%   ORIGINAL: h4/ieee/ccode__case__def_c3
% 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/ieee/Un__def: h4/ieee/Un = h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/ieee/num2ccode__thm_c3: h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/ieee/Un
% Assm: h4/ieee/ccode2num__thm_c3: h4/ieee/ccode2num h4/ieee/Un = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/ieee/ccode__CASE0: !x v3 v2 v1 v0. h4/ieee/ccode__CASE x v0 v1 v2 v3 = (\m. h4/bool/COND (h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v0 (h4/bool/COND (h4/prim__rec/_3C m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) v1 (h4/bool/COND (m = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) v2 v3))) (h4/ieee/ccode2num x)
% Assm: h4/numeral/numeral__distrib_c22: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/ieee/ccode2num__num2ccode: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/ieee/ccode2num (h4/ieee/num2ccode r) = r
% Assm: h4/numeral/numeral__lt_c3: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/ieee/ccode__case__def_c1: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Lt v0 v1 v2 v3 = v1
% Assm: h4/ieee/ccode__case__def_c0: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Gt v0 v1 v2 v3 = v0
% Assm: h4/ieee/ccode__case__def_c2: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Eq v0 v1 v2 v3 = v2
% Assm: h4/ieee/ccode__BIJ_c0: !a. h4/ieee/num2ccode (h4/ieee/ccode2num a) = a
% Assm: h4/ieee/ccode__BIJ_c1: !r. (\n. h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) r <=> h4/ieee/ccode2num (h4/ieee/num2ccode r) = r
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/ieee/ccode2num__thm_c0: h4/ieee/ccode2num h4/ieee/Gt = h4/num/0
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/ieee/Gt__def: h4/ieee/Gt = h4/ieee/num2ccode h4/num/0
% Assm: h4/ieee/Eq__def: h4/ieee/Eq = h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/ieee/Lt__def: h4/ieee/Lt = h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/ieee/ccode__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\n. h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) rep
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/ieee/ccode2num__thm_c1: h4/ieee/ccode2num h4/ieee/Lt = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/ieee/ccode2num__thm_c2: h4/ieee/ccode2num h4/ieee/Eq = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/numeral/numeral__lt_c4: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) <=> h4/prim__rec/_3C n m
% 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/ieee/ccode2num__11: !a_27 a. h4/ieee/ccode2num a = h4/ieee/ccode2num a_27 <=> a = a_27
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/numeral/numeral__lt_c6: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/ieee/num2ccode__ccode2num: !a. h4/ieee/num2ccode (h4/ieee/ccode2num a) = a
% Assm: h4/ieee/num2ccode__thm_c2: h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/ieee/Eq
% Assm: h4/ieee/num2ccode__thm_c0: h4/ieee/num2ccode h4/num/0 = h4/ieee/Gt
% Assm: h4/ieee/ccode__EQ__ccode: !a_27 a. a = a_27 <=> h4/ieee/ccode2num a = h4/ieee/ccode2num a_27
% Assm: h4/ieee/num2ccode__thm_c1: h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/ieee/Lt
% Assm: h4/ieee/num2ccode__11: !r_27 r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> h4/prim__rec/_3C r_27 (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> (h4/ieee/num2ccode r = h4/ieee/num2ccode r_27 <=> r = r_27)
% Assm: h4/ieee/ccode__size__def: !x. h4/ieee/ccode__size x = h4/num/0
% Assm: h4/ieee/num2ccode__ONTO: !a. ?r. a = h4/ieee/num2ccode r /\ h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/ieee/ccode2num__ONTO: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?a. r = h4/ieee/ccode2num a)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/prim__rec/measure__thm: !y x f. h4/prim__rec/measure f x y <=> h4/prim__rec/_3C (f x) (f y)
% Assm: h4/prim__rec/measure__def: h4/prim__rec/measure = h4/relation/inv__image h4/prim__rec/_3C
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/arithmetic/FUNPOW__1: !x f. h4/arithmetic/FUNPOW f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x = f x
% Assm: h4/arithmetic/ONE: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm: h4/arithmetic/FUNPOW0_c1: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = h4/arithmetic/FUNPOW f n (f x)
% Assm: h4/arithmetic/FUNPOW0_c0: !x f. h4/arithmetic/FUNPOW f h4/num/0 x = x
% Assm: h4/list/LIST__TO__SET__FILTER: !l P. h4/list/LIST__TO__SET (h4/list/FILTER P l) = h4/pred__set/INTER (h4/pred__set/GSPEC (\x. h4/pair/_2C x (P x))) (h4/list/LIST__TO__SET l)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/list/MEM__FILTER: !x P L. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/FILTER P L)) <=> P x /\ h4/bool/IN x (h4/list/LIST__TO__SET L)
% Assm: h4/pred__set/IN__INTER: !x t s. h4/bool/IN x (h4/pred__set/INTER s t) <=> h4/bool/IN x s /\ h4/bool/IN x t
% Assm: h4/pred__set/GSPECIFICATION: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = f x)
% Assm: h4/pred__set/EXTENSION: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm: h4/pair/PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/list/LIST__REL__def_c1: !as a R. h4/list/LIST__REL R (h4/list/CONS a as) h4/list/NIL <=> F
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/list/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% 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/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/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/list/LIST__REL__def0: h4/list/LIST__REL = (\R a0 a1. !LIST__REL_27. (!a00 a10. a00 = h4/list/NIL /\ a10 = h4/list/NIL \/ (?h1 h2 t1 t2. a00 = h4/list/CONS h1 t1 /\ a10 = h4/list/CONS h2 t2 /\ R h1 h2 /\ LIST__REL_27 t1 t2) ==> LIST__REL_27 a00 a10) ==> LIST__REL_27 a0 a1)
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/pred__set/IMAGE__applied: !y s f. h4/pred__set/IMAGE f s y <=> (?x. y = f x /\ h4/bool/IN x s)
% Assm: h4/bool/IN__DEF: h4/bool/IN = (\x f. f x)
% Assm: h4/pred__set/IN__IMAGE: !y s f. h4/bool/IN y (h4/pred__set/IMAGE f s) <=> (?x. y = f x /\ h4/bool/IN x s)
% Assm: h4/marker/Cong__def: !x. h4/marker/Cong x <=> x
% Assm: h4/combin/APPLY__UPDATE__ID: !f a. h4/combin/UPDATE a (f a) f = f
% Assm: h4/combin/UPDATE__APPLY__ID: !f b a. f a = b <=> h4/combin/UPDATE a b f = f
% Assm: h4/list/LAST__APPEND__CONS: !l2 l1 h. h4/list/LAST (h4/list/APPEND l1 (h4/list/CONS h l2)) = h4/list/LAST (h4/list/CONS h l2)
% Assm: h4/list/LAST__CONS__cond: !t h. h4/list/LAST (h4/list/CONS h t) = h4/bool/COND (t = h4/list/NIL) h (h4/list/LAST t)
% Assm: h4/list/APPEND__eq__NIL_c0: !l2 l1. h4/list/NIL = h4/list/APPEND l1 l2 <=> l1 = h4/list/NIL /\ l2 = h4/list/NIL
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/list/MEM__FLAT: !x L. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/FLAT L)) <=> (?l. h4/bool/IN l (h4/list/LIST__TO__SET L) /\ h4/bool/IN x (h4/list/LIST__TO__SET l))
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/list/MEM__APPEND: !l2 l1 e. h4/bool/IN e (h4/list/LIST__TO__SET (h4/list/APPEND l1 l2)) <=> h4/bool/IN e (h4/list/LIST__TO__SET l1) \/ h4/bool/IN e (h4/list/LIST__TO__SET l2)
% Assm: h4/list/LIST__TO__SET0_c1: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm: h4/list/LIST__TO__SET0_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/list/FLAT0_c0: h4/list/FLAT h4/list/NIL = h4/list/NIL
% Assm: h4/pred__set/IN__INSERT: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/list/FLAT0_c1: !t h. h4/list/FLAT (h4/list/CONS h t) = h4/list/APPEND h (h4/list/FLAT t)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Goal: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Un v0 v1 v2 v3 = v3
%   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_ieees_Unu_u_def]: h4/ieee/Un = h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_ieees_num2ccodeu_u_thmu_c3]: h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/ieee/Un
% Assm [h4s_ieees_ccode2numu_u_thmu_c3]: h4/ieee/ccode2num h4/ieee/Un = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_ieees_ccodeu_u_CASE0]: !x v3 v2 v1 v0. ?v. (v <=> h4/ieee/ccode2num x = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ h4/ieee/ccode__CASE x v0 v1 v2 v3 = h4/bool/COND (happ (happ h4/prim__rec/_3C (h4/ieee/ccode2num x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v0 (h4/bool/COND (happ (happ h4/prim__rec/_3C (h4/ieee/ccode2num x)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) v1 (h4/bool/COND v v2 v3))
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/NUMERAL n)) (h4/arithmetic/NUMERAL m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. happ (happ h4/prim__rec/_3C n) h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT2 m) <=> ~happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_ieees_ccode2numu_u_num2ccode]: !r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/ieee/ccode2num (h4/ieee/num2ccode r) = r
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_ieees_ccodeu_u_caseu_u_defu_c1]: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Lt v0 v1 v2 v3 = v1
% Assm [h4s_ieees_ccodeu_u_caseu_u_defu_c0]: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Gt v0 v1 v2 v3 = v0
% Assm [h4s_ieees_ccodeu_u_caseu_u_defu_c2]: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Eq v0 v1 v2 v3 = v2
% Assm [h4s_ieees_ccodeu_u_BIJu_c0]: !a. h4/ieee/num2ccode (h4/ieee/ccode2num a) = a
% Assm [h4s_ieees_ccodeu_u_BIJu_c1]: !r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/ieee/ccode2num (h4/ieee/num2ccode r) = r
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. happ (happ h4/prim__rec/_3C h4/num/0) (h4/arithmetic/NUMERAL n) <=> happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) n
% Assm [h4s_ieees_ccode2numu_u_thmu_c0]: h4/ieee/ccode2num h4/ieee/Gt = h4/num/0
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_ieees_Gtu_u_def]: h4/ieee/Gt = h4/ieee/num2ccode h4/num/0
% Assm [h4s_ieees_Equ_u_def]: h4/ieee/Eq = h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_ieees_Ltu_u_def]: h4/ieee/Lt = h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_ieees_ccodeu_u_TYu_u_DEF]: !_0. (!n. happ _0 n <=> happ (happ h4/prim__rec/_3C n) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep)
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_ieees_ccode2numu_u_thmu_c1]: h4/ieee/ccode2num h4/ieee/Lt = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_ieees_ccode2numu_u_thmu_c2]: h4/ieee/ccode2num h4/ieee/Eq = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_numerals_numeralu_u_ltu_c4]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT2 n)) (h4/arithmetic/BIT2 m) <=> happ (happ h4/prim__rec/_3C n) m
% 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_ieees_ccode2numu_u_11]: !a_27 a. h4/ieee/ccode2num a = h4/ieee/ccode2num a_27 <=> a = a_27
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c6]: !n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/BIT2 n)) (h4/arithmetic/BIT1 m) <=> happ (happ h4/prim__rec/_3C n) m
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_ieees_num2ccodeu_u_ccode2num]: !a. h4/ieee/num2ccode (h4/ieee/ccode2num a) = a
% Assm [h4s_ieees_num2ccodeu_u_thmu_c2]: h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/ieee/Eq
% Assm [h4s_ieees_num2ccodeu_u_thmu_c0]: h4/ieee/num2ccode h4/num/0 = h4/ieee/Gt
% Assm [h4s_ieees_ccodeu_u_EQu_u_ccode]: !a_27 a. a = a_27 <=> h4/ieee/ccode2num a = h4/ieee/ccode2num a_27
% Assm [h4s_ieees_num2ccodeu_u_thmu_c1]: h4/ieee/num2ccode (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/ieee/Lt
% Assm [h4s_ieees_num2ccodeu_u_11]: !r_27 r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> happ (happ h4/prim__rec/_3C r_27) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> (h4/ieee/num2ccode r = h4/ieee/num2ccode r_27 <=> r = r_27)
% Assm [h4s_ieees_ccodeu_u_sizeu_u_def]: !x. h4/ieee/ccode__size x = h4/num/0
% Assm [h4s_ieees_num2ccodeu_u_ONTO]: !a. ?r. a = h4/ieee/num2ccode r /\ happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_ieees_ccode2numu_u_ONTO]: !r. happ (happ h4/prim__rec/_3C r) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?a. r = h4/ieee/ccode2num a)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_primu_u_recs_measureu_u_thm]: !y x f. happ (happ (happ h4/prim__rec/measure f) x) y <=> happ (happ h4/prim__rec/_3C (happ f x)) (happ f y)
% Assm [h4s_primu_u_recs_measureu_u_def]: h4/prim__rec/measure = h4/relation/inv__image h4/prim__rec/_3C
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (happ (h4/relation/inv__image R) f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_arithmetics_FUNPOWu_u_1]: !x f. h4/arithmetic/FUNPOW f (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x = happ f x
% Assm [h4s_arithmetics_ONE]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/num/SUC h4/num/0
% Assm [h4s_arithmetics_FUNPOW0u_c1]: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = h4/arithmetic/FUNPOW f n (happ f x)
% Assm [h4s_arithmetics_FUNPOW0u_c0]: !x f. h4/arithmetic/FUNPOW f h4/num/0 x = x
% Assm [h4s_lists_LISTu_u_TOu_u_SETu_u_FILTER]: !_0. (!P x. happ (happ _0 P) x = h4/pair/_2C x (happ P x)) ==> (!l P. h4/list/LIST__TO__SET (h4/list/FILTER P l) = h4/pred__set/INTER (h4/pred__set/GSPEC (happ _0 P)) (h4/list/LIST__TO__SET l))
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_lists_MEMu_u_FILTER]: !x P L. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/FILTER P L)) <=> happ P x /\ h4/bool/IN x (h4/list/LIST__TO__SET L)
% Assm [h4s_predu_u_sets_INu_u_INTER]: !x t s. h4/bool/IN x (h4/pred__set/INTER s t) <=> h4/bool/IN x s /\ h4/bool/IN x t
% Assm [h4s_predu_u_sets_GSPECIFICATION]: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = happ f x)
% Assm [h4s_predu_u_sets_EXTENSION]: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm [h4s_pairs_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_lists_LISTu_u_RELu_u_defu_c1]: !as a R. h4/list/LIST__REL R (happ (happ h4/list/CONS a) as) h4/list/NIL <=> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% 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_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_lists_LISTu_u_RELu_u_def0]: !x x x. h4/list/LIST__REL x x x <=> (!LIST__REL_27. (!a00 a10. a00 = h4/list/NIL /\ a10 = h4/list/NIL \/ (?h1 h2 t1 t2. a00 = happ (happ h4/list/CONS h1) t1 /\ a10 = happ (happ h4/list/CONS h2) t2 /\ happ (happ x h1) h2 /\ happ (happ LIST__REL_27 t1) t2) ==> happ (happ LIST__REL_27 a00) a10) ==> happ (happ LIST__REL_27 x) x)
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_predu_u_sets_IMAGEu_u_applied]: !y s f. happ (h4/pred__set/IMAGE f s) y <=> (?x. y = happ f x /\ h4/bool/IN x s)
% Assm [h4s_bools_INu_u_DEF]: !x x. h4/bool/IN x x <=> happ x x
% Assm [h4s_predu_u_sets_INu_u_IMAGE]: !y s f. h4/bool/IN y (h4/pred__set/IMAGE f s) <=> (?x. y = happ f x /\ h4/bool/IN x s)
% Assm [h4s_markers_Congu_u_def]: !x. h4/marker/Cong x <=> x
% Assm [h4s_combins_APPLYu_u_UPDATEu_u_ID]: !f a. h4/combin/UPDATE a (happ f a) f = f
% Assm [h4s_combins_UPDATEu_u_APPLYu_u_ID]: !f b a. happ f a = b <=> h4/combin/UPDATE a b f = f
% Assm [h4s_lists_LASTu_u_APPENDu_u_CONS]: !l2 l1 h. h4/list/LAST (h4/list/APPEND l1 (happ (happ h4/list/CONS h) l2)) = h4/list/LAST (happ (happ h4/list/CONS h) l2)
% Assm [h4s_lists_LASTu_u_CONSu_u_cond]: !t h. ?v. (v <=> t = h4/list/NIL) /\ h4/list/LAST (happ (happ h4/list/CONS h) t) = h4/bool/COND v h (h4/list/LAST t)
% Assm [h4s_lists_APPENDu_u_equ_u_NILu_c0]: !l2 l1. h4/list/NIL = h4/list/APPEND l1 l2 <=> l1 = h4/list/NIL /\ l2 = h4/list/NIL
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_lists_MEMu_u_FLAT]: !x L. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/FLAT L)) <=> (?l. h4/bool/IN l (h4/list/LIST__TO__SET L) /\ h4/bool/IN x (h4/list/LIST__TO__SET l))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_lists_MEMu_u_APPEND]: !l2 l1 e. h4/bool/IN e (h4/list/LIST__TO__SET (h4/list/APPEND l1 l2)) <=> h4/bool/IN e (h4/list/LIST__TO__SET l1) \/ h4/bool/IN e (h4/list/LIST__TO__SET l2)
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c1]: !t h. h4/list/LIST__TO__SET (happ (happ h4/list/CONS h) t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_lists_FLAT0u_c0]: h4/list/FLAT h4/list/NIL = h4/list/NIL
% Assm [h4s_predu_u_sets_INu_u_INSERT]: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_lists_FLAT0u_c1]: !t h. h4/list/FLAT (happ (happ h4/list/CONS h) t) = h4/list/APPEND h (h4/list/FLAT t)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Goal: !v3 v2 v1 v0. h4/ieee/ccode__CASE h4/ieee/Un v0 v1 v2 v3 = v3
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_Q1233271,TV_Q1233267]: ![V_f, V_g]: (![V_x]: s(TV_Q1233267,happ(s(t_fun(TV_Q1233271,TV_Q1233267),V_f),s(TV_Q1233271,V_x))) = s(TV_Q1233267,happ(s(t_fun(TV_Q1233271,TV_Q1233267),V_g),s(TV_Q1233271,V_x))) => s(t_fun(TV_Q1233271,TV_Q1233267),V_f) = s(t_fun(TV_Q1233271,TV_Q1233267),V_g))).
fof(ah4s_ieees_Unu_u_def, axiom, s(t_h4s_ieees_ccode,h4s_ieees_un) = s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))).
fof(ah4s_ieees_num2ccodeu_u_thmu_c3, axiom, s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) = s(t_h4s_ieees_ccode,h4s_ieees_un)).
fof(ah4s_ieees_ccode2numu_u_thmu_c3, axiom, s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,h4s_ieees_un))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_ieees_ccodeu_u_CASE0, axiom, ![TV_u_27a]: ![V_x, V_v3, V_v2, V_v1, V_v0]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_x))) = 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(TV_u_27a,h4s_ieees_ccodeu_u_case(s(t_h4s_ieees_ccode,V_x),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2),s(TV_u_27a,V_v3))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_x))))),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(TV_u_27a,V_v0),s(TV_u_27a,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_x))))),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(TV_u_27a,V_v1),s(TV_u_27a,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_v2),s(TV_u_27a,V_v3))))))))).
fof(ah4s_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),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_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m)))))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_ieees_ccode2numu_u_num2ccode, axiom, ![V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_numerals_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
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_ieees_ccodeu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v3, V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_ieees_ccodeu_u_case(s(t_h4s_ieees_ccode,h4s_ieees_lt),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2),s(TV_u_27a,V_v3))) = s(TV_u_27a,V_v1)).
fof(ah4s_ieees_ccodeu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v3, V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_ieees_ccodeu_u_case(s(t_h4s_ieees_ccode,h4s_ieees_gt),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2),s(TV_u_27a,V_v3))) = s(TV_u_27a,V_v0)).
fof(ah4s_ieees_ccodeu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v3, V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_ieees_ccodeu_u_case(s(t_h4s_ieees_ccode,h4s_ieees_eq),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2),s(TV_u_27a,V_v3))) = s(TV_u_27a,V_v2)).
fof(ah4s_ieees_ccodeu_u_BIJu_c0, axiom, ![V_a]: s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_a))))) = s(t_h4s_ieees_ccode,V_a)).
fof(ah4s_ieees_ccodeu_u_BIJu_c1, axiom, ![V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_ieees_ccode2numu_u_thmu_c0, axiom, s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,h4s_ieees_gt))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_ieees_Gtu_u_def, axiom, s(t_h4s_ieees_ccode,h4s_ieees_gt) = s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_ieees_Equ_u_def, axiom, s(t_h4s_ieees_ccode,h4s_ieees_eq) = s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(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_ieees_Ltu_u_def, axiom, s(t_h4s_ieees_ccode,h4s_ieees_lt) = s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(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_ieees_ccodeu_u_TYu_u_DEF, axiom, ![V_uu_0]: (![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_ieees_ccode,t_h4s_nums_num),V_rep)))))).
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_ieees_ccode2numu_u_thmu_c1, axiom, s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,h4s_ieees_lt))) = 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_ieees_ccode2numu_u_thmu_c2, axiom, s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,h4s_ieees_eq))) = 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_numerals_numeralu_u_ltu_c4, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
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_ieees_ccode2numu_u_11, axiom, ![V_au_27, V_a]: (s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_a))) = s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_au_27))) <=> s(t_h4s_ieees_ccode,V_a) = s(t_h4s_ieees_ccode,V_au_27))).
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_numerals_numeralu_u_ltu_c6, axiom, ![V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_zero))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
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_ieees_num2ccodeu_u_ccode2num, axiom, ![V_a]: s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_a))))) = s(t_h4s_ieees_ccode,V_a)).
fof(ah4s_ieees_num2ccodeu_u_thmu_c2, axiom, s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(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_ieees_ccode,h4s_ieees_eq)).
fof(ah4s_ieees_num2ccodeu_u_thmu_c0, axiom, s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_ieees_ccode,h4s_ieees_gt)).
fof(ah4s_ieees_ccodeu_u_EQu_u_ccode, axiom, ![V_au_27, V_a]: (s(t_h4s_ieees_ccode,V_a) = s(t_h4s_ieees_ccode,V_au_27) <=> s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_a))) = s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_au_27))))).
fof(ah4s_ieees_num2ccodeu_u_thmu_c1, axiom, s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(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_ieees_ccode,h4s_ieees_lt)).
fof(ah4s_ieees_num2ccodeu_u_11, axiom, ![V_ru_27, V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) => (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_ru_27))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) => (s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,V_r))) = s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,V_ru_27))) <=> s(t_h4s_nums_num,V_r) = s(t_h4s_nums_num,V_ru_27))))).
fof(ah4s_ieees_ccodeu_u_sizeu_u_def, axiom, ![V_x]: s(t_h4s_nums_num,h4s_ieees_ccodeu_u_size(s(t_h4s_ieees_ccode,V_x))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_ieees_num2ccodeu_u_ONTO, axiom, ![V_a]: ?[V_r]: (s(t_h4s_ieees_ccode,V_a) = s(t_h4s_ieees_ccode,h4s_ieees_num2ccode(s(t_h4s_nums_num,V_r))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_ieees_ccode2numu_u_ONTO, axiom, ![V_r]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_r))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))) <=> ?[V_a]: s(t_h4s_nums_num,V_r) = s(t_h4s_nums_num,h4s_ieees_ccode2num(s(t_h4s_ieees_ccode,V_a))))).
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_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_primu_u_recs_measureu_u_thm, axiom, ![TV_u_27a]: ![V_y, V_x, V_f]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_primu_u_recs_measure),s(t_fun(TV_u_27a,t_h4s_nums_num),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_x))))),s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_y)))))).
fof(ah4s_primu_u_recs_measureu_u_def, axiom, ![TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_primu_u_recs_measure) = s(t_fun(t_fun(TV_u_27a,t_h4s_nums_num),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_relations_invu_u_image(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c)))).
fof(ah4s_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_arithmetics_FUNPOWu_u_1, axiom, ![TV_u_27a]: ![V_x, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),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(TV_u_27a,V_x))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_x)))).
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(ah4s_arithmetics_FUNPOW0u_c1, axiom, ![TV_u_27a]: ![V_x, V_n, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_x))) = s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,V_n),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_x)))))).
fof(ah4s_arithmetics_FUNPOW0u_c0, axiom, ![TV_u_27a]: ![V_x, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_LISTu_u_TOu_u_SETu_u_FILTER, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => ![V_l, V_P]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))))),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))).
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_lists_MEMu_u_FILTER, axiom, ![TV_u_27a]: ![V_x, V_P, V_L]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_L)))))))) <=> (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,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_L))))))))).
fof(ah4s_predu_u_sets_INu_u_INTER, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_GSPECIFICATION, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_v),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f)))))) <=> ?[V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_v),s(t_bool,t))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f),s(TV_u_27b,V_x))))).
fof(ah4s_predu_u_sets_EXTENSION, axiom, ![TV_u_27a]: ![V_t, V_s]: (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),V_t) <=> ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))).
fof(ah4s_pairs_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_lists_LISTu_u_RELu_u_defu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_as, V_a, V_R]: s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27a),V_as))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))) = s(t_bool,f)).
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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: 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) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
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_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: 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_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: 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_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: 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_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, 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)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),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)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
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_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,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_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_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_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,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_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_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
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_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_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_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_lists_LISTu_u_RELu_u_def0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_x0, V_x1]: (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_x),s(t_h4s_lists_list(TV_u_27a),V_x0),s(t_h4s_lists_list(TV_u_27b),V_x1)))) <=> ![V_LISTu_u_RELu_27]: (![V_a00, V_a10]: (((s(t_h4s_lists_list(TV_u_27a),V_a00) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27b),V_a10) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)) | ?[V_h1, V_h2, V_t1, V_t2]: (s(t_h4s_lists_list(TV_u_27a),V_a00) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_h1))),s(t_h4s_lists_list(TV_u_27a),V_t1))) & (s(t_h4s_lists_list(TV_u_27b),V_a10) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h2))),s(t_h4s_lists_list(TV_u_27b),V_t2))) & (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_x),s(TV_u_27a,V_h1))),s(TV_u_27b,V_h2)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_t1))),s(t_h4s_lists_list(TV_u_27b),V_t2)))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_a00))),s(t_h4s_lists_list(TV_u_27b),V_a10))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_h4s_lists_list(TV_u_27b),V_x1))))))).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
fof(ah4s_predu_u_sets_IMAGEu_u_applied, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_s, V_f]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_image(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,V_y)))) <=> ?[V_x]: (s(TV_u_27b,V_y) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_bools_INu_u_DEF, axiom, ![TV_u_27a]: ![V_x, V_x0]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_x0))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x0),s(TV_u_27a,V_x)))).
fof(ah4s_predu_u_sets_INu_u_IMAGE, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_s, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27b,V_y),s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_image(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s)))))) <=> ?[V_x]: (s(TV_u_27b,V_y) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_markers_Congu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_cong(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_combins_APPLYu_u_UPDATEu_u_ID, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_a]: s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_update(s(TV_u_27a,V_a),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a))),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,TV_u_27b),V_f)).
fof(ah4s_combins_UPDATEu_u_APPLYu_u_ID, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_b, V_a]: (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a))) = s(TV_u_27b,V_b) <=> s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_update(s(TV_u_27a,V_a),s(TV_u_27b,V_b),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_fun(TV_u_27a,TV_u_27b),V_f))).
fof(ah4s_lists_LASTu_u_APPENDu_u_CONS, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l2))))))) = s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_LASTu_u_CONSu_u_cond, axiom, ![TV_u_27a]: ![V_t, V_h]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(TV_u_27a),V_t) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) & s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_h),s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_APPENDu_u_equ_u_NILu_c0, axiom, ![TV_u_27a]: ![V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) <=> (s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(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),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_lists_MEMu_u_FLAT, axiom, ![TV_u_27a]: ![V_x, V_L]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_L)))))))) <=> ?[V_l]: (p(s(t_bool,h4s_bools_in(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_L)))))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
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_lists_MEMu_u_APPEND, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_e]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l1)))))) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l2))))))))).
fof(ah4s_lists_LISTu_u_TOu_u_SET0u_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h))),s(t_h4s_lists_list(TV_u_27b),V_t))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_h),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),V_t)))))).
fof(ah4s_lists_LISTu_u_TOu_u_SET0u_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_lists_FLAT0u_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_predu_u_sets_INu_u_INSERT, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s)))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_lists_FLAT0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)))),h4s_lists_cons),s(t_h4s_lists_list(TV_u_27a),V_h))),s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_t))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_t)))))).
fof(ah4s_bools_NOTu_u_EXISTSu_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_bools_LEFTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, 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)))) & p(s(t_bool,V_Q))) <=> ![V_x]: (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,V_Q))))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, 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)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),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)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ?[V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
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_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, 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)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: 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,V_Q))))).
fof(ah4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) & ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) | ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
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_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_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
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_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_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_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(ch4s_ieees_ccodeu_u_caseu_u_defu_c3, conjecture, ![TV_u_27a]: ![V_v3, V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_ieees_ccodeu_u_case(s(t_h4s_ieees_ccode,h4s_ieees_un),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2),s(TV_u_27a,V_v3))) = s(TV_u_27a,V_v3)).
