))))))
  'none/option.simps_1' 'none/rev_is_rev_conv' 'none/Basic_BNF_LFPs.xtor_inject' 'none/principal_inject' 'none/Rep_filter_inject' 'none/pred.simps_1'
6: (!V2, (((C0 V2) V2) (^V1, (^V0, (V1 = V0)))))
  'none/right_total_eq' 'none/left_total_eq' 'none/bi_total_eq' 'none/left_unique_eq' 'none/bi_unique_eq' 'none/right_unique_eq'
6: (!V1, ((C0 V1) = (^V0, V0)))
  'none/id_apply' 'none/id_bnf_apply' 'none/BNF_Composition.id_bnf_def' 'none/Basic_BNF_LFPs.ctor_rec_def' 'none/id_def' 'none/Basic_BNF_LFPs.xtor_def'
6: (!V2, ((((C0 V2) V2) (^V1, (^V0, (V1 = V0)))) = (^V1, (^V0, (V1 = V0)))))
  'none/rel_filter_eq' 'none/list_all2_eq' 'none/list.rel_eq' 'none/option.rel_eq' 'none/rel_set_eq' 'none/conversep_eq'
5: (!V0, (!V2, (V0 = ((((C0 V2) V2) (^V1, V1)) V0))))
  'none/image_ident' 'none/list.map_ident' 'none/filtermap_ident' 'none/option.map_ident' 'none/vimage_ident'
5: (!V1, (!V0, ((~ ((C0 V1) = (C0 V0))) | (V1 = V0))))
  'none/Suc_Rep_inject' 'none/natural_eqI' 'none/integer_eqI' 'none/Suc_inject' 'none/quotient_of_inject'
5: (!V2, ((C0 V2) (^V1, (^V0, (V1 = V0)))))
  'none/identity_equivp' 'none/reflp_equality' 'none/is_equality_eq' 'none/DEADID.rel_symp' 'none/transp_equality'
5: (!V3, (!V2, (!V1, (!V4, (!V0, (((((C0 V3) V2) V1) V4) | ((~ ((((C0 V3) V2) V0) V4)) | (~ ((((C0 V3) V2) V1) V0)))))))))
  'none/transitive_closurep_trans\'_1' 'none/POS_trans' 'none/map_le_trans' 'none/NEG_trans' 'none/transitive_closurep_trans\'_2'
Property of 2 constants: 
19: (!V0, (V0 = (C1 (C0 V0))))
  'none/natural_of_nat_of_natural_inverse' 'none/nat_of_natural_of_nat_inverse' 'none/Rep_unit_inverse' 'none/Rep_real_inverse' 'none/explode_inverse' 'none/nibble_of_nat_of_nibble' 'none/nat_of_natural_inverse' 'none/Rep_Nat_inverse' 'none/Rep_int_inverse' 'none/int_of_integer_inverse' 'none/int_of_integer_integer_of_int' 'none/holds_if_pred' 'none/natural_of_integer_of_natural' 'none/nat_of_num_inverse' 'none/Rep_rat_inverse' 'none/integer_of_int_int_of_integer' 'none/char_of_nat_of_char' 'none/if_pred_holds' 'none/nat_of_integer_integer_of_nat'
18: (!V2, (!V1, (!V0, ((((C1 V2) V1) V0) | (~ (((C0 V2) V1) V0))))))
  'none/folding_idem.axioms_2' 'none/folding_idem.axioms_1' 'none/monoid.axioms_2' 'none/comm_monoid_set.axioms' 'none/card_order_on_well_order_on' 'none/comm_monoid_list_set.axioms_2' 'none/comm_monoid_list_set.axioms_1' 'none/comm_monoid_set.intro' 'none/comm_monoid.axioms_2' 'none/comp_fun_idem.axioms_2' 'none/comp_fun_idem.axioms_1' 'none/semilattice_neutr_set.axioms' 'none/monoid_list.axioms' 'none/monoid_list.intro' 'none/semilattice_neutr.axioms_2' 'none/comm_monoid_list.axioms_2' 'none/comm_monoid_list.axioms_1' 'none/semilattice_neutr_set.intro'
11: (!V1, (!V0, (((C1 V1) V0) | (~ ((C0 V1) V0)))))
  'none/wo_rel.TRANS' 'none/semilattice_set.axioms' 'none/semilattice.axioms_2' 'none/semilattice.axioms_1' 'none/abel_semigroup.axioms_2' 'none/abel_semigroup.axioms_1' 'none/equivp_implies_part_equivp' 'none/wf_acyclic' 'none/wo_rel.ANTISYM' 'none/equivp_reflp2' 'none/semilattice_set.intro'
10: (!V1, (!V0, ((C1 V1) ((C0 V1) V0))))
  'none/trans_trancl' 'none/trans_Id_on' 'none/distinct_remdups' 'none/wf_measure' 'none/is_filter_Rep_filter' 'none/wf_measures' 'none/sym_Id_on' 'none/List.finite_set' 'none/trans_rtrancl' 'none/antisym_Id_on'
9: (!V1, (!V2, (!V0, (((C0 V1) (((C1 V1) V2) V0)) | (~ ((C0 V1) V0))))))
  'none/wf_mlex' 'none/distinct_take' 'none/distinct_removeAll' 'none/finite.intros_2' 'none/distinct_takeWhile' 'none/distinct_dropWhile' 'none/distinct_filter' 'none/distinct_remove1' 'none/distinct_drop'
8: (!V0, ((C1 V0) (C0 V0)))
  'none/sym_Id' 'none/distinct.simps_1' 'none/trans_Id' 'none/null_rec_2' 'none/is_none_code_1' 'none/is_none_simps_1' 'none/antisym_Id' 'none/null.simps_1'
8: (!V1, (!V0, (((C1 V1) V0) = ((C1 V1) ((C0 V1) V0)))))
  'none/set_rev' 'none/distinct1_rotate' 'none/hd_remdups_adj' 'none/trancl_rtrancl_absorb' 'none/distinct_rev' 'none/set_remdups' 'none/remdups_adj_set' 'none/set_rotate1'
8: (C1 = C0)
  'none/fact_rel_dict' 'none/int.pcr_cr_eq' 'none/rat.pcr_cr_eq' 'none/integer.pcr_cr_eq' 'none/implode_def' 'none/real.pcr_cr_eq' 'none/literal.pcr_cr_eq' 'none/natural.pcr_cr_eq'
8: ((C1 C0) = (^V0, V0))
  'none/size_nat_def' 'none/inverse_finite_2_def' 'none/sgn_finite_2_def' 'none/inverse_finite_3_def' 'none/abs_finite_2_def' 'none/uminus_finite_2_def' 'none/abs_finite_3_def' 'none/of_nat_id'
7: (!V0, (~ (C1 = (C0 V0))))
  'none/rel_simps_19' 'none/rel_simps_18' 'none/rel_simps_17' 'none/rel_simps_16' 'none/num.simps_6' 'none/num.simps_4' 'none/Suc_Rep_not_Zero_Rep'
Property: 
44: (!V1, (!V0, ((C0 (((C2 C3) V1) V0)) = (((C2 C1) (C0 V1)) (C0 V0)))))
  'none/plus_int_code_6' 'none/plus_int_code_3' 'none/nat_of_num_add' 'none/divide_natural.abs_eq' 'none/plus_integer_code_6' 'none/plus_integer_code_3' 'none/times_natural.rep_eq' 'none/mod_integer.rep_eq' 'none/plus_natural.abs_eq' 'none/minus_integer.abs_eq' 'none/real_plus_code' 'none/nat_of_natural_min' 'none/divide_natural.rep_eq' 'none/nat_of_natural_max' 'none/mod_natural.abs_eq' 'none/plus_complex.sel_2' 'none/plus_complex.sel_1' 'none/minus_complex.sel_2' 'none/minus_complex.sel_1' 'none/real_times_code' 'none/times_integer.abs_eq' 'none/divide_integer.rep_eq' 'none/plus_natural.rep_eq' 'none/real_minus_code' 'none/minus_integer.rep_eq' 'none/times_int_code_3' 'none/divide_integer.abs_eq' 'none/lcm_integer.abs_eq' 'none/mod_natural.rep_eq' 'none/nat_of_num_mult' 'none/times_integer.rep_eq' 'none/minus_natural.abs_eq' 'none/plus_integer.abs_eq' 'none/gcd_integer.abs_eq' 'none/times_integer_code_3' 'none/lcm_integer.rep_eq' 'none/times_natural.abs_eq' 'none/mod_integer.abs_eq' 'none/minus_natural.rep_eq' 'none/int_of_integer_min' 'none/int_of_integer_max' 'none/plus_integer.rep_eq' 'none/gcd_integer.rep_eq' 'none/real_divide_code'
29: (!V0, ((((C4 V0) (C3 V0)) (C2 V0)) | (~ ((C1 V0) (C0 V0)))))
  'none/sup_bot.comm_monoid_axioms' 'none/zero_le_one' 'none/order.ordering_axioms' 'none/mult.monoid_axioms' 'none/add.monoid_axioms' 'none/setsum.comm_monoid_set_axioms' 'none/Nats_1' 'none/Nats_0' 'none/inf_top.semilattice_neutr_axioms' 'none/sup_bot.semilattice_neutr_axioms' 'none/listprod.comm_monoid_list_axioms' 'none/inf_top.comm_monoid_axioms' 'none/mult.comm_monoid_axioms' 'none/zero_less_one' 'none/setprod.comm_monoid_list_set_axioms' 'none/setsum.comm_monoid_list_set_axioms' 'none/Ints_1' 'none/Ints_0' 'none/setprod.comm_monoid_set_axioms' 'none/Rats_1' 'none/Rats_0' 'none/listprod.monoid_list_axioms' 'none/sup_bot.monoid_axioms' 'none/add.comm_monoid_axioms' 'none/listsum.monoid_list_axioms' 'none/listsum.comm_monoid_list_axioms' 'none/Reals_1' 'none/Reals_0' 'none/inf_top.monoid_axioms'
28: (!V0, (((C3 V0) (C2 V0)) | (~ ((C1 V0) (C0 V0)))))
  'none/mult.semigroup_axioms' 'none/max.semigroup_axioms' 'none/measure_size' 'none/gcd.semigroup_axioms' 'none/lcm.abel_semigroup_axioms' 'none/sup.semigroup_axioms' 'none/min.semigroup_axioms' 'none/inf.abel_semigroup_axioms' 'none/max.abel_semigroup_axioms' 'none/is_num.intros_1' 'none/add.semigroup_axioms' 'none/iszero_0' 'none/sup.abel_semigroup_axioms' 'none/min.semilattice_axioms' 'none/Min.semilattice_set_axioms' 'none/sup.semilattice_axioms' 'none/Sup_fin.semilattice_set_axioms' 'none/inf.semigroup_axioms' 'none/Inf_fin.semilattice_set_axioms' 'none/inf.semilattice_axioms' 'none/max.semilattice_axioms' 'none/mult.abel_semigroup_axioms' 'none/min.abel_semigroup_axioms' 'none/gcd.abel_semigroup_axioms' 'none/add.abel_semigroup_axioms' 'none/sorted.intros_1' 'none/Max.semilattice_set_axioms' 'none/lcm.semigroup_axioms'
28: ((C3 C2) = (C1 C0))
  'none/nibble.size_9' 'none/nibble.size_8' 'none/nibble.size_7' 'none/nibble.size_6' 'none/nibble.size_5' 'none/nibble.size_4' 'none/nibble.size_3' 'none/nibble.size_2' 'none/nibble.size_1' 'none/pred_numeral_simps_1' 'none/nibble.size_16' 'none/nibble.size_15' 'none/nibble.size_14' 'none/nibble.size_13' 'none/nibble.size_12' 'none/one_int_code' 'none/nibble.size_11' 'none/nibble.size_10' 'none/nat_of_nibble.simps_2' 'none/nat_of_nibble.simps_1' 'none/one_integer_code' 'none/nat_of_num_code_1' 'none/integer_of_num_1' 'none/ii.sel_2' 'none/ii.sel_1' 'none/unit.size_1' 'none/num.size_1' 'none/Zero_nat_def'
27: ((C2 C0) = (C1 C0))
  'none/sup_rat_def' 'none/real_scaleR_def' 'none/inf_real_def' 'none/bot_nat_def' 'none/normalize_int_def' 'none/inf_rat_def' 'none/sup_finite_3_def' 'none/inf_nat_def' 'none/bdd_above_nat' 'none/of_rat_eq_id' 'none/minus_finite_2_def' 'none/sup_int_def' 'none/Sup_nat_def' 'none/has_field_derivative_iff_has_vector_derivative' 'none/sup_nat_def' 'none/of_nat_eq_id' 'none/of_real_eq_id' 'none/sup_real_def' 'none/unit_factor_int_def' 'none/inf_int_def' 'none/divide_finite_2_def' 'none/normalize_nat_def' 'none/cofinite_eq_sequentially' 'none/inc.simps_1' 'none/inf_finite_3_def' 'none/of_int_eq_id' 'none/real_norm_def'
24: (!V2, (!V3, (!V1, (!V0, ((~ ((C3 V2) (C2 V2))) | ((((C0 V2) (((C1 V2) V3) V1)) V0) = (((C1 V2) (((C0 V2) V3) V0)) (((C0 V2) V1) V0))))))))
  'none/semiring_normalization_rules_8' 'none/semiring_normalization_rules_1' 'none/power_mult_distrib' 'none/distrib_4' 'none/distrib_2' 'none/linordered_field_class.sign_simps_39' 'none/linordered_field_class.sign_simps_37' 'none/linordered_field_class.sign_simps_35' 'none/left_diff_distrib' 'none/semiring_normalization_rules_30' 'none/min_diff_distrib_left' 'none/mult_mod_left' 'none/min_max_distrib1' 'none/left_diff_distrib\'' 'none/diff_divide_distrib' 'none/min_add_distrib_left' 'none/max_diff_distrib_left' 'none/power_divide' 'none/add_divide_distrib' 'none/ring_class.ring_distribs_2' 'none/comm_semiring_class.distrib' 'none/max_add_distrib_left' 'none/distrib_right' 'none/max_min_distrib1'
23: (!V1, (!V0, ((V1 = V0) = ((C0 V1) = (C0 V0)))))
  'none/Rep_real_inject' 'none/Rep_unit_inject' 'none/natural.simps_1' 'none/nat_of_nibble_eq_iff' 'none/STR_inject\'' 'none/int_of_integer_inject' 'none/arctan_eq_iff' 'none/Suc_Rep_inject\'' 'none/real_sqrt_eq_iff' 'none/Rep_rat_inject' 'none/rel_simps_23' 'none/rel_simps_20' 'none/num.simps_2' 'none/num.simps_1' 'none/Rep_int_inject' 'none/old.nat.inject' 'none/explode_inject' 'none/nat_of_natural_inject' 'none/quotient_of_inject_eq' 'none/nat_of_char_eq_iff' 'none/Rep_Nat_inject' 'none/nat.simps_1' 'none/complex_cnj_cancel_iff'
21: ((C1 C3) = (C2 (C1 C0)))
  'none/zero_real_code' 'none/natural.size_1' 'none/zero_natural.rep_eq' 'none/sin_coeff_0' 'none/transfer_nat_int_numerals_2' 'none/one_natural.rep_eq' 'none/integer_of_nat_1' 'none/integer_of_nat_0' 'none/zero_natural_def' 'none/nat_code_2' 'none/zero_integer_def' 'none/arg_zero' 'none/one_real_code' 'none/zero_integer.rep_eq' 'none/transfer_nat_int_list_functions_2' 'none/zero_complex.sel_2' 'none/zero_complex.sel_1' 'none/one_complex.sel_1' 'none/one_natural_def' 'none/one_integer.rep_eq' 'none/one_integer_def'
21: (!V2, (!V1, (!V0, ((((C0 (C2 V2)) (C2 V1)) (((C1 V2) V1) V0)) | (~ (((C0 V2) V1) V0))))))
  'none/option.right_total_rel' 'none/list.bi_total_rel' 'none/option.left_unique_rel' 'none/bi_total_rel_set' 'none/right_unique_rel_set' 'none/list.bi_unique_rel' 'none/option.bi_unique_rel' 'none/option.left_total_rel' 'none/bi_unique_rel_set' 'none/bi_unique_rel_filter' 'none/left_unique_rel_set' 'none/right_total_rel_set' 'none/list.right_total_rel' 'none/list.left_unique_rel' 'none/left_unique_rel_filter' 'none/right_unique_rel_filter' 'none/list.left_total_rel' 'none/left_total_rel_set' 'none/list.right_unique_rel' 'none/option.right_unique_rel' 'none/option.bi_total_rel'
21: (!V3, (!V2, (!V1, (!V0, ((~ ((C2 V3) (C1 V3))) | ((((C0 V3) V2) (((C0 V3) V1) V0)) = (((C0 V3) (((C0 V3) V2) V1)) V0)))))))
  'none/min.assoc' 'none/linordered_field_class.sign_simps_26' 'none/linordered_field_class.sign_simps_23' 'none/inf_sup_aci_6' 'none/inf_sup_aci_2' 'none/semiring_normalization_rules_25' 'none/semiring_normalization_rules_21' 'none/semiring_normalization_rules_18' 'none/semiring_normalization_rules_17' 'none/is_num_normalize_1' 'none/sup_aci_2' 'none/Groups.add_ac_1' 'none/max.assoc' 'none/sup.assoc' 'none/ab_semigroup_add_class.add_ac_1' 'none/gcd.assoc' 'none/ab_semigroup_mult_class.mult_ac_1' 'none/inf_aci_2' 'none/lcm.assoc' 'none/inf.assoc' 'none/Groups.mult_ac_1'
