% 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/Fundamental_Theorem_Algebra/prob_292__5370416_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:58.854

% Could-be-implicit typings (4)
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (29)
thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint, type,
    one_one_int : int).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
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_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_If_001t__Int__Oint, type,
    if_int : $o > int > int > int).
thf(sy_c_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_If_001t__Real__Oreal, type,
    if_real : $o > real > real > real).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint, type,
    numeral_numeral_int : num > int).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
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_Orderings_Oord__class_Oless_001t__Num__Onum, type,
    ord_less_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint, type,
    ord_less_eq_int : int > int > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum, type,
    ord_less_eq_num : num > num > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint, type,
    divide_divide_int : int > int > int).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat, type,
    divide_divide_nat : nat > nat > nat).
thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal, type,
    divide_divide_real : real > real > real).
thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint, type,
    zero_n1994027371ol_int : $o > int).
thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat, type,
    zero_n1356753679ol_nat : $o > nat).
thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal, type,
    zero_n797941355l_real : $o > real).
thf(sy_v_e____, type,
    e : real).

% Relevant facts (213)
thf(fact_0_that, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % that
thf(fact_1_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_2_half__gt__zero, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))))))). % half_gt_zero
thf(fact_3_half__gt__zero__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ (numeral_numeral_real @ (bit0 @ one)))) = (ord_less_real @ zero_zero_real @ A))))). % half_gt_zero_iff
thf(fact_4_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_5_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_6_div__0, axiom,
    ((![A : real]: ((divide_divide_real @ zero_zero_real @ A) = zero_zero_real)))). % div_0
thf(fact_7_div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % div_0
thf(fact_8_div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % div_0
thf(fact_9_divide__eq__0__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % divide_eq_0_iff
thf(fact_10_div__by__0, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % div_by_0
thf(fact_11_div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % div_by_0
thf(fact_12_div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % div_by_0
thf(fact_13_divide__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((divide_divide_real @ C @ A) = (divide_divide_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_left
thf(fact_14_bits__div__0, axiom,
    ((![A : int]: ((divide_divide_int @ zero_zero_int @ A) = zero_zero_int)))). % bits_div_0
thf(fact_15_bits__div__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % bits_div_0
thf(fact_16_divide__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((divide_divide_real @ A @ C) = (divide_divide_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % divide_cancel_right
thf(fact_17_bits__div__by__0, axiom,
    ((![A : int]: ((divide_divide_int @ A @ zero_zero_int) = zero_zero_int)))). % bits_div_by_0
thf(fact_18_bits__div__by__0, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % bits_div_by_0
thf(fact_19_division__ring__divide__zero, axiom,
    ((![A : real]: ((divide_divide_real @ A @ zero_zero_real) = zero_zero_real)))). % division_ring_divide_zero
thf(fact_20_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_21_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_int @ M) = (numeral_numeral_int @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_22_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_23_semiring__norm_I78_J, axiom,
    ((![M : num, N : num]: ((ord_less_num @ (bit0 @ M) @ (bit0 @ N)) = (ord_less_num @ M @ N))))). % semiring_norm(78)
thf(fact_24_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_25_semiring__norm_I75_J, axiom,
    ((![M : num]: (~ ((ord_less_num @ M @ one)))))). % semiring_norm(75)
thf(fact_26_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_27_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_28_numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_num @ M @ N))))). % numeral_less_iff
thf(fact_29_half__negative__int__iff, axiom,
    ((![K : int]: ((ord_less_int @ (divide_divide_int @ K @ (numeral_numeral_int @ (bit0 @ one))) @ zero_zero_int) = (ord_less_int @ K @ zero_zero_int))))). % half_negative_int_iff
thf(fact_30_semiring__norm_I76_J, axiom,
    ((![N : num]: (ord_less_num @ one @ (bit0 @ N))))). % semiring_norm(76)
thf(fact_31_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y2 : real]: ((~ ((X3 = Y2))) => ((~ ((ord_less_real @ X3 @ Y2))) => (ord_less_real @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_32_linorder__neqE__linordered__idom, axiom,
    ((![X3 : int, Y2 : int]: ((~ ((X3 = Y2))) => ((~ ((ord_less_int @ X3 @ Y2))) => (ord_less_int @ Y2 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_33_linordered__field__no__ub, axiom,
    ((![X4 : real]: (?[X_12 : real]: (ord_less_real @ X4 @ X_12))))). % linordered_field_no_ub
thf(fact_34_linordered__field__no__lb, axiom,
    ((![X4 : real]: (?[Y3 : real]: (ord_less_real @ Y3 @ X4))))). % linordered_field_no_lb
thf(fact_35_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_36_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_37_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_38_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N))))))). % zero_neq_numeral
thf(fact_39_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_int = (numeral_numeral_int @ N))))))). % zero_neq_numeral
thf(fact_40_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_41_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_42_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_int @ (numeral_numeral_int @ N) @ zero_zero_int)))))). % not_numeral_less_zero
thf(fact_43_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_44_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_less_numeral
thf(fact_45_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_int @ zero_zero_int @ (numeral_numeral_int @ N))))). % zero_less_numeral
thf(fact_46_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_less_numeral
thf(fact_47_divide__strict__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono_neg
thf(fact_48_divide__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_strict_right_mono
thf(fact_49_zero__less__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ zero_zero_real @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ B @ zero_zero_real))))))))). % zero_less_divide_iff
thf(fact_50_divide__less__cancel, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A)))) & ((~ ((C = zero_zero_real))))))))))). % divide_less_cancel
thf(fact_51_divide__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_real @ B @ zero_zero_real)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_real @ zero_zero_real @ B))))))))). % divide_less_0_iff
thf(fact_52_divide__pos__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_pos_pos
thf(fact_53_divide__pos__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ X3) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_pos_neg
thf(fact_54_divide__neg__pos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ Y2) => (ord_less_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_neg_pos
thf(fact_55_divide__neg__neg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_real @ X3 @ zero_zero_real) => ((ord_less_real @ Y2 @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_neg_neg
thf(fact_56_divide__numeral__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ (numeral_numeral_real @ one)) = A)))). % divide_numeral_1
thf(fact_57_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_58_numeral__Bit0__div__2, axiom,
    ((![N : num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ N)) @ (numeral_numeral_int @ (bit0 @ one))) = (numeral_numeral_int @ N))))). % numeral_Bit0_div_2
thf(fact_59_numeral__Bit0__div__2, axiom,
    ((![N : num]: ((divide_divide_nat @ (numeral_numeral_nat @ (bit0 @ N)) @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ N))))). % numeral_Bit0_div_2
thf(fact_60_zdiv__numeral__Bit0, axiom,
    ((![V : num, W : num]: ((divide_divide_int @ (numeral_numeral_int @ (bit0 @ V)) @ (numeral_numeral_int @ (bit0 @ W))) = (divide_divide_int @ (numeral_numeral_int @ V) @ (numeral_numeral_int @ W)))))). % zdiv_numeral_Bit0
thf(fact_61_verit__eq__simplify_I8_J, axiom,
    ((![X22 : num, Y22 : num]: (((bit0 @ X22) = (bit0 @ Y22)) = (X22 = Y22))))). % verit_eq_simplify(8)
thf(fact_62_pos2, axiom,
    ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))))). % pos2
thf(fact_63_verit__eq__simplify_I10_J, axiom,
    ((![X22 : num]: (~ ((one = (bit0 @ X22))))))). % verit_eq_simplify(10)
thf(fact_64_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_65_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_66_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_67_div__less, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => ((divide_divide_nat @ M @ N) = zero_zero_nat))))). % div_less
thf(fact_68_div__neg__pos__less0, axiom,
    ((![A : int, B : int]: ((ord_less_int @ A @ zero_zero_int) => ((ord_less_int @ zero_zero_int @ B) => (ord_less_int @ (divide_divide_int @ A @ B) @ zero_zero_int)))))). % div_neg_pos_less0
thf(fact_69_neg__imp__zdiv__neg__iff, axiom,
    ((![B : int, A : int]: ((ord_less_int @ B @ zero_zero_int) => ((ord_less_int @ (divide_divide_int @ A @ B) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A)))))). % neg_imp_zdiv_neg_iff
thf(fact_70_pos__imp__zdiv__neg__iff, axiom,
    ((![B : int, A : int]: ((ord_less_int @ zero_zero_int @ B) => ((ord_less_int @ (divide_divide_int @ A @ B) @ zero_zero_int) = (ord_less_int @ A @ zero_zero_int)))))). % pos_imp_zdiv_neg_iff
thf(fact_71_Euclidean__Division_Odiv__eq__0__iff, axiom,
    ((![M : nat, N : nat]: (((divide_divide_nat @ M @ N) = zero_zero_nat) = (((ord_less_nat @ M @ N)) | ((N = zero_zero_nat))))))). % Euclidean_Division.div_eq_0_iff
thf(fact_72_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_73_zero__reorient, axiom,
    ((![X3 : int]: ((zero_zero_int = X3) = (X3 = zero_zero_int))))). % zero_reorient
thf(fact_74_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_75_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_76_verit__comp__simplify1_I1_J, axiom,
    ((![A : num]: (~ ((ord_less_num @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_77_verit__comp__simplify1_I1_J, axiom,
    ((![A : int]: (~ ((ord_less_int @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_78_verit__comp__simplify1_I1_J, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_79_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_80_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_81_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_82_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_83_less__int__code_I1_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_int_code(1)
thf(fact_84_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_85_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_86_linorder__neqE__nat, axiom,
    ((![X3 : nat, Y2 : nat]: ((~ ((X3 = Y2))) => ((~ ((ord_less_nat @ X3 @ Y2))) => (ord_less_nat @ Y2 @ X3)))))). % linorder_neqE_nat
thf(fact_87_infinite__descent, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P @ N2))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N2) & (~ ((P @ M2))))))) => (P @ N))))). % infinite_descent
thf(fact_88_nat__less__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((![M2 : nat]: ((ord_less_nat @ M2 @ N2) => (P @ M2))) => (P @ N2))) => (P @ N))))). % nat_less_induct
thf(fact_89_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_90_less__not__refl3, axiom,
    ((![S2 : nat, T : nat]: ((ord_less_nat @ S2 @ T) => (~ ((S2 = T))))))). % less_not_refl3
thf(fact_91_less__not__refl2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ N @ M) => (~ ((M = N))))))). % less_not_refl2
thf(fact_92_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_93_nat__neq__iff, axiom,
    ((![M : nat, N : nat]: ((~ ((M = N))) = (((ord_less_nat @ M @ N)) | ((ord_less_nat @ N @ M))))))). % nat_neq_iff
thf(fact_94_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_95_infinite__descent0, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P @ N2))) => (?[M2 : nat]: ((ord_less_nat @ M2 @ N2) & (~ ((P @ M2)))))))) => (P @ N)))))). % infinite_descent0
thf(fact_96_gr__implies__not0, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_97_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_98_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_99_field__lbound__gt__zero, axiom,
    ((![D1 : real, D2 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D2) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D2))))))))). % field_lbound_gt_zero
thf(fact_100_half__nonnegative__int__iff, axiom,
    ((![K : int]: ((ord_less_eq_int @ zero_zero_int @ (divide_divide_int @ K @ (numeral_numeral_int @ (bit0 @ one)))) = (ord_less_eq_int @ zero_zero_int @ K))))). % half_nonnegative_int_iff
thf(fact_101_bits__1__div__2, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % bits_1_div_2
thf(fact_102_bits__1__div__2, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % bits_1_div_2
thf(fact_103_one__div__two__eq__zero, axiom,
    (((divide_divide_int @ one_one_int @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int))). % one_div_two_eq_zero
thf(fact_104_one__div__two__eq__zero, axiom,
    (((divide_divide_nat @ one_one_nat @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat))). % one_div_two_eq_zero
thf(fact_105_of__bool__half__eq__0, axiom,
    ((![B : $o]: ((divide_divide_int @ (zero_n1994027371ol_int @ B) @ (numeral_numeral_int @ (bit0 @ one))) = zero_zero_int)))). % of_bool_half_eq_0
thf(fact_106_of__bool__half__eq__0, axiom,
    ((![B : $o]: ((divide_divide_nat @ (zero_n1356753679ol_nat @ B) @ (numeral_numeral_nat @ (bit0 @ one))) = zero_zero_nat)))). % of_bool_half_eq_0
thf(fact_107_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_108_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_109_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_110_numeral__le__iff, axiom,
    ((![M : num, N : num]: ((ord_less_eq_int @ (numeral_numeral_int @ M) @ (numeral_numeral_int @ N)) = (ord_less_eq_num @ M @ N))))). % numeral_le_iff
thf(fact_111_div__by__1, axiom,
    ((![A : real]: ((divide_divide_real @ A @ one_one_real) = A)))). % div_by_1
thf(fact_112_div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % div_by_1
thf(fact_113_div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % div_by_1
thf(fact_114_bits__div__by__1, axiom,
    ((![A : int]: ((divide_divide_int @ A @ one_one_int) = A)))). % bits_div_by_1
thf(fact_115_bits__div__by__1, axiom,
    ((![A : nat]: ((divide_divide_nat @ A @ one_one_nat) = A)))). % bits_div_by_1
thf(fact_116_less__one, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ one_one_nat) = (N = zero_zero_nat))))). % less_one
thf(fact_117_of__bool__eq_I1_J, axiom,
    (((zero_n797941355l_real @ $false) = zero_zero_real))). % of_bool_eq(1)
thf(fact_118_of__bool__eq_I1_J, axiom,
    (((zero_n1994027371ol_int @ $false) = zero_zero_int))). % of_bool_eq(1)
thf(fact_119_of__bool__eq_I1_J, axiom,
    (((zero_n1356753679ol_nat @ $false) = zero_zero_nat))). % of_bool_eq(1)
thf(fact_120_of__bool__eq_I2_J, axiom,
    (((zero_n1356753679ol_nat @ $true) = one_one_nat))). % of_bool_eq(2)
thf(fact_121_of__bool__eq_I2_J, axiom,
    (((zero_n1994027371ol_int @ $true) = one_one_int))). % of_bool_eq(2)
thf(fact_122_divide__eq__1__iff, axiom,
    ((![A : real, B : real]: (((divide_divide_real @ A @ B) = one_one_real) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % divide_eq_1_iff
thf(fact_123_div__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % div_self
thf(fact_124_div__self, axiom,
    ((![A : int]: ((~ ((A = zero_zero_int))) => ((divide_divide_int @ A @ A) = one_one_int))))). % div_self
thf(fact_125_div__self, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => ((divide_divide_nat @ A @ A) = one_one_nat))))). % div_self
thf(fact_126_one__eq__divide__iff, axiom,
    ((![A : real, B : real]: ((one_one_real = (divide_divide_real @ A @ B)) = (((~ ((B = zero_zero_real)))) & ((A = B))))))). % one_eq_divide_iff
thf(fact_127_divide__self, axiom,
    ((![A : real]: ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real))))). % divide_self
thf(fact_128_divide__self__if, axiom,
    ((![A : real]: (((A = zero_zero_real) => ((divide_divide_real @ A @ A) = zero_zero_real)) & ((~ ((A = zero_zero_real))) => ((divide_divide_real @ A @ A) = one_one_real)))))). % divide_self_if
thf(fact_129_divide__eq__eq__1, axiom,
    ((![B : real, A : real]: (((divide_divide_real @ B @ A) = one_one_real) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % divide_eq_eq_1
thf(fact_130_eq__divide__eq__1, axiom,
    ((![B : real, A : real]: ((one_one_real = (divide_divide_real @ B @ A)) = (((~ ((A = zero_zero_real)))) & ((A = B))))))). % eq_divide_eq_1
thf(fact_131_one__divide__eq__0__iff, axiom,
    ((![A : real]: (((divide_divide_real @ one_one_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % one_divide_eq_0_iff
thf(fact_132_zero__eq__1__divide__iff, axiom,
    ((![A : real]: ((zero_zero_real = (divide_divide_real @ one_one_real @ A)) = (A = zero_zero_real))))). % zero_eq_1_divide_iff
thf(fact_133_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_real @ N) = one_one_real) = (N = one))))). % numeral_eq_one_iff
thf(fact_134_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_int @ N) = one_one_int) = (N = one))))). % numeral_eq_one_iff
thf(fact_135_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_136_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_real = (numeral_numeral_real @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_137_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_int = (numeral_numeral_int @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_138_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_139_zero__le__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_divide_1_iff
thf(fact_140_divide__le__0__1__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % divide_le_0_1_iff
thf(fact_141_divide__less__0__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ (divide_divide_real @ one_one_real @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % divide_less_0_1_iff
thf(fact_142_divide__less__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ A @ B)))))). % divide_less_eq_1_neg
thf(fact_143_divide__less__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_real @ B @ A)))))). % divide_less_eq_1_pos
thf(fact_144_less__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ B @ A)))))). % less_divide_eq_1_neg
thf(fact_145_less__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_real @ A @ B)))))). % less_divide_eq_1_pos
thf(fact_146_zero__less__divide__1__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (divide_divide_real @ one_one_real @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_divide_1_iff
thf(fact_147_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_real @ (numeral_numeral_real @ N) @ one_one_real) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_148_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_149_numeral__le__one__iff, axiom,
    ((![N : num]: ((ord_less_eq_int @ (numeral_numeral_int @ N) @ one_one_int) = (ord_less_eq_num @ N @ one))))). % numeral_le_one_iff
thf(fact_150_div__neg__neg__trivial, axiom,
    ((![K : int, L : int]: ((ord_less_eq_int @ K @ zero_zero_int) => ((ord_less_int @ L @ K) => ((divide_divide_int @ K @ L) = zero_zero_int)))))). % div_neg_neg_trivial
thf(fact_151_div__pos__pos__trivial, axiom,
    ((![K : int, L : int]: ((ord_less_eq_int @ zero_zero_int @ K) => ((ord_less_int @ K @ L) => ((divide_divide_int @ K @ L) = zero_zero_int)))))). % div_pos_pos_trivial
thf(fact_152_divide__le__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ A @ B)))))). % divide_le_eq_1_neg
thf(fact_153_divide__le__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (ord_less_eq_real @ B @ A)))))). % divide_le_eq_1_pos
thf(fact_154_le__divide__eq__1__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ B @ A)))))). % le_divide_eq_1_neg
thf(fact_155_le__divide__eq__1__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (ord_less_eq_real @ A @ B)))))). % le_divide_eq_1_pos
thf(fact_156_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_real @ one_one_real @ (numeral_numeral_real @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_157_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_int @ one_one_int @ (numeral_numeral_int @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_158_one__less__numeral__iff, axiom,
    ((![N : num]: ((ord_less_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (ord_less_num @ one @ N))))). % one_less_numeral_iff
thf(fact_159_less__eq__int__code_I1_J, axiom,
    ((ord_less_eq_int @ zero_zero_int @ zero_zero_int))). % less_eq_int_code(1)
thf(fact_160_int__one__le__iff__zero__less, axiom,
    ((![Z2 : int]: ((ord_less_eq_int @ one_one_int @ Z2) = (ord_less_int @ zero_zero_int @ Z2))))). % int_one_le_iff_zero_less
thf(fact_161_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_162_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat))). % le_numeral_extra(3)
thf(fact_163_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_int @ zero_zero_int @ zero_zero_int))). % le_numeral_extra(3)
thf(fact_164_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_165_verit__comp__simplify1_I3_J, axiom,
    ((![B2 : real, A2 : real]: ((~ ((ord_less_eq_real @ B2 @ A2))) = (ord_less_real @ A2 @ B2))))). % verit_comp_simplify1(3)
thf(fact_166_verit__comp__simplify1_I3_J, axiom,
    ((![B2 : num, A2 : num]: ((~ ((ord_less_eq_num @ B2 @ A2))) = (ord_less_num @ A2 @ B2))))). % verit_comp_simplify1(3)
thf(fact_167_verit__comp__simplify1_I3_J, axiom,
    ((![B2 : nat, A2 : nat]: ((~ ((ord_less_eq_nat @ B2 @ A2))) = (ord_less_nat @ A2 @ B2))))). % verit_comp_simplify1(3)
thf(fact_168_verit__comp__simplify1_I3_J, axiom,
    ((![B2 : int, A2 : int]: ((~ ((ord_less_eq_int @ B2 @ A2))) = (ord_less_int @ A2 @ B2))))). % verit_comp_simplify1(3)
thf(fact_169_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_170_zero__neq__one, axiom,
    ((~ ((zero_zero_int = one_one_int))))). % zero_neq_one
thf(fact_171_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_172_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_173_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_int @ one_one_int @ one_one_int))))). % less_numeral_extra(4)
thf(fact_174_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ one_one_nat))))). % less_numeral_extra(4)
thf(fact_175_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_nat @ one_one_nat @ one_one_nat))). % le_numeral_extra(4)
thf(fact_176_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_int @ one_one_int @ one_one_int))). % le_numeral_extra(4)
thf(fact_177_one__reorient, axiom,
    ((![X3 : nat]: ((one_one_nat = X3) = (X3 = one_one_nat))))). % one_reorient
thf(fact_178_one__reorient, axiom,
    ((![X3 : int]: ((one_one_int = X3) = (X3 = one_one_int))))). % one_reorient
thf(fact_179_verit__la__generic, axiom,
    ((![A : int, X3 : int]: ((ord_less_eq_int @ A @ X3) | ((A = X3) | (ord_less_eq_int @ X3 @ A)))))). % verit_la_generic
thf(fact_180_verit__la__disequality, axiom,
    ((![A : int, B : int]: ((A = B) | ((~ ((ord_less_eq_int @ A @ B))) | (~ ((ord_less_eq_int @ B @ A)))))))). % verit_la_disequality
thf(fact_181_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_182_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_nat @ one_one_nat @ zero_zero_nat))))). % not_one_le_zero
thf(fact_183_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_int @ one_one_int @ zero_zero_int))))). % not_one_le_zero
thf(fact_184_one__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_real @ one_one_real @ (numeral_numeral_real @ N))))). % one_le_numeral
thf(fact_185_one__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ N))))). % one_le_numeral
thf(fact_186_one__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_int @ one_one_int @ (numeral_numeral_int @ N))))). % one_le_numeral
thf(fact_187_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_188_zero__le__one, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ one_one_nat))). % zero_le_one
thf(fact_189_zero__le__one, axiom,
    ((ord_less_eq_int @ zero_zero_int @ one_one_int))). % zero_le_one
thf(fact_190_split__of__bool__asm, axiom,
    ((![P : real > $o, P2 : $o]: ((P @ (zero_n797941355l_real @ P2)) = (~ (((((P2) & ((~ ((P @ one_one_real)))))) | ((((~ (P2))) & ((~ ((P @ zero_zero_real))))))))))))). % split_of_bool_asm
thf(fact_191_split__of__bool__asm, axiom,
    ((![P : int > $o, P2 : $o]: ((P @ (zero_n1994027371ol_int @ P2)) = (~ (((((P2) & ((~ ((P @ one_one_int)))))) | ((((~ (P2))) & ((~ ((P @ zero_zero_int))))))))))))). % split_of_bool_asm
thf(fact_192_split__of__bool__asm, axiom,
    ((![P : nat > $o, P2 : $o]: ((P @ (zero_n1356753679ol_nat @ P2)) = (~ (((((P2) & ((~ ((P @ one_one_nat)))))) | ((((~ (P2))) & ((~ ((P @ zero_zero_nat))))))))))))). % split_of_bool_asm
thf(fact_193_split__of__bool, axiom,
    ((![P : real > $o, P2 : $o]: ((P @ (zero_n797941355l_real @ P2)) = ((((P2) => ((P @ one_one_real)))) & ((((~ (P2))) => ((P @ zero_zero_real))))))))). % split_of_bool
thf(fact_194_split__of__bool, axiom,
    ((![P : int > $o, P2 : $o]: ((P @ (zero_n1994027371ol_int @ P2)) = ((((P2) => ((P @ one_one_int)))) & ((((~ (P2))) => ((P @ zero_zero_int))))))))). % split_of_bool
thf(fact_195_split__of__bool, axiom,
    ((![P : nat > $o, P2 : $o]: ((P @ (zero_n1356753679ol_nat @ P2)) = ((((P2) => ((P @ one_one_nat)))) & ((((~ (P2))) => ((P @ zero_zero_nat))))))))). % split_of_bool
thf(fact_196_of__bool__def, axiom,
    ((zero_n797941355l_real = (^[P3 : $o]: (if_real @ P3 @ one_one_real @ zero_zero_real))))). % of_bool_def
thf(fact_197_of__bool__def, axiom,
    ((zero_n1994027371ol_int = (^[P3 : $o]: (if_int @ P3 @ one_one_int @ zero_zero_int))))). % of_bool_def
thf(fact_198_of__bool__def, axiom,
    ((zero_n1356753679ol_nat = (^[P3 : $o]: (if_nat @ P3 @ one_one_nat @ zero_zero_nat))))). % of_bool_def
thf(fact_199_divide__le__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (divide_divide_real @ B @ A) @ one_one_real) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ A)))) | ((((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ A @ B)))) | ((A = zero_zero_real))))))))). % divide_le_eq_1
thf(fact_200_le__divide__eq__1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ one_one_real @ (divide_divide_real @ B @ A)) = (((((ord_less_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ A @ B)))) | ((((ord_less_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ A))))))))). % le_divide_eq_1
thf(fact_201_zero__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_le_numeral
thf(fact_202_zero__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_le_numeral
thf(fact_203_zero__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_int @ zero_zero_int @ (numeral_numeral_int @ N))))). % zero_le_numeral
thf(fact_204_not__numeral__le__zero, axiom,
    ((![N : num]: (~ ((ord_less_eq_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_le_zero
thf(fact_205_not__numeral__le__zero, axiom,
    ((![N : num]: (~ ((ord_less_eq_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_le_zero
thf(fact_206_not__numeral__le__zero, axiom,
    ((![N : num]: (~ ((ord_less_eq_int @ (numeral_numeral_int @ N) @ zero_zero_int)))))). % not_numeral_le_zero
thf(fact_207_divide__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (divide_divide_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % divide_le_0_iff
thf(fact_208_divide__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (divide_divide_real @ A @ C) @ (divide_divide_real @ B @ C))))))). % divide_right_mono
thf(fact_209_zero__le__divide__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_divide_iff
thf(fact_210_divide__nonneg__nonneg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y2) => (ord_less_eq_real @ zero_zero_real @ (divide_divide_real @ X3 @ Y2))))))). % divide_nonneg_nonneg
thf(fact_211_divide__nonneg__nonpos, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ Y2 @ zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_nonneg_nonpos
thf(fact_212_divide__nonpos__nonneg, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ Y2) => (ord_less_eq_real @ (divide_divide_real @ X3 @ Y2) @ zero_zero_real)))))). % divide_nonpos_nonneg

% Helper facts (7)
thf(help_If_2_1_If_001t__Int__Oint_T, axiom,
    ((![X3 : int, Y2 : int]: ((if_int @ $false @ X3 @ Y2) = Y2)))).
thf(help_If_1_1_If_001t__Int__Oint_T, axiom,
    ((![X3 : int, Y2 : int]: ((if_int @ $true @ X3 @ Y2) = X3)))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X3 : nat, Y2 : nat]: ((if_nat @ $false @ X3 @ Y2) = Y2)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X3 : nat, Y2 : nat]: ((if_nat @ $true @ X3 @ Y2) = X3)))).
thf(help_If_3_1_If_001t__Real__Oreal_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Real__Oreal_T, axiom,
    ((![X3 : real, Y2 : real]: ((if_real @ $false @ X3 @ Y2) = Y2)))).
thf(help_If_1_1_If_001t__Real__Oreal_T, axiom,
    ((![X3 : real, Y2 : real]: ((if_real @ $true @ X3 @ Y2) = X3)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ zero_zero_real @ (divide_divide_real @ e @ (numeral_numeral_real @ (bit0 @ one)))))).
