% 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/FFT/prob_126__3223916_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:09:19.813

% Could-be-implicit typings (3)
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).

% Explicit typings (20)
thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat, type,
    minus_minus_nat : nat > nat > nat).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum, type,
    times_times_num : num > num > num).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal, type,
    uminus_uminus_real : real > real).
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_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_Num_Onumeral__class_Onumeral_001t__Real__Oreal, type,
    numeral_numeral_real : num > real).
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_Transcendental_Oarsinh_001t__Real__Oreal, type,
    arsinh_real : real > real).
thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal, type,
    artanh_real : real > real).
thf(sy_c_Transcendental_Opi, type,
    pi : real).
thf(sy_c_Transcendental_Osin_001t__Real__Oreal, type,
    sin_real : real > real).
thf(sy_v_x, type,
    x : real).

% Relevant facts (179)
thf(fact_0_pi1, axiom,
    ((ord_less_real @ pi @ x))). % pi1
thf(fact_1__C0_C, axiom,
    ((ord_less_real @ zero_zero_real @ x))). % "0"
thf(fact_2_pi2, axiom,
    ((ord_less_real @ x @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)))). % pi2
thf(fact_3_diff__gt__0__iff__gt, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_4_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_5_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_6_zero__diff, axiom,
    ((![A : nat]: ((minus_minus_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % zero_diff
thf(fact_7_diff__zero, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ zero_zero_nat) = A)))). % diff_zero
thf(fact_8_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_9_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : nat]: ((minus_minus_nat @ A @ A) = zero_zero_nat)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_10_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_11_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_12_calculation_I1_J, axiom,
    (((ord_less_real @ zero_zero_real @ x) => ((ord_less_real @ x @ pi) => (~ (((sin_real @ x) = zero_zero_real))))))). % calculation(1)
thf(fact_13_pi__gt__zero, axiom,
    ((ord_less_real @ zero_zero_real @ pi))). % pi_gt_zero
thf(fact_14_pi__not__less__zero, axiom,
    ((~ ((ord_less_real @ pi @ zero_zero_real))))). % pi_not_less_zero
thf(fact_15_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A2 : real]: (^[B2 : real]: (ord_less_real @ (minus_minus_real @ A2 @ B2) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_16_sin__zero, axiom,
    (((sin_real @ zero_zero_real) = zero_zero_real))). % sin_zero
thf(fact_17_sin__pi, axiom,
    (((sin_real @ pi) = zero_zero_real))). % sin_pi
thf(fact_18_sin__pi__minus, axiom,
    ((![X : real]: ((sin_real @ (minus_minus_real @ pi @ X)) = (sin_real @ X))))). % sin_pi_minus
thf(fact_19_sin__two__pi, axiom,
    (((sin_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) = zero_zero_real))). % sin_two_pi
thf(fact_20_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_21_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_22_mult_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_23_mult_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((times_times_nat @ (times_times_nat @ A @ B) @ C) = (times_times_nat @ A @ (times_times_nat @ B @ C)))))). % mult.assoc
thf(fact_24_mult_Ocommute, axiom,
    ((times_times_real = (^[A2 : real]: (^[B2 : real]: (times_times_real @ B2 @ A2)))))). % mult.commute
thf(fact_25_mult_Ocommute, axiom,
    ((times_times_nat = (^[A2 : nat]: (^[B2 : nat]: (times_times_nat @ B2 @ A2)))))). % mult.commute
thf(fact_26_mult_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((times_times_real @ B @ (times_times_real @ A @ C)) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_27_mult_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((times_times_nat @ B @ (times_times_nat @ A @ C)) = (times_times_nat @ A @ (times_times_nat @ B @ C)))))). % mult.left_commute
thf(fact_28_sin__gt__zero__02, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ (numeral_numeral_real @ (bit0 @ one))) => (ord_less_real @ zero_zero_real @ (sin_real @ X))))))). % sin_gt_zero_02
thf(fact_29_sin__lt__zero, axiom,
    ((![X : real]: ((ord_less_real @ pi @ X) => ((ord_less_real @ X @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi)) => (ord_less_real @ (sin_real @ X) @ zero_zero_real)))))). % sin_lt_zero
thf(fact_30_pi__less__4, axiom,
    ((ord_less_real @ pi @ (numeral_numeral_real @ (bit0 @ (bit0 @ one)))))). % pi_less_4
thf(fact_31_sin__gt__zero, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ X) => ((ord_less_real @ X @ pi) => (ord_less_real @ zero_zero_real @ (sin_real @ X))))))). % sin_gt_zero
thf(fact_32_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_33_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_34_diff__right__commute, axiom,
    ((![A : real, C : real, B : real]: ((minus_minus_real @ (minus_minus_real @ A @ C) @ B) = (minus_minus_real @ (minus_minus_real @ A @ B) @ C))))). % diff_right_commute
thf(fact_35_diff__right__commute, axiom,
    ((![A : nat, C : nat, B : nat]: ((minus_minus_nat @ (minus_minus_nat @ A @ C) @ B) = (minus_minus_nat @ (minus_minus_nat @ A @ B) @ C))))). % diff_right_commute
thf(fact_36_diff__eq__diff__eq, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((A = B) = (C = D)))))). % diff_eq_diff_eq
thf(fact_37_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_38_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_39_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_40_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_41_eq__iff__diff__eq__0, axiom,
    (((^[Y : real]: (^[Z : real]: (Y = Z))) = (^[A2 : real]: (^[B2 : real]: ((minus_minus_real @ A2 @ B2) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_42_diff__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_43_diff__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => (ord_less_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_44_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C : real, D : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D)))))). % diff_eq_diff_less
thf(fact_45_diff__strict__mono, axiom,
    ((![A : real, B : real, D : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D))))))). % diff_strict_mono
thf(fact_46_pi__neq__zero, axiom,
    ((~ ((pi = zero_zero_real))))). % pi_neq_zero
thf(fact_47_not__real__square__gt__zero, axiom,
    ((![X : real]: ((~ ((ord_less_real @ zero_zero_real @ (times_times_real @ X @ X)))) = (X = zero_zero_real))))). % not_real_square_gt_zero
thf(fact_48_right__diff__distrib__numeral, axiom,
    ((![V : num, B : real, C : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ V) @ B) @ (times_times_real @ (numeral_numeral_real @ V) @ C)))))). % right_diff_distrib_numeral
thf(fact_49_left__diff__distrib__numeral, axiom,
    ((![A : real, B : real, V : num]: ((times_times_real @ (minus_minus_real @ A @ B) @ (numeral_numeral_real @ V)) = (minus_minus_real @ (times_times_real @ A @ (numeral_numeral_real @ V)) @ (times_times_real @ B @ (numeral_numeral_real @ V))))))). % left_diff_distrib_numeral
thf(fact_50_semiring__norm_I85_J, axiom,
    ((![M : num]: (~ (((bit0 @ M) = one)))))). % semiring_norm(85)
thf(fact_51_semiring__norm_I83_J, axiom,
    ((![N : num]: (~ ((one = (bit0 @ N))))))). % semiring_norm(83)
thf(fact_52_semiring__norm_I76_J, axiom,
    ((![N : num]: (ord_less_num @ one @ (bit0 @ N))))). % semiring_norm(76)
thf(fact_53_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z2 : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (numeral_numeral_real @ W) @ Z2)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Z2))))). % mult_numeral_left_semiring_numeral
thf(fact_54_mult__numeral__left__semiring__numeral, axiom,
    ((![V : num, W : num, Z2 : nat]: ((times_times_nat @ (numeral_numeral_nat @ V) @ (times_times_nat @ (numeral_numeral_nat @ W) @ Z2)) = (times_times_nat @ (numeral_numeral_nat @ (times_times_num @ V @ W)) @ Z2))))). % mult_numeral_left_semiring_numeral
thf(fact_55_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (numeral_numeral_real @ N)) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_56_numeral__times__numeral, axiom,
    ((![M : num, N : num]: ((times_times_nat @ (numeral_numeral_nat @ M) @ (numeral_numeral_nat @ N)) = (numeral_numeral_nat @ (times_times_num @ M @ N)))))). % numeral_times_numeral
thf(fact_57_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_58_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_59_mult__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_right
thf(fact_60_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_61_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_real @ M) = (numeral_numeral_real @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_62_numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((numeral_numeral_nat @ M) = (numeral_numeral_nat @ N)) = (M = N))))). % numeral_eq_iff
thf(fact_63_semiring__norm_I87_J, axiom,
    ((![M : num, N : num]: (((bit0 @ M) = (bit0 @ N)) = (M = N))))). % semiring_norm(87)
thf(fact_64_mult__zero__left, axiom,
    ((![A : real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real)))). % mult_zero_left
thf(fact_65_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_66_mult__zero__right, axiom,
    ((![A : real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_67_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_68_mult__eq__0__iff, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % mult_eq_0_iff
thf(fact_69_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_70_mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((times_times_real @ C @ A) = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_left
thf(fact_71_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left
thf(fact_72_semiring__norm_I13_J, axiom,
    ((![M : num, N : num]: ((times_times_num @ (bit0 @ M) @ (bit0 @ N)) = (bit0 @ (bit0 @ (times_times_num @ M @ N))))))). % semiring_norm(13)
thf(fact_73_semiring__norm_I11_J, axiom,
    ((![M : num]: ((times_times_num @ M @ one) = M)))). % semiring_norm(11)
thf(fact_74_semiring__norm_I12_J, axiom,
    ((![N : num]: ((times_times_num @ one @ N) = N)))). % semiring_norm(12)
thf(fact_75_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_76_semiring__norm_I75_J, axiom,
    ((![M : num]: (~ ((ord_less_num @ M @ one)))))). % semiring_norm(75)
thf(fact_77_num__double, axiom,
    ((![N : num]: ((times_times_num @ (bit0 @ one) @ N) = (bit0 @ N))))). % num_double
thf(fact_78_pos2, axiom,
    ((ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ (bit0 @ one))))). % pos2
thf(fact_79_linorder__neqE__linordered__idom, axiom,
    ((![X : real, Y2 : real]: ((~ ((X = Y2))) => ((~ ((ord_less_real @ X @ Y2))) => (ord_less_real @ Y2 @ X)))))). % linorder_neqE_linordered_idom
thf(fact_80_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_81_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_82_mult__not__zero, axiom,
    ((![A : real, B : real]: ((~ (((times_times_real @ A @ B) = zero_zero_real))) => ((~ ((A = zero_zero_real))) & (~ ((B = zero_zero_real)))))))). % mult_not_zero
thf(fact_83_mult__not__zero, axiom,
    ((![A : nat, B : nat]: ((~ (((times_times_nat @ A @ B) = zero_zero_nat))) => ((~ ((A = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_84_divisors__zero, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = zero_zero_real) => ((A = zero_zero_real) | (B = zero_zero_real)))))). % divisors_zero
thf(fact_85_divisors__zero, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_86_no__zero__divisors, axiom,
    ((![A : real, B : real]: ((~ ((A = zero_zero_real))) => ((~ ((B = zero_zero_real))) => (~ (((times_times_real @ A @ B) = zero_zero_real)))))))). % no_zero_divisors
thf(fact_87_no__zero__divisors, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_88_mult__left__cancel, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ C @ A) = (times_times_real @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_89_mult__left__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_90_mult__right__cancel, axiom,
    ((![C : real, A : real, B : real]: ((~ ((C = zero_zero_real))) => (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_91_mult__right__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_92_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_real = (numeral_numeral_real @ N))))))). % zero_neq_numeral
thf(fact_93_zero__neq__numeral, axiom,
    ((![N : num]: (~ ((zero_zero_nat = (numeral_numeral_nat @ N))))))). % zero_neq_numeral
thf(fact_94_left__diff__distrib, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (minus_minus_real @ A @ B) @ C) = (minus_minus_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)))))). % left_diff_distrib
thf(fact_95_right__diff__distrib, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)))))). % right_diff_distrib
thf(fact_96_left__diff__distrib_H, axiom,
    ((![B : real, C : real, A : real]: ((times_times_real @ (minus_minus_real @ B @ C) @ A) = (minus_minus_real @ (times_times_real @ B @ A) @ (times_times_real @ C @ A)))))). % left_diff_distrib'
thf(fact_97_left__diff__distrib_H, axiom,
    ((![B : nat, C : nat, A : nat]: ((times_times_nat @ (minus_minus_nat @ B @ C) @ A) = (minus_minus_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)))))). % left_diff_distrib'
thf(fact_98_right__diff__distrib_H, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ A @ (minus_minus_real @ B @ C)) = (minus_minus_real @ (times_times_real @ A @ B) @ (times_times_real @ A @ C)))))). % right_diff_distrib'
thf(fact_99_right__diff__distrib_H, axiom,
    ((![A : nat, B : nat, C : nat]: ((times_times_nat @ A @ (minus_minus_nat @ B @ C)) = (minus_minus_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)))))). % right_diff_distrib'
thf(fact_100_mult__neg__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_neg_neg
thf(fact_101_not__square__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (times_times_real @ A @ A) @ zero_zero_real)))))). % not_square_less_zero
thf(fact_102_mult__less__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (times_times_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))))))))). % mult_less_0_iff
thf(fact_103_mult__neg__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_neg_pos
thf(fact_104_mult__neg__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_neg_pos
thf(fact_105_mult__pos__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_pos_neg
thf(fact_106_mult__pos__neg, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ A @ B) @ zero_zero_nat)))))). % mult_pos_neg
thf(fact_107_mult__pos__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_pos_pos
thf(fact_108_mult__pos__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B))))))). % mult_pos_pos
thf(fact_109_mult__pos__neg2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (times_times_real @ B @ A) @ zero_zero_real)))))). % mult_pos_neg2
thf(fact_110_mult__pos__neg2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (times_times_nat @ B @ A) @ zero_zero_nat)))))). % mult_pos_neg2
thf(fact_111_zero__less__mult__iff, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (times_times_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_mult_iff
thf(fact_112_zero__less__mult__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ A @ B)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos
thf(fact_113_zero__less__mult__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ A @ B)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)))))). % zero_less_mult_pos
thf(fact_114_zero__less__mult__pos2, axiom,
    ((![B : real, A : real]: ((ord_less_real @ zero_zero_real @ (times_times_real @ B @ A)) => ((ord_less_real @ zero_zero_real @ A) => (ord_less_real @ zero_zero_real @ B)))))). % zero_less_mult_pos2
thf(fact_115_zero__less__mult__pos2, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ zero_zero_nat @ (times_times_nat @ B @ A)) => ((ord_less_nat @ zero_zero_nat @ A) => (ord_less_nat @ zero_zero_nat @ B)))))). % zero_less_mult_pos2
thf(fact_116_mult__less__cancel__left__neg, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ B @ A)))))). % mult_less_cancel_left_neg
thf(fact_117_mult__less__cancel__left__pos, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_real @ A @ B)))))). % mult_less_cancel_left_pos
thf(fact_118_mult__strict__left__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ zero_zero_real) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono_neg
thf(fact_119_mult__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_strict_left_mono
thf(fact_120_mult__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % mult_strict_left_mono
thf(fact_121_mult__less__cancel__left__disj, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) & ((ord_less_real @ A @ B)))) | ((((ord_less_real @ C @ zero_zero_real)) & ((ord_less_real @ B @ A))))))))). % mult_less_cancel_left_disj
thf(fact_122_mult__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 @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono_neg
thf(fact_123_mult__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 @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_strict_right_mono
thf(fact_124_mult__strict__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ C))))))). % mult_strict_right_mono
thf(fact_125_mult__less__cancel__right__disj, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_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))))))))). % mult_less_cancel_right_disj
thf(fact_126_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_127_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ zero_zero_nat @ C) => (ord_less_nat @ (times_times_nat @ C @ A) @ (times_times_nat @ C @ B))))))). % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
thf(fact_128_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_real @ zero_zero_real @ (numeral_numeral_real @ N))))). % zero_less_numeral
thf(fact_129_zero__less__numeral, axiom,
    ((![N : num]: (ord_less_nat @ zero_zero_nat @ (numeral_numeral_nat @ N))))). % zero_less_numeral
thf(fact_130_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_real @ (numeral_numeral_real @ N) @ zero_zero_real)))))). % not_numeral_less_zero
thf(fact_131_not__numeral__less__zero, axiom,
    ((![N : num]: (~ ((ord_less_nat @ (numeral_numeral_nat @ N) @ zero_zero_nat)))))). % not_numeral_less_zero
thf(fact_132_mult__numeral__1__right, axiom,
    ((![A : real]: ((times_times_real @ A @ (numeral_numeral_real @ one)) = A)))). % mult_numeral_1_right
thf(fact_133_mult__numeral__1__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ (numeral_numeral_nat @ one)) = A)))). % mult_numeral_1_right
thf(fact_134_mult__numeral__1, axiom,
    ((![A : real]: ((times_times_real @ (numeral_numeral_real @ one) @ A) = A)))). % mult_numeral_1
thf(fact_135_mult__numeral__1, axiom,
    ((![A : nat]: ((times_times_nat @ (numeral_numeral_nat @ one) @ A) = A)))). % mult_numeral_1
thf(fact_136_arsinh__0, axiom,
    (((arsinh_real @ zero_zero_real) = zero_zero_real))). % arsinh_0
thf(fact_137_artanh__0, axiom,
    (((artanh_real @ zero_zero_real) = zero_zero_real))). % artanh_0
thf(fact_138_mult__less__iff1, axiom,
    ((![Z2 : real, X : real, Y2 : real]: ((ord_less_real @ zero_zero_real @ Z2) => ((ord_less_real @ (times_times_real @ X @ Z2) @ (times_times_real @ Y2 @ Z2)) = (ord_less_real @ X @ Y2)))))). % mult_less_iff1
thf(fact_139_sin__2pi__minus, axiom,
    ((![X : real]: ((sin_real @ (minus_minus_real @ (times_times_real @ (numeral_numeral_real @ (bit0 @ one)) @ pi) @ X)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_2pi_minus
thf(fact_140_verit__eq__simplify_I8_J, axiom,
    ((![X2 : num, Y22 : num]: (((bit0 @ X2) = (bit0 @ Y22)) = (X2 = Y22))))). % verit_eq_simplify(8)
thf(fact_141_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_142_neg__equal__iff__equal, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = (uminus_uminus_real @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_143_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_144_arsinh__minus__real, axiom,
    ((![X : real]: ((arsinh_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (arsinh_real @ X)))))). % arsinh_minus_real
thf(fact_145_neg__equal__zero, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = A) = (A = zero_zero_real))))). % neg_equal_zero
thf(fact_146_equal__neg__zero, axiom,
    ((![A : real]: ((A = (uminus_uminus_real @ A)) = (A = zero_zero_real))))). % equal_neg_zero
thf(fact_147_neg__equal__0__iff__equal, axiom,
    ((![A : real]: (((uminus_uminus_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % neg_equal_0_iff_equal
thf(fact_148_neg__0__equal__iff__equal, axiom,
    ((![A : real]: ((zero_zero_real = (uminus_uminus_real @ A)) = (zero_zero_real = A))))). % neg_0_equal_iff_equal
thf(fact_149_add_Oinverse__neutral, axiom,
    (((uminus_uminus_real @ zero_zero_real) = zero_zero_real))). % add.inverse_neutral
thf(fact_150_neg__less__iff__less, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ B))))). % neg_less_iff_less
thf(fact_151_mult__minus__left, axiom,
    ((![A : real, B : real]: ((times_times_real @ (uminus_uminus_real @ A) @ B) = (uminus_uminus_real @ (times_times_real @ A @ B)))))). % mult_minus_left
thf(fact_152_minus__mult__minus, axiom,
    ((![A : real, B : real]: ((times_times_real @ (uminus_uminus_real @ A) @ (uminus_uminus_real @ B)) = (times_times_real @ A @ B))))). % minus_mult_minus
thf(fact_153_mult__minus__right, axiom,
    ((![A : real, B : real]: ((times_times_real @ A @ (uminus_uminus_real @ B)) = (uminus_uminus_real @ (times_times_real @ A @ B)))))). % mult_minus_right
thf(fact_154_neg__numeral__eq__iff, axiom,
    ((![M : num, N : num]: (((uminus_uminus_real @ (numeral_numeral_real @ M)) = (uminus_uminus_real @ (numeral_numeral_real @ N))) = (M = N))))). % neg_numeral_eq_iff
thf(fact_155_minus__diff__eq, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (minus_minus_real @ A @ B)) = (minus_minus_real @ B @ A))))). % minus_diff_eq
thf(fact_156_nat__mult__less__cancel__disj, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_nat @ (times_times_nat @ K @ M) @ (times_times_nat @ K @ N)) = (((ord_less_nat @ zero_zero_nat @ K)) & ((ord_less_nat @ M @ N))))))). % nat_mult_less_cancel_disj
thf(fact_157_sin__minus, axiom,
    ((![X : real]: ((sin_real @ (uminus_uminus_real @ X)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_minus
thf(fact_158_neg__less__0__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ zero_zero_real) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_0_iff_less
thf(fact_159_neg__0__less__iff__less, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % neg_0_less_iff_less
thf(fact_160_neg__less__pos, axiom,
    ((![A : real]: ((ord_less_real @ (uminus_uminus_real @ A) @ A) = (ord_less_real @ zero_zero_real @ A))))). % neg_less_pos
thf(fact_161_less__neg__neg, axiom,
    ((![A : real]: ((ord_less_real @ A @ (uminus_uminus_real @ A)) = (ord_less_real @ A @ zero_zero_real))))). % less_neg_neg
thf(fact_162_verit__minus__simplify_I3_J, axiom,
    ((![B : real]: ((minus_minus_real @ zero_zero_real @ B) = (uminus_uminus_real @ B))))). % verit_minus_simplify(3)
thf(fact_163_diff__0, axiom,
    ((![A : real]: ((minus_minus_real @ zero_zero_real @ A) = (uminus_uminus_real @ A))))). % diff_0
thf(fact_164_semiring__norm_I172_J, axiom,
    ((![V : num, W : num, Y2 : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y2)) = (times_times_real @ (numeral_numeral_real @ (times_times_num @ V @ W)) @ Y2))))). % semiring_norm(172)
thf(fact_165_semiring__norm_I171_J, axiom,
    ((![V : num, W : num, Y2 : real]: ((times_times_real @ (numeral_numeral_real @ V) @ (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ W)) @ Y2)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ V @ W))) @ Y2))))). % semiring_norm(171)
thf(fact_166_semiring__norm_I170_J, axiom,
    ((![V : num, W : num, Y2 : real]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ V)) @ (times_times_real @ (numeral_numeral_real @ W) @ Y2)) = (times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ V @ W))) @ Y2))))). % semiring_norm(170)
thf(fact_167_mult__neg__numeral__simps_I3_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (numeral_numeral_real @ M) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(3)
thf(fact_168_mult__neg__numeral__simps_I2_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (numeral_numeral_real @ N)) = (uminus_uminus_real @ (numeral_numeral_real @ (times_times_num @ M @ N))))))). % mult_neg_numeral_simps(2)
thf(fact_169_mult__neg__numeral__simps_I1_J, axiom,
    ((![M : num, N : num]: ((times_times_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (numeral_numeral_real @ (times_times_num @ M @ N)))))). % mult_neg_numeral_simps(1)
thf(fact_170_neg__numeral__less__iff, axiom,
    ((![M : num, N : num]: ((ord_less_real @ (uminus_uminus_real @ (numeral_numeral_real @ M)) @ (uminus_uminus_real @ (numeral_numeral_real @ N))) = (ord_less_num @ N @ M))))). % neg_numeral_less_iff
thf(fact_171_sin__periodic__pi__diff, axiom,
    ((![X : real]: ((sin_real @ (minus_minus_real @ X @ pi)) = (uminus_uminus_real @ (sin_real @ X)))))). % sin_periodic_pi_diff
thf(fact_172_nat__mult__eq__cancel1, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ K) => (((times_times_nat @ K @ M) = (times_times_nat @ K @ N)) = (M = N)))))). % nat_mult_eq_cancel1
thf(fact_173_nat__mult__less__cancel1, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ K) => ((ord_less_nat @ (times_times_nat @ K @ M) @ (times_times_nat @ K @ N)) = (ord_less_nat @ M @ N)))))). % nat_mult_less_cancel1
thf(fact_174_nat__mult__eq__cancel__disj, axiom,
    ((![K : nat, M : nat, N : nat]: (((times_times_nat @ K @ M) = (times_times_nat @ K @ N)) = (((K = zero_zero_nat)) | ((M = N))))))). % nat_mult_eq_cancel_disj
thf(fact_175_verit__negate__coefficient_I2_J, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % verit_negate_coefficient(2)
thf(fact_176_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_177_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_178_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ zero_zero_real @ (minus_minus_real @ x @ pi)))).
