% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/StrongNorm/prob_200__5211384_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:38:19.309

% Could-be-implicit typings (5)
thf(ty_n_t__List__Olist_It__Lambda__OdB_J, type,
    list_dB : $tType).
thf(ty_n_t__Set__Oset_It__Lambda__OdB_J, type,
    set_dB : $tType).
thf(ty_n_t__Lambda__OdB, type,
    dB : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (34)
thf(sy_c_Fun_Ofun__upd_001t__Lambda__OdB_001t__Lambda__OdB, type,
    fun_upd_dB_dB : (dB > dB) > dB > dB > dB > dB).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint, type,
    uminus_uminus_int : int > int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint, type,
    zero_zero_int : int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_InductTermi_OIT, type,
    it : dB > $o).
thf(sy_c_Int_Onat, type,
    nat2 : int > nat).
thf(sy_c_Lambda_OdB_OVar, type,
    var : nat > dB).
thf(sy_c_Lambda_OdB_Osize__dB, type,
    size_dB : dB > nat).
thf(sy_c_Lambda_Olift, type,
    lift : dB > nat > dB).
thf(sy_c_Lambda_Oliftn, type,
    liftn : nat > dB > nat > dB).
thf(sy_c_Lambda_Osubst, type,
    subst : dB > dB > nat > dB).
thf(sy_c_Lambda_Osubstn, type,
    substn : dB > dB > nat > dB).
thf(sy_c_List_Obind_001t__Lambda__OdB_001t__Lambda__OdB, type,
    bind_dB_dB : list_dB > (dB > list_dB) > list_dB).
thf(sy_c_List_Ocount__list_001t__Lambda__OdB, type,
    count_list_dB : list_dB > dB > nat).
thf(sy_c_List_Ogen__length_001t__Lambda__OdB, type,
    gen_length_dB : nat > list_dB > nat).
thf(sy_c_List_Olist_ONil_001t__Lambda__OdB, type,
    nil_dB : list_dB).
thf(sy_c_List_Olist_Omap_001t__Lambda__OdB_001t__Lambda__OdB, type,
    map_dB_dB : (dB > dB) > list_dB > list_dB).
thf(sy_c_List_Olist_Oset_001t__Lambda__OdB, type,
    set_dB2 : list_dB > set_dB).
thf(sy_c_List_Olist__ex1_001t__Lambda__OdB, type,
    list_ex1_dB : (dB > $o) > list_dB > $o).
thf(sy_c_List_Olistsp_001t__Lambda__OdB, type,
    listsp_dB : (dB > $o) > list_dB > $o).
thf(sy_c_List_Omap__tailrec_001t__Lambda__OdB_001t__Lambda__OdB, type,
    map_tailrec_dB_dB : (dB > dB) > list_dB > list_dB).
thf(sy_c_List_Omember_001t__Lambda__OdB, type,
    member_dB : list_dB > dB > $o).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint, type,
    semiri2019852685at_int : nat > int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__Lambda__OdB, type,
    size_size_dB : dB > nat).
thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Lambda__OdB_J, type,
    size_size_list_dB : list_dB > nat).
thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint, type,
    ord_less_int : int > int > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_member_001t__Lambda__OdB, type,
    member_dB2 : dB > set_dB > $o).
thf(sy_v_i____, type,
    i : nat).
thf(sy_v_n____, type,
    n : nat).
thf(sy_v_t____, type,
    t : dB).
thf(sy_v_u1____, type,
    u1 : dB).
thf(sy_v_u____, type,
    u : dB).

% Relevant facts (127)
thf(fact_0__092_060open_062IT_At_092_060close_062, axiom,
    ((it @ t))). % \<open>IT t\<close>
thf(fact_1_Var_Oprems_I2_J, axiom,
    ((it @ u1))). % Var.prems(2)
thf(fact_2_False, axiom,
    ((~ ((n = i))))). % False
thf(fact_3_uIT, axiom,
    ((it @ u))). % uIT
thf(fact_4_listsp__simps_I1_J, axiom,
    ((![A : dB > $o]: (listsp_dB @ A @ nil_dB)))). % listsp_simps(1)
thf(fact_5_Nil__is__map__conv, axiom,
    ((![F : dB > dB, Xs : list_dB]: ((nil_dB = (map_dB_dB @ F @ Xs)) = (Xs = nil_dB))))). % Nil_is_map_conv
thf(fact_6_map__is__Nil__conv, axiom,
    ((![F : dB > dB, Xs : list_dB]: (((map_dB_dB @ F @ Xs) = nil_dB) = (Xs = nil_dB))))). % map_is_Nil_conv
thf(fact_7_list_Omap__disc__iff, axiom,
    ((![F : dB > dB, A2 : list_dB]: (((map_dB_dB @ F @ A2) = nil_dB) = (A2 = nil_dB))))). % list.map_disc_iff
thf(fact_8_listsp__conj__eq, axiom,
    ((![A : dB > $o, B : dB > $o]: ((listsp_dB @ (^[X : dB]: (((A @ X)) & ((B @ X))))) = (^[X : list_dB]: (((listsp_dB @ A @ X)) & ((listsp_dB @ B @ X)))))))). % listsp_conj_eq
thf(fact_9_map__ident, axiom,
    (((map_dB_dB @ (^[X : dB]: X)) = (^[Xs2 : list_dB]: Xs2)))). % map_ident
thf(fact_10_listsp_ONil, axiom,
    ((![A : dB > $o]: (listsp_dB @ A @ nil_dB)))). % listsp.Nil
thf(fact_11_list_Osimps_I8_J, axiom,
    ((![F : dB > dB]: ((map_dB_dB @ F @ nil_dB) = nil_dB)))). % list.simps(8)
thf(fact_12_list_Omap__ident, axiom,
    ((![T : list_dB]: ((map_dB_dB @ (^[X : dB]: X) @ T) = T)))). % list.map_ident
thf(fact_13_lifts__IT, axiom,
    ((![Ts : list_dB]: ((listsp_dB @ it @ Ts) => (listsp_dB @ it @ (map_dB_dB @ (^[T2 : dB]: (lift @ T2 @ zero_zero_nat)) @ Ts)))))). % lifts_IT
thf(fact_14_subst__Var__IT, axiom,
    ((![R : dB, I : nat, J : nat]: ((it @ R) => (it @ (subst @ R @ (var @ I) @ J)))))). % subst_Var_IT
thf(fact_15_lift__IT, axiom,
    ((![T : dB, I : nat]: ((it @ T) => (it @ (lift @ T @ I)))))). % lift_IT
thf(fact_16_Var__IT, axiom,
    ((![N : nat]: (it @ (var @ N))))). % Var_IT
thf(fact_17_subst__lift, axiom,
    ((![T : dB, K : nat, S : dB]: ((subst @ (lift @ T @ K) @ S @ K) = T)))). % subst_lift
thf(fact_18_subst__eq, axiom,
    ((![K : nat, U : dB]: ((subst @ (var @ K) @ U @ K) = U)))). % subst_eq
thf(fact_19_dB_Oinject_I1_J, axiom,
    ((![X1 : nat, Y1 : nat]: (((var @ X1) = (var @ Y1)) = (X1 = Y1))))). % dB.inject(1)
thf(fact_20_map__eq__map__tailrec, axiom,
    ((map_dB_dB = map_tailrec_dB_dB))). % map_eq_map_tailrec
thf(fact_21_list__ex1__simps_I1_J, axiom,
    ((![P : dB > $o]: (~ ((list_ex1_dB @ P @ nil_dB)))))). % list_ex1_simps(1)
thf(fact_22_count__list_Osimps_I1_J, axiom,
    ((![Y : dB]: ((count_list_dB @ nil_dB @ Y) = zero_zero_nat)))). % count_list.simps(1)
thf(fact_23_bind__simps_I1_J, axiom,
    ((![F : dB > list_dB]: ((bind_dB_dB @ nil_dB @ F) = nil_dB)))). % bind_simps(1)
thf(fact_24_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_25_zero__reorient, axiom,
    ((![X2 : int]: ((zero_zero_int = X2) = (X2 = zero_zero_int))))). % zero_reorient
thf(fact_26_dB_Osize__gen_I1_J, axiom,
    ((![X1 : nat]: ((size_dB @ (var @ X1)) = zero_zero_nat)))). % dB.size_gen(1)
thf(fact_27_substn__subst__0, axiom,
    ((![T : dB, S : dB]: ((substn @ T @ S @ zero_zero_nat) = (subst @ T @ S @ zero_zero_nat))))). % substn_subst_0
thf(fact_28_dB_Osize_I4_J, axiom,
    ((![X1 : nat]: ((size_size_dB @ (var @ X1)) = zero_zero_nat)))). % dB.size(4)
thf(fact_29_zero__natural_Orsp, axiom,
    ((zero_zero_nat = zero_zero_nat))). % zero_natural.rsp
thf(fact_30_member__rec_I2_J, axiom,
    ((![Y : dB]: (~ ((member_dB @ nil_dB @ Y)))))). % member_rec(2)
thf(fact_31_subst__lt, axiom,
    ((![J : nat, I : nat, U : dB]: ((ord_less_nat @ J @ I) => ((subst @ (var @ J) @ U @ I) = (var @ J)))))). % subst_lt
thf(fact_32_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_33_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_34_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_35_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A2 : nat]: ((~ ((A2 = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A2))))). % bot_nat_0.not_eq_extremum
thf(fact_36_map__eq__conv, axiom,
    ((![F : dB > dB, Xs : list_dB, G : dB > dB]: (((map_dB_dB @ F @ Xs) = (map_dB_dB @ G @ Xs)) = (![X : dB]: (((member_dB2 @ X @ (set_dB2 @ Xs))) => (((F @ X) = (G @ X))))))))). % map_eq_conv
thf(fact_37_in__listspI, axiom,
    ((![Xs : list_dB, A : dB > $o]: ((![X3 : dB]: ((member_dB2 @ X3 @ (set_dB2 @ Xs)) => (A @ X3))) => (listsp_dB @ A @ Xs))))). % in_listspI
thf(fact_38_bot__nat__0_Oextremum__strict, axiom,
    ((![A2 : nat]: (~ ((ord_less_nat @ A2 @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_39_infinite__descent0, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P @ M)))))))) => (P @ N)))))). % infinite_descent0
thf(fact_40_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_41_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_42_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_43_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_44_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_45_nat__neq__iff, axiom,
    ((![M2 : nat, N : nat]: ((~ ((M2 = N))) = (((ord_less_nat @ M2 @ N)) | ((ord_less_nat @ N @ M2))))))). % nat_neq_iff
thf(fact_46_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_47_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_48_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_49_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_50_nat__less__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((![M : nat]: ((ord_less_nat @ M @ N2) => (P @ M))) => (P @ N2))) => (P @ N))))). % nat_less_induct
thf(fact_51_infinite__descent, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P @ M))))))) => (P @ N))))). % infinite_descent
thf(fact_52_linorder__neqE__nat, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((X2 = Y))) => ((~ ((ord_less_nat @ X2 @ Y))) => (ord_less_nat @ Y @ X2)))))). % linorder_neqE_nat
thf(fact_53_size__neq__size__imp__neq, axiom,
    ((![X2 : dB, Y : dB]: ((~ (((size_size_dB @ X2) = (size_size_dB @ Y)))) => (~ ((X2 = Y))))))). % size_neq_size_imp_neq
thf(fact_54_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_55_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_56_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_57_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_58_list_Oinj__map__strong, axiom,
    ((![X2 : list_dB, Xa : list_dB, F : dB > dB, Fa : dB > dB]: ((![Z : dB, Za : dB]: ((member_dB2 @ Z @ (set_dB2 @ X2)) => ((member_dB2 @ Za @ (set_dB2 @ Xa)) => (((F @ Z) = (Fa @ Za)) => (Z = Za))))) => (((map_dB_dB @ F @ X2) = (map_dB_dB @ Fa @ Xa)) => (X2 = Xa)))))). % list.inj_map_strong
thf(fact_59_list_Omap__cong0, axiom,
    ((![X2 : list_dB, F : dB > dB, G : dB > dB]: ((![Z : dB]: ((member_dB2 @ Z @ (set_dB2 @ X2)) => ((F @ Z) = (G @ Z)))) => ((map_dB_dB @ F @ X2) = (map_dB_dB @ G @ X2)))))). % list.map_cong0
thf(fact_60_list_Omap__cong, axiom,
    ((![X2 : list_dB, Ya : list_dB, F : dB > dB, G : dB > dB]: ((X2 = Ya) => ((![Z : dB]: ((member_dB2 @ Z @ (set_dB2 @ Ya)) => ((F @ Z) = (G @ Z)))) => ((map_dB_dB @ F @ X2) = (map_dB_dB @ G @ Ya))))))). % list.map_cong
thf(fact_61_ex__map__conv, axiom,
    ((![Ys : list_dB, F : dB > dB]: ((?[Xs2 : list_dB]: (Ys = (map_dB_dB @ F @ Xs2))) = (![X : dB]: (((member_dB2 @ X @ (set_dB2 @ Ys))) => ((?[Y2 : dB]: (X = (F @ Y2)))))))))). % ex_map_conv
thf(fact_62_map__cong, axiom,
    ((![Xs : list_dB, Ys : list_dB, F : dB > dB, G : dB > dB]: ((Xs = Ys) => ((![X3 : dB]: ((member_dB2 @ X3 @ (set_dB2 @ Ys)) => ((F @ X3) = (G @ X3)))) => ((map_dB_dB @ F @ Xs) = (map_dB_dB @ G @ Ys))))))). % map_cong
thf(fact_63_map__idI, axiom,
    ((![Xs : list_dB, F : dB > dB]: ((![X3 : dB]: ((member_dB2 @ X3 @ (set_dB2 @ Xs)) => ((F @ X3) = X3))) => ((map_dB_dB @ F @ Xs) = Xs))))). % map_idI
thf(fact_64_map__ext, axiom,
    ((![Xs : list_dB, F : dB > dB, G : dB > dB]: ((![X3 : dB]: ((member_dB2 @ X3 @ (set_dB2 @ Xs)) => ((F @ X3) = (G @ X3)))) => ((map_dB_dB @ F @ Xs) = (map_dB_dB @ G @ Xs)))))). % map_ext
thf(fact_65_in__listsp__conv__set, axiom,
    ((listsp_dB = (^[A3 : dB > $o]: (^[Xs2 : list_dB]: (![X : dB]: (((member_dB2 @ X @ (set_dB2 @ Xs2))) => ((A3 @ X))))))))). % in_listsp_conv_set
thf(fact_66_in__listspD, axiom,
    ((![A : dB > $o, Xs : list_dB]: ((listsp_dB @ A @ Xs) => (![X4 : dB]: ((member_dB2 @ X4 @ (set_dB2 @ Xs)) => (A @ X4))))))). % in_listspD
thf(fact_67_substn__subst__n, axiom,
    ((substn = (^[T2 : dB]: (^[S2 : dB]: (^[N3 : nat]: (subst @ T2 @ (liftn @ N3 @ S2 @ zero_zero_nat) @ N3))))))). % substn_subst_n
thf(fact_68_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_69_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_70_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_71_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_int @ zero_zero_int @ (semiri2019852685at_int @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_72_length__greater__0__conv, axiom,
    ((![Xs : list_dB]: ((ord_less_nat @ zero_zero_nat @ (size_size_list_dB @ Xs)) = (~ ((Xs = nil_dB))))))). % length_greater_0_conv
thf(fact_73_map__fun__upd, axiom,
    ((![Y : dB, Xs : list_dB, F : dB > dB, V : dB]: ((~ ((member_dB2 @ Y @ (set_dB2 @ Xs)))) => ((map_dB_dB @ (fun_upd_dB_dB @ F @ Y @ V) @ Xs) = (map_dB_dB @ F @ Xs)))))). % map_fun_upd
thf(fact_74_of__nat__eq__iff, axiom,
    ((![M2 : nat, N : nat]: (((semiri2019852685at_int @ M2) = (semiri2019852685at_int @ N)) = (M2 = N))))). % of_nat_eq_iff
thf(fact_75_length__map, axiom,
    ((![F : dB > dB, Xs : list_dB]: ((size_size_list_dB @ (map_dB_dB @ F @ Xs)) = (size_size_list_dB @ Xs))))). % length_map
thf(fact_76_liftn__0, axiom,
    ((![T : dB, K : nat]: ((liftn @ zero_zero_nat @ T @ K) = T)))). % liftn_0
thf(fact_77_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri1382578993at_nat @ M2) = zero_zero_nat) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_78_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri2019852685at_int @ M2) = zero_zero_int) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_79_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_nat = (semiri1382578993at_nat @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_80_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_int = (semiri2019852685at_int @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_81_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_82_of__nat__0, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % of_nat_0
thf(fact_83_of__nat__less__iff, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ M2 @ N))))). % of_nat_less_iff
thf(fact_84_of__nat__less__iff, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_int @ (semiri2019852685at_int @ M2) @ (semiri2019852685at_int @ N)) = (ord_less_nat @ M2 @ N))))). % of_nat_less_iff
thf(fact_85_length__0__conv, axiom,
    ((![Xs : list_dB]: (((size_size_list_dB @ Xs) = zero_zero_nat) = (Xs = nil_dB))))). % length_0_conv
thf(fact_86_map__eq__imp__length__eq, axiom,
    ((![F : dB > dB, Xs : list_dB, G : dB > dB, Ys : list_dB]: (((map_dB_dB @ F @ Xs) = (map_dB_dB @ G @ Ys)) => ((size_size_list_dB @ Xs) = (size_size_list_dB @ Ys)))))). % map_eq_imp_length_eq
thf(fact_87_of__nat__less__0__iff, axiom,
    ((![M2 : nat]: (~ ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ zero_zero_nat)))))). % of_nat_less_0_iff
thf(fact_88_of__nat__less__0__iff, axiom,
    ((![M2 : nat]: (~ ((ord_less_int @ (semiri2019852685at_int @ M2) @ zero_zero_int)))))). % of_nat_less_0_iff
thf(fact_89_of__nat__less__imp__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)) => (ord_less_nat @ M2 @ N))))). % of_nat_less_imp_less
thf(fact_90_of__nat__less__imp__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_int @ (semiri2019852685at_int @ M2) @ (semiri2019852685at_int @ N)) => (ord_less_nat @ M2 @ N))))). % of_nat_less_imp_less
thf(fact_91_less__imp__of__nat__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)))))). % less_imp_of_nat_less
thf(fact_92_less__imp__of__nat__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_int @ (semiri2019852685at_int @ M2) @ (semiri2019852685at_int @ N)))))). % less_imp_of_nat_less
thf(fact_93_list_Osize_I3_J, axiom,
    (((size_size_list_dB @ nil_dB) = zero_zero_nat))). % list.size(3)
thf(fact_94_zero__less__imp__eq__int, axiom,
    ((![K : int]: ((ord_less_int @ zero_zero_int @ K) => (?[N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) & (K = (semiri2019852685at_int @ N2)))))))). % zero_less_imp_eq_int
thf(fact_95_pos__int__cases, axiom,
    ((![K : int]: ((ord_less_int @ zero_zero_int @ K) => (~ ((![N2 : nat]: ((K = (semiri2019852685at_int @ N2)) => (~ ((ord_less_nat @ zero_zero_nat @ N2))))))))))). % pos_int_cases
thf(fact_96_gen__length__code_I1_J, axiom,
    ((![N : nat]: ((gen_length_dB @ N @ nil_dB) = N)))). % gen_length_code(1)
thf(fact_97_nat__less__as__int, axiom,
    ((ord_less_nat = (^[A4 : nat]: (^[B2 : nat]: (ord_less_int @ (semiri2019852685at_int @ A4) @ (semiri2019852685at_int @ B2))))))). % nat_less_as_int
thf(fact_98_nat__int__comparison_I2_J, axiom,
    ((ord_less_nat = (^[A4 : nat]: (^[B2 : nat]: (ord_less_int @ (semiri2019852685at_int @ A4) @ (semiri2019852685at_int @ B2))))))). % nat_int_comparison(2)
thf(fact_99_verit__comp__simplify1_I1_J, axiom,
    ((![A2 : nat]: (~ ((ord_less_nat @ A2 @ A2)))))). % verit_comp_simplify1(1)
thf(fact_100_verit__comp__simplify1_I1_J, axiom,
    ((![A2 : int]: (~ ((ord_less_int @ A2 @ A2)))))). % verit_comp_simplify1(1)
thf(fact_101_int__ops_I1_J, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % int_ops(1)
thf(fact_102_neg__int__cases, axiom,
    ((![K : int]: ((ord_less_int @ K @ zero_zero_int) => (~ ((![N2 : nat]: ((K = (uminus_uminus_int @ (semiri2019852685at_int @ N2))) => (~ ((ord_less_nat @ zero_zero_nat @ N2))))))))))). % neg_int_cases
thf(fact_103_zero__less__nat__eq, axiom,
    ((![Z2 : int]: ((ord_less_nat @ zero_zero_nat @ (nat2 @ Z2)) = (ord_less_int @ zero_zero_int @ Z2))))). % zero_less_nat_eq
thf(fact_104_add_Oinverse__inverse, axiom,
    ((![A2 : int]: ((uminus_uminus_int @ (uminus_uminus_int @ A2)) = A2)))). % add.inverse_inverse
thf(fact_105_neg__equal__iff__equal, axiom,
    ((![A2 : int, B3 : int]: (((uminus_uminus_int @ A2) = (uminus_uminus_int @ B3)) = (A2 = B3))))). % neg_equal_iff_equal
thf(fact_106_neg__equal__zero, axiom,
    ((![A2 : int]: (((uminus_uminus_int @ A2) = A2) = (A2 = zero_zero_int))))). % neg_equal_zero
thf(fact_107_equal__neg__zero, axiom,
    ((![A2 : int]: ((A2 = (uminus_uminus_int @ A2)) = (A2 = zero_zero_int))))). % equal_neg_zero
thf(fact_108_neg__equal__0__iff__equal, axiom,
    ((![A2 : int]: (((uminus_uminus_int @ A2) = zero_zero_int) = (A2 = zero_zero_int))))). % neg_equal_0_iff_equal
thf(fact_109_neg__0__equal__iff__equal, axiom,
    ((![A2 : int]: ((zero_zero_int = (uminus_uminus_int @ A2)) = (zero_zero_int = A2))))). % neg_0_equal_iff_equal
thf(fact_110_add_Oinverse__neutral, axiom,
    (((uminus_uminus_int @ zero_zero_int) = zero_zero_int))). % add.inverse_neutral
thf(fact_111_neg__less__iff__less, axiom,
    ((![B3 : int, A2 : int]: ((ord_less_int @ (uminus_uminus_int @ B3) @ (uminus_uminus_int @ A2)) = (ord_less_int @ A2 @ B3))))). % neg_less_iff_less
thf(fact_112_less__neg__neg, axiom,
    ((![A2 : int]: ((ord_less_int @ A2 @ (uminus_uminus_int @ A2)) = (ord_less_int @ A2 @ zero_zero_int))))). % less_neg_neg
thf(fact_113_neg__less__pos, axiom,
    ((![A2 : int]: ((ord_less_int @ (uminus_uminus_int @ A2) @ A2) = (ord_less_int @ zero_zero_int @ A2))))). % neg_less_pos
thf(fact_114_neg__0__less__iff__less, axiom,
    ((![A2 : int]: ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ A2)) = (ord_less_int @ A2 @ zero_zero_int))))). % neg_0_less_iff_less
thf(fact_115_neg__less__0__iff__less, axiom,
    ((![A2 : int]: ((ord_less_int @ (uminus_uminus_int @ A2) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A2))))). % neg_less_0_iff_less
thf(fact_116_negative__eq__positive, axiom,
    ((![N : nat, M2 : nat]: (((uminus_uminus_int @ (semiri2019852685at_int @ N)) = (semiri2019852685at_int @ M2)) = (((N = zero_zero_nat)) & ((M2 = zero_zero_nat))))))). % negative_eq_positive
thf(fact_117_zless__nat__conj, axiom,
    ((![W : int, Z2 : int]: ((ord_less_nat @ (nat2 @ W) @ (nat2 @ Z2)) = (((ord_less_int @ zero_zero_int @ Z2)) & ((ord_less_int @ W @ Z2))))))). % zless_nat_conj
thf(fact_118_nat__zminus__int, axiom,
    ((![N : nat]: ((nat2 @ (uminus_uminus_int @ (semiri2019852685at_int @ N))) = zero_zero_nat)))). % nat_zminus_int
thf(fact_119_nat__zero__as__int, axiom,
    ((zero_zero_nat = (nat2 @ zero_zero_int)))). % nat_zero_as_int
thf(fact_120_verit__negate__coefficient_I2_J, axiom,
    ((![A2 : int, B3 : int]: ((ord_less_int @ A2 @ B3) => (ord_less_int @ (uminus_uminus_int @ B3) @ (uminus_uminus_int @ A2)))))). % verit_negate_coefficient(2)
thf(fact_121_equation__minus__iff, axiom,
    ((![A2 : int, B3 : int]: ((A2 = (uminus_uminus_int @ B3)) = (B3 = (uminus_uminus_int @ A2)))))). % equation_minus_iff
thf(fact_122_minus__equation__iff, axiom,
    ((![A2 : int, B3 : int]: (((uminus_uminus_int @ A2) = B3) = ((uminus_uminus_int @ B3) = A2))))). % minus_equation_iff
thf(fact_123_less__minus__iff, axiom,
    ((![A2 : int, B3 : int]: ((ord_less_int @ A2 @ (uminus_uminus_int @ B3)) = (ord_less_int @ B3 @ (uminus_uminus_int @ A2)))))). % less_minus_iff
thf(fact_124_minus__less__iff, axiom,
    ((![A2 : int, B3 : int]: ((ord_less_int @ (uminus_uminus_int @ A2) @ B3) = (ord_less_int @ (uminus_uminus_int @ B3) @ A2))))). % minus_less_iff
thf(fact_125_nat__mono__iff, axiom,
    ((![Z2 : int, W : int]: ((ord_less_int @ zero_zero_int @ Z2) => ((ord_less_nat @ (nat2 @ W) @ (nat2 @ Z2)) = (ord_less_int @ W @ Z2)))))). % nat_mono_iff
thf(fact_126_zless__nat__eq__int__zless, axiom,
    ((![M2 : nat, Z2 : int]: ((ord_less_nat @ M2 @ (nat2 @ Z2)) = (ord_less_int @ (semiri2019852685at_int @ M2) @ Z2))))). % zless_nat_eq_int_zless

% Conjectures (1)
thf(conj_0, conjecture,
    ((listsp_dB @ it @ (map_dB_dB @ (^[X : dB]: (subst @ X @ u @ i)) @ nil_dB)))).
