%   ORIGINAL: h4/toto/num__dtOrd0_c5
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/toto/bit10: h4/toto/bit1 = h4/toto/_20_40ind__typetoto1
% Assm: h4/toto/bit20: h4/toto/bit2 = h4/toto/_20_40ind__typetoto2
% Assm: h4/toto/hidden____20__40ind____typetoto2____def: h4/toto/_20_40ind__typetoto2 = (\a. h4/toto/_20_40ind__typetoto3 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/toto/_20_40ind__typetoto4 a)))
% Assm: h4/toto/num__dt__repfns_c0: !a. h4/toto/_20_40ind__typetoto3 (h4/toto/_20_40ind__typetoto4 a) = a
% Assm: h4/toto/hidden____20__40ind____typetoto1____def: h4/toto/_20_40ind__typetoto1 = (\a. h4/toto/_20_40ind__typetoto3 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/toto/_20_40ind__typetoto4 a)))
% Assm: h4/toto/num__dtOrd__tupled__primitive: h4/toto/num__dtOrd__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!y x. R (h4/pair/_2C x y) (h4/pair/_2C (h4/toto/bit1 x) (h4/toto/bit1 y))) /\ (!y x. R (h4/pair/_2C x y) (h4/pair/_2C (h4/toto/bit2 x) (h4/toto/bit2 y))))) (\num__dtOrd__tupled a. h4/pair/pair__CASE a (\v v1. h4/toto/num__dt__CASE v (h4/toto/num__dt__CASE v1 (h4/combin/I h4/toto/EQUAL) (\x. h4/combin/I h4/toto/LESS) (\x_27. h4/combin/I h4/toto/LESS)) (\x_27_27. h4/toto/num__dt__CASE v1 (h4/combin/I h4/toto/GREATER) (\y_27_27. h4/combin/I (num__dtOrd__tupled (h4/pair/_2C x_27_27 y_27_27))) (\y. h4/combin/I h4/toto/LESS)) (\x_27_27_27. h4/toto/num__dt__CASE v1 (h4/combin/I h4/toto/GREATER) (\y_27. h4/combin/I h4/toto/GREATER) (\y_27_27_27. h4/combin/I (num__dtOrd__tupled (h4/pair/_2C x_27_27_27 y_27_27_27))))))
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/toto/zer0: h4/toto/zer = h4/toto/_20_40ind__typetoto0
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/toto/hidden____20__40ind____typetoto0____def: h4/toto/_20_40ind__typetoto0 = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% 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/toto/num__dt__repfns_c1: !r. (\a0. !_27num__dt_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27num__dt_27 a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27num__dt_27 a) ==> _27num__dt_27 a00) ==> _27num__dt_27 a0) r <=> h4/toto/_20_40ind__typetoto4 (h4/toto/_20_40ind__typetoto3 r) = r
% Assm: h4/toto/num__dtOrd0_c2: !x. h4/toto/num__dtOrd h4/toto/zer (h4/toto/bit2 x) = h4/toto/LESS
% Assm: h4/toto/num__dtOrd0_c1: !x. h4/toto/num__dtOrd h4/toto/zer (h4/toto/bit1 x) = h4/toto/LESS
% Assm: h4/toto/num__dtOrd0_c3: !x. h4/toto/num__dtOrd (h4/toto/bit1 x) h4/toto/zer = h4/toto/GREATER
% Assm: h4/toto/num__dtOrd0_c4: !x. h4/toto/num__dtOrd (h4/toto/bit2 x) h4/toto/zer = h4/toto/GREATER
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/toto/num__dt__case__def_c2: !v f1 f a. h4/toto/num__dt__CASE (h4/toto/bit2 a) v f f1 = f1 a
% Assm: h4/toto/num__dt__case__def_c1: !v f1 f a. h4/toto/num__dt__CASE (h4/toto/bit1 a) v f f1 = f a
% Assm: h4/toto/num__dt__nchotomy: !nn. nn = h4/toto/zer \/ (?n. nn = h4/toto/bit1 n) \/ (?n. nn = h4/toto/bit2 n)
% Assm: h4/toto/num__dt__Axiom: !f2 f1 f0. ?fn. fn h4/toto/zer = f0 /\ (!a. fn (h4/toto/bit1 a) = f1 a (fn a)) /\ (!a. fn (h4/toto/bit2 a) = f2 a (fn a))
% Assm: h4/toto/num__dt__distinct_c2: !a_27 a. ~(h4/toto/bit1 a = h4/toto/bit2 a_27)
% Assm: h4/toto/num__dt__case__cong: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/toto/zer ==> v = v_27) /\ (!a. M_27 = h4/toto/bit1 a ==> f a = f_27 a) /\ (!a. M_27 = h4/toto/bit2 a ==> f1 a = f1_27 a) ==> h4/toto/num__dt__CASE M v f f1 = h4/toto/num__dt__CASE M_27 v_27 f_27 f1_27
% Assm: h4/toto/num__dtOrd__ind: !P. P h4/toto/zer h4/toto/zer /\ (!x. P h4/toto/zer (h4/toto/bit1 x)) /\ (!x. P h4/toto/zer (h4/toto/bit2 x)) /\ (!x. P (h4/toto/bit1 x) h4/toto/zer) /\ (!x. P (h4/toto/bit2 x) h4/toto/zer) /\ (!x y. P (h4/toto/bit1 x) (h4/toto/bit2 y)) /\ (!x y. P (h4/toto/bit2 x) (h4/toto/bit1 y)) /\ (!x y. P x y ==> P (h4/toto/bit1 x) (h4/toto/bit1 y)) /\ (!x y. P x y ==> P (h4/toto/bit2 x) (h4/toto/bit2 y)) ==> (!v v1. P v v1)
% Assm: h4/toto/num__dt__induction: !P. P h4/toto/zer /\ (!n. P n ==> P (h4/toto/bit1 n)) /\ (!n. P n ==> P (h4/toto/bit2 n)) ==> (!n. P n)
% Assm: h4/toto/num__dtOrd__curried: !x1 x. h4/toto/num__dtOrd x x1 = h4/toto/num__dtOrd__tupled (h4/pair/_2C x x1)
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/toto/num__dt__size__def_c1: !a. h4/toto/num__dt__size (h4/toto/bit1 a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/toto/num__dt__size a)
% Assm: h4/toto/num__dt__size__def_c2: !a. h4/toto/num__dt__size (h4/toto/bit2 a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/toto/num__dt__size a)
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% 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/toto/datatype__num__dt: !num__dt. h4/bool/DATATYPE (num__dt h4/toto/zer h4/toto/bit1 h4/toto/bit2)
% Assm: h4/toto/num__dtOrd0_c0: h4/toto/num__dtOrd h4/toto/zer h4/toto/zer = h4/toto/EQUAL
% Assm: h4/toto/num__dt__11_c0: !a_27 a. h4/toto/bit1 a = h4/toto/bit1 a_27 <=> a = a_27
% Assm: h4/toto/num__dt__distinct_c1: !a. ~(h4/toto/zer = h4/toto/bit2 a)
% Assm: h4/toto/num__dt__11_c1: !a_27 a. h4/toto/bit2 a = h4/toto/bit2 a_27 <=> a = a_27
% Assm: h4/toto/num__dt__distinct_c0: !a. ~(h4/toto/zer = h4/toto/bit1 a)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/toto/num__dt__case__def_c0: !v f1 f. h4/toto/num__dt__CASE h4/toto/zer v f f1 = v
% Assm: h4/toto/num__to__dt__primitive: h4/toto/num__to__dt = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!n. ~(n = h4/num/0) /\ h4/arithmetic/ODD n ==> R (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) n) /\ (!n. ~(n = h4/num/0) /\ ~h4/arithmetic/ODD n ==> R (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))) n))) (\num__to__dt n. h4/combin/I (h4/bool/COND (n = h4/num/0) h4/toto/zer (h4/bool/COND (h4/arithmetic/ODD n) (h4/toto/bit1 (num__to__dt (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (h4/toto/bit2 (num__to__dt (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)))))))))
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% 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/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/toto/num__dt__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0. !_27num__dt_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27num__dt_27 a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27num__dt_27 a) ==> _27num__dt_27 a00) ==> _27num__dt_27 a0) rep
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/toto/totoLEtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/toto/totoLLtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__antisym: !y x c. h4/toto/apto c x y = h4/toto/GREATER <=> h4/toto/apto c y x = h4/toto/LESS
% Assm: h4/toto/toto__glneq_c0: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm: h4/toto/toto__glneq_c1: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm: h4/toto/toto__cpn__eqn_c1: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm: h4/toto/totoLGtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/cpn__distinct_c1: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm: h4/toto/toto__trans__less_c4: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/aplextoto: !y2 y1 x2 x1 v c. h4/toto/apto (h4/toto/lextoto c v) (h4/pair/_2C x1 x2) (h4/pair/_2C y1 y2) = h4/toto/cpn__CASE (h4/toto/apto c x1 y1) h4/toto/LESS (h4/toto/apto v x2 y2) h4/toto/GREATER
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% 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/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/relation/WF__INDUCTION__THM: !R. h4/relation/WF R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/toto/cpn__EQ__cpn: !a_27 a. a = a_27 <=> h4/toto/cpn2num a = h4/toto/cpn2num a_27
% Assm: h4/toto/cpn2num__thm_c2: h4/toto/cpn2num h4/toto/GREATER = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/toto/cpn2num__thm_c0: h4/toto/cpn2num h4/toto/LESS = h4/num/0
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% 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
% Goal: !y x. h4/toto/num__dtOrd (h4/toto/bit1 x) (h4/toto/bit2 y) = h4/toto/LESS
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_totos_bit10]: h4/toto/bit1 = h4/toto/_20_40ind__typetoto1
% Assm [h4s_totos_bit20]: h4/toto/bit2 = h4/toto/_20_40ind__typetoto2
% Assm [h4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/toto/_20_40ind__typetoto2 x = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS (h4/toto/_20_40ind__typetoto4 x) _0)))
% Assm [h4s_totos_numu_u_dtu_u_repfnsu_c0]: !a. h4/toto/_20_40ind__typetoto3 (h4/toto/_20_40ind__typetoto4 a) = a
% Assm [h4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/toto/_20_40ind__typetoto1 x = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS (h4/toto/_20_40ind__typetoto4 x) _0)))
% Assm [h4s_totos_numu_u_dtOrdu_u_tupledu_u_primitive]: !_9. (!y_27. happ _9 y_27 = h4/combin/I h4/toto/GREATER) ==> (!_8. (!v1 _7 num__dtOrd__tupled x_27_27_27. happ (happ (happ (happ _8 v1) _7) num__dtOrd__tupled) x_27_27_27 = h4/toto/num__dt__CASE v1 (h4/combin/I h4/toto/GREATER) _9 (happ (happ _7 num__dtOrd__tupled) x_27_27_27)) ==> (!_7. (!num__dtOrd__tupled x_27_27 y_27_27. happ (happ (happ _7 num__dtOrd__tupled) x_27_27) y_27_27 = h4/combin/I (happ num__dtOrd__tupled (h4/pair/_2C x_27_27 y_27_27))) ==> (!_6. (!v1 num__dtOrd__tupled _5 x_27_27. happ (happ (happ (happ _6 v1) num__dtOrd__tupled) _5) x_27_27 = h4/toto/num__dt__CASE v1 (h4/combin/I h4/toto/GREATER) (happ (happ _7 num__dtOrd__tupled) x_27_27) _5) ==> (!_5. (!x. happ _5 x = h4/combin/I h4/toto/LESS) ==> (!_4. (!v num__dtOrd__tupled v1. happ (happ (happ _4 v) num__dtOrd__tupled) v1 = h4/toto/num__dt__CASE v (h4/toto/num__dt__CASE v1 (h4/combin/I h4/toto/EQUAL) _5 _5) (happ (happ (happ _6 v1) num__dtOrd__tupled) _5) (happ (happ (happ _8 v1) _7) num__dtOrd__tupled)) ==> (!_3. (!num__dtOrd__tupled v. happ (happ _3 num__dtOrd__tupled) v = happ (happ _4 v) num__dtOrd__tupled) ==> (!_2. (!num__dtOrd__tupled a. happ (happ _2 num__dtOrd__tupled) a = h4/pair/pair__CASE a (happ _3 num__dtOrd__tupled)) ==> (!_1. (!num__dtOrd__tupled. happ _1 num__dtOrd__tupled = happ _2 num__dtOrd__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!y x. happ (happ R (h4/pair/_2C x y)) (h4/pair/_2C (happ h4/toto/bit1 x) (happ h4/toto/bit1 y))) /\ (!y x. happ (happ R (h4/pair/_2C x y)) (h4/pair/_2C (happ h4/toto/bit2 x) (happ h4/toto/bit2 y)))) ==> h4/toto/num__dtOrd__tupled = h4/relation/WFREC (h4/min/_40 _0) _1)))))))))
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_totos_zer0]: h4/toto/zer = h4/toto/_20_40ind__typetoto0
% 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_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/toto/_20_40ind__typetoto0 = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% 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_totos_numu_u_dtu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27num__dt_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a _0) /\ happ _27num__dt_27 a) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a _0) /\ happ _27num__dt_27 a) ==> happ _27num__dt_27 a00) ==> happ _27num__dt_27 r) <=> h4/toto/_20_40ind__typetoto4 (h4/toto/_20_40ind__typetoto3 r) = r)
% Assm [h4s_totos_numu_u_dtOrd0u_c2]: !x. h4/toto/num__dtOrd h4/toto/zer (happ h4/toto/bit2 x) = h4/toto/LESS
% Assm [h4s_totos_numu_u_dtOrd0u_c1]: !x. h4/toto/num__dtOrd h4/toto/zer (happ h4/toto/bit1 x) = h4/toto/LESS
% Assm [h4s_totos_numu_u_dtOrd0u_c3]: !x. h4/toto/num__dtOrd (happ h4/toto/bit1 x) h4/toto/zer = h4/toto/GREATER
% Assm [h4s_totos_numu_u_dtOrd0u_c4]: !x. h4/toto/num__dtOrd (happ h4/toto/bit2 x) h4/toto/zer = h4/toto/GREATER
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_defu_c2]: !v f1 f a. h4/toto/num__dt__CASE (happ h4/toto/bit2 a) v f f1 = happ f1 a
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_defu_c1]: !v f1 f a. h4/toto/num__dt__CASE (happ h4/toto/bit1 a) v f f1 = happ f a
% Assm [h4s_totos_numu_u_dtu_u_nchotomy]: !nn. nn = h4/toto/zer \/ (?n. nn = happ h4/toto/bit1 n) \/ (?n. nn = happ h4/toto/bit2 n)
% Assm [h4s_totos_numu_u_dtu_u_Axiom]: !f2 f1 f0. ?fn. happ fn h4/toto/zer = f0 /\ (!a. happ fn (happ h4/toto/bit1 a) = happ (happ f1 a) (happ fn a)) /\ (!a. happ fn (happ h4/toto/bit2 a) = happ (happ f2 a) (happ fn a))
% Assm [h4s_totos_numu_u_dtu_u_distinctu_c2]: !a_27 a. ~(happ h4/toto/bit1 a = happ h4/toto/bit2 a_27)
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_cong]: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/toto/zer ==> v = v_27) /\ (!a. M_27 = happ h4/toto/bit1 a ==> happ f a = happ f_27 a) /\ (!a. M_27 = happ h4/toto/bit2 a ==> happ f1 a = happ f1_27 a) ==> h4/toto/num__dt__CASE M v f f1 = h4/toto/num__dt__CASE M_27 v_27 f_27 f1_27
% Assm [h4s_totos_numu_u_dtOrdu_u_ind]: !P. happ (happ P h4/toto/zer) h4/toto/zer /\ (!x. happ (happ P h4/toto/zer) (happ h4/toto/bit1 x)) /\ (!x. happ (happ P h4/toto/zer) (happ h4/toto/bit2 x)) /\ (!x. happ (happ P (happ h4/toto/bit1 x)) h4/toto/zer) /\ (!x. happ (happ P (happ h4/toto/bit2 x)) h4/toto/zer) /\ (!x y. happ (happ P (happ h4/toto/bit1 x)) (happ h4/toto/bit2 y)) /\ (!x y. happ (happ P (happ h4/toto/bit2 x)) (happ h4/toto/bit1 y)) /\ (!x y. happ (happ P x) y ==> happ (happ P (happ h4/toto/bit1 x)) (happ h4/toto/bit1 y)) /\ (!x y. happ (happ P x) y ==> happ (happ P (happ h4/toto/bit2 x)) (happ h4/toto/bit2 y)) ==> (!v v1. happ (happ P v) v1)
% Assm [h4s_totos_numu_u_dtu_u_induction]: !P. happ P h4/toto/zer /\ (!n. happ P n ==> happ P (happ h4/toto/bit1 n)) /\ (!n. happ P n ==> happ P (happ h4/toto/bit2 n)) ==> (!n. happ P n)
% Assm [h4s_totos_numu_u_dtOrdu_u_curried]: !x1 x. h4/toto/num__dtOrd x x1 = happ h4/toto/num__dtOrd__tupled (h4/pair/_2C x x1)
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_totos_numu_u_dtu_u_sizeu_u_defu_c1]: !a. h4/toto/num__dt__size (happ h4/toto/bit1 a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/toto/num__dt__size a)
% Assm [h4s_totos_numu_u_dtu_u_sizeu_u_defu_c2]: !a. h4/toto/num__dt__size (happ h4/toto/bit2 a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/toto/num__dt__size a)
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% 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_totos_datatypeu_u_numu_u_dt]: !num__dt. h4/bool/DATATYPE (happ (happ (happ num__dt h4/toto/zer) h4/toto/bit1) h4/toto/bit2)
% Assm [h4s_totos_numu_u_dtOrd0u_c0]: h4/toto/num__dtOrd h4/toto/zer h4/toto/zer = h4/toto/EQUAL
% Assm [h4s_totos_numu_u_dtu_u_11u_c0]: !a_27 a. happ h4/toto/bit1 a = happ h4/toto/bit1 a_27 <=> a = a_27
% Assm [h4s_totos_numu_u_dtu_u_distinctu_c1]: !a. ~(h4/toto/zer = happ h4/toto/bit2 a)
% Assm [h4s_totos_numu_u_dtu_u_11u_c1]: !a_27 a. happ h4/toto/bit2 a = happ h4/toto/bit2 a_27 <=> a = a_27
% Assm [h4s_totos_numu_u_dtu_u_distinctu_c0]: !a. ~(h4/toto/zer = happ h4/toto/bit1 a)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_defu_c0]: !v f1 f. h4/toto/num__dt__CASE h4/toto/zer v f f1 = v
% Assm [h4s_totos_numu_u_tou_u_dtu_u_primitive]: !_2. (!num__to__dt n. ?v. (v <=> n = h4/num/0) /\ happ (happ _2 num__to__dt) n = h4/combin/I (h4/bool/COND v h4/toto/zer (h4/bool/COND (h4/arithmetic/ODD n) (happ h4/toto/bit1 (happ num__to__dt (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (happ h4/toto/bit2 (happ num__to__dt (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))))))) ==> (!_1. (!num__to__dt. happ _1 num__to__dt = happ _2 num__to__dt) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!n. ~(n = h4/num/0) /\ h4/arithmetic/ODD n ==> happ (happ R (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) n) /\ (!n. ~(n = h4/num/0) /\ ~h4/arithmetic/ODD n ==> happ (happ R (h4/arithmetic/DIV2 (h4/arithmetic/_2D n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) n)) ==> h4/toto/num__to__dt = h4/relation/WFREC (h4/min/_40 _0) _1))
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. happ (happ h4/prim__rec/_3C h4/arithmetic/ZERO) (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% 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_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_totos_numu_u_dtu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0. happ _0 a0 <=> (!_27num__dt_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _1 \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a _1) /\ happ _27num__dt_27 a) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a _1) /\ happ _27num__dt_27 a) ==> happ _27num__dt_27 a00) ==> happ _27num__dt_27 a0)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_totos_totoLEtrans]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_totos_totoLLtrans]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_totos_totou_u_antisym]: !y x c. h4/toto/apto c x y = h4/toto/GREATER <=> h4/toto/apto c y x = h4/toto/LESS
% Assm [h4s_totos_totou_u_glnequ_c0]: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm [h4s_totos_totou_u_glnequ_c1]: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm [h4s_totos_totou_u_cpnu_u_eqnu_c1]: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm [h4s_totos_totoLGtrans]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_totos_cpnu_u_distinctu_c1]: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm [h4s_totos_totou_u_transu_u_lessu_c4]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_totos_aplextoto]: !y2 y1 x2 x1 v c. h4/toto/apto (h4/toto/lextoto c v) (h4/pair/_2C x1 x2) (h4/pair/_2C y1 y2) = h4/toto/cpn__CASE (h4/toto/apto c x1 y1) h4/toto/LESS (h4/toto/apto v x2 y2) h4/toto/GREATER
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% 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_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_relations_WFu_u_INDUCTIONu_u_THM]: !R. h4/relation/WF R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P x))
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_totos_cpnu_u_EQu_u_cpn]: !a_27 a. a = a_27 <=> h4/toto/cpn2num a = h4/toto/cpn2num a_27
% Assm [h4s_totos_cpn2numu_u_thmu_c2]: h4/toto/cpn2num h4/toto/GREATER = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_totos_cpn2numu_u_thmu_c0]: h4/toto/cpn2num h4/toto/LESS = h4/num/0
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% 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
% Goal: !y x. h4/toto/num__dtOrd (happ h4/toto/bit1 x) (happ h4/toto/bit2 y) = h4/toto/LESS
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_Q1345360,TV_Q1345356]: ![V_f, V_g]: (![V_x]: s(TV_Q1345356,happ(s(t_fun(TV_Q1345360,TV_Q1345356),V_f),s(TV_Q1345360,V_x))) = s(TV_Q1345356,happ(s(t_fun(TV_Q1345360,TV_Q1345356),V_g),s(TV_Q1345360,V_x))) => s(t_fun(TV_Q1345360,TV_Q1345356),V_f) = s(t_fun(TV_Q1345360,TV_Q1345356),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_totos_bit10, axiom, s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1) = s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto1)).
fof(ah4s_totos_bit20, axiom, s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2) = s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto2)).
fof(ah4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto2u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto2),s(t_h4s_totos_numu_u_dt,V_x))) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),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(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))))).
fof(ah4s_totos_numu_u_dtu_u_repfnsu_c0, axiom, ![V_a]: s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,V_a))))) = s(t_h4s_totos_numu_u_dt,V_a)).
fof(ah4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto1u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto1),s(t_h4s_totos_numu_u_dt,V_x))) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))))).
fof(ah4s_totos_numu_u_dtOrdu_u_tupledu_u_primitive, axiom, ![V_uu_9]: (![V_yu_27]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_9),s(t_h4s_totos_numu_u_dt,V_yu_27))) = s(t_h4s_totos_cpn,h4s_combins_i(s(t_h4s_totos_cpn,h4s_totos_greater))) => ![V_uu_8]: (![V_v1, V_uu_7, V_numu_u_dtOrdu_u_tupled, V_xu_27u_27u_27]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)))),V_uu_8),s(t_h4s_totos_numu_u_dt,V_v1))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_7))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_totos_numu_u_dt,V_xu_27u_27u_27))) = s(t_h4s_totos_cpn,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_v1),s(t_h4s_totos_cpn,h4s_combins_i(s(t_h4s_totos_cpn,h4s_totos_greater))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_9),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_totos_numu_u_dt,V_xu_27u_27u_27))))) => ![V_uu_7]: (![V_numu_u_dtOrdu_u_tupled, V_xu_27u_27, V_yu_27u_27]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_totos_numu_u_dt,V_xu_27u_27))),s(t_h4s_totos_numu_u_dt,V_yu_27u_27))) = s(t_h4s_totos_cpn,h4s_combins_i(s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_pairs_u_2c(s(t_h4s_totos_numu_u_dt,V_xu_27u_27),s(t_h4s_totos_numu_u_dt,V_yu_27u_27))))))) => ![V_uu_6]: (![V_v1, V_numu_u_dtOrdu_u_tupled, V_uu_5, V_xu_27u_27]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)))),V_uu_6),s(t_h4s_totos_numu_u_dt,V_v1))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_5))),s(t_h4s_totos_numu_u_dt,V_xu_27u_27))) = s(t_h4s_totos_cpn,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_v1),s(t_h4s_totos_cpn,h4s_combins_i(s(t_h4s_totos_cpn,h4s_totos_greater))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_totos_numu_u_dt,V_xu_27u_27))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_5))) => ![V_uu_5]: (![V_x]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_5),s(t_h4s_totos_numu_u_dt,V_x))) = s(t_h4s_totos_cpn,h4s_combins_i(s(t_h4s_totos_cpn,h4s_totos_less))) => ![V_uu_4]: (![V_v, V_numu_u_dtOrdu_u_tupled, V_v1]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_4),s(t_h4s_totos_numu_u_dt,V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_totos_numu_u_dt,V_v1))) = s(t_h4s_totos_cpn,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_v),s(t_h4s_totos_cpn,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_v1),s(t_h4s_totos_cpn,h4s_combins_i(s(t_h4s_totos_cpn,h4s_totos_equal))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_5),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_5))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)))),V_uu_6),s(t_h4s_totos_numu_u_dt,V_v1))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),V_uu_5))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)))),V_uu_8),s(t_h4s_totos_numu_u_dt,V_v1))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_7))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))))) => ![V_uu_3]: (![V_numu_u_dtOrdu_u_tupled, V_v]: s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_totos_numu_u_dt,V_v))) = s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_4),s(t_h4s_totos_numu_u_dt,V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))) => ![V_uu_2]: (![V_numu_u_dtOrdu_u_tupled, V_a]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),V_a))) = s(t_h4s_totos_cpn,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),V_a),s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_cpn))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))))) => ![V_uu_1]: (![V_numu_u_dtOrdu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),V_numu_u_dtOrdu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),V_R)))) & (![V_y, V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_pairs_u_2c(s(t_h4s_totos_numu_u_dt,V_x),s(t_h4s_totos_numu_u_dt,V_y))))),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_pairs_u_2c(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_y)))))))) & ![V_y, V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_pairs_u_2c(s(t_h4s_totos_numu_u_dt,V_x),s(t_h4s_totos_numu_u_dt,V_y))))),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_pairs_u_2c(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_y))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),h4s_totos_numu_u_dtordu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn)),V_uu_1)))))))))))))).
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_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_totos_zer0, axiom, s(t_h4s_totos_numu_u_dt,h4s_totos_zer) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto0)).
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_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto0u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto0) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))).
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_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_totos_numu_u_dtu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27numu_u_dtu_27]: (![V_a00]: ((s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))) | ?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),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(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),V_r))))) = s(t_h4s_indu_u_types_recspace(t_bool),V_r)))).
fof(ah4s_totos_numu_u_dtOrd0u_c2, axiom, ![V_x]: s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,h4s_totos_zer),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x))))) = s(t_h4s_totos_cpn,h4s_totos_less)).
fof(ah4s_totos_numu_u_dtOrd0u_c1, axiom, ![V_x]: s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,h4s_totos_zer),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))))) = s(t_h4s_totos_cpn,h4s_totos_less)).
fof(ah4s_totos_numu_u_dtOrd0u_c3, axiom, ![V_x]: s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))) = s(t_h4s_totos_cpn,h4s_totos_greater)).
fof(ah4s_totos_numu_u_dtOrd0u_c4, axiom, ![V_x]: s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))) = s(t_h4s_totos_cpn,h4s_totos_greater)).
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_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_totos_numu_u_dtu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1),s(t_h4s_totos_numu_u_dt,V_a)))).
fof(ah4s_totos_numu_u_dtu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_h4s_totos_numu_u_dt,V_a)))).
fof(ah4s_totos_numu_u_dtu_u_nchotomy, axiom, ![V_nn]: (s(t_h4s_totos_numu_u_dt,V_nn) = s(t_h4s_totos_numu_u_dt,h4s_totos_zer) | (?[V_n]: s(t_h4s_totos_numu_u_dt,V_nn) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_n))) | ?[V_n]: s(t_h4s_totos_numu_u_dt,V_nn) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_n)))))).
fof(ah4s_totos_numu_u_dtu_u_Axiom, axiom, ![TV_u_27a]: ![V_f2, V_f1, V_f0]: ?[V_fn]: (s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fn),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))) = s(TV_u_27a,V_f0) & (![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fn),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(TV_u_27a,TV_u_27a)),V_f1),s(t_h4s_totos_numu_u_dt,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fn),s(t_h4s_totos_numu_u_dt,V_a))))) & ![V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fn),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(TV_u_27a,TV_u_27a)),V_f2),s(t_h4s_totos_numu_u_dt,V_a))),s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fn),s(t_h4s_totos_numu_u_dt,V_a)))))))).
fof(ah4s_totos_numu_u_dtu_u_distinctu_c2, axiom, ![V_au_27, V_a]: ~ (s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_au_27))))).
fof(ah4s_totos_numu_u_dtu_u_caseu_u_cong, axiom, ![TV_u_27a]: ![V_vu_27, V_v, V_f1u_27, V_f1, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_totos_numu_u_dt,V_M) = s(t_h4s_totos_numu_u_dt,V_Mu_27) & ((s(t_h4s_totos_numu_u_dt,V_Mu_27) = s(t_h4s_totos_numu_u_dt,h4s_totos_zer) => s(TV_u_27a,V_v) = s(TV_u_27a,V_vu_27)) & (![V_a]: (s(t_h4s_totos_numu_u_dt,V_Mu_27) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_h4s_totos_numu_u_dt,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fu_27),s(t_h4s_totos_numu_u_dt,V_a)))) & ![V_a]: (s(t_h4s_totos_numu_u_dt,V_Mu_27) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1),s(t_h4s_totos_numu_u_dt,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1u_27),s(t_h4s_totos_numu_u_dt,V_a))))))) => s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_M),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_Mu_27),s(TV_u_27a,V_vu_27),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fu_27),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1u_27))))).
fof(ah4s_totos_numu_u_dtOrdu_u_ind, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))),s(t_h4s_totos_numu_u_dt,h4s_totos_zer)))) & (![V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x)))))) & (![V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x)))))) & (![V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))))),s(t_h4s_totos_numu_u_dt,h4s_totos_zer)))) & (![V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x))))),s(t_h4s_totos_numu_u_dt,h4s_totos_zer)))) & (![V_x, V_y]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_y)))))) & (![V_x, V_y]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x))))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_y)))))) & (![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,V_y)))) => p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_y))))))) & ![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,V_y)))) => p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_x))))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_y))))))))))))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_h4s_totos_numu_u_dt,t_bool)),V_P),s(t_h4s_totos_numu_u_dt,V_v))),s(t_h4s_totos_numu_u_dt,V_v1)))))).
fof(ah4s_totos_numu_u_dtu_u_induction, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),V_P),s(t_h4s_totos_numu_u_dt,h4s_totos_zer)))) & (![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),V_P),s(t_h4s_totos_numu_u_dt,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_n))))))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),V_P),s(t_h4s_totos_numu_u_dt,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),V_P),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_n))))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_bool),V_P),s(t_h4s_totos_numu_u_dt,V_n)))))).
fof(ah4s_totos_numu_u_dtOrdu_u_curried, axiom, ![V_x1, V_x]: s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,V_x),s(t_h4s_totos_numu_u_dt,V_x1))) = s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_h4s_totos_cpn),h4s_totos_numu_u_dtordu_u_tupled),s(t_h4s_pairs_prod(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_pairs_u_2c(s(t_h4s_totos_numu_u_dt,V_x),s(t_h4s_totos_numu_u_dt,V_x1)))))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_totos_numu_u_dtu_u_sizeu_u_defu_c1, axiom, ![V_a]: s(t_h4s_nums_num,h4s_totos_numu_u_dtu_u_size(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,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,h4s_totos_numu_u_dtu_u_size(s(t_h4s_totos_numu_u_dt,V_a)))))).
fof(ah4s_totos_numu_u_dtu_u_sizeu_u_defu_c2, axiom, ![V_a]: s(t_h4s_nums_num,h4s_totos_numu_u_dtu_u_size(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,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,h4s_totos_numu_u_dtu_u_size(s(t_h4s_totos_numu_u_dt,V_a)))))).
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_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_totos_datatypeu_u_numu_u_dt, axiom, ![V_numu_u_dt]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool),happ(s(t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool)),happ(s(t_fun(t_h4s_totos_numu_u_dt,t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_fun(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),t_bool))),V_numu_u_dt),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1))),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2))))))).
fof(ah4s_totos_numu_u_dtOrd0u_c0, axiom, s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,h4s_totos_zer),s(t_h4s_totos_numu_u_dt,h4s_totos_zer))) = s(t_h4s_totos_cpn,h4s_totos_equal)).
fof(ah4s_totos_numu_u_dtu_u_11u_c0, axiom, ![V_au_27, V_a]: (s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_au_27))) <=> s(t_h4s_totos_numu_u_dt,V_a) = s(t_h4s_totos_numu_u_dt,V_au_27))).
fof(ah4s_totos_numu_u_dtu_u_distinctu_c1, axiom, ![V_a]: ~ (s(t_h4s_totos_numu_u_dt,h4s_totos_zer) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))))).
fof(ah4s_totos_numu_u_dtu_u_11u_c1, axiom, ![V_au_27, V_a]: (s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_au_27))) <=> s(t_h4s_totos_numu_u_dt,V_a) = s(t_h4s_totos_numu_u_dt,V_au_27))).
fof(ah4s_totos_numu_u_dtu_u_distinctu_c0, axiom, ![V_a]: ~ (s(t_h4s_totos_numu_u_dt,h4s_totos_zer) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_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_totos_numu_u_dtu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f]: s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,h4s_totos_zer),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,V_v)).
fof(ah4s_totos_numu_u_tou_u_dtu_u_primitive, axiom, ![V_uu_2]: (![V_numu_u_tou_u_dt, V_n]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt)),V_uu_2),s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),V_numu_u_tou_u_dt))),s(t_h4s_nums_num,V_n))) = s(t_h4s_totos_numu_u_dt,h4s_combins_i(s(t_h4s_totos_numu_u_dt,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_totos_numu_u_dt,h4s_totos_zer),s(t_h4s_totos_numu_u_dt,h4s_bools_cond(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),V_numu_u_tou_u_dt),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),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_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),V_numu_u_tou_u_dt),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_zero)))))))))))))))))))) => ![V_uu_1]: (![V_numu_u_tou_u_dt]: s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt)),V_uu_1),s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),V_numu_u_tou_u_dt))) = s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt)),V_uu_2),s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),V_numu_u_tou_u_dt))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_R)))) & (![V_n]: ((~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n))))) => 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)),V_R),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,V_n))))) & ![V_n]: ((~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & ~ (p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,V_n)))))) => 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)),V_R),s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_zero))))))))))),s(t_h4s_nums_num,V_n)))))))) => s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),h4s_totos_numu_u_tou_u_dt) = s(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),h4s_relations_wfrec(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt),t_fun(t_h4s_nums_num,t_h4s_totos_numu_u_dt)),V_uu_1))))))).
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_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
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_arithmetics_NOTu_u_LESS, 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,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
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_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
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_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = 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,V_n)))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQ, 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,V_m))),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(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(TV_u_27a,V_x)).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),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(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
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_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_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_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_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_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_bools_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_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
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)),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_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_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(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)))))))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
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_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: 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),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),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_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (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_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),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))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_totos_numu_u_dtu_u_TYu_u_DEF, axiom, ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_bool),V_a0)))) <=> ![V_uu_27numu_u_dtu_27]: (![V_a00]: ((s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_1))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))) | ?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),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(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a0)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_0),s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_indu_u_types_recspace(t_bool)),V_rep))))))).
fof(ah4s_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_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_totos_totoLEtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_equal)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
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_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_totos_totoLLtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_totou_u_antisym, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_totou_u_glnequ_c0, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_glnequ_c1, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_cpnu_u_eqnu_c1, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totoLGtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_z),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_cpnu_u_distinctu_c1, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_greater))).
fof(ah4s_totos_totou_u_transu_u_lessu_c4, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_equal)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_aplextoto, axiom, ![TV_u_27a,TV_u_27b]: ![V_y2, V_y1, V_x2, V_x1, V_v, V_c]: s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_lextoto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(t_h4s_totos_toto(TV_u_27b),V_v))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(TV_u_27b,V_x2))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_y1),s(TV_u_27b,V_y2))))) = s(t_h4s_totos_cpn,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x1),s(TV_u_27a,V_y1))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27b),V_v),s(TV_u_27b,V_x2),s(TV_u_27b,V_y2))),s(t_h4s_totos_cpn,h4s_totos_greater)))).
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_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_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_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_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_q),s(TV_u_27b,V_r)))).
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_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_relations_WFu_u_INDUCTIONu_u_THM, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_P]: (![V_x]: (![V_y]: (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_y))),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,V_y))))) => 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_numerals_numeralu_u_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_c18, axiom, ![V_n]: (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_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_totos_cpnu_u_EQu_u_cpn, axiom, ![V_au_27, V_a]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,V_au_27) <=> s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))) = s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_au_27))))).
fof(ah4s_totos_cpn2numu_u_thmu_c2, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_greater))) = 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_totos_cpn2numu_u_thmu_c0, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_less))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(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_x)))).
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(ch4s_totos_numu_u_dtOrd0u_c5, conjecture, ![V_y, V_x]: s(t_h4s_totos_cpn,h4s_totos_numu_u_dtord(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_x))),s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_y))))) = s(t_h4s_totos_cpn,h4s_totos_less)).
