%   ORIGINAL: h4/extreal/datatype__extreal
% 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/extreal/Normal0: h4/extreal/Normal = h4/extreal/_20_40ind__typeextreal2
% Assm: h4/extreal/NegInf0: h4/extreal/NegInf = h4/extreal/_20_40ind__typeextreal0
% Assm: h4/extreal/PosInf0: h4/extreal/PosInf = h4/extreal/_20_40ind__typeextreal1
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/extreal/extreal__repfns_c1: !r. (\a0. !_27extreal_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) a1 (\n. h4/ind__type/BOTTOM)) a) ==> _27extreal_27 a00) ==> _27extreal_27 a0) r <=> h4/extreal/_20_40ind__typeextreal4 (h4/extreal/_20_40ind__typeextreal3 r) = r
% Assm: h4/extreal/hidden____20__40ind____typeextreal2____def: h4/extreal/_20_40ind__typeextreal2 = (\a. h4/extreal/_20_40ind__typeextreal3 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/extreal/hidden____20__40ind____typeextreal1____def: h4/extreal/_20_40ind__typeextreal1 = h4/extreal/_20_40ind__typeextreal3 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/extreal/hidden____20__40ind____typeextreal0____def: h4/extreal/_20_40ind__typeextreal0 = h4/extreal/_20_40ind__typeextreal3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/bool/DATATYPE__TAG__DEF: h4/bool/DATATYPE = (\x. T)
% Assm: h4/bool/TRUTH: T
% Assm: h4/extreal/extreal__case__def_c0: !v1 v f. h4/extreal/extreal__CASE h4/extreal/NegInf v v1 f = v
% Assm: h4/extreal/extreal__case__def_c1: !v1 v f. h4/extreal/extreal__CASE h4/extreal/PosInf v v1 f = v1
% Assm: h4/extreal/extreal__size__def_c1: h4/extreal/extreal__size h4/extreal/PosInf = h4/num/0
% Assm: h4/extreal/extreal__size__def_c0: h4/extreal/extreal__size h4/extreal/NegInf = h4/num/0
% Assm: h4/extreal/extreal__size__def_c2: !a. h4/extreal/extreal__size (h4/extreal/Normal a) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/extreal/extreal__case__def_c2: !v1 v f a. h4/extreal/extreal__CASE (h4/extreal/Normal a) v v1 f = f a
% Assm: h4/extreal/extreal__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0. !_27extreal_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) a1 (\n. h4/ind__type/BOTTOM)) a) ==> _27extreal_27 a00) ==> _27extreal_27 a0) rep
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/sum/datatype__sum: !sum. h4/bool/DATATYPE (sum h4/sum/INL h4/sum/INR)
% Assm: h4/pair/datatype__pair: !pair. h4/bool/DATATYPE (pair h4/pair/_2C)
% Assm: h4/list/datatype__list: !list. h4/bool/DATATYPE (list h4/list/NIL h4/list/CONS)
% Assm: h4/bool/DATATYPE__BOOL: !bool. h4/bool/DATATYPE (bool T F) <=> T
% Assm: h4/arithmetic/datatype__num: !num. h4/bool/DATATYPE (num h4/num/0 h4/num/SUC)
% Assm: h4/option/datatype__option: !option. h4/bool/DATATYPE (option h4/option/NONE h4/option/SOME)
% Assm: h4/extreal/extreal__repfns_c0: !a. h4/extreal/_20_40ind__typeextreal3 (h4/extreal/_20_40ind__typeextreal4 a) = a
% Assm: h4/real/REAL__MUL__SYM: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm: h4/lim/DIFF__CMUL: !x l f c. h4/lim/diffl f l x ==> h4/lim/diffl (\x0. h4/realax/real__mul c (f x0)) (h4/realax/real__mul c l) x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/real/REAL__ADD__LID: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/lim/DIFF__MUL: !x m l g f. h4/lim/diffl f l x /\ h4/lim/diffl g m x ==> h4/lim/diffl (\x0. h4/realax/real__mul (f x0) (g x0)) (h4/realax/real__add (h4/realax/real__mul l (g x)) (h4/realax/real__mul m (f x))) x
% Assm: h4/lim/DIFF__CONST: !x k. h4/lim/diffl (\x0. k) (h4/real/real__of__num h4/num/0) 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/transc/SQRT__POS__LE: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/transc/sqrt x)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/real/REAL__LE__LT: !y x. h4/real/real__lte x y <=> h4/realax/real__lt x y \/ x = y
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/transc/SQRT__POS__LT: !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/transc/sqrt x)
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/transc/SQRT__0: h4/transc/sqrt (h4/real/real__of__num h4/num/0) = h4/real/real__of__num h4/num/0
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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__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__INV__LT1: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> h4/realax/real__lt (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/realax/inv x)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/real/REAL__LT__MUL2: !y2 y1 x2 x1. h4/real/real__lte (h4/real/real__of__num h4/num/0) x1 /\ h4/real/real__lte (h4/real/real__of__num h4/num/0) y1 /\ h4/realax/real__lt x1 x2 /\ h4/realax/real__lt y1 y2 ==> h4/realax/real__lt (h4/realax/real__mul x1 y1) (h4/realax/real__mul x2 y2)
% Assm: h4/real/REAL__INV1: h4/realax/inv (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__LT__IMP__NE: !y x. h4/realax/real__lt x y ==> ~(x = y)
% 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/real/REAL__INVINV: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/inv (h4/realax/inv x) = x
% Assm: h4/real/REAL__NOT__LT: !y x. ~h4/realax/real__lt x y <=> h4/real/real__lte y 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__LT__REFL: !x. ~h4/realax/real__lt x x
% 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/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/bool/NOT__IMP: !B A. ~(A ==> B) <=> A /\ ~B
% Assm: h4/util__prob/POW__HALF__POS: !n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/pow (h4/real/_2F (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) n)
% Assm: h4/util__prob/HALF__POS: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm: h4/real/REAL__OF__NUM__LE: !n m. h4/real/real__lte (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm: h4/real/REAL__OF__NUM__MUL: !n m. h4/realax/real__mul (h4/real/real__of__num m) (h4/real/real__of__num n) = h4/real/real__of__num (h4/arithmetic/_2A m n)
% Assm: h4/real/REAL__LE__RNEG: !y x. h4/real/real__lte x (h4/realax/real__neg y) <=> h4/real/real__lte (h4/realax/real__add x y) (h4/real/real__of__num h4/num/0)
% Assm: h4/real/REAL__LE__NEG2: !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__NEG__NEG: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/real/REAL__MUL__RNEG: !y x. h4/realax/real__mul x (h4/realax/real__neg y) = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/real/REAL__MUL__LNEG: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm: h4/real/POW__POS__LT: !x n. 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/real/pow x (h4/num/SUC n))
% Assm: h4/real/pow0_c1: !x n. h4/real/pow x (h4/num/SUC n) = h4/realax/real__mul x (h4/real/pow x n)
% Assm: h4/real/REAL__ADD: !n m. h4/realax/real__add (h4/real/real__of__num m) (h4/real/real__of__num n) = h4/real/real__of__num (h4/arithmetic/_2B m n)
% Assm: h4/real/real__lt: !y x. h4/realax/real__lt x y <=> ~h4/real/real__lte y x
% Assm: h4/real/pow0_c0: !x. h4/real/pow x h4/num/0 = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/real/REAL__LE__ANTISYM: !y x. h4/real/real__lte x y /\ h4/real/real__lte y x <=> x = y
% Assm: h4/real/REAL__LE__LNEG: !y x. h4/real/real__lte (h4/realax/real__neg x) y <=> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/realax/real__add x y)
% 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/numeral/numeral__mult_c2: !n m. h4/arithmetic/_2A (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/arithmetic/_2A n m)) m)
% Assm: h4/numeral/numeral__mult_c0: !n. h4/arithmetic/_2A h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c5: !n m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2A n m)
% Assm: h4/numeral/numeral__distrib_c17: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm: h4/arithmetic/LE_c0: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm: h4/arithmetic/num__CASES: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__EQ__0: !n m. h4/arithmetic/_2B m n = h4/num/0 <=> m = h4/num/0 /\ n = h4/num/0
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% 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/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/real/REAL__LT__RADD: !z y x. h4/realax/real__lt (h4/realax/real__add x z) (h4/realax/real__add y z) <=> h4/realax/real__lt x y
% Assm: h4/real/real__lte0: !y x. h4/real/real__lte x y <=> ~h4/realax/real__lt y x
% Goal: !extreal. h4/bool/DATATYPE (extreal h4/extreal/NegInf h4/extreal/PosInf h4/extreal/Normal)
%   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_extreals_Normal0]: h4/extreal/Normal = h4/extreal/_20_40ind__typeextreal2
% Assm [h4s_extreals_NegInf0]: h4/extreal/NegInf = h4/extreal/_20_40ind__typeextreal0
% Assm [h4s_extreals_PosInf0]: h4/extreal/PosInf = h4/extreal/_20_40ind__typeextreal1
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_extreals_extrealu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27extreal_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ a00 = h4/ind__type/CONSTR (happ h4/num/SUC h4/num/0) h4/bool/ARB _0 \/ (?a. a00 = h4/ind__type/CONSTR (happ h4/num/SUC (happ h4/num/SUC h4/num/0)) a _0) ==> happ _27extreal_27 a00) ==> happ _27extreal_27 r) <=> h4/extreal/_20_40ind__typeextreal4 (h4/extreal/_20_40ind__typeextreal3 r) = r)
% Assm [h4s_extreals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeextreal2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/extreal/_20_40ind__typeextreal2 x = h4/extreal/_20_40ind__typeextreal3 (h4/ind__type/CONSTR (happ h4/num/SUC (happ h4/num/SUC h4/num/0)) x _0))
% Assm [h4s_extreals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeextreal1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/extreal/_20_40ind__typeextreal1 = h4/extreal/_20_40ind__typeextreal3 (h4/ind__type/CONSTR (happ h4/num/SUC h4/num/0) h4/bool/ARB _0)
% Assm [h4s_extreals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeextreal0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/extreal/_20_40ind__typeextreal0 = h4/extreal/_20_40ind__typeextreal3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. h4/ind__type/FCONS a f (happ h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_DEF]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_extreals_extrealu_u_caseu_u_defu_c0]: !v1 v f. h4/extreal/extreal__CASE h4/extreal/NegInf v v1 f = v
% Assm [h4s_extreals_extrealu_u_caseu_u_defu_c1]: !v1 v f. h4/extreal/extreal__CASE h4/extreal/PosInf v v1 f = v1
% Assm [h4s_extreals_extrealu_u_sizeu_u_defu_c1]: h4/extreal/extreal__size h4/extreal/PosInf = h4/num/0
% Assm [h4s_extreals_extrealu_u_sizeu_u_defu_c0]: h4/extreal/extreal__size h4/extreal/NegInf = h4/num/0
% Assm [h4s_extreals_extrealu_u_sizeu_u_defu_c2]: !a. h4/extreal/extreal__size (happ h4/extreal/Normal a) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_extreals_extrealu_u_caseu_u_defu_c2]: !v1 v f a. h4/extreal/extreal__CASE (happ h4/extreal/Normal a) v v1 f = happ f a
% Assm [h4s_extreals_extrealu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0. happ _0 a0 <=> (!_27extreal_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _1 \/ a00 = h4/ind__type/CONSTR (happ h4/num/SUC h4/num/0) h4/bool/ARB _1 \/ (?a. a00 = h4/ind__type/CONSTR (happ h4/num/SUC (happ h4/num/SUC h4/num/0)) a _1) ==> happ _27extreal_27 a00) ==> happ _27extreal_27 a0)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_sums_datatypeu_u_sum]: !sum. h4/bool/DATATYPE (happ (happ sum h4/sum/INL) h4/sum/INR)
% Assm [h4s_pairs_datatypeu_u_pair]: !pair. h4/bool/DATATYPE (happ pair h4/pair/_2C)
% Assm [h4s_lists_datatypeu_u_list]: !list. h4/bool/DATATYPE (happ (happ list h4/list/NIL) h4/list/CONS)
% Assm [h4s_bools_DATATYPEu_u_BOOL]: !bool. h4/bool/DATATYPE (happ (happ bool T) F) <=> T
% Assm [h4s_arithmetics_datatypeu_u_num]: !num. h4/bool/DATATYPE (happ (happ num h4/num/0) h4/num/SUC)
% Assm [h4s_options_datatypeu_u_option]: !option. h4/bool/DATATYPE (happ (happ option h4/option/NONE) h4/option/SOME)
% Assm [h4s_extreals_extrealu_u_repfnsu_c0]: !a. h4/extreal/_20_40ind__typeextreal3 (h4/extreal/_20_40ind__typeextreal4 a) = a
% Assm [h4s_reals_REALu_u_MULu_u_SYM]: !y x. h4/realax/real__mul x y = h4/realax/real__mul y x
% Assm [h4s_lims_DIFFu_u_CMUL]: !_0. (!c f x0. happ (happ (happ _0 c) f) x0 = h4/realax/real__mul c (happ f x0)) ==> (!x l f c. h4/lim/diffl f l x ==> h4/lim/diffl (happ (happ _0 c) f) (h4/realax/real__mul c l) x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_reals_REALu_u_ADDu_u_LID]: !x. h4/realax/real__add (h4/real/real__of__num h4/num/0) x = x
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_lims_DIFFu_u_MUL]: !_0. (!f g x0. happ (happ (happ _0 f) g) x0 = h4/realax/real__mul (happ f x0) (happ g x0)) ==> (!x m l g f. h4/lim/diffl f l x /\ h4/lim/diffl g m x ==> h4/lim/diffl (happ (happ _0 f) g) (h4/realax/real__add (h4/realax/real__mul l (happ g x)) (h4/realax/real__mul m (happ f x))) x)
% Assm [h4s_lims_DIFFu_u_CONST]: !_0. (!k x0. happ (happ _0 k) x0 = k) ==> (!x k. h4/lim/diffl (happ _0 k) (h4/real/real__of__num h4/num/0) 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_transcs_SQRTu_u_POSu_u_LE]: !x. h4/real/real__lte (h4/real/real__of__num h4/num/0) x ==> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/transc/sqrt x)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_reals_REALu_u_LEu_u_LT]: !y x. h4/real/real__lte x y <=> h4/realax/real__lt x y \/ x = y
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_transcs_SQRTu_u_POSu_u_LT]: !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/transc/sqrt x)
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_transcs_SQRTu_u_0]: h4/transc/sqrt (h4/real/real__of__num h4/num/0) = h4/real/real__of__num h4/num/0
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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_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_INVu_u_LT1]: !x. h4/realax/real__lt (h4/real/real__of__num h4/num/0) x /\ h4/realax/real__lt x (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> h4/realax/real__lt (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/realax/inv x)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_reals_REALu_u_LTu_u_MUL2]: !y2 y1 x2 x1. h4/real/real__lte (h4/real/real__of__num h4/num/0) x1 /\ h4/real/real__lte (h4/real/real__of__num h4/num/0) y1 /\ h4/realax/real__lt x1 x2 /\ h4/realax/real__lt y1 y2 ==> h4/realax/real__lt (h4/realax/real__mul x1 y1) (h4/realax/real__mul x2 y2)
% Assm [h4s_reals_REALu_u_INV1]: h4/realax/inv (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% 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_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_reals_REALu_u_INVINV]: !x. ~(x = h4/real/real__of__num h4/num/0) ==> h4/realax/inv (h4/realax/inv x) = x
% Assm [h4s_reals_REALu_u_NOTu_u_LT]: !y x. ~h4/realax/real__lt x y <=> h4/real/real__lte y 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_LTu_u_REFL]: !x. ~h4/realax/real__lt x x
% 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_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_bools_NOTu_u_IMP]: !B A. ~(A ==> B) <=> A /\ ~B
% Assm [h4s_utilu_u_probs_POWu_u_HALFu_u_POS]: !n. h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/pow (h4/real/_2F (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) n)
% Assm [h4s_utilu_u_probs_HALFu_u_POS]: h4/realax/real__lt (h4/real/real__of__num h4/num/0) (h4/real/_2F (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Assm [h4s_reals_REALu_u_OFu_u_NUMu_u_LE]: !n m. h4/real/real__lte (h4/real/real__of__num m) (h4/real/real__of__num n) <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_reals_REALu_u_OFu_u_NUMu_u_MUL]: !n m. h4/realax/real__mul (h4/real/real__of__num m) (h4/real/real__of__num n) = h4/real/real__of__num (h4/arithmetic/_2A m n)
% Assm [h4s_reals_REALu_u_LEu_u_RNEG]: !y x. h4/real/real__lte x (h4/realax/real__neg y) <=> h4/real/real__lte (h4/realax/real__add x y) (h4/real/real__of__num h4/num/0)
% Assm [h4s_reals_REALu_u_LEu_u_NEG2]: !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_NEGu_u_NEG]: !x. h4/realax/real__neg (h4/realax/real__neg x) = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_reals_REALu_u_MULu_u_RNEG]: !y x. h4/realax/real__mul x (h4/realax/real__neg y) = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_reals_REALu_u_MULu_u_LNEG]: !y x. h4/realax/real__mul (h4/realax/real__neg x) y = h4/realax/real__neg (h4/realax/real__mul x y)
% Assm [h4s_reals_POWu_u_POSu_u_LT]: !x n. 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/real/pow x (happ h4/num/SUC n))
% Assm [h4s_reals_pow0u_c1]: !x n. h4/real/pow x (happ h4/num/SUC n) = h4/realax/real__mul x (h4/real/pow x n)
% Assm [h4s_reals_REALu_u_ADD]: !n m. h4/realax/real__add (h4/real/real__of__num m) (h4/real/real__of__num n) = h4/real/real__of__num (h4/arithmetic/_2B m n)
% Assm [h4s_reals_realu_u_lt]: !y x. h4/realax/real__lt x y <=> ~h4/real/real__lte y x
% Assm [h4s_reals_pow0u_c0]: !x. h4/real/pow x h4/num/0 = h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_reals_REALu_u_LEu_u_ANTISYM]: !y x. h4/real/real__lte x y /\ h4/real/real__lte y x <=> x = y
% Assm [h4s_reals_REALu_u_LEu_u_LNEG]: !y x. h4/real/real__lte (h4/realax/real__neg x) y <=> h4/real/real__lte (h4/real/real__of__num h4/num/0) (h4/realax/real__add x y)
% 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_numerals_numeralu_u_multu_c2]: !n m. h4/arithmetic/_2A (h4/arithmetic/BIT1 n) m = h4/numeral/iZ (h4/arithmetic/_2B (h4/numeral/iDUB (h4/arithmetic/_2A n m)) m)
% Assm [h4s_numerals_numeralu_u_multu_c0]: !n. h4/arithmetic/_2A h4/arithmetic/ZERO n = h4/arithmetic/ZERO
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c5]: !n m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/arithmetic/_2A n m)
% Assm [h4s_numerals_numeralu_u_distribu_c17]: !n. h4/arithmetic/NUMERAL n = h4/num/0 <=> n = h4/arithmetic/ZERO
% Assm [h4s_arithmetics_LEu_c0]: !n. h4/arithmetic/_3C_3D n h4/num/0 <=> n = h4/num/0
% Assm [h4s_arithmetics_numu_u_CASES]: !m. m = h4/num/0 \/ (?n. m = happ h4/num/SUC n)
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_EQu_u_0]: !n m. h4/arithmetic/_2B m n = h4/num/0 <=> m = h4/num/0 /\ n = h4/num/0
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% 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_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_reals_REALu_u_LTu_u_RADD]: !z y x. h4/realax/real__lt (h4/realax/real__add x z) (h4/realax/real__add y z) <=> h4/realax/real__lt x y
% Assm [h4s_reals_realu_u_lte0]: !y x. h4/real/real__lte x y <=> ~h4/realax/real__lt y x
% Goal: !extreal. h4/bool/DATATYPE (happ (happ (happ extreal h4/extreal/NegInf) h4/extreal/PosInf) h4/extreal/Normal)
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_Q1260927,TV_Q1260923]: ![V_f, V_g]: (![V_x]: s(TV_Q1260923,happ(s(t_fun(TV_Q1260927,TV_Q1260923),V_f),s(TV_Q1260927,V_x))) = s(TV_Q1260923,happ(s(t_fun(TV_Q1260927,TV_Q1260923),V_g),s(TV_Q1260927,V_x))) => s(t_fun(TV_Q1260927,TV_Q1260923),V_f) = s(t_fun(TV_Q1260927,TV_Q1260923),V_g))).
fof(ah4s_extreals_Normal0, axiom, s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal) = s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_u_20u_40indu_u_typeextreal2)).
fof(ah4s_extreals_NegInf0, axiom, s(t_h4s_extreals_extreal,h4s_extreals_neginf) = s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal0)).
fof(ah4s_extreals_PosInf0, axiom, s(t_h4s_extreals_extreal,h4s_extreals_posinf) = s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal1)).
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_extreals_extrealu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27extrealu_27]: (![V_a00]: ((s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))) | (s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))) | ?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_realaxs_real,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_27extrealu_27),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_27extrealu_27),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_extreals_u_20u_40indu_u_typeextreal4(s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal3(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_r)))).
fof(ah4s_extreals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeextreal2u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_u_20u_40indu_u_typeextreal2),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal3(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_realaxs_real,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))))).
fof(ah4s_extreals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeextreal1u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal1) = s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal3(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))))).
fof(ah4s_extreals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeextreal0u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal0) = s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal3(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_0))))))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => 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,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_extreals_extrealu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f]: s(TV_u_27a,h4s_extreals_extrealu_u_case(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(TV_u_27a,V_v),s(TV_u_27a,V_v1),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f))) = s(TV_u_27a,V_v)).
fof(ah4s_extreals_extrealu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f]: s(TV_u_27a,h4s_extreals_extrealu_u_case(s(t_h4s_extreals_extreal,h4s_extreals_posinf),s(TV_u_27a,V_v),s(TV_u_27a,V_v1),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f))) = s(TV_u_27a,V_v1)).
fof(ah4s_extreals_extrealu_u_sizeu_u_defu_c1, axiom, s(t_h4s_nums_num,h4s_extreals_extrealu_u_size(s(t_h4s_extreals_extreal,h4s_extreals_posinf))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_extreals_extrealu_u_sizeu_u_defu_c0, axiom, s(t_h4s_nums_num,h4s_extreals_extrealu_u_size(s(t_h4s_extreals_extreal,h4s_extreals_neginf))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_extreals_extrealu_u_sizeu_u_defu_c2, axiom, ![V_a]: s(t_h4s_nums_num,h4s_extreals_extrealu_u_size(s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,V_a))))) = 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_extreals_extrealu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v1, V_v, V_f, V_a]: s(TV_u_27a,h4s_extreals_extrealu_u_case(s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,V_a))),s(TV_u_27a,V_v),s(TV_u_27a,V_v1),s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f))) = s(TV_u_27a,happ(s(t_fun(t_h4s_realaxs_real,TV_u_27a),V_f),s(t_h4s_realaxs_real,V_a)))).
fof(ah4s_extreals_extrealu_u_TYu_u_DEF, axiom, ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a0)))) <=> ![V_uu_27extrealu_27]: (![V_a00]: ((s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_1))) | (s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_1))) | ?[V_a]: s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00) = s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_indu_u_types_constr(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_realaxs_real,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_uu_1))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_27extrealu_27),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_27extrealu_27),s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),V_a0)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),t_bool),V_uu_0),s(t_fun(t_h4s_extreals_extreal,t_h4s_indu_u_types_recspace(t_h4s_realaxs_real)),V_rep))))))).
fof(ah4s_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_sums_datatypeu_u_sum, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_sum]: p(s(t_bool,h4s_bools_datatype(s(TV_u_27c,happ(s(t_fun(t_fun(TV_u_27b,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),t_fun(t_fun(TV_u_27b,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),TV_u_27c)),V_sum),s(t_fun(TV_u_27a,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_sums_inl))),s(t_fun(TV_u_27b,t_h4s_sums_sum(TV_u_27a,TV_u_27b)),h4s_sums_inr))))))).
fof(ah4s_pairs_datatypeu_u_pair, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_pair]: p(s(t_bool,h4s_bools_datatype(s(TV_u_27c,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),TV_u_27c),V_pair),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c))))))).
fof(ah4s_lists_datatypeu_u_list, axiom, ![TV_u_27a]: ![V_list]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),t_bool)),V_list),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))),s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons))))))).
fof(ah4s_bools_DATATYPEu_u_BOOL, axiom, ![V_bool]: s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_bool),s(t_bool,t))),s(t_bool,f))))) = s(t_bool,t)).
fof(ah4s_arithmetics_datatypeu_u_num, axiom, ![TV_u_27a]: ![V_num]: p(s(t_bool,h4s_bools_datatype(s(TV_u_27a,happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_h4s_nums_num),TV_u_27a)),V_num),s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc))))))).
fof(ah4s_options_datatypeu_u_option, axiom, ![TV_u_27b,TV_u_27a]: ![V_option]: p(s(t_bool,h4s_bools_datatype(s(TV_u_27b,happ(s(t_fun(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),TV_u_27b),happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_fun(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),TV_u_27b)),V_option),s(t_h4s_options_option(TV_u_27a),h4s_options_none))),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),h4s_options_some))))))).
fof(ah4s_extreals_extrealu_u_repfnsu_c0, axiom, ![V_a]: s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal3(s(t_h4s_indu_u_types_recspace(t_h4s_realaxs_real),h4s_extreals_u_20u_40indu_u_typeextreal4(s(t_h4s_extreals_extreal,V_a))))) = s(t_h4s_extreals_extreal,V_a)).
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_lims_DIFFu_u_CMUL, axiom, ![V_uu_0]: (![V_c, 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)),happ(s(t_fun(t_h4s_realaxs_real,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_h4s_realaxs_real,V_c))),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_mul(s(t_h4s_realaxs_real,V_c),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, V_c]: (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)),happ(s(t_fun(t_h4s_realaxs_real,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_h4s_realaxs_real,V_c))),s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_f))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_c),s(t_h4s_realaxs_real,V_l))),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_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_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
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_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_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_reals_REALu_u_ADDu_u_LID, axiom, ![V_x]: 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_nums_0))),s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,V_x)).
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_lims_DIFFu_u_MUL, axiom, ![V_uu_0]: (![V_f, V_g, 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)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),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_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(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))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x0))))) => ![V_x, V_m, V_l, V_g, 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),V_g),s(t_h4s_realaxs_real,V_m),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)),happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),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_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g))),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_l),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_realaxs_real),V_g),s(t_h4s_realaxs_real,V_x))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_m),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_x))))))).
fof(ah4s_lims_DIFFu_u_CONST, axiom, ![V_uu_0]: (![V_k, V_x0]: 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)),V_uu_0),s(t_h4s_realaxs_real,V_k))),s(t_h4s_realaxs_real,V_x0))) = s(t_h4s_realaxs_real,V_k) => ![V_x, V_k]: p(s(t_bool,h4s_lims_diffl(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)),V_uu_0),s(t_h4s_realaxs_real,V_k))),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_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_transcs_SQRTu_u_POSu_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_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_reals_REALu_u_LEu_u_LT, axiom, ![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_x),s(t_h4s_realaxs_real,V_y)))) | s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y)))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_transcs_SQRTu_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,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_sqrt(s(t_h4s_realaxs_real,V_x)))))))).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_transcs_SQRTu_u_0, axiom, s(t_h4s_realaxs_real,h4s_transcs_sqrt(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_nums_0)))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
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_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_INVu_u_LT1, 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,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))))))))))) => 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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x)))))))).
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_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_reals_REALu_u_LTu_u_MUL2, axiom, ![V_y2, V_y1, V_x2, V_x1]: ((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_x1)))) & (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_y1)))) & (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x1),s(t_h4s_realaxs_real,V_x2)))) & p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_y1),s(t_h4s_realaxs_real,V_y2))))))) => p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x1),s(t_h4s_realaxs_real,V_y1))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x2),s(t_h4s_realaxs_real,V_y2)))))))).
fof(ah4s_reals_REALu_u_INV1, axiom, s(t_h4s_realaxs_real,h4s_realaxs_inv(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
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_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_reals_REALu_u_INVINV, 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,h4s_realaxs_inv(s(t_h4s_realaxs_real,V_x))))) = s(t_h4s_realaxs_real,V_x))).
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_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_LTu_u_REFL, axiom, ![V_x]: ~ (p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_x)))))).
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_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_bools_NOTu_u_IMP, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) => p(s(t_bool,V_B)))) <=> (p(s(t_bool,V_A)) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_utilu_u_probs_POWu_u_HALFu_u_POS, axiom, ![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,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_u_2f(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_utilu_u_probs_HALFu_u_POS, 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_u_2f(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))).
fof(ah4s_reals_REALu_u_OFu_u_NUMu_u_LE, axiom, ![V_n, V_m]: 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,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_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_reals_REALu_u_OFu_u_NUMu_u_MUL, axiom, ![V_n, V_m]: 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_m))),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_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_reals_REALu_u_LEu_u_RNEG, axiom, ![V_y, V_x]: s(t_bool,h4s_reals_realu_u_lte(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,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)))))).
fof(ah4s_reals_REALu_u_LEu_u_NEG2, 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_NEGu_u_NEG, 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_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_reals_REALu_u_MULu_u_RNEG, 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,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,V_y))))) = 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)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_reals_REALu_u_MULu_u_LNEG, axiom, ![V_y, V_x]: 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))) = 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)))))).
fof(ah4s_reals_POWu_u_POSu_u_LT, 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)))) => 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_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_reals_pow0u_c1, axiom, ![V_x, V_n]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n))))) = s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_reals_REALu_u_ADD, axiom, ![V_n, V_m]: 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,V_m))),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_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_reals_realu_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_reals_pow0u_c0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,V_x),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_reals_REALu_u_LEu_u_ANTISYM, axiom, ![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_reals_realu_u_lte(s(t_h4s_realaxs_real,V_y),s(t_h4s_realaxs_real,V_x))))) <=> s(t_h4s_realaxs_real,V_x) = s(t_h4s_realaxs_real,V_y))).
fof(ah4s_reals_REALu_u_LEu_u_LNEG, 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,V_y))) = 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,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_y)))))).
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_numerals_numeralu_u_multu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_numeralu_u_multu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_c5, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_numeralu_u_distribu_c17, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_arithmetics_LEu_c0, axiom, ![V_n]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0)))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_arithmetics_numu_u_CASES, axiom, ![V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0) | ?[V_n]: s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,V_n))))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_ADDu_u_EQu_u_0, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0) <=> (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0) & s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_sats_pthu_u_no2, 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_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_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_no1, 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_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
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_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_reals_REALu_u_LTu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,V_z))),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_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_lte0, axiom, ![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_x))))))).
fof(ch4s_extreals_datatypeu_u_extreal, conjecture, ![V_extreal]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),t_bool)),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_fun(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),t_bool))),V_extreal),s(t_h4s_extreals_extreal,h4s_extreals_neginf))),s(t_h4s_extreals_extreal,h4s_extreals_posinf))),s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal))))))).
