%   ORIGINAL: h4/transc/LN__LT__X
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/transc/EXP__LN: !x. h4/transc/exp (h4/transc/ln x) = x <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm: h4/bool/TRUTH: T
% Assm: h4/transc/EXP__INJ: !y x. h4/transc/exp x = h4/transc/exp y <=> x = y
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/transc/LN__MUL: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/transc/ln (h4/realax/real__mul x y) = h4/realax/real__add (h4/transc/ln x) (h4/transc/ln y)
% Assm: h4/transc/LN__INV: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/ln (h4/realax/inv x) = h4/realax/real__neg (h4/transc/ln x)
% Assm: h4/transc/LN__EXP: !x. h4/transc/ln (h4/transc/exp x) = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/transc/ln0: !x. h4/transc/ln x = h4/min/_40 (\u. h4/transc/exp u = x)
% Assm: h4/transc/LN__MONO__LE: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/real/real__lte (h4/transc/ln x) (h4/transc/ln y) <=> h4/real/real__lte x y)
% Assm: h4/transc/LN__MONO__LT: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/realax/real__lt (h4/transc/ln x) (h4/transc/ln y) <=> h4/realax/real__lt x y)
% Assm: h4/transc/LN__DIV: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/transc/ln (h4/real/_2F x y) = h4/real/real__sub (h4/transc/ln x) (h4/transc/ln y)
% Assm: h4/transc/LN__POW: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/ln (h4/real/pow x n) = h4/realax/real__mul (h4/real/real__of__num n) (h4/transc/ln x)
% Assm: h4/transc/LN__INJ: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/transc/ln x = h4/transc/ln y <=> x = y)
% Assm: h4/transc/EXP__MONO__LT: !y x. h4/realax/real__lt (h4/transc/exp x) (h4/transc/exp y) <=> h4/realax/real__lt x y
% Assm: h4/transc/EXP__MONO__LE: !y x. h4/real/real__lte (h4/transc/exp x) (h4/transc/exp y) <=> h4/real/real__lte x y
% Assm: h4/transc/EXP__TOTAL: !y. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?x. h4/transc/exp x = y)
% Assm: h4/transc/LN__1: h4/transc/ln (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__INV__POS: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/inv x)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/transc/EXP__POS__LT: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/transc/exp x)
% Assm: h4/transc/EXP__N: !x n. h4/transc/exp (h4/realax/real__mul (h4/real/real__of__num n) x) = h4/real/pow (h4/transc/exp x) n
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/transc/LN__LE: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/transc/ln (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x)) x
% Assm: h4/real/real__div: !y x. h4/real/_2F x y = h4/realax/real__mul x (h4/realax/inv y)
% Assm: h4/real/real__sub0: !y x. h4/real/real__sub x y = h4/realax/real__add x (h4/realax/real__neg y)
% Assm: h4/real/REAL__LT__MUL: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y)
% Assm: h4/transc/EXP__ADD: !y x. h4/transc/exp (h4/realax/real__add x y) = h4/realax/real__mul (h4/transc/exp x) (h4/transc/exp y)
% Assm: h4/real/REAL__POS__NZ: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> ~(x = h4/real/real__of__num h4/num/0)
% Assm: h4/real/REAL__MUL__RINV: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul x (h4/realax/inv x) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__RNEG__UNIQ: !y x. h4/realax/real__add x y = h4/real/real__of__num h4/num/0 <=> y = h4/realax/real__neg x
% Assm: h4/real/REAL__LT__01: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/real/REAL__LT__ADDL: !y x. h4/realax/real__lt y (h4/realax/real__add x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm: h4/transc/EXP__0: h4/transc/exp (h4/real/real__of__num h4/num/0) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/real/REAL__LE__LMUL: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (h4/real/real__lte (h4/realax/real__mul x y) (h4/realax/real__mul x z) <=> h4/real/real__lte y z)
% Assm: h4/transc/EXP__LE__X: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) (h4/transc/exp x)
% Assm: h4/real/REAL__LET__TRANS: !z y x. h4/real/real__lte x y /\ h4/realax/real__lt y z ==> h4/realax/real__lt x z
% Assm: h4/lim/DIFF__LMAX: !x l f. h4/lim/diffl f l x /\ (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> h4/real/real__lte (f y) (f x))) ==> l = h4/real/real__of__num h4/num/0
% Assm: h4/real/REAL__MUL__SYM: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm: h4/real/REAL__LT__ADDR: !y x. h4/realax/real__lt x (h4/realax/real__add x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) y
% Assm: h4/real/REAL__ADD__SYM: !y x. h4/realax/real__add x y = h4/realax/real__add y x
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/real/REAL__DOWN2: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?z. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z /\ h4/realax/real__lt z x /\ h4/realax/real__lt z y)
% Assm: h4/real/ABS__SIGN: !y x. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) y ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm: h4/lim/DIFF__LINC: !x l f. h4/lim/diffl f l x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) l ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!h. h4/realax/real__lt (h4/real/real__of__num h4/num/0) h /\ h4/realax/real__lt h d ==> h4/realax/real__lt (f x) (f (h4/realax/real__add x h))))
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/real/REAL__SUP__SOMEPOS: !P. (?x. P x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) x) /\ (?z. !x. P x ==> h4/realax/real__lt x z) ==> (?s. !y. (?x. P x /\ h4/realax/real__lt y x) <=> h4/realax/real__lt y s)
% Assm: h4/real/REAL__LE__RMUL: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z ==> (h4/real/real__lte (h4/realax/real__mul x z) (h4/realax/real__mul y z) <=> h4/real/real__lte x y)
% Assm: h4/topology/MTOP__OPEN: !m S_27. h4/topology/open (h4/topology/mtop m) S_27 <=> (!x. S_27 x ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e ==> S_27 y)))
% Assm: h4/real/REAL__LT__TOTAL: !y x. x = y \/ h4/realax/real__lt x y \/ h4/realax/real__lt y x
% Assm: h4/real/REAL__LT__LMUL__0: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) y)
% Assm: h4/real/REAL__LT__HALF2: !d. h4/realax/real__lt (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) d <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm: h4/lim/DIFF__LCONST: !x l f. h4/lim/diffl f l x /\ (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> f y = f x)) ==> l = h4/real/real__of__num h4/num/0
% Assm: h4/topology/BALL__NEIGH: !x m e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> h4/topology/neigh (h4/topology/mtop m) (h4/pair/_2C (h4/topology/B m (h4/pair/_2C x e)) x)
% Assm: h4/lim/DIFF__LMIN: !x l f. h4/lim/diffl f l x /\ (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> h4/real/real__lte (f x) (f y))) ==> l = h4/real/real__of__num h4/num/0
% Assm: h4/arithmetic/TWO: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__NOT__LT: !y x. ~h4/realax/real__lt x y <=> h4/real/real__lte y x
% Assm: h4/seq/cauchy0: !f. h4/seq/cauchy f <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?N. !m n. h4/arithmetic/_3E_3D m N /\ h4/arithmetic/_3E_3D n N ==> h4/realax/real__lt (h4/real/abs (h4/real/real__sub (f m) (f n))) e))
% Assm: h4/real/REAL__LT__HALF1: !d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/lim/CONT__INJ__LEMMA2: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> g (f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> ~(!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/real/real__lte (f x) (f z))
% Assm: h4/real/REAL__LT__MULTIPLE: !n d. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n ==> (h4/realax/real__lt d (h4/realax/real__mul (h4/real/real__of__num n) d) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d)
% Assm: h4/real/REAL__LT__TRANS: !z y x. h4/realax/real__lt x y /\ h4/realax/real__lt y z ==> h4/realax/real__lt x z
% Assm: h4/real/REAL__LT__LMUL: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (h4/realax/real__lt (h4/realax/real__mul x y) (h4/realax/real__mul x z) <=> h4/realax/real__lt y z)
% Assm: h4/real/ABS__BOUND: !y x d. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> h4/realax/real__lt y (h4/realax/real__add x d)
% Assm: h4/real/REAL__LE__NEG: !y x. h4/real/real__lte (h4/realax/real__neg x) (h4/realax/real__neg y) <=> h4/real/real__lte y x
% Assm: h4/real/REAL__LE__REFL: !x. h4/real/real__lte x x
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/real/REAL__LT__IMP__NE: !y x. h4/realax/real__lt x y ==> ~(x = y)
% Assm: h4/real/REAL__MUL__LINV: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul (h4/realax/inv x) x = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/topology/mtop__istopology: !m. h4/topology/istopology (\S_27. !x. S_27 x ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e ==> S_27 y)))
% Assm: h4/topology/mtop0: !m. h4/topology/mtop m = h4/topology/topology0 (\S_27. !x. S_27 x ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e ==> S_27 y)))
% Assm: h4/topology/topology__tybij_c1: !r. h4/topology/istopology r <=> h4/topology/open (h4/topology/topology0 r) = r
% Assm: h4/real/REAL__DOWN: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (?y. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y /\ h4/realax/real__lt y x)
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/real/REAL__LT__FRACTION: !n d. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n ==> (h4/realax/real__lt (h4/real/_2F d (h4/real/real__of__num n)) d <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d)
% Assm: h4/prim__rec/LESS__SUC__REFL: !n. h4/prim__rec/_3C n (h4/num/SUC n)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/real/REAL__SUP__ALLPOS: !P. (!x. P x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x) /\ (?x. P x) /\ (?z. !x. P x ==> h4/realax/real__lt x z) ==> (?s. !y. (?x. P x /\ h4/realax/real__lt y x) <=> h4/realax/real__lt y s)
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/real/abs0: !x. h4/real/abs x = h4/bool/COND (h4/real/real__lte (h4/real/real__of__num h4/num/0) x) x (h4/realax/real__neg x)
% Assm: h4/real/REAL__LT__IMP__LE: !y x. h4/realax/real__lt x y ==> h4/real/real__lte x y
% Assm: h4/real/REAL__INV__NZ: !x. ~(x = h4/real/real__of__num h4/num/0) ==> ~(h4/realax/inv x = h4/real/real__of__num h4/num/0)
% Assm: h4/real/REAL__NEG__GT0: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__neg x) <=> h4/realax/real__lt x (h4/real/real__of__num h4/num/0)
% Assm: h4/real/REAL__NEG__LMUL: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/real__neg x) y
% Assm: h4/real/REAL__LT__ANTISYM: !y x. ~(h4/realax/real__lt x y /\ h4/realax/real__lt y x)
% Assm: h4/topology/ball: !x m e. h4/topology/B m (h4/pair/_2C x e) = (\y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e)
% Assm: h4/topology/METRIC__SAME: !x m. h4/topology/dist m (h4/pair/_2C x x) = h4/real/real__of__num h4/num/0
% Assm: h4/topology/BALL__OPEN: !x m e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> h4/topology/open (h4/topology/mtop m) (h4/topology/B m (h4/pair/_2C x e))
% Assm: h4/topology/neigh0: !x top N. h4/topology/neigh top (h4/pair/_2C N x) <=> (?P. h4/topology/open top P /\ h4/pred__set/SUBSET P N /\ P x)
% Assm: h4/pred__set/SUBSET__REFL: !s. h4/pred__set/SUBSET s s
% Assm: h4/lim/DIFF__NEG: !x l f. h4/lim/diffl f l x ==> h4/lim/diffl (\x0. h4/realax/real__neg (f x0)) (h4/realax/real__neg l) x
% Assm: h4/real/REAL__NEG__EQ0: !x. h4/realax/real__neg x = h4/real/real__of__num h4/num/0 <=> x = h4/real/real__of__num h4/num/0
% Assm: h4/lim/diffl0: !x l f. h4/lim/diffl f l x <=> h4/lim/tends__real__real (\h. h4/real/_2F (h4/real/real__sub (f (h4/realax/real__add x h)) (f x)) h) l (h4/real/real__of__num h4/num/0)
% Assm: h4/lim/LIM: !y0 x0 f. h4/lim/tends__real__real f y0 x0 <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/abs (h4/real/real__sub x x0)) /\ h4/realax/real__lt (h4/real/abs (h4/real/real__sub x x0)) d ==> h4/realax/real__lt (h4/real/abs (h4/real/real__sub (f x) y0)) e)))
% Assm: h4/real/REAL__SUB__RZERO: !x. h4/real/real__sub x (h4/real/real__of__num h4/num/0) = x
% Assm: h4/real/REAL__LT__RMUL: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z ==> (h4/realax/real__lt (h4/realax/real__mul x z) (h4/realax/real__mul y z) <=> h4/realax/real__lt x y)
% Assm: h4/real/REAL__SUB__LT: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/real__sub x y) <=> h4/realax/real__lt y x
% Assm: h4/real/REAL__MUL__LZERO: !x. h4/realax/real__mul (h4/real/real__of__num h4/num/0) x = h4/real/real__of__num h4/num/0
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/real/REAL__LT__FRACTION__0: !n d. ~(n = h4/num/0) ==> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F d (h4/real/real__of__num n)) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d)
% Assm: h4/num/NOT__SUC: !n. ~(h4/num/SUC n = h4/num/0)
% Assm: h4/real/REAL__MUL__ASSOC: !z y x. h4/realax/real__mul x (h4/realax/real__mul y z) = h4/realax/real__mul (h4/realax/real__mul x y) z
% Assm: h4/real/REAL__MUL__LID: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm: h4/lim/CONT__INJ__LEMMA: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> g (f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> ~(!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/real/real__lte (f z) (f x))
% Assm: h4/lim/CONT__NEG: !x f. h4/lim/contl f x ==> h4/lim/contl (\x0. h4/realax/real__neg (f x0)) x
% Assm: h4/real/REAL__NEGNEG: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/lim/DIFF__LDEC: !x l f. h4/lim/diffl f l x /\ h4/realax/real__lt l (h4/real/real__of__num h4/num/0) ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!h. h4/realax/real__lt (h4/real/real__of__num h4/num/0) h /\ h4/realax/real__lt h d ==> h4/realax/real__lt (f x) (f (h4/real/real__sub x h))))
% Assm: h4/real/ABS__NEG: !x. h4/real/abs (h4/realax/real__neg x) = h4/real/abs x
% Assm: h4/real/REAL__ADD__SUB2: !y x. h4/real/real__sub x (h4/realax/real__add x y) = h4/realax/real__neg y
% Assm: h4/real/REAL__SUB__SUB2: !y x. h4/real/real__sub x (h4/real/real__sub x y) = y
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/real/REAL__LT: !n m. h4/realax/real__lt (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/prim__rec/_3C m n
% Assm: h4/real/REAL__LT__RMUL__0: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x)
% Assm: h4/real/REAL__MUL__RID: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm: h4/arithmetic/LESS__TRANS: !p n m. h4/prim__rec/_3C m n /\ h4/prim__rec/_3C n p ==> h4/prim__rec/_3C m p
% Assm: h4/real/REAL__LDISTRIB: !z y x. h4/realax/real__mul x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Goal: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/transc/ln x) x
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_transcs_EXPu_u_LN]: !x. h4/transc/exp (h4/transc/ln x) = x <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_transcs_EXPu_u_INJ]: !y x. h4/transc/exp x = h4/transc/exp y <=> x = y
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_transcs_LNu_u_MUL]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/transc/ln (h4/realax/real__mul x y) = h4/realax/real__add (h4/transc/ln x) (h4/transc/ln y)
% Assm [h4s_transcs_LNu_u_INV]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/ln (h4/realax/inv x) = h4/realax/real__neg (h4/transc/ln x)
% Assm [h4s_transcs_LNu_u_EXP]: !x. h4/transc/ln (h4/transc/exp x) = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_transcs_ln0]: !_0. (!x u. happ (happ _0 x) u <=> h4/transc/exp u = x) ==> (!x. h4/transc/ln x = h4/min/_40 (happ _0 x))
% Assm [h4s_transcs_LNu_u_MONOu_u_LE]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/real/real__lte (h4/transc/ln x) (h4/transc/ln y) <=> h4/real/real__lte x y)
% Assm [h4s_transcs_LNu_u_MONOu_u_LT]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/realax/real__lt (h4/transc/ln x) (h4/transc/ln y) <=> h4/realax/real__lt x y)
% Assm [h4s_transcs_LNu_u_DIV]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/transc/ln (h4/real/_2F x y) = h4/real/real__sub (h4/transc/ln x) (h4/transc/ln y)
% Assm [h4s_transcs_LNu_u_POW]: !x n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/transc/ln (h4/real/pow x n) = h4/realax/real__mul (h4/real/real__of__num n) (h4/transc/ln x)
% Assm [h4s_transcs_LNu_u_INJ]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/transc/ln x = h4/transc/ln y <=> x = y)
% Assm [h4s_transcs_EXPu_u_MONOu_u_LT]: !y x. h4/realax/real__lt (h4/transc/exp x) (h4/transc/exp y) <=> h4/realax/real__lt x y
% Assm [h4s_transcs_EXPu_u_MONOu_u_LE]: !y x. h4/real/real__lte (h4/transc/exp x) (h4/transc/exp y) <=> h4/real/real__lte x y
% Assm [h4s_transcs_EXPu_u_TOTAL]: !y. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?x. h4/transc/exp x = y)
% Assm [h4s_transcs_LNu_u_1]: h4/transc/ln (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_INVu_u_POS]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/inv x)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_transcs_EXPu_u_POSu_u_LT]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/transc/exp x)
% Assm [h4s_transcs_EXPu_u_N]: !x n. h4/transc/exp (h4/realax/real__mul (h4/real/real__of__num n) x) = h4/real/pow (h4/transc/exp x) n
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_transcs_LNu_u_LE]: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/transc/ln (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x)) x
% Assm [h4s_reals_realu_u_div]: !y x. h4/real/_2F x y = h4/realax/real__mul x (h4/realax/inv y)
% Assm [h4s_reals_realu_u_sub0]: !y x. h4/real/real__sub x y = h4/realax/real__add x (h4/realax/real__neg y)
% Assm [h4s_reals_REALu_u_LTu_u_MUL]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y)
% Assm [h4s_transcs_EXPu_u_ADD]: !y x. h4/transc/exp (h4/realax/real__add x y) = h4/realax/real__mul (h4/transc/exp x) (h4/transc/exp y)
% Assm [h4s_reals_REALu_u_POSu_u_NZ]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> ~(x = h4/real/real__of__num h4/num/0)
% Assm [h4s_reals_REALu_u_MULu_u_RINV]: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul x (h4/realax/inv x) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_REALu_u_RNEGu_u_UNIQ]: !y x. h4/realax/real__add x y = h4/real/real__of__num h4/num/0 <=> y = h4/realax/real__neg x
% Assm [h4s_reals_REALu_u_LTu_u_01]: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_reals_REALu_u_LTu_u_ADDL]: !y x. h4/realax/real__lt y (h4/realax/real__add x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm [h4s_transcs_EXPu_u_0]: h4/transc/exp (h4/real/real__of__num h4/num/0) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_reals_REALu_u_LEu_u_LMUL]: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (h4/real/real__lte (h4/realax/real__mul x y) (h4/realax/real__mul x z) <=> h4/real/real__lte y z)
% Assm [h4s_transcs_EXPu_u_LEu_u_X]: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/realax/real__add (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x) (h4/transc/exp x)
% Assm [h4s_reals_REALu_u_LETu_u_TRANS]: !z y x. h4/real/real__lte x y /\ h4/realax/real__lt y z ==> h4/realax/real__lt x z
% Assm [h4s_lims_DIFFu_u_LMAX]: !x l f. h4/lim/diffl f l x /\ (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> h4/real/real__lte (happ f y) (happ f x))) ==> l = h4/real/real__of__num h4/num/0
% Assm [h4s_reals_REALu_u_MULu_u_SYM]: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm [h4s_reals_REALu_u_LTu_u_ADDR]: !y x. h4/realax/real__lt x (h4/realax/real__add x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) y
% Assm [h4s_reals_REALu_u_ADDu_u_SYM]: !y x. h4/realax/real__add x y = h4/realax/real__add y x
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_reals_REALu_u_DOWN2]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (?z. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z /\ h4/realax/real__lt z x /\ h4/realax/real__lt z y)
% Assm [h4s_reals_ABSu_u_SIGN]: !y x. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) y ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x
% Assm [h4s_lims_DIFFu_u_LINC]: !x l f. h4/lim/diffl f l x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) l ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!h. h4/realax/real__lt (h4/real/real__of__num h4/num/0) h /\ h4/realax/real__lt h d ==> h4/realax/real__lt (happ f x) (happ f (h4/realax/real__add x h))))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_reals_REALu_u_SUPu_u_SOMEPOS]: !P. (?x. happ P x /\ h4/realax/real__lt (h4/real/real__of__num h4/num/0) x) /\ (?z. !x. happ P x ==> h4/realax/real__lt x z) ==> (?s. !y. (?x. happ P x /\ h4/realax/real__lt y x) <=> h4/realax/real__lt y s)
% Assm [h4s_reals_REALu_u_LEu_u_RMUL]: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z ==> (h4/real/real__lte (h4/realax/real__mul x z) (h4/realax/real__mul y z) <=> h4/real/real__lte x y)
% Assm [h4s_topologys_MTOPu_u_OPEN]: !m S_27. happ (h4/topology/open (h4/topology/mtop m)) S_27 <=> (!x. happ S_27 x ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e ==> happ S_27 y)))
% Assm [h4s_reals_REALu_u_LTu_u_TOTAL]: !y x. x = y \/ h4/realax/real__lt x y \/ h4/realax/real__lt y x
% Assm [h4s_reals_REALu_u_LTu_u_LMULu_u_0]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) y)
% Assm [h4s_reals_REALu_u_LTu_u_HALF2]: !d. h4/realax/real__lt (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) d <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm [h4s_lims_DIFFu_u_LCONST]: !x l f. h4/lim/diffl f l x /\ (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> happ f y = happ f x)) ==> l = h4/real/real__of__num h4/num/0
% Assm [h4s_topologys_BALLu_u_NEIGH]: !x m e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> h4/topology/neigh (h4/topology/mtop m) (h4/pair/_2C (h4/topology/B m (h4/pair/_2C x e)) x)
% Assm [h4s_lims_DIFFu_u_LMIN]: !x l f. h4/lim/diffl f l x /\ (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!y. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> h4/real/real__lte (happ f x) (happ f y))) ==> l = h4/real/real__of__num h4/num/0
% Assm [h4s_arithmetics_TWO]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_REALu_u_NOTu_u_LT]: !y x. ~h4/realax/real__lt x y <=> h4/real/real__lte y x
% Assm [h4s_seqs_cauchy0]: !f. h4/seq/cauchy f <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?N. !m n. h4/arithmetic/_3E_3D m N /\ h4/arithmetic/_3E_3D n N ==> h4/realax/real__lt (h4/real/abs (h4/real/real__sub (happ f m) (happ f n))) e))
% Assm [h4s_reals_REALu_u_LTu_u_HALF1]: !d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F d (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_lims_CONTu_u_INJu_u_LEMMA2]: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> happ g (happ f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> ~(!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/real/real__lte (happ f x) (happ f z))
% Assm [h4s_reals_REALu_u_LTu_u_MULTIPLE]: !n d. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n ==> (h4/realax/real__lt d (h4/realax/real__mul (h4/real/real__of__num n) d) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d)
% Assm [h4s_reals_REALu_u_LTu_u_TRANS]: !z y x. h4/realax/real__lt x y /\ h4/realax/real__lt y z ==> h4/realax/real__lt x z
% Assm [h4s_reals_REALu_u_LTu_u_LMUL]: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (h4/realax/real__lt (h4/realax/real__mul x y) (h4/realax/real__mul x z) <=> h4/realax/real__lt y z)
% Assm [h4s_reals_ABSu_u_BOUND]: !y x d. h4/realax/real__lt (h4/real/abs (h4/real/real__sub x y)) d ==> h4/realax/real__lt y (h4/realax/real__add x d)
% Assm [h4s_reals_REALu_u_LEu_u_NEG]: !y x. h4/real/real__lte (h4/realax/real__neg x) (h4/realax/real__neg y) <=> h4/real/real__lte y x
% Assm [h4s_reals_REALu_u_LEu_u_REFL]: !x. h4/real/real__lte x x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_reals_REALu_u_LTu_u_IMPu_u_NE]: !y x. h4/realax/real__lt x y ==> ~(x = y)
% Assm [h4s_reals_REALu_u_MULu_u_LINV]: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/real__mul (h4/realax/inv x) x = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_topologys_mtopu_u_istopology]: !_0. (!m S_27. happ (happ _0 m) S_27 <=> (!x. happ S_27 x ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e ==> happ S_27 y)))) ==> (!m. h4/topology/istopology (happ _0 m))
% Assm [h4s_topologys_mtop0]: !_0. (!m S_27. happ (happ _0 m) S_27 <=> (!x. happ S_27 x ==> (?e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e /\ (!y. h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x y)) e ==> happ S_27 y)))) ==> (!m. h4/topology/mtop m = h4/topology/topology0 (happ _0 m))
% Assm [h4s_topologys_topologyu_u_tybiju_c1]: !r. h4/topology/istopology r <=> h4/topology/open (h4/topology/topology0 r) = r
% Assm [h4s_reals_REALu_u_DOWN]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> (?y. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y /\ h4/realax/real__lt y x)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_reals_REALu_u_LTu_u_FRACTION]: !n d. h4/prim__rec/_3C (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n ==> (h4/realax/real__lt (h4/real/_2F d (h4/real/real__of__num n)) d <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d)
% Assm [h4s_primu_u_recs_LESSu_u_SUCu_u_REFL]: !n. h4/prim__rec/_3C n (h4/num/SUC n)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_reals_REALu_u_SUPu_u_ALLPOS]: !P. (!x. happ P x ==> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x) /\ (?x. happ P x) /\ (?z. !x. happ P x ==> h4/realax/real__lt x z) ==> (?s. !y. (?x. happ P x /\ h4/realax/real__lt y x) <=> h4/realax/real__lt y s)
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_reals_abs0]: !x. h4/real/abs x = h4/bool/COND (h4/real/real__lte (h4/real/real__of__num h4/num/0) x) x (h4/realax/real__neg x)
% Assm [h4s_reals_REALu_u_LTu_u_IMPu_u_LE]: !y x. h4/realax/real__lt x y ==> h4/real/real__lte x y
% Assm [h4s_reals_REALu_u_INVu_u_NZ]: !x. ~(x = h4/real/real__of__num h4/num/0) ==> ~(h4/realax/inv x = h4/real/real__of__num h4/num/0)
% Assm [h4s_reals_REALu_u_NEGu_u_GT0]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__neg x) <=> h4/realax/real__lt x (h4/real/real__of__num h4/num/0)
% Assm [h4s_reals_REALu_u_NEGu_u_LMUL]: !y x. h4/realax/real__neg (h4/realax/real__mul x y) = h4/realax/real__mul (h4/realax/real__neg x) y
% Assm [h4s_reals_REALu_u_LTu_u_ANTISYM]: !y x. ~(h4/realax/real__lt x y /\ h4/realax/real__lt y x)
% Assm [h4s_topologys_ball]: !x m e x'. happ (h4/topology/B m (h4/pair/_2C x e)) x' <=> h4/realax/real__lt (h4/topology/dist m (h4/pair/_2C x x')) e
% Assm [h4s_topologys_METRICu_u_SAME]: !x m. h4/topology/dist m (h4/pair/_2C x x) = h4/real/real__of__num h4/num/0
% Assm [h4s_topologys_BALLu_u_OPEN]: !x m e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> happ (h4/topology/open (h4/topology/mtop m)) (h4/topology/B m (h4/pair/_2C x e))
% Assm [h4s_topologys_neigh0]: !x top N. h4/topology/neigh top (h4/pair/_2C N x) <=> (?P. happ (h4/topology/open top) P /\ h4/pred__set/SUBSET P N /\ happ P x)
% Assm [h4s_predu_u_sets_SUBSETu_u_REFL]: !s. h4/pred__set/SUBSET s s
% Assm [h4s_lims_DIFFu_u_NEG]: !_0. (!f x0. happ (happ _0 f) x0 = h4/realax/real__neg (happ f x0)) ==> (!x l f. h4/lim/diffl f l x ==> h4/lim/diffl (happ _0 f) (h4/realax/real__neg l) x)
% Assm [h4s_reals_REALu_u_NEGu_u_EQ0]: !x. h4/realax/real__neg x = h4/real/real__of__num h4/num/0 <=> x = h4/real/real__of__num h4/num/0
% Assm [h4s_lims_diffl0]: !_0. (!f x h. happ (happ (happ _0 f) x) h = h4/real/_2F (h4/real/real__sub (happ f (h4/realax/real__add x h)) (happ f x)) h) ==> (!x l f. h4/lim/diffl f l x <=> h4/lim/tends__real__real (happ (happ _0 f) x) l (h4/real/real__of__num h4/num/0))
% Assm [h4s_lims_LIM]: !y0 x0 f. h4/lim/tends__real__real f y0 x0 <=> (!e. h4/realax/real__lt (h4/real/real__of__num h4/num/0) e ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/abs (h4/real/real__sub x x0)) /\ h4/realax/real__lt (h4/real/abs (h4/real/real__sub x x0)) d ==> h4/realax/real__lt (h4/real/abs (h4/real/real__sub (happ f x) y0)) e)))
% Assm [h4s_reals_REALu_u_SUBu_u_RZERO]: !x. h4/real/real__sub x (h4/real/real__of__num h4/num/0) = x
% Assm [h4s_reals_REALu_u_LTu_u_RMUL]: !z y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) z ==> (h4/realax/real__lt (h4/realax/real__mul x z) (h4/realax/real__mul y z) <=> h4/realax/real__lt x y)
% Assm [h4s_reals_REALu_u_SUBu_u_LT]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/real__sub x y) <=> h4/realax/real__lt y x
% Assm [h4s_reals_REALu_u_MULu_u_LZERO]: !x. h4/realax/real__mul (h4/real/real__of__num h4/num/0) x = h4/real/real__of__num h4/num/0
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_reals_REALu_u_LTu_u_FRACTIONu_u_0]: !n d. ~(n = h4/num/0) ==> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F d (h4/real/real__of__num n)) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) d)
% Assm [h4s_nums_NOTu_u_SUC]: !n. ~(h4/num/SUC n = h4/num/0)
% Assm [h4s_reals_REALu_u_MULu_u_ASSOC]: !z y x. h4/realax/real__mul x (h4/realax/real__mul y z) = h4/realax/real__mul (h4/realax/real__mul x y) z
% Assm [h4s_reals_REALu_u_MULu_u_LID]: !x. h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) x = x
% Assm [h4s_lims_CONTu_u_INJu_u_LEMMA]: !x g f d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> happ g (happ f z) = z) /\ (!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/lim/contl f z) ==> ~(!z. h4/real/real__lte (h4/real/abs (h4/real/real__sub z x)) d ==> h4/real/real__lte (happ f z) (happ f x))
% Assm [h4s_lims_CONTu_u_NEG]: !_0. (!f x0. happ (happ _0 f) x0 = h4/realax/real__neg (happ f x0)) ==> (!x f. h4/lim/contl f x ==> h4/lim/contl (happ _0 f) x)
% Assm [h4s_reals_REALu_u_NEGNEG]: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_lims_DIFFu_u_LDEC]: !x l f. h4/lim/diffl f l x /\ h4/realax/real__lt l (h4/real/real__of__num h4/num/0) ==> (?d. h4/realax/real__lt (h4/real/real__of__num h4/num/0) d /\ (!h. h4/realax/real__lt (h4/real/real__of__num h4/num/0) h /\ h4/realax/real__lt h d ==> h4/realax/real__lt (happ f x) (happ f (h4/real/real__sub x h))))
% Assm [h4s_reals_ABSu_u_NEG]: !x. h4/real/abs (h4/realax/real__neg x) = h4/real/abs x
% Assm [h4s_reals_REALu_u_ADDu_u_SUB2]: !y x. h4/real/real__sub x (h4/realax/real__add x y) = h4/realax/real__neg y
% Assm [h4s_reals_REALu_u_SUBu_u_SUB2]: !y x. h4/real/real__sub x (h4/real/real__sub x y) = y
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_reals_REALu_u_LT]: !n m. h4/realax/real__lt (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/prim__rec/_3C m n
% Assm [h4s_reals_REALu_u_LTu_u_RMULu_u_0]: !y x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) y ==> (h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/realax/real__mul x y) <=> h4/realax/real__lt (h4/real/real__of__num h4/num/0) x)
% Assm [h4s_reals_REALu_u_MULu_u_RID]: !x. h4/realax/real__mul x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = x
% Assm [h4s_arithmetics_LESSu_u_TRANS]: !p n m. h4/prim__rec/_3C m n /\ h4/prim__rec/_3C n p ==> h4/prim__rec/_3C m p
% Assm [h4s_reals_REALu_u_LDISTRIB]: !z y x. h4/realax/real__mul x (h4/realax/real__add y z) = h4/realax/real__add (h4/realax/real__mul x y) (h4/realax/real__mul x z)
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Goal: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x ==> h4/realax/real__lt (h4/transc/ln x) x
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1282833,TV_Q1282829]: ![V_f, V_g]: (![V_x]: s(TV_Q1282829,happ(s(t_fun(TV_Q1282833,TV_Q1282829),V_f),s(TV_Q1282833,V_x))) = s(TV_Q1282829,happ(s(t_fun(TV_Q1282833,TV_Q1282829),V_g),s(TV_Q1282833,V_x))) => s(t_fun(TV_Q1282833,TV_Q1282829),V_f) = s(t_fun(TV_Q1282833,TV_Q1282829),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_transcs_EXPu_u_LN, axiom, ![V_x]: (s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x) <=> p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_transcs_EXPu_u_INJ, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_y))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_transcs_LNu_u_MUL, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_transcs_LNu_u_INV, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_LNu_u_EXP, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_transcs_ln0, axiom, ![V_uu_0]: (![V_x, V_u]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool)),V_uu_0),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_u)))) <=> s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_u))) = s(t_h4s_realaxs_real,V_x)) => ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_mins_u_40(s(t_fun(t_h4s_realaxs_real,t_bool),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_bool)),V_uu_0),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_LNu_u_MONOu_u_LE, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_transcs_LNu_u_MONOu_u_LT, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_transcs_LNu_u_DIV, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_transcs_LNu_u_POW, axiom, ![V_x, V_n]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_n))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_LNu_u_INJ, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => (s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_y))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_EXPu_u_MONOu_u_LT, axiom, ![V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_EXPu_u_MONOu_u_LE, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_transcs_EXPu_u_TOTAL, axiom, ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y)))) => ?[V_x]: s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_transcs_LNu_u_1, axiom, s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_reals_REALu_u_INVu_u_POS, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_transcs_EXPu_u_POSu_u_LT, axiom, ![V_x]: p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_transcs_EXPu_u_N, axiom, ![V_x, V_n]: s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_transcs_LNu_u_LE, axiom, ![V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_reals_realu_u_div, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_realu_u_sub0, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_LTu_u_MUL, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))))).
fof(ah4s_transcs_EXPu_u_ADD, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_POSu_u_NZ, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => ~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_reals_REALu_u_MULu_u_RINV, axiom, ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_reals_REALu_u_RNEGu_u_UNIQ, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_realaxs_real,V_y) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_reals_REALu_u_LTu_u_01, axiom, p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_reals_REALu_u_LTu_u_ADDL, axiom, ![V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_transcs_EXPu_u_0, axiom, s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_reals_REALu_u_LEu_u_LMUL, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))).
fof(ah4s_transcs_EXPu_u_LEu_u_X, axiom, ![V_x]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_exp(s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_reals_REALu_u_LETu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_lims_DIFFu_u_LMAX, axiom, ![V_x, V_l, V_f]: ((p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))))))))) => s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_reals_REALu_u_MULu_u_SYM, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_LTu_u_ADDR, axiom, ![V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_ADDu_u_SYM, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_reals_REALu_u_DOWN2, axiom, ![V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))) => ?[V_z]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_z)))) & (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_y)))))))).
fof(ah4s_reals_ABSu_u_SIGN, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))),s(t_h4s_realaxs_real,V_y)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_lims_DIFFu_u_LINC, axiom, ![V_x, V_l, V_f]: ((p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_l))))) => ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_h]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_h)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_h),s(t_h4s_realaxs_real,V_d))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_h)))))))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_reals_REALu_u_SUPu_u_SOMEPOS, axiom, ![V_P]: ((?[V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))))) & ?[V_z]: ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))) => ?[V_s]: ![V_y]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))) <=> p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_s))))))).
fof(ah4s_reals_REALu_u_LEu_u_RMUL, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_z)))) => s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_topologys_MTOPu_u_OPEN, axiom, ![TV_u_27a]: ![V_m, V_Su_27]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_mtop(s(t_h4s_topologys_metric(TV_u_27a),V_m))))),s(t_fun(TV_u_27a,t_bool),V_Su_27)))) <=> ![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Su_27),s(TV_u_27a,V_x)))) => ?[V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) & ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_y))))),s(t_h4s_realaxs_real,V_e)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Su_27),s(TV_u_27a,V_y))))))))).
fof(ah4s_reals_REALu_u_LTu_u_TOTAL, axiom, ![V_y, V_x]: (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y) | (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) | p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_LTu_u_LMULu_u_0, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_reals_REALu_u_LTu_u_HALF2, axiom, ![V_d]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_realaxs_real,V_d))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))).
fof(ah4s_lims_DIFFu_u_LCONST, axiom, ![V_x, V_l, V_f]: ((p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_y))) = s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))) => s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_topologys_BALLu_u_NEIGH, axiom, ![TV_u_27a]: ![V_x, V_m, V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) => p(s(t_bool,h4s_topologys_neigh(s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_mtop(s(t_h4s_topologys_metric(TV_u_27a),V_m))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27a),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),h4s_topologys_b(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_realaxs_real),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_realaxs_real,V_e))))),s(TV_u_27a,V_x)))))))).
fof(ah4s_lims_DIFFu_u_LMIN, axiom, ![V_x, V_l, V_f]: ((p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_y))))))))) => s(t_h4s_realaxs_real,V_l) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_arithmetics_TWO, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_reals_REALu_u_NOTu_u_LT, axiom, ![V_y, V_x]: (~ (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) <=> p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_seqs_cauchy0, axiom, ![V_f]: (p(s(t_bool,h4s_seqs_cauchy(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f)))) <=> ![V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) => ?[V_N]: ![V_m, V_n]: ((p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_N)))) & p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_N))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f),s(t_h4s_nums_num,V_m))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),V_f),s(t_h4s_nums_num,V_n))))))),s(t_h4s_realaxs_real,V_e)))))))).
fof(ah4s_reals_REALu_u_LTu_u_HALF1, axiom, ![V_d]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_lims_CONTu_u_INJu_u_LEMMA2, axiom, ![V_x, V_g, V_f, V_d]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z)) & ![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))))) => ~ (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z)))))))))).
fof(ah4s_reals_REALu_u_LTu_u_MULTIPLE, axiom, ![V_n, V_d]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_realaxs_real,V_d))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d))))).
fof(ah4s_reals_REALu_u_LTu_u_TRANS, axiom, ![V_z, V_y, V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_reals_REALu_u_LTu_u_LMUL, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))).
fof(ah4s_reals_ABSu_u_BOUND, axiom, ![V_y, V_x, V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_d)))))))).
fof(ah4s_reals_REALu_u_LEu_u_NEG, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_LEu_u_REFL, axiom, ![V_x]: p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_reals_REALu_u_LTu_u_IMPu_u_NE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) => ~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_MULu_u_LINV, axiom, ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))).
fof(ah4s_topologys_mtopu_u_istopology, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_m, V_Su_27]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),happ(s(t_fun(t_h4s_topologys_metric(TV_u_27a),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_uu_0),s(t_h4s_topologys_metric(TV_u_27a),V_m))),s(t_fun(TV_u_27a,t_bool),V_Su_27)))) <=> ![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Su_27),s(TV_u_27a,V_x)))) => ?[V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) & ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_y))))),s(t_h4s_realaxs_real,V_e)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Su_27),s(TV_u_27a,V_y)))))))) => ![V_m]: p(s(t_bool,h4s_topologys_istopology(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),happ(s(t_fun(t_h4s_topologys_metric(TV_u_27a),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_uu_0),s(t_h4s_topologys_metric(TV_u_27a),V_m)))))))).
fof(ah4s_topologys_mtop0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_m, V_Su_27]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),happ(s(t_fun(t_h4s_topologys_metric(TV_u_27a),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_uu_0),s(t_h4s_topologys_metric(TV_u_27a),V_m))),s(t_fun(TV_u_27a,t_bool),V_Su_27)))) <=> ![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Su_27),s(TV_u_27a,V_x)))) => ?[V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) & ![V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_y))))),s(t_h4s_realaxs_real,V_e)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Su_27),s(TV_u_27a,V_y)))))))) => ![V_m]: s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_mtop(s(t_h4s_topologys_metric(TV_u_27a),V_m))) = s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_topology0(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),happ(s(t_fun(t_h4s_topologys_metric(TV_u_27a),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_uu_0),s(t_h4s_topologys_metric(TV_u_27a),V_m))))))).
fof(ah4s_topologys_topologyu_u_tybiju_c1, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,h4s_topologys_istopology(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_r)))) <=> s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_topology0(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_r))))) = s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_r))).
fof(ah4s_reals_REALu_u_DOWN, axiom, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => ?[V_y]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_reals_REALu_u_LTu_u_FRACTION, axiom, ![V_n, V_d]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_realaxs_real,V_d))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d))))).
fof(ah4s_primu_u_recs_LESSu_u_SUCu_u_REFL, axiom, ![V_n]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_reals_REALu_u_SUPu_u_ALLPOS, axiom, ![V_P]: ((![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))))) & (?[V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) & ?[V_z]: ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))))))) => ?[V_s]: ![V_y]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_realaxs_real,t_bool),V_P),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))) <=> p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_s))))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_reals_abs0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x)))))).
fof(ah4s_reals_REALu_u_LTu_u_IMPu_u_LE, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
fof(ah4s_reals_REALu_u_INVu_u_NZ, axiom, ![V_x]: (~ (s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))) => ~ (s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_reals_REALu_u_NEGu_u_GT0, axiom, ![V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_reals_REALu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_LTu_u_ANTISYM, axiom, ![V_y, V_x]: ~ ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_topologys_ball, axiom, ![TV_u_27a]: ![V_x, V_m, V_e, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),h4s_topologys_b(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_realaxs_real),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_realaxs_real,V_e))))),s(TV_u_27a,V_xi_))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_xi_))))),s(t_h4s_realaxs_real,V_e)))).
fof(ah4s_topologys_METRICu_u_SAME, axiom, ![TV_u_27a]: ![V_x, V_m]: s(t_h4s_realaxs_real,h4s_topologys_dist(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_topologys_BALLu_u_OPEN, axiom, ![TV_u_27a]: ![V_x, V_m, V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) => p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(TV_u_27a),h4s_topologys_mtop(s(t_h4s_topologys_metric(TV_u_27a),V_m))))),s(t_fun(TV_u_27a,t_bool),h4s_topologys_b(s(t_h4s_topologys_metric(TV_u_27a),V_m),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_realaxs_real),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_realaxs_real,V_e)))))))))).
fof(ah4s_topologys_neigh0, axiom, ![TV_u_27a]: ![V_x, V_top, V_N]: (p(s(t_bool,h4s_topologys_neigh(s(t_h4s_topologys_topology(TV_u_27a),V_top),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27a),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),V_N),s(TV_u_27a,V_x)))))) <=> ?[V_P]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),h4s_topologys_open(s(t_h4s_topologys_topology(TV_u_27a),V_top))),s(t_fun(TV_u_27a,t_bool),V_P)))) & (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_N)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))))))).
fof(ah4s_predu_u_sets_SUBSETu_u_REFL, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_lims_DIFFu_u_NEG, axiom, ![V_uu_0]: (![V_f, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_l, V_f]: (p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_l))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_NEGu_u_EQ0, axiom, ![V_x]: (s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_lims_diffl0, axiom, ![V_uu_0]: (![V_f, V_x, V_h]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_h))) = s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_h))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_h))) => ![V_x, V_l, V_f]: s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x))) = s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real))),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))).
fof(ah4s_lims_LIM, axiom, ![V_y0, V_x0, V_f]: (p(s(t_bool,h4s_lims_tendsu_u_realu_u_real(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_y0),s(t_h4s_realaxs_real,V_x0)))) <=> ![V_e]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_e)))) => ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_x]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x0)))))))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x0))))),s(t_h4s_realaxs_real,V_d))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_y0))))),s(t_h4s_realaxs_real,V_e))))))))).
fof(ah4s_reals_REALu_u_SUBu_u_RZERO, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_reals_REALu_u_LTu_u_RMUL, axiom, ![V_z, V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_z)))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))).
fof(ah4s_reals_REALu_u_SUBu_u_LT, axiom, ![V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_MULu_u_LZERO, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_reals_REALu_u_LTu_u_FRACTIONu_u_0, axiom, ![V_n, V_d]: (~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,V_d),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d))))).
fof(ah4s_nums_NOTu_u_SUC, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_reals_REALu_u_MULu_u_ASSOC, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,V_z)))).
fof(ah4s_reals_REALu_u_MULu_u_LID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_lims_CONTu_u_INJu_u_LEMMA, axiom, ![V_x, V_g, V_f, V_d]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,V_z)) & ![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))))))) => ~ (![V_z]: (p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_z),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,V_d)))) => p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_z))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))))))))).
fof(ah4s_lims_CONTu_u_NEG, axiom, ![V_uu_0]: (![V_f, V_x0]: s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_f]: (p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_lims_contl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real)),V_uu_0),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,V_x))))))).
fof(ah4s_reals_REALu_u_NEGNEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_lims_DIFFu_u_LDEC, axiom, ![V_x, V_l, V_f]: ((p(s(t_bool,h4s_lims_diffl(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,V_x)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_l),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))) => ?[V_d]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_d)))) & ![V_h]: ((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_h)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_h),s(t_h4s_realaxs_real,V_d))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_h)))))))))))).
fof(ah4s_reals_ABSu_u_NEG, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_reals_REALu_u_ADDu_u_SUB2, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_reals_REALu_u_SUBu_u_SUB2, axiom, ![V_y, V_x]: s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,V_y)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_reals_REALu_u_LT, axiom, ![V_n, V_m]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_reals_REALu_u_LTu_u_RMULu_u_0, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_y)))) => s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))))) = s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x))))).
fof(ah4s_reals_REALu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) = s(t_h4s_realaxs_real,V_x)).
fof(ah4s_arithmetics_LESSu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_reals_REALu_u_LDISTRIB, axiom, ![V_z, V_y, V_x]: s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_z))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z)))))).
fof(ah4s_arithmetics_ONE, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_transcs_LNu_u_LTu_u_X, conjecture, ![V_x]: (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,V_x)))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_transcs_ln(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,V_x)))))).
