%   ORIGINAL: h4/binary__ieee/float__compare__case__def_c0
% 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/binary__ieee/LT__def: h4/binary__ieee/LT = h4/binary__ieee/num2float__compare h4/num/0
% Assm: h4/binary__ieee/float__compare2num__thm_c0: h4/binary__ieee/float__compare2num h4/binary__ieee/LT = h4/num/0
% Assm: h4/binary__ieee/num2float__compare__thm_c0: h4/binary__ieee/num2float__compare h4/num/0 = h4/binary__ieee/LT
% Assm: h4/binary__ieee/float__compare__CASE0: !x v3 v2 v1 v0. h4/binary__ieee/float__compare__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/binary__ieee/float__compare2num x)
% Assm: h4/bool/TRUTH: T
% Assm: h4/binary__ieee/float__compare2num__num2float__compare: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/binary__ieee/float__compare2num (h4/binary__ieee/num2float__compare 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/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/binary__ieee/float__compare__BIJ_c0: !a. h4/binary__ieee/num2float__compare (h4/binary__ieee/float__compare2num a) = a
% Assm: h4/binary__ieee/float__compare__BIJ_c1: !r. (\n. h4/prim__rec/_3C n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) r <=> h4/binary__ieee/float__compare2num (h4/binary__ieee/num2float__compare r) = r
% Assm: h4/binary__ieee/EQ__def: h4/binary__ieee/EQ = h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/GT__def: h4/binary__ieee/GT = h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/UN__def: h4/binary__ieee/UN = h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/binary__ieee/float__compare__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/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/binary__ieee/float__compare2num__11: !a_27 a. h4/binary__ieee/float__compare2num a = h4/binary__ieee/float__compare2num a_27 <=> a = a_27
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = 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/binary__ieee/num2float__compare__ONTO: !a. ?r. a = h4/binary__ieee/num2float__compare r /\ h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/binary__ieee/float__compare2num__thm_c3: h4/binary__ieee/float__compare2num h4/binary__ieee/UN = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/float__compare__size__def: !x. h4/binary__ieee/float__compare__size x = h4/num/0
% Assm: h4/binary__ieee/num2float__compare__thm_c2: h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/binary__ieee/EQ
% Assm: h4/binary__ieee/num2float__compare__thm_c1: h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/binary__ieee/GT
% Assm: h4/binary__ieee/float__compare2num__thm_c2: h4/binary__ieee/float__compare2num h4/binary__ieee/EQ = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/binary__ieee/num2float__compare__float__compare2num: !a. h4/binary__ieee/num2float__compare (h4/binary__ieee/float__compare2num a) = a
% Assm: h4/binary__ieee/float__compare2num__thm_c1: h4/binary__ieee/float__compare2num h4/binary__ieee/GT = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/binary__ieee/float__compare__EQ__float__compare: !a_27 a. a = a_27 <=> h4/binary__ieee/float__compare2num a = h4/binary__ieee/float__compare2num a_27
% Assm: h4/binary__ieee/float__compare2num__ONTO: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?a. r = h4/binary__ieee/float__compare2num a)
% Assm: h4/binary__ieee/num2float__compare__thm_c3: h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/binary__ieee/UN
% Assm: h4/binary__ieee/num2float__compare__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/binary__ieee/num2float__compare r = h4/binary__ieee/num2float__compare r_27 <=> r = r_27)
% 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/numeral/numeral__lt_c2: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% 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/prim__rec/num__Axiom: !f e. ?fn. fn h4/num/0 = e /\ (!n. fn (h4/num/SUC n) = f n (fn n))
% Assm: h4/rich__list/LASTN0_c1: !x n l. h4/rich__list/LASTN (h4/num/SUC n) (h4/list/SNOC x l) = h4/list/SNOC x (h4/rich__list/LASTN n l)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~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/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/list/FRONT__SNOC: !x l. h4/list/FRONT (h4/list/SNOC x l) = l
% Assm: h4/list/LAST__SNOC: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/bool/IN__DEF: h4/bool/IN = (\x f. f x)
% Assm: h4/pred__set/INSERT__applied: !y x s. h4/pred__set/INSERT y s x <=> x = y \/ h4/bool/IN x s
% 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/marker/Cong__def: !x. h4/marker/Cong x <=> x
% Assm: h4/fcp/bit1__size__def_c0: !f a. h4/fcp/bit1__size f (h4/fcp/BIT1A a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (f a)
% Assm: h4/fcp/hidden____20__40ind____typefcp6____def: h4/fcp/_20_40ind__typefcp6 = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/fcp/hidden____20__40ind____typefcp4____def: h4/fcp/_20_40ind__typefcp4 = (\a. h4/fcp/_20_40ind__typefcp7 ((\a0. h4/ind__type/CONSTR h4/num/0 a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/fcp/hidden____20__40ind____typefcp5____def: h4/fcp/_20_40ind__typefcp5 = (\a. h4/fcp/_20_40ind__typefcp7 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/fcp/BIT1B0: h4/fcp/BIT1B = h4/fcp/_20_40ind__typefcp5
% Assm: h4/fcp/bit1__repfns_c1: !r. (\a0. !_27bit1_27. (!a00. (?a. a00 = (\a1. h4/ind__type/CONSTR h4/num/0 a1 (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (\n. h4/ind__type/BOTTOM)) a) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM) ==> _27bit1_27 a00) ==> _27bit1_27 a0) r <=> h4/fcp/_20_40ind__typefcp8 (h4/fcp/_20_40ind__typefcp7 r) = r
% Assm: h4/fcp/BIT1C0: h4/fcp/BIT1C = h4/fcp/_20_40ind__typefcp6
% Assm: h4/fcp/BIT1A0: h4/fcp/BIT1A = h4/fcp/_20_40ind__typefcp4
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% 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/arithmetic/NRC__SUC__RECURSE__LEFT: !y x n R. h4/arithmetic/NRC R (h4/num/SUC n) x y <=> (?z. h4/arithmetic/NRC R n x z /\ R z y)
% Assm: h4/arithmetic/NRC__1: !y x R. h4/arithmetic/NRC R (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x y <=> R x y
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/arithmetic/ADD1: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/NRC__ADD__EQN: !z x n m R. h4/arithmetic/NRC R (h4/arithmetic/_2B m n) x z <=> (?y. h4/arithmetic/NRC R m x y /\ h4/arithmetic/NRC R n y z)
% Assm: h4/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/rich__list/ELL__LENGTH__SNOC: !x l. h4/rich__list/ELL (h4/list/LENGTH l) (h4/list/SNOC x l) = h4/bool/COND (h4/list/NULL l) x (h4/list/HD l)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/rich__list/ELL__LENGTH__CONS: !x l. h4/rich__list/ELL (h4/list/LENGTH l) (h4/list/CONS x l) = x
% Assm: h4/rich__list/ELL__SUC__SNOC: !x n l. h4/rich__list/ELL (h4/num/SUC n) (h4/list/SNOC x l) = h4/rich__list/ELL n l
% Assm: h4/rich__list/ELL__0__SNOC: !x l. h4/rich__list/ELL h4/num/0 (h4/list/SNOC x l) = x
% Assm: h4/list/NULL0_c0: h4/list/NULL h4/list/NIL
% Assm: h4/list/NULL0_c1: !t h. ~h4/list/NULL (h4/list/CONS h t)
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/list/HD0: !t h. h4/list/HD (h4/list/CONS h t) = h
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/list/LAST__CONS_c0: !x. h4/list/LAST (h4/list/CONS x h4/list/NIL) = x
% Assm: h4/list/LAST__DEF: !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/NOT__CONS__NIL: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/sum/IS__SUM__REP0: !f. h4/sum/IS__SUM__REP f <=> (?v1 v2. f = (\b x y. x = v1 /\ b) \/ f = (\b x y. y = v2 /\ ~b))
% Assm: h4/operator/ASSOC__DEF: !f. h4/operator/ASSOC f <=> (!x y z. f x (f y z) = f (f x y) z)
% Assm: h4/operator/ASSOC__SYM: !f. h4/operator/ASSOC f <=> (!x y z. f (f x y) z = f x (f y z))
% Assm: h4/list/MEM__REVERSE: !x l. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/REVERSE l)) <=> h4/bool/IN x (h4/list/LIST__TO__SET l)
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/list/REVERSE__DEF_c1: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm: h4/list/REVERSE__DEF_c0: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/list/LIST__TO__SET0_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/list/MEM_c0: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% 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/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/list/REVERSE__SNOC: !x l. h4/list/REVERSE (h4/list/SNOC x l) = h4/list/CONS x (h4/list/REVERSE l)
% Assm: h4/list/REVERSE__REVERSE: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm: h4/rich__list/SNOC__REVERSE__CONS: !x l. h4/list/SNOC x l = h4/list/REVERSE (h4/list/CONS x (h4/list/REVERSE l))
% Assm: h4/quotient/RESPECTS: !x R. h4/quotient/respects R x <=> R x x
% Assm: h4/quotient/respects__def: h4/quotient/respects = h4/combin/W
% Assm: h4/combin/W__THM: !x f. h4/combin/W f x = f x x
% Assm: h4/pred__set/SPECIFICATION: !x P. h4/bool/IN x P <=> P x
% Goal: !v3 v2 v1 v0. h4/binary__ieee/float__compare__CASE h4/binary__ieee/LT v0 v1 v2 v3 = v0
%   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_binaryu_u_ieees_LTu_u_def]: h4/binary__ieee/LT = h4/binary__ieee/num2float__compare h4/num/0
% Assm [h4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c0]: h4/binary__ieee/float__compare2num h4/binary__ieee/LT = h4/num/0
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c0]: h4/binary__ieee/num2float__compare h4/num/0 = h4/binary__ieee/LT
% Assm [h4s_binaryu_u_ieees_floatu_u_compareu_u_CASE0]: !x v3 v2 v1 v0. ?v. (v <=> h4/binary__ieee/float__compare2num x = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) /\ h4/binary__ieee/float__compare__CASE x v0 v1 v2 v3 = h4/bool/COND (h4/prim__rec/_3C (h4/binary__ieee/float__compare2num x) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) v0 (h4/bool/COND (h4/prim__rec/_3C (h4/binary__ieee/float__compare2num x) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) v1 (h4/bool/COND v v2 v3))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_binaryu_u_ieees_floatu_u_compare2numu_u_num2floatu_u_compare]: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/binary__ieee/float__compare2num (h4/binary__ieee/num2float__compare r) = r
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_binaryu_u_ieees_floatu_u_compareu_u_BIJu_c0]: !a. h4/binary__ieee/num2float__compare (h4/binary__ieee/float__compare2num a) = a
% Assm [h4s_binaryu_u_ieees_floatu_u_compareu_u_BIJu_c1]: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> h4/binary__ieee/float__compare2num (h4/binary__ieee/num2float__compare r) = r
% Assm [h4s_binaryu_u_ieees_EQu_u_def]: h4/binary__ieee/EQ = h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_GTu_u_def]: h4/binary__ieee/GT = h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_UNu_u_def]: h4/binary__ieee/UN = h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_binaryu_u_ieees_floatu_u_compareu_u_TYu_u_DEF]: !_0. (!n. happ _0 n <=> 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_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_binaryu_u_ieees_floatu_u_compare2numu_u_11]: !a_27 a. h4/binary__ieee/float__compare2num a = h4/binary__ieee/float__compare2num a_27 <=> a = a_27
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_numerals_numeralu_u_distribu_c22]: !n m. h4/prim__rec/_3C (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/prim__rec/_3C n m
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_ONTO]: !a. ?r. a = h4/binary__ieee/num2float__compare r /\ h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c3]: h4/binary__ieee/float__compare2num h4/binary__ieee/UN = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_floatu_u_compareu_u_sizeu_u_def]: !x. h4/binary__ieee/float__compare__size x = h4/num/0
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c2]: h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) = h4/binary__ieee/EQ
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c1]: h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/binary__ieee/GT
% Assm [h4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c2]: h4/binary__ieee/float__compare2num h4/binary__ieee/EQ = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_floatu_u_compare2num]: !a. h4/binary__ieee/num2float__compare (h4/binary__ieee/float__compare2num a) = a
% Assm [h4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c1]: h4/binary__ieee/float__compare2num h4/binary__ieee/GT = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_binaryu_u_ieees_floatu_u_compareu_u_EQu_u_floatu_u_compare]: !a_27 a. a = a_27 <=> h4/binary__ieee/float__compare2num a = h4/binary__ieee/float__compare2num a_27
% Assm [h4s_binaryu_u_ieees_floatu_u_compare2numu_u_ONTO]: !r. h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) <=> (?a. r = h4/binary__ieee/float__compare2num a)
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c3]: h4/binary__ieee/num2float__compare (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/binary__ieee/UN
% Assm [h4s_binaryu_u_ieees_num2floatu_u_compareu_u_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/binary__ieee/num2float__compare r = h4/binary__ieee/num2float__compare r_27 <=> r = r_27)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm [h4s_numerals_numeralu_u_ltu_c2]: !n. h4/prim__rec/_3C n h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_numerals_numeralu_u_ltu_c4]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_numerals_numeralu_u_ltu_c3]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) <=> h4/prim__rec/_3C n m
% Assm [h4s_primu_u_recs_numu_u_Axiom]: !f e. ?fn. happ fn h4/num/0 = e /\ (!n. happ fn (h4/num/SUC n) = happ (happ f n) (happ fn n))
% Assm [h4s_richu_u_lists_LASTN0u_c1]: !x n l. h4/rich__list/LASTN (h4/num/SUC n) (h4/list/SNOC x l) = h4/list/SNOC x (h4/rich__list/LASTN n l)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~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_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% 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_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_lists_FRONTu_u_SNOC]: !x l. h4/list/FRONT (h4/list/SNOC x l) = l
% Assm [h4s_lists_LASTu_u_SNOC]: !x l. h4/list/LAST (h4/list/SNOC x l) = x
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = happ f n
% Assm [h4s_bools_INu_u_DEF]: !x x. h4/bool/IN x x <=> happ x x
% Assm [h4s_predu_u_sets_INSERTu_u_applied]: !y x s. happ (h4/pred__set/INSERT y s) x <=> x = y \/ h4/bool/IN x s
% 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_markers_Congu_u_def]: !x. h4/marker/Cong x <=> x
% Assm [h4s_fcps_bit1u_u_sizeu_u_defu_c0]: !f a. h4/fcp/bit1__size f (happ h4/fcp/BIT1A a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (happ f a)
% Assm [h4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/fcp/_20_40ind__typefcp6 = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0)
% Assm [h4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/fcp/_20_40ind__typefcp4 x = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR h4/num/0 x _0))
% Assm [h4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/fcp/_20_40ind__typefcp5 x = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x _0))
% Assm [h4s_fcps_BIT1B0]: h4/fcp/BIT1B = h4/fcp/_20_40ind__typefcp5
% Assm [h4s_fcps_bit1u_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27bit1_27. (!a00. (?a. a00 = h4/ind__type/CONSTR h4/num/0 a _0) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a _0) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0 ==> happ _27bit1_27 a00) ==> happ _27bit1_27 r) <=> h4/fcp/_20_40ind__typefcp8 (h4/fcp/_20_40ind__typefcp7 r) = r)
% Assm [h4s_fcps_BIT1C0]: h4/fcp/BIT1C = h4/fcp/_20_40ind__typefcp6
% Assm [h4s_fcps_BIT1A0]: h4/fcp/BIT1A = h4/fcp/_20_40ind__typefcp4
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% 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_arithmetics_NRCu_u_SUCu_u_RECURSEu_u_LEFT]: !y x n R. h4/arithmetic/NRC R (h4/num/SUC n) x y <=> (?z. h4/arithmetic/NRC R n x z /\ happ (happ R z) y)
% Assm [h4s_arithmetics_NRCu_u_1]: !y x R. h4/arithmetic/NRC R (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) x y <=> happ (happ R x) y
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_arithmetics_ADD1]: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_NRCu_u_ADDu_u_EQN]: !z x n m R. h4/arithmetic/NRC R (h4/arithmetic/_2B m n) x z <=> (?y. h4/arithmetic/NRC R m x y /\ h4/arithmetic/NRC R n y z)
% Assm [h4s_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_richu_u_lists_ELLu_u_LENGTHu_u_SNOC]: !x l. h4/rich__list/ELL (h4/list/LENGTH l) (h4/list/SNOC x l) = h4/bool/COND (h4/list/NULL l) x (h4/list/HD l)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_richu_u_lists_ELLu_u_LENGTHu_u_CONS]: !x l. h4/rich__list/ELL (h4/list/LENGTH l) (h4/list/CONS x l) = x
% Assm [h4s_richu_u_lists_ELLu_u_SUCu_u_SNOC]: !x n l. h4/rich__list/ELL (h4/num/SUC n) (h4/list/SNOC x l) = h4/rich__list/ELL n l
% Assm [h4s_richu_u_lists_ELLu_u_0u_u_SNOC]: !x l. h4/rich__list/ELL h4/num/0 (h4/list/SNOC x l) = x
% Assm [h4s_lists_NULL0u_c0]: h4/list/NULL h4/list/NIL
% Assm [h4s_lists_NULL0u_c1]: !t h. ~h4/list/NULL (h4/list/CONS h t)
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_lists_HD0]: !t h. h4/list/HD (h4/list/CONS h t) = h
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_lists_LASTu_u_CONSu_c0]: !x. h4/list/LAST (h4/list/CONS x h4/list/NIL) = x
% Assm [h4s_lists_LASTu_u_DEF]: !t h. ?v. (v <=> t = h4/list/NIL) /\ h4/list/LAST (h4/list/CONS h t) = h4/bool/COND v h (h4/list/LAST t)
% Assm [h4s_lists_NOTu_u_CONSu_u_NIL]: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_sums_ISu_u_SUMu_u_REP0]: !f. h4/sum/IS__SUM__REP f <=> (?v1 v2. (!x x x. happ (happ (happ f x) x) x <=> x = v1 /\ x) \/ (!x x x. happ (happ (happ f x) x) x <=> x = v2 /\ ~x))
% Assm [h4s_operators_ASSOCu_u_DEF]: !f. h4/operator/ASSOC f <=> (!x y z. happ (happ f x) (happ (happ f y) z) = happ (happ f (happ (happ f x) y)) z)
% Assm [h4s_operators_ASSOCu_u_SYM]: !f. h4/operator/ASSOC f <=> (!x y z. happ (happ f (happ (happ f x) y)) z = happ (happ f x) (happ (happ f y) z))
% Assm [h4s_lists_MEMu_u_REVERSE]: !x l. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/REVERSE l)) <=> h4/bool/IN x (h4/list/LIST__TO__SET l)
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_lists_REVERSEu_u_DEFu_c1]: !t h. h4/list/REVERSE (h4/list/CONS h t) = h4/list/APPEND (h4/list/REVERSE t) (h4/list/CONS h h4/list/NIL)
% Assm [h4s_lists_REVERSEu_u_DEFu_c0]: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_lists_MEMu_c0]: !x. h4/bool/IN x (h4/list/LIST__TO__SET h4/list/NIL) <=> F
% 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_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_lists_REVERSEu_u_SNOC]: !x l. h4/list/REVERSE (h4/list/SNOC x l) = h4/list/CONS x (h4/list/REVERSE l)
% Assm [h4s_lists_REVERSEu_u_REVERSE]: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm [h4s_richu_u_lists_SNOCu_u_REVERSEu_u_CONS]: !x l. h4/list/SNOC x l = h4/list/REVERSE (h4/list/CONS x (h4/list/REVERSE l))
% Assm [h4s_quotients_RESPECTS]: !x R. happ (happ h4/quotient/respects R) x <=> happ (happ R x) x
% Assm [h4s_quotients_respectsu_u_def]: h4/quotient/respects = h4/combin/W
% Assm [h4s_combins_Wu_u_THM]: !x f. happ (happ h4/combin/W f) x = happ (happ f x) x
% Assm [h4s_predu_u_sets_SPECIFICATION]: !x P. h4/bool/IN x P <=> happ P x
% Goal: !v3 v2 v1 v0. h4/binary__ieee/float__compare__CASE h4/binary__ieee/LT v0 v1 v2 v3 = v0
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_Q1181922,TV_Q1181918]: ![V_f, V_g]: (![V_x]: s(TV_Q1181918,happ(s(t_fun(TV_Q1181922,TV_Q1181918),V_f),s(TV_Q1181922,V_x))) = s(TV_Q1181918,happ(s(t_fun(TV_Q1181922,TV_Q1181918),V_g),s(TV_Q1181922,V_x))) => s(t_fun(TV_Q1181922,TV_Q1181918),V_f) = s(t_fun(TV_Q1181922,TV_Q1181918),V_g))).
fof(ah4s_binaryu_u_ieees_LTu_u_def, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_lt) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c0, axiom, s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_lt))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c0, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_lt)).
fof(ah4s_binaryu_u_ieees_floatu_u_compareu_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_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,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_binaryu_u_ieees_floatu_u_compareu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_compare,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,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,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,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,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_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_binaryu_u_ieees_floatu_u_compare2numu_u_num2floatu_u_compare, axiom, ![V_r]: (p(s(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_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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,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,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(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_binaryu_u_ieees_floatu_u_compareu_u_BIJu_c0, axiom, ![V_a]: s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a))))) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a)).
fof(ah4s_binaryu_u_ieees_floatu_u_compareu_u_BIJu_c1, axiom, ![V_r]: (p(s(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_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,V_r))))) = s(t_h4s_nums_num,V_r))).
fof(ah4s_binaryu_u_ieees_EQu_u_def, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_eq) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_binaryu_u_ieees_GTu_u_def, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_gt) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_binaryu_u_ieees_UNu_u_def, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_un) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_binaryu_u_ieees_floatu_u_compareu_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,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_binaryu_u_ieees_floatu_u_compare,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_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_binaryu_u_ieees_floatu_u_compare2numu_u_11, axiom, ![V_au_27, V_a]: (s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a))) = s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_au_27))) <=> s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_au_27))).
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_numerals_numeralu_u_distribu_c22, axiom, ![V_n, V_m]: s(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,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_binaryu_u_ieees_num2floatu_u_compareu_u_ONTO, axiom, ![V_a]: ?[V_r]: (s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,V_r))) & p(s(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_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c3, axiom, s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_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_binaryu_u_ieees_floatu_u_compareu_u_sizeu_u_def, axiom, ![V_x]: s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compareu_u_size(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_x))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c2, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_eq)).
fof(ah4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c1, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_gt)).
fof(ah4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c2, axiom, s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_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_binaryu_u_ieees_num2floatu_u_compareu_u_floatu_u_compare2num, axiom, ![V_a]: s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a))))) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a)).
fof(ah4s_binaryu_u_ieees_floatu_u_compare2numu_u_thmu_c1, axiom, s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_gt))) = 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_binaryu_u_ieees_floatu_u_compareu_u_EQu_u_floatu_u_compare, axiom, ![V_au_27, V_a]: (s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_au_27) <=> s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a))) = s(t_h4s_nums_num,h4s_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_au_27))))).
fof(ah4s_binaryu_u_ieees_floatu_u_compare2numu_u_ONTO, axiom, ![V_r]: (p(s(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_binaryu_u_ieees_floatu_u_compare2num(s(t_h4s_binaryu_u_ieees_floatu_u_compare,V_a))))).
fof(ah4s_binaryu_u_ieees_num2floatu_u_compareu_u_thmu_c3, axiom, s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_un)).
fof(ah4s_binaryu_u_ieees_num2floatu_u_compareu_u_11, axiom, ![V_ru_27, V_r]: (p(s(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,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_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(s(t_h4s_nums_num,V_r))) = s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_ieees_num2floatu_u_compare(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_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,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,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_ltu_c2, axiom, ![V_n]: s(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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_numerals_numeralu_u_ltu_c4, axiom, ![V_n, V_m]: s(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,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_c0, axiom, ![V_n]: s(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_numerals_numeralu_u_ltu_c3, axiom, ![V_n, V_m]: s(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,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_primu_u_recs_numu_u_Axiom, axiom, ![TV_u_27a]: ![V_f, V_e]: ?[V_fn]: (s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_fn),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_e) & ![V_n]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_fn),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,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(t_h4s_nums_num,TV_u_27a),V_fn),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_richu_u_lists_LASTN0u_c1, axiom, ![TV_u_27a]: ![V_x, V_n, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_lastn(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_lastn(s(t_h4s_nums_num,V_n),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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (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_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_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_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_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_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_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_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_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_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_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_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
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_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_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_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_bools_EXISTSu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_x)))))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_lists_FRONTu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_front(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_LASTu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_RIGHTu_u_ANDu_u_FORALLu_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_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,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_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_INSERTu_u_applied, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,happ(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_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_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_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_fcps_bit1u_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_fcps_bit1u_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a)))))).
fof(ah4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp6u_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_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp6) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(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_suc(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_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp4u_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]: s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp4),s(TV_u_27a,V_x))) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(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,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp5u_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]: s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp5),s(TV_u_27a,V_x))) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(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)),V_uu_0))))))).
fof(ah4s_fcps_BIT1B0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b) = s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp5)).
fof(ah4s_fcps_bit1u_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_27bit1u_27]: (![V_a00]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = 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,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = 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_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = 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_suc(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))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27bit1u_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27bit1u_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp8(s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(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_fcps_BIT1C0, axiom, ![TV_u_27a]: s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp6)).
fof(ah4s_fcps_BIT1A0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a) = s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp4)).
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_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_arithmetics_NRCu_u_SUCu_u_RECURSEu_u_LEFT, axiom, ![TV_u_27a]: ![V_y, V_x, V_n, V_R]: (p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),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,V_y)))) <=> ?[V_z]: (p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_h4s_nums_num,V_n),s(TV_u_27a,V_x),s(TV_u_27a,V_z)))) & p(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)),V_R),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))))))).
fof(ah4s_arithmetics_NRCu_u_1, axiom, ![TV_u_27a]: ![V_y, V_x, V_R]: s(t_bool,h4s_arithmetics_nrc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),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,V_y))) = 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)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))).
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_arithmetics_ADD1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),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_arithmetics_NRCu_u_ADDu_u_EQN, axiom, ![TV_u_27a]: ![V_z, V_x, V_n, V_m, V_R]: (p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_x),s(TV_u_27a,V_z)))) <=> ?[V_y]: (p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_h4s_nums_num,V_m),s(TV_u_27a,V_x),s(TV_u_27a,V_y)))) & p(s(t_bool,h4s_arithmetics_nrc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_h4s_nums_num,V_n),s(TV_u_27a,V_y),s(TV_u_27a,V_z))))))).
fof(ah4s_bools_LEFTu_u_ORu_u_OVERu_u_AND, 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_A)) | p(s(t_bool,V_C)))))).
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_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_richu_u_lists_ELLu_u_LENGTHu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),V_l))),s(TV_u_27a,V_x),s(TV_u_27a,h4s_lists_hd(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_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_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(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)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
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_richu_u_lists_ELLu_u_LENGTHu_u_CONS, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,V_x)).
fof(ah4s_richu_u_lists_ELLu_u_SUCu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_n, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_richu_u_lists_ELLu_u_0u_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(TV_u_27a,h4s_richu_u_lists_ell(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_NULL0u_c0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))).
fof(ah4s_lists_NULL0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: ~ (p(s(t_bool,h4s_lists_null(s(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)))))))).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(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(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_HD0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(TV_u_27a,h4s_lists_hd(s(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,V_h)).
fof(ah4s_lists_LENGTH0u_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_LASTu_u_CONSu_c0, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_LASTu_u_DEF, 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),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_NOTu_u_CONSu_u_NIL, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
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_sums_ISu_u_SUMu_u_REP0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: (p(s(t_bool,h4s_sums_isu_u_sumu_u_rep(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_f)))) <=> ?[V_v1, V_v2]: (![V_x, V_x0, V_x1]: (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)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_f),s(t_bool,V_x))),s(TV_u_27a,V_x0))),s(TV_u_27b,V_x1)))) <=> (s(TV_u_27a,V_x0) = s(TV_u_27a,V_v1) & p(s(t_bool,V_x)))) | ![V_x, V_x0, V_x1]: (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)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_f),s(t_bool,V_x))),s(TV_u_27a,V_x0))),s(TV_u_27b,V_x1)))) <=> (s(TV_u_27b,V_x1) = s(TV_u_27b,V_v2) & ~ (p(s(t_bool,V_x)))))))).
fof(ah4s_operators_ASSOCu_u_DEF, axiom, ![TV_u_27a]: ![V_f]: (p(s(t_bool,h4s_operators_assoc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f)))) <=> ![V_x, V_y, V_z]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))),s(TV_u_27a,V_z))))).
fof(ah4s_operators_ASSOCu_u_SYM, axiom, ![TV_u_27a]: ![V_f]: (p(s(t_bool,h4s_operators_assoc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f)))) <=> ![V_x, V_y, V_z]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))),s(TV_u_27a,V_z))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))))))).
fof(ah4s_lists_MEMu_u_REVERSE, axiom, ![TV_u_27a]: ![V_x, V_l]: 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_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))))) = 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_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_REVERSEu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(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(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_t))),s(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_nil)))))).
fof(ah4s_lists_REVERSEu_u_DEFu_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (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_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | 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_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_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_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_lists_MEMu_c0, axiom, ![TV_u_27a]: ![V_x]: 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_nil))))) = s(t_bool,f)).
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_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_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_REVERSEu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_REVERSEu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_richu_u_lists_SNOCu_u_REVERSEu_u_CONS, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l)))))))).
fof(ah4s_quotients_RESPECTS, axiom, ![TV_u_27a]: ![V_x, V_R]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))) = 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)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_x)))).
fof(ah4s_quotients_respectsu_u_def, axiom, ![TV_u_27a,TV_u_27b]: s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,TV_u_27b)),h4s_quotients_respects) = s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,TV_u_27b)),h4s_combins_w)).
fof(ah4s_combins_Wu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,TV_u_27b)),h4s_combins_w),s(t_fun(TV_u_27a,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),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_x)))).
fof(ah4s_predu_u_sets_SPECIFICATION, axiom, ![TV_u_27a]: ![V_x, V_P]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))).
fof(ch4s_binaryu_u_ieees_floatu_u_compareu_u_caseu_u_defu_c0, conjecture, ![TV_u_27a]: ![V_v3, V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_binaryu_u_ieees_floatu_u_compareu_u_case(s(t_h4s_binaryu_u_ieees_floatu_u_compare,h4s_binaryu_u_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_v0)).
