% 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_30__5366932_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:26:24.499

% Could-be-implicit typings (6)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_a : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Set__Oset_It__Real__Oreal_J, type,
    set_real : $tType).
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (18)
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    zero_z2096148049poly_a : poly_poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
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__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001tf__a, type,
    real_V1022479215norm_a : a > real).
thf(sy_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_r, type,
    r : real).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (143)
thf(fact_0_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_1_pCons_Ohyps_I2_J, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M))))))). % pCons.hyps(2)
thf(fact_2_order__refl, axiom,
    ((![X : real]: (ord_less_eq_real @ X @ X)))). % order_refl
thf(fact_3_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_4_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_5_norm__ge__zero, axiom,
    ((![X : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X))))). % norm_ge_zero
thf(fact_6_complete__real, axiom,
    ((![S : set_real]: ((?[X2 : real]: (member_real @ X2 @ S)) => ((?[Z : real]: (![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Z)))) => (?[Y : real]: ((![X2 : real]: ((member_real @ X2 @ S) => (ord_less_eq_real @ X2 @ Y))) & (![Z : real]: ((![X3 : real]: ((member_real @ X3 @ S) => (ord_less_eq_real @ X3 @ Z))) => (ord_less_eq_real @ Y @ Z)))))))))). % complete_real
thf(fact_7_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_8_norm__le__zero__iff, axiom,
    ((![X : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ X) @ zero_zero_real) = (X = zero_zero_a))))). % norm_le_zero_iff
thf(fact_9_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_10_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_11_verit__la__disequality, axiom,
    ((![A : real, B : real]: ((A = B) | ((~ ((ord_less_eq_real @ A @ B))) | (~ ((ord_less_eq_real @ B @ A)))))))). % verit_la_disequality
thf(fact_12_norm__eq__zero, axiom,
    ((![X : a]: (((real_V1022479215norm_a @ X) = zero_zero_real) = (X = zero_zero_a))))). % norm_eq_zero
thf(fact_13_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_14_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_15_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_16_poly__0, axiom,
    ((![X : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X) = zero_zero_poly_a)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_18_poly__0, axiom,
    ((![X : a]: ((poly_a2 @ zero_zero_poly_a @ X) = zero_zero_a)))). % poly_0
thf(fact_19_zero__less__norm__iff, axiom,
    ((![X : a]: ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ X)) = (~ ((X = zero_zero_a))))))). % zero_less_norm_iff
thf(fact_20_zero__less__norm__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X)) = (~ ((X = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_21_verit__comp__simplify1_I1_J, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_22_poly__IVT__neg, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_23_poly__IVT__pos, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X3 : real]: ((ord_less_real @ A @ X3) & ((ord_less_real @ X3 @ B) & ((poly_real2 @ P @ X3) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_24_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_25_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_real @ X3 @ Y) => (ord_less_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_26_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_real @ X3 @ Y) => (ord_less_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_27_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_real @ X3 @ Y) => (ord_less_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_28_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_real @ X3 @ Y) => (ord_less_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_29_lt__ex, axiom,
    ((![X : real]: (?[Y : real]: (ord_less_real @ Y @ X))))). % lt_ex
thf(fact_30_gt__ex, axiom,
    ((![X : real]: (?[X_1 : real]: (ord_less_real @ X @ X_1))))). % gt_ex
thf(fact_31_neqE, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % neqE
thf(fact_32_neq__iff, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) = (((ord_less_real @ X @ Y2)) | ((ord_less_real @ Y2 @ X))))))). % neq_iff
thf(fact_33_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_34_dense, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (?[Z2 : real]: ((ord_less_real @ X @ Z2) & (ord_less_real @ Z2 @ Y2))))))). % dense
thf(fact_35_less__imp__neq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_neq
thf(fact_36_less__asym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_asym
thf(fact_37_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_38_less__trans, axiom,
    ((![X : real, Y2 : real, Z3 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z3) => (ord_less_real @ X @ Z3)))))). % less_trans
thf(fact_39_less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) | ((X = Y2) | (ord_less_real @ Y2 @ X)))))). % less_linear
thf(fact_40_less__irrefl, axiom,
    ((![X : real]: (~ ((ord_less_real @ X @ X)))))). % less_irrefl
thf(fact_41_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_42_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_43_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_44_less__imp__not__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((X = Y2))))))). % less_imp_not_eq
thf(fact_45_less__not__sym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_not_sym
thf(fact_46_antisym__conv3, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_real @ Y2 @ X))) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv3
thf(fact_47_mem__Collect__eq, axiom,
    ((![A : real, P2 : real > $o]: ((member_real @ A @ (collect_real @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_48_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X4 : real]: (member_real @ X4 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_49_less__imp__not__eq2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((Y2 = X))))))). % less_imp_not_eq2
thf(fact_50_less__imp__triv, axiom,
    ((![X : real, Y2 : real, P2 : $o]: ((ord_less_real @ X @ Y2) => ((ord_less_real @ Y2 @ X) => P2))))). % less_imp_triv
thf(fact_51_linorder__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((~ ((X = Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_cases
thf(fact_52_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_53_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_54_less__imp__not__less, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (~ ((ord_less_real @ Y2 @ X))))))). % less_imp_not_less
thf(fact_55_linorder__less__wlog, axiom,
    ((![P2 : real > real > $o, A : real, B : real]: ((![A3 : real, B2 : real]: ((ord_less_real @ A3 @ B2) => (P2 @ A3 @ B2))) => ((![A3 : real]: (P2 @ A3 @ A3)) => ((![A3 : real, B2 : real]: ((P2 @ B2 @ A3) => (P2 @ A3 @ B2))) => (P2 @ A @ B))))))). % linorder_less_wlog
thf(fact_56_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_57_not__less__iff__gr__or__eq, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (((ord_less_real @ Y2 @ X)) | ((X = Y2))))))). % not_less_iff_gr_or_eq
thf(fact_58_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_59_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_60_norm__not__less__zero, axiom,
    ((![X : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_61_norm__not__less__zero, axiom,
    ((![X : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_62_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X4 : real]: ((poly_real2 @ P @ X4) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_63_order_Onot__eq__order__implies__strict, axiom,
    ((![A : real, B : real]: ((~ ((A = B))) => ((ord_less_eq_real @ A @ B) => (ord_less_real @ A @ B)))))). % order.not_eq_order_implies_strict
thf(fact_64_dual__order_Ostrict__implies__order, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (ord_less_eq_real @ B @ A))))). % dual_order.strict_implies_order
thf(fact_65_dual__order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[B3 : real]: (^[A4 : real]: (((ord_less_eq_real @ B3 @ A4)) & ((~ ((A4 = B3)))))))))). % dual_order.strict_iff_order
thf(fact_66_dual__order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[B3 : real]: (^[A4 : real]: (((ord_less_real @ B3 @ A4)) | ((A4 = B3)))))))). % dual_order.order_iff_strict
thf(fact_67_order_Ostrict__implies__order, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_eq_real @ A @ B))))). % order.strict_implies_order
thf(fact_68_dense__le__bounded, axiom,
    ((![X : real, Y2 : real, Z3 : real]: ((ord_less_real @ X @ Y2) => ((![W : real]: ((ord_less_real @ X @ W) => ((ord_less_real @ W @ Y2) => (ord_less_eq_real @ W @ Z3)))) => (ord_less_eq_real @ Y2 @ Z3)))))). % dense_le_bounded
thf(fact_69_dense__ge__bounded, axiom,
    ((![Z3 : real, X : real, Y2 : real]: ((ord_less_real @ Z3 @ X) => ((![W : real]: ((ord_less_real @ Z3 @ W) => ((ord_less_real @ W @ X) => (ord_less_eq_real @ Y2 @ W)))) => (ord_less_eq_real @ Y2 @ Z3)))))). % dense_ge_bounded
thf(fact_70_dual__order_Ostrict__trans2, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans2
thf(fact_71_dual__order_Ostrict__trans1, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans1
thf(fact_72_order_Ostrict__iff__order, axiom,
    ((ord_less_real = (^[A4 : real]: (^[B3 : real]: (((ord_less_eq_real @ A4 @ B3)) & ((~ ((A4 = B3)))))))))). % order.strict_iff_order
thf(fact_73_order_Oorder__iff__strict, axiom,
    ((ord_less_eq_real = (^[A4 : real]: (^[B3 : real]: (((ord_less_real @ A4 @ B3)) | ((A4 = B3)))))))). % order.order_iff_strict
thf(fact_74_order_Ostrict__trans2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans2
thf(fact_75_order_Ostrict__trans1, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans1
thf(fact_76_not__le__imp__less, axiom,
    ((![Y2 : real, X : real]: ((~ ((ord_less_eq_real @ Y2 @ X))) => (ord_less_real @ X @ Y2))))). % not_le_imp_less
thf(fact_77_less__le__not__le, axiom,
    ((ord_less_real = (^[X4 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X4 @ Y3)) & ((~ ((ord_less_eq_real @ Y3 @ X4)))))))))). % less_le_not_le
thf(fact_78_le__imp__less__or__eq, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ X @ Y2) | (X = Y2)))))). % le_imp_less_or_eq
thf(fact_79_le__less__linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_real @ Y2 @ X))))). % le_less_linear
thf(fact_80_dense__le, axiom,
    ((![Y2 : real, Z3 : real]: ((![X3 : real]: ((ord_less_real @ X3 @ Y2) => (ord_less_eq_real @ X3 @ Z3))) => (ord_less_eq_real @ Y2 @ Z3))))). % dense_le
thf(fact_81_dense__ge, axiom,
    ((![Z3 : real, Y2 : real]: ((![X3 : real]: ((ord_less_real @ Z3 @ X3) => (ord_less_eq_real @ Y2 @ X3))) => (ord_less_eq_real @ Y2 @ Z3))))). % dense_ge
thf(fact_82_less__le__trans, axiom,
    ((![X : real, Y2 : real, Z3 : real]: ((ord_less_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z3) => (ord_less_real @ X @ Z3)))))). % less_le_trans
thf(fact_83_le__less__trans, axiom,
    ((![X : real, Y2 : real, Z3 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_real @ Y2 @ Z3) => (ord_less_real @ X @ Z3)))))). % le_less_trans
thf(fact_84_less__imp__le, axiom,
    ((![X : real, Y2 : real]: ((ord_less_real @ X @ Y2) => (ord_less_eq_real @ X @ Y2))))). % less_imp_le
thf(fact_85_antisym__conv2, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((~ ((ord_less_real @ X @ Y2))) = (X = Y2)))))). % antisym_conv2
thf(fact_86_antisym__conv1, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv1
thf(fact_87_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_88_not__less, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) = (ord_less_eq_real @ Y2 @ X))))). % not_less
thf(fact_89_not__le, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) = (ord_less_real @ Y2 @ X))))). % not_le
thf(fact_90_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_real @ X3 @ Y) => (ord_less_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_91_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_92_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_93_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_real @ X3 @ Y) => (ord_less_real @ (F @ X3) @ (F @ Y)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_94_less__le, axiom,
    ((ord_less_real = (^[X4 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X4 @ Y3)) & ((~ ((X4 = Y3)))))))))). % less_le
thf(fact_95_le__less, axiom,
    ((ord_less_eq_real = (^[X4 : real]: (^[Y3 : real]: (((ord_less_real @ X4 @ Y3)) | ((X4 = Y3)))))))). % le_less
thf(fact_96_leI, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % leI
thf(fact_97_leD, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_real @ X @ Y2))))))). % leD
thf(fact_98_verit__comp__simplify1_I3_J, axiom,
    ((![B4 : real, A5 : real]: ((~ ((ord_less_eq_real @ B4 @ A5))) = (ord_less_real @ A5 @ B4))))). % verit_comp_simplify1(3)
thf(fact_99_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X4 : real]: (^[Y3 : real]: (((ord_less_real @ X4 @ Y3)) | ((X4 = Y3)))))))). % less_eq_real_def
thf(fact_100_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_101_dual__order_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z4 : real]: (Y4 = Z4))) = (^[A4 : real]: (^[B3 : real]: (((ord_less_eq_real @ B3 @ A4)) & ((ord_less_eq_real @ A4 @ B3)))))))). % dual_order.eq_iff
thf(fact_102_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_103_linorder__wlog, axiom,
    ((![P2 : real > real > $o, A : real, B : real]: ((![A3 : real, B2 : real]: ((ord_less_eq_real @ A3 @ B2) => (P2 @ A3 @ B2))) => ((![A3 : real, B2 : real]: ((P2 @ B2 @ A3) => (P2 @ A3 @ B2))) => (P2 @ A @ B)))))). % linorder_wlog
thf(fact_104_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_105_order__trans, axiom,
    ((![X : real, Y2 : real, Z3 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ Z3) => (ord_less_eq_real @ X @ Z3)))))). % order_trans
thf(fact_106_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_107_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_108_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_109_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z4 : real]: (Y4 = Z4))) = (^[A4 : real]: (^[B3 : real]: (((ord_less_eq_real @ A4 @ B3)) & ((ord_less_eq_real @ B3 @ A4)))))))). % order_class.order.eq_iff
thf(fact_110_antisym__conv, axiom,
    ((![Y2 : real, X : real]: ((ord_less_eq_real @ Y2 @ X) => ((ord_less_eq_real @ X @ Y2) = (X = Y2)))))). % antisym_conv
thf(fact_111_le__cases3, axiom,
    ((![X : real, Y2 : real, Z3 : real]: (((ord_less_eq_real @ X @ Y2) => (~ ((ord_less_eq_real @ Y2 @ Z3)))) => (((ord_less_eq_real @ Y2 @ X) => (~ ((ord_less_eq_real @ X @ Z3)))) => (((ord_less_eq_real @ X @ Z3) => (~ ((ord_less_eq_real @ Z3 @ Y2)))) => (((ord_less_eq_real @ Z3 @ Y2) => (~ ((ord_less_eq_real @ Y2 @ X)))) => (((ord_less_eq_real @ Y2 @ Z3) => (~ ((ord_less_eq_real @ Z3 @ X)))) => (~ (((ord_less_eq_real @ Z3 @ X) => (~ ((ord_less_eq_real @ X @ Y2)))))))))))))). % le_cases3
thf(fact_112_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_113_le__cases, axiom,
    ((![X : real, Y2 : real]: ((~ ((ord_less_eq_real @ X @ Y2))) => (ord_less_eq_real @ Y2 @ X))))). % le_cases
thf(fact_114_eq__refl, axiom,
    ((![X : real, Y2 : real]: ((X = Y2) => (ord_less_eq_real @ X @ Y2))))). % eq_refl
thf(fact_115_linear, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) | (ord_less_eq_real @ Y2 @ X))))). % linear
thf(fact_116_antisym, axiom,
    ((![X : real, Y2 : real]: ((ord_less_eq_real @ X @ Y2) => ((ord_less_eq_real @ Y2 @ X) => (X = Y2)))))). % antisym
thf(fact_117_eq__iff, axiom,
    (((^[Y4 : real]: (^[Z4 : real]: (Y4 = Z4))) = (^[X4 : real]: (^[Y3 : real]: (((ord_less_eq_real @ X4 @ Y3)) & ((ord_less_eq_real @ Y3 @ X4)))))))). % eq_iff
thf(fact_118_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_119_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X3 : real, Y : real]: ((ord_less_eq_real @ X3 @ Y) => (ord_less_eq_real @ (F @ X3) @ (F @ Y)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_120_complete__interval, axiom,
    ((![A : real, B : real, P2 : real > $o]: ((ord_less_real @ A @ B) => ((P2 @ A) => ((~ ((P2 @ B))) => (?[C2 : real]: ((ord_less_eq_real @ A @ C2) & ((ord_less_eq_real @ C2 @ B) & ((![X2 : real]: (((ord_less_eq_real @ A @ X2) & (ord_less_real @ X2 @ C2)) => (P2 @ X2))) & (![D : real]: ((![X3 : real]: (((ord_less_eq_real @ A @ X3) & (ord_less_real @ X3 @ D)) => (P2 @ X3))) => (ord_less_eq_real @ D @ C2))))))))))))). % complete_interval
thf(fact_121_pinf_I6_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => (~ ((ord_less_eq_real @ X2 @ T))))))))). % pinf(6)
thf(fact_122_pinf_I8_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => (ord_less_eq_real @ T @ X2))))))). % pinf(8)
thf(fact_123_minf_I6_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => (ord_less_eq_real @ X2 @ T))))))). % minf(6)
thf(fact_124_minf_I8_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => (~ ((ord_less_eq_real @ T @ X2))))))))). % minf(8)
thf(fact_125_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_126_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_127_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_128_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_129_ex__gt__or__lt, axiom,
    ((![A : real]: (?[B2 : real]: ((ord_less_real @ A @ B2) | (ord_less_real @ B2 @ A)))))). % ex_gt_or_lt
thf(fact_130_pinf_I1_J, axiom,
    ((![P2 : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X3 : real]: ((ord_less_real @ Z @ X3) => ((P2 @ X3) = (P3 @ X3))))) => ((?[Z : real]: (![X3 : real]: ((ord_less_real @ Z @ X3) => ((Q2 @ X3) = (Q3 @ X3))))) => (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => ((((P2 @ X2)) & ((Q2 @ X2))) = (((P3 @ X2)) & ((Q3 @ X2)))))))))))). % pinf(1)
thf(fact_131_pinf_I2_J, axiom,
    ((![P2 : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X3 : real]: ((ord_less_real @ Z @ X3) => ((P2 @ X3) = (P3 @ X3))))) => ((?[Z : real]: (![X3 : real]: ((ord_less_real @ Z @ X3) => ((Q2 @ X3) = (Q3 @ X3))))) => (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => ((((P2 @ X2)) | ((Q2 @ X2))) = (((P3 @ X2)) | ((Q3 @ X2)))))))))))). % pinf(2)
thf(fact_132_pinf_I3_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => (~ ((X2 = T))))))))). % pinf(3)
thf(fact_133_pinf_I4_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => (~ ((X2 = T))))))))). % pinf(4)
thf(fact_134_pinf_I5_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => (~ ((ord_less_real @ X2 @ T))))))))). % pinf(5)
thf(fact_135_pinf_I7_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ Z2 @ X2) => (ord_less_real @ T @ X2))))))). % pinf(7)
thf(fact_136_minf_I1_J, axiom,
    ((![P2 : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X3 : real]: ((ord_less_real @ X3 @ Z) => ((P2 @ X3) = (P3 @ X3))))) => ((?[Z : real]: (![X3 : real]: ((ord_less_real @ X3 @ Z) => ((Q2 @ X3) = (Q3 @ X3))))) => (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => ((((P2 @ X2)) & ((Q2 @ X2))) = (((P3 @ X2)) & ((Q3 @ X2)))))))))))). % minf(1)
thf(fact_137_minf_I2_J, axiom,
    ((![P2 : real > $o, P3 : real > $o, Q2 : real > $o, Q3 : real > $o]: ((?[Z : real]: (![X3 : real]: ((ord_less_real @ X3 @ Z) => ((P2 @ X3) = (P3 @ X3))))) => ((?[Z : real]: (![X3 : real]: ((ord_less_real @ X3 @ Z) => ((Q2 @ X3) = (Q3 @ X3))))) => (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => ((((P2 @ X2)) | ((Q2 @ X2))) = (((P3 @ X2)) | ((Q3 @ X2)))))))))))). % minf(2)
thf(fact_138_minf_I3_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => (~ ((X2 = T))))))))). % minf(3)
thf(fact_139_minf_I4_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => (~ ((X2 = T))))))))). % minf(4)
thf(fact_140_minf_I5_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => (ord_less_real @ X2 @ T))))))). % minf(5)
thf(fact_141_minf_I7_J, axiom,
    ((![T : real]: (?[Z2 : real]: (![X2 : real]: ((ord_less_real @ X2 @ Z2) => (~ ((ord_less_real @ T @ X2))))))))). % minf(7)
thf(fact_142_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![M2 : real]: ((![Z2 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z2) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z2)) @ M2))) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
