% 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_564__5373582_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:31:10.670

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Num__Onum, type,
    num : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (22)
thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat, type,
    semiri50953410ct_nat : nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001tf__a_001tf__a, type,
    fundam236050252nt_a_a : (a > a) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001tf__a, type,
    fundam247907092size_a : poly_a > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    one_one_poly_nat : poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum, type,
    plus_plus_num : num > num > num).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    plus_plus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_Itf__a_J, type,
    plus_plus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Oplus__class_Oplus_001tf__a, type,
    plus_plus_a : a > a > a).
thf(sy_c_Num_Onum_OBit0, type,
    bit0 : num > num).
thf(sy_c_Num_Onum_OOne, type,
    one : num).
thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat, type,
    numeral_numeral_nat : num > nat).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Nat__Onat_J, type,
    ord_less_eq_o_nat : ($o > nat) > ($o > nat) > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Num__Onum_J, type,
    ord_less_eq_o_num : ($o > num) > ($o > num) > $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_Oorder__class_OGreatest_001t__Nat__Onat, type,
    order_Greatest_nat : (nat > $o) > nat).
thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Num__Onum, type,
    order_Greatest_num : (num > $o) > num).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_v_p, type,
    p : poly_a).

% Relevant facts (131)
thf(fact_0_constant__def, axiom,
    ((fundam236050252nt_a_a = (^[F : a > a]: (![X : a]: (![Y : a]: ((F @ X) = (F @ Y)))))))). % constant_def
thf(fact_1_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_2_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_3_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_4_verit__eq__simplify_I8_J, axiom,
    ((![X2 : num, Y2 : num]: (((bit0 @ X2) = (bit0 @ Y2)) = (X2 = Y2))))). % verit_eq_simplify(8)
thf(fact_5_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_6_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_7_order__refl, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ X3 @ X3)))). % order_refl
thf(fact_8_order__refl, axiom,
    ((![X3 : num]: (ord_less_eq_num @ X3 @ X3)))). % order_refl
thf(fact_9_verit__eq__simplify_I10_J, axiom,
    ((![X2 : num]: (~ ((one = (bit0 @ X2))))))). % verit_eq_simplify(10)
thf(fact_10_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_11_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_12_semiring__norm_I71_J, axiom,
    ((![M : num, N : num]: ((ord_less_eq_num @ (bit0 @ M) @ (bit0 @ N)) = (ord_less_eq_num @ M @ N))))). % semiring_norm(71)
thf(fact_13_semiring__norm_I68_J, axiom,
    ((![N : num]: (ord_less_eq_num @ one @ N)))). % semiring_norm(68)
thf(fact_14_semiring__norm_I69_J, axiom,
    ((![M : num]: (~ ((ord_less_eq_num @ (bit0 @ M) @ one)))))). % semiring_norm(69)
thf(fact_15_le__num__One__iff, axiom,
    ((![X3 : num]: ((ord_less_eq_num @ X3 @ one) = (X3 = one))))). % le_num_One_iff
thf(fact_16_dual__order_Oantisym, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_17_dual__order_Oantisym, axiom,
    ((![B : num, A : num]: ((ord_less_eq_num @ B @ A) => ((ord_less_eq_num @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_18_dual__order_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_19_dual__order_Oeq__iff, axiom,
    (((^[Y3 : num]: (^[Z : num]: (Y3 = Z))) = (^[A2 : num]: (^[B2 : num]: (((ord_less_eq_num @ B2 @ A2)) & ((ord_less_eq_num @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_20_dual__order_Otrans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))))). % dual_order.trans
thf(fact_21_dual__order_Otrans, axiom,
    ((![B : num, A : num, C : num]: ((ord_less_eq_num @ B @ A) => ((ord_less_eq_num @ C @ B) => (ord_less_eq_num @ C @ A)))))). % dual_order.trans
thf(fact_22_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_eq_nat @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : nat, B3 : nat]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_23_linorder__wlog, axiom,
    ((![P : num > num > $o, A : num, B : num]: ((![A3 : num, B3 : num]: ((ord_less_eq_num @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : num, B3 : num]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_24_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_25_dual__order_Orefl, axiom,
    ((![A : num]: (ord_less_eq_num @ A @ A)))). % dual_order.refl
thf(fact_26_order__trans, axiom,
    ((![X3 : nat, Y4 : nat, Z2 : nat]: ((ord_less_eq_nat @ X3 @ Y4) => ((ord_less_eq_nat @ Y4 @ Z2) => (ord_less_eq_nat @ X3 @ Z2)))))). % order_trans
thf(fact_27_order__trans, axiom,
    ((![X3 : num, Y4 : num, Z2 : num]: ((ord_less_eq_num @ X3 @ Y4) => ((ord_less_eq_num @ Y4 @ Z2) => (ord_less_eq_num @ X3 @ Z2)))))). % order_trans
thf(fact_28_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_29_order__class_Oorder_Oantisym, axiom,
    ((![A : num, B : num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_30_ord__le__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C)))))). % ord_le_eq_trans
thf(fact_31_ord__le__eq__trans, axiom,
    ((![A : num, B : num, C : num]: ((ord_less_eq_num @ A @ B) => ((B = C) => (ord_less_eq_num @ A @ C)))))). % ord_le_eq_trans
thf(fact_32_ord__eq__le__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % ord_eq_le_trans
thf(fact_33_ord__eq__le__trans, axiom,
    ((![A : num, B : num, C : num]: ((A = B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C)))))). % ord_eq_le_trans
thf(fact_34_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((ord_less_eq_nat @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_35_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : num]: (^[Z : num]: (Y3 = Z))) = (^[A2 : num]: (^[B2 : num]: (((ord_less_eq_num @ A2 @ B2)) & ((ord_less_eq_num @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_36_antisym__conv, axiom,
    ((![Y4 : nat, X3 : nat]: ((ord_less_eq_nat @ Y4 @ X3) => ((ord_less_eq_nat @ X3 @ Y4) = (X3 = Y4)))))). % antisym_conv
thf(fact_37_antisym__conv, axiom,
    ((![Y4 : num, X3 : num]: ((ord_less_eq_num @ Y4 @ X3) => ((ord_less_eq_num @ X3 @ Y4) = (X3 = Y4)))))). % antisym_conv
thf(fact_38_le__cases3, axiom,
    ((![X3 : nat, Y4 : nat, Z2 : nat]: (((ord_less_eq_nat @ X3 @ Y4) => (~ ((ord_less_eq_nat @ Y4 @ Z2)))) => (((ord_less_eq_nat @ Y4 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Z2)))) => (((ord_less_eq_nat @ X3 @ Z2) => (~ ((ord_less_eq_nat @ Z2 @ Y4)))) => (((ord_less_eq_nat @ Z2 @ Y4) => (~ ((ord_less_eq_nat @ Y4 @ X3)))) => (((ord_less_eq_nat @ Y4 @ Z2) => (~ ((ord_less_eq_nat @ Z2 @ X3)))) => (~ (((ord_less_eq_nat @ Z2 @ X3) => (~ ((ord_less_eq_nat @ X3 @ Y4)))))))))))))). % le_cases3
thf(fact_39_le__cases3, axiom,
    ((![X3 : num, Y4 : num, Z2 : num]: (((ord_less_eq_num @ X3 @ Y4) => (~ ((ord_less_eq_num @ Y4 @ Z2)))) => (((ord_less_eq_num @ Y4 @ X3) => (~ ((ord_less_eq_num @ X3 @ Z2)))) => (((ord_less_eq_num @ X3 @ Z2) => (~ ((ord_less_eq_num @ Z2 @ Y4)))) => (((ord_less_eq_num @ Z2 @ Y4) => (~ ((ord_less_eq_num @ Y4 @ X3)))) => (((ord_less_eq_num @ Y4 @ Z2) => (~ ((ord_less_eq_num @ Z2 @ X3)))) => (~ (((ord_less_eq_num @ Z2 @ X3) => (~ ((ord_less_eq_num @ X3 @ Y4)))))))))))))). % le_cases3
thf(fact_40_order_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % order.trans
thf(fact_41_order_Otrans, axiom,
    ((![A : num, B : num, C : num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ B @ C) => (ord_less_eq_num @ A @ C)))))). % order.trans
thf(fact_42_le__cases, axiom,
    ((![X3 : nat, Y4 : nat]: ((~ ((ord_less_eq_nat @ X3 @ Y4))) => (ord_less_eq_nat @ Y4 @ X3))))). % le_cases
thf(fact_43_le__cases, axiom,
    ((![X3 : num, Y4 : num]: ((~ ((ord_less_eq_num @ X3 @ Y4))) => (ord_less_eq_num @ Y4 @ X3))))). % le_cases
thf(fact_44_eq__refl, axiom,
    ((![X3 : nat, Y4 : nat]: ((X3 = Y4) => (ord_less_eq_nat @ X3 @ Y4))))). % eq_refl
thf(fact_45_eq__refl, axiom,
    ((![X3 : num, Y4 : num]: ((X3 = Y4) => (ord_less_eq_num @ X3 @ Y4))))). % eq_refl
thf(fact_46_linear, axiom,
    ((![X3 : nat, Y4 : nat]: ((ord_less_eq_nat @ X3 @ Y4) | (ord_less_eq_nat @ Y4 @ X3))))). % linear
thf(fact_47_linear, axiom,
    ((![X3 : num, Y4 : num]: ((ord_less_eq_num @ X3 @ Y4) | (ord_less_eq_num @ Y4 @ X3))))). % linear
thf(fact_48_antisym, axiom,
    ((![X3 : nat, Y4 : nat]: ((ord_less_eq_nat @ X3 @ Y4) => ((ord_less_eq_nat @ Y4 @ X3) => (X3 = Y4)))))). % antisym
thf(fact_49_antisym, axiom,
    ((![X3 : num, Y4 : num]: ((ord_less_eq_num @ X3 @ Y4) => ((ord_less_eq_num @ Y4 @ X3) => (X3 = Y4)))))). % antisym
thf(fact_50_eq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[X : nat]: (^[Y : nat]: (((ord_less_eq_nat @ X @ Y)) & ((ord_less_eq_nat @ Y @ X)))))))). % eq_iff
thf(fact_51_eq__iff, axiom,
    (((^[Y3 : num]: (^[Z : num]: (Y3 = Z))) = (^[X : num]: (^[Y : num]: (((ord_less_eq_num @ X @ Y)) & ((ord_less_eq_num @ Y @ X)))))))). % eq_iff
thf(fact_52_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_53_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > num, C : num]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_54_ord__le__eq__subst, axiom,
    ((![A : num, B : num, F2 : num > nat, C : nat]: ((ord_less_eq_num @ A @ B) => (((F2 @ B) = C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_55_ord__le__eq__subst, axiom,
    ((![A : num, B : num, F2 : num > num, C : num]: ((ord_less_eq_num @ A @ B) => (((F2 @ B) = C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_56_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_57_ord__eq__le__subst, axiom,
    ((![A : num, F2 : nat > num, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_58_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : num > nat, B : num, C : num]: ((A = (F2 @ B)) => ((ord_less_eq_num @ B @ C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_59_ord__eq__le__subst, axiom,
    ((![A : num, F2 : num > num, B : num, C : num]: ((A = (F2 @ B)) => ((ord_less_eq_num @ B @ C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_60_verit__la__disequality, axiom,
    ((![A : nat, B : nat]: ((A = B) | ((~ ((ord_less_eq_nat @ A @ B))) | (~ ((ord_less_eq_nat @ B @ A)))))))). % verit_la_disequality
thf(fact_61_verit__la__disequality, axiom,
    ((![A : num, B : num]: ((A = B) | ((~ ((ord_less_eq_num @ A @ B))) | (~ ((ord_less_eq_num @ B @ A)))))))). % verit_la_disequality
thf(fact_62_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_63_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > num, C : num]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_num @ (F2 @ B) @ C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_64_order__subst2, axiom,
    ((![A : num, B : num, F2 : num > nat, C : nat]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_65_order__subst2, axiom,
    ((![A : num, B : num, F2 : num > num, C : num]: ((ord_less_eq_num @ A @ B) => ((ord_less_eq_num @ (F2 @ B) @ C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_66_order__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_67_order__subst1, axiom,
    ((![A : nat, F2 : num > nat, B : num, C : num]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_num @ B @ C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_68_order__subst1, axiom,
    ((![A : num, F2 : nat > num, B : nat, C : nat]: ((ord_less_eq_num @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y5 : nat]: ((ord_less_eq_nat @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_69_order__subst1, axiom,
    ((![A : num, F2 : num > num, B : num, C : num]: ((ord_less_eq_num @ A @ (F2 @ B)) => ((ord_less_eq_num @ B @ C) => ((![X4 : num, Y5 : num]: ((ord_less_eq_num @ X4 @ Y5) => (ord_less_eq_num @ (F2 @ X4) @ (F2 @ Y5)))) => (ord_less_eq_num @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_70_Nat_Oex__has__greatest__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ B))) => (?[X4 : nat]: ((P @ X4) & (![Y6 : nat]: ((P @ Y6) => (ord_less_eq_nat @ Y6 @ X4)))))))))). % Nat.ex_has_greatest_nat
thf(fact_71_nat__le__linear, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) | (ord_less_eq_nat @ N @ M))))). % nat_le_linear
thf(fact_72_le__antisym, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((ord_less_eq_nat @ N @ M) => (M = N)))))). % le_antisym
thf(fact_73_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_74_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_75_Greatest__equality, axiom,
    ((![P : num > $o, X3 : num]: ((P @ X3) => ((![Y5 : num]: ((P @ Y5) => (ord_less_eq_num @ Y5 @ X3))) => ((order_Greatest_num @ P) = X3)))))). % Greatest_equality
thf(fact_76_Greatest__equality, axiom,
    ((![P : nat > $o, X3 : nat]: ((P @ X3) => ((![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ X3))) => ((order_Greatest_nat @ P) = X3)))))). % Greatest_equality
thf(fact_77_GreatestI2__order, axiom,
    ((![P : num > $o, X3 : num, Q : num > $o]: ((P @ X3) => ((![Y5 : num]: ((P @ Y5) => (ord_less_eq_num @ Y5 @ X3))) => ((![X4 : num]: ((P @ X4) => ((![Y6 : num]: ((P @ Y6) => (ord_less_eq_num @ Y6 @ X4))) => (Q @ X4)))) => (Q @ (order_Greatest_num @ P)))))))). % GreatestI2_order
thf(fact_78_GreatestI2__order, axiom,
    ((![P : nat > $o, X3 : nat, Q : nat > $o]: ((P @ X3) => ((![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ X3))) => ((![X4 : nat]: ((P @ X4) => ((![Y6 : nat]: ((P @ Y6) => (ord_less_eq_nat @ Y6 @ X4))) => (Q @ X4)))) => (Q @ (order_Greatest_nat @ P)))))))). % GreatestI2_order
thf(fact_79_bounded__Max__nat, axiom,
    ((![P : nat > $o, X3 : nat, M2 : nat]: ((P @ X3) => ((![X4 : nat]: ((P @ X4) => (ord_less_eq_nat @ X4 @ M2))) => (~ ((![M3 : nat]: ((P @ M3) => (~ ((![X5 : nat]: ((P @ X5) => (ord_less_eq_nat @ X5 @ M3)))))))))))))). % bounded_Max_nat
thf(fact_80_fact__2, axiom,
    (((semiri50953410ct_nat @ (numeral_numeral_nat @ (bit0 @ one))) = (numeral_numeral_nat @ (bit0 @ one))))). % fact_2
thf(fact_81_le__rel__bool__arg__iff, axiom,
    ((ord_less_eq_o_nat = (^[X6 : $o > nat]: (^[Y7 : $o > nat]: (((ord_less_eq_nat @ (X6 @ $false) @ (Y7 @ $false))) & ((ord_less_eq_nat @ (X6 @ $true) @ (Y7 @ $true))))))))). % le_rel_bool_arg_iff
thf(fact_82_le__rel__bool__arg__iff, axiom,
    ((ord_less_eq_o_num = (^[X6 : $o > num]: (^[Y7 : $o > num]: (((ord_less_eq_num @ (X6 @ $false) @ (Y7 @ $false))) & ((ord_less_eq_num @ (X6 @ $true) @ (Y7 @ $true))))))))). % le_rel_bool_arg_iff
thf(fact_83_semiring__norm_I6_J, axiom,
    ((![M : num, N : num]: ((plus_plus_num @ (bit0 @ M) @ (bit0 @ N)) = (bit0 @ (plus_plus_num @ M @ N)))))). % semiring_norm(6)
thf(fact_84_nat__add__left__cancel__le, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N)) = (ord_less_eq_nat @ M @ N))))). % nat_add_left_cancel_le
thf(fact_85_numeral__plus__numeral, axiom,
    ((![M : num, N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ M @ N)))))). % numeral_plus_numeral
thf(fact_86_add__numeral__left, axiom,
    ((![V : num, W : num, Z2 : nat]: ((plus_plus_nat @ (numeral_numeral_nat @ V) @ (plus_plus_nat @ (numeral_numeral_nat @ W) @ Z2)) = (plus_plus_nat @ (numeral_numeral_nat @ (plus_plus_num @ V @ W)) @ Z2))))). % add_numeral_left
thf(fact_87_semiring__norm_I2_J, axiom,
    (((plus_plus_num @ one @ one) = (bit0 @ one)))). % semiring_norm(2)
thf(fact_88_fact__1, axiom,
    (((semiri50953410ct_nat @ one_one_nat) = one_one_nat))). % fact_1
thf(fact_89_poly__add, axiom,
    ((![P2 : poly_a, Q2 : poly_a, X3 : a]: ((poly_a2 @ (plus_plus_poly_a @ P2 @ Q2) @ X3) = (plus_plus_a @ (poly_a2 @ P2 @ X3) @ (poly_a2 @ Q2 @ X3)))))). % poly_add
thf(fact_90_poly__add, axiom,
    ((![P2 : poly_nat, Q2 : poly_nat, X3 : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P2 @ Q2) @ X3) = (plus_plus_nat @ (poly_nat2 @ P2 @ X3) @ (poly_nat2 @ Q2 @ X3)))))). % poly_add
thf(fact_91_poly__1, axiom,
    ((![X3 : nat]: ((poly_nat2 @ one_one_poly_nat @ X3) = one_one_nat)))). % poly_1
thf(fact_92_numeral__eq__one__iff, axiom,
    ((![N : num]: (((numeral_numeral_nat @ N) = one_one_nat) = (N = one))))). % numeral_eq_one_iff
thf(fact_93_one__eq__numeral__iff, axiom,
    ((![N : num]: ((one_one_nat = (numeral_numeral_nat @ N)) = (one = N))))). % one_eq_numeral_iff
thf(fact_94_numeral__plus__one, axiom,
    ((![N : num]: ((plus_plus_nat @ (numeral_numeral_nat @ N) @ one_one_nat) = (numeral_numeral_nat @ (plus_plus_num @ N @ one)))))). % numeral_plus_one
thf(fact_95_one__plus__numeral, axiom,
    ((![N : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (plus_plus_num @ one @ N)))))). % one_plus_numeral
thf(fact_96_one__add__one, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % one_add_one
thf(fact_97_fact__ge__1, axiom,
    ((![N : nat]: (ord_less_eq_nat @ one_one_nat @ (semiri50953410ct_nat @ N))))). % fact_ge_1
thf(fact_98_one__plus__numeral__commute, axiom,
    ((![X3 : num]: ((plus_plus_nat @ one_one_nat @ (numeral_numeral_nat @ X3)) = (plus_plus_nat @ (numeral_numeral_nat @ X3) @ one_one_nat))))). % one_plus_numeral_commute
thf(fact_99_fact__ge__self, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ (semiri50953410ct_nat @ N))))). % fact_ge_self
thf(fact_100_fact__mono__nat, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (semiri50953410ct_nat @ M) @ (semiri50953410ct_nat @ N)))))). % fact_mono_nat
thf(fact_101_add__One__commute, axiom,
    ((![N : num]: ((plus_plus_num @ one @ N) = (plus_plus_num @ N @ one))))). % add_One_commute
thf(fact_102_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_nat @ one_one_nat @ one_one_nat))). % le_numeral_extra(4)
thf(fact_103_add__leE, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N) => (~ (((ord_less_eq_nat @ M @ N) => (~ ((ord_less_eq_nat @ K @ N)))))))))). % add_leE
thf(fact_104_le__add1, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ N @ (plus_plus_nat @ N @ M))))). % le_add1
thf(fact_105_le__add2, axiom,
    ((![N : nat, M : nat]: (ord_less_eq_nat @ N @ (plus_plus_nat @ M @ N))))). % le_add2
thf(fact_106_add__leD1, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N) => (ord_less_eq_nat @ M @ N))))). % add_leD1
thf(fact_107_add__leD2, axiom,
    ((![M : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N) => (ord_less_eq_nat @ K @ N))))). % add_leD2
thf(fact_108_le__Suc__ex, axiom,
    ((![K : nat, L : nat]: ((ord_less_eq_nat @ K @ L) => (?[N2 : nat]: (L = (plus_plus_nat @ K @ N2))))))). % le_Suc_ex
thf(fact_109_add__le__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ K @ L) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L))))))). % add_le_mono
thf(fact_110_add__le__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ K)))))). % add_le_mono1
thf(fact_111_trans__le__add1, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ J @ M)))))). % trans_le_add1
thf(fact_112_trans__le__add2, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ M @ J)))))). % trans_le_add2
thf(fact_113_nat__le__iff__add, axiom,
    ((ord_less_eq_nat = (^[M4 : nat]: (^[N3 : nat]: (?[K2 : nat]: (N3 = (plus_plus_nat @ M4 @ K2)))))))). % nat_le_iff_add
thf(fact_114_fact__mono, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => (ord_less_eq_nat @ (semiri50953410ct_nat @ M) @ (semiri50953410ct_nat @ N)))))). % fact_mono
thf(fact_115_nat__1__add__1, axiom,
    (((plus_plus_nat @ one_one_nat @ one_one_nat) = (numeral_numeral_nat @ (bit0 @ one))))). % nat_1_add_1
thf(fact_116_numeral__Bit0, axiom,
    ((![N : num]: ((numeral_numeral_nat @ (bit0 @ N)) = (plus_plus_nat @ (numeral_numeral_nat @ N) @ (numeral_numeral_nat @ N)))))). % numeral_Bit0
thf(fact_117_one__le__numeral, axiom,
    ((![N : num]: (ord_less_eq_nat @ one_one_nat @ (numeral_numeral_nat @ N))))). % one_le_numeral
thf(fact_118_numeral__One, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numeral_One
thf(fact_119_numerals_I1_J, axiom,
    (((numeral_numeral_nat @ one) = one_one_nat))). % numerals(1)
thf(fact_120_GreatestI__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ B))) => (P @ (order_Greatest_nat @ P))))))). % GreatestI_nat
thf(fact_121_Greatest__le__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ B))) => (ord_less_eq_nat @ K @ (order_Greatest_nat @ P))))))). % Greatest_le_nat
thf(fact_122_GreatestI__ex__nat, axiom,
    ((![P : nat > $o, B : nat]: ((?[X_1 : nat]: (P @ X_1)) => ((![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ B))) => (P @ (order_Greatest_nat @ P))))))). % GreatestI_ex_nat
thf(fact_123_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_124_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_125_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_126_add__le__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_127_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_128_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_129_group__cancel_Oadd1, axiom,
    ((![A4 : nat, K : nat, A : nat, B : nat]: ((A4 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A4 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_130_group__cancel_Oadd2, axiom,
    ((![B4 : nat, K : nat, B : nat, A : nat]: ((B4 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B4) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2

% Conjectures (2)
thf(conj_0, hypothesis,
    ((~ ((fundam236050252nt_a_a @ (poly_a2 @ p)))))).
thf(conj_1, conjecture,
    ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ (fundam247907092size_a @ p)))).
