%   ORIGINAL: h4/state__transformer/JOIN__MAP
% 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/state__transformer/BIND__DEF: !g f. h4/state__transformer/BIND g f = h4/combin/o (h4/pair/UNCURRY f) g
% Assm: h4/state__transformer/MMAP__DEF: !m f. h4/state__transformer/MMAP f m = h4/state__transformer/BIND m (h4/combin/o h4/state__transformer/UNIT f)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/state__transformer/JOIN__DEF: !z. h4/state__transformer/JOIN z = h4/state__transformer/BIND z h4/combin/I
% Assm: h4/state__transformer/BIND__LEFT__UNIT: !x k. h4/state__transformer/BIND (h4/state__transformer/UNIT x) k = k x
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__EXT: !g f. (!x. f x = g x) ==> f = g
% Assm: h4/state__transformer/IGNORE__BIND__DEF: !g f. h4/state__transformer/IGNORE__BIND f g = h4/state__transformer/BIND f (\x. g)
% Assm: h4/state__transformer/JOIN__MAP__JOIN: h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP h4/state__transformer/JOIN) = h4/combin/o h4/state__transformer/JOIN h4/state__transformer/JOIN
% Assm: h4/state__transformer/MMAP__JOIN: !f. h4/combin/o (h4/state__transformer/MMAP f) h4/state__transformer/JOIN = h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP (h4/state__transformer/MMAP f))
% Assm: h4/state__transformer/JOIN__MMAP__UNIT: h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP h4/state__transformer/UNIT) = h4/combin/I
% Assm: h4/state__transformer/WIDEN__def: !f. h4/state__transformer/WIDEN f = h4/pair/UNCURRY (\s1 s2. h4/bool/LET (h4/pair/UNCURRY (\r s3. h4/pair/_2C r (h4/pair/_2C s1 s3))) (f s2))
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/state__transformer/BIND__ASSOC: !n m k. h4/state__transformer/BIND k (\a. h4/state__transformer/BIND (m a) n) = h4/state__transformer/BIND (h4/state__transformer/BIND k m) n
% Assm: h4/state__transformer/JOIN__UNIT: h4/combin/o h4/state__transformer/JOIN h4/state__transformer/UNIT = h4/combin/I
% Assm: h4/state__transformer/BIND__RIGHT__UNIT: !k. h4/state__transformer/BIND k h4/state__transformer/UNIT = k
% Assm: h4/state__transformer/MMAP__UNIT: !f. h4/combin/o (h4/state__transformer/MMAP f) h4/state__transformer/UNIT = h4/combin/o h4/state__transformer/UNIT f
% Assm: h4/state__transformer/MMAP__COMP: !g f. h4/state__transformer/MMAP (h4/combin/o f g) = h4/combin/o (h4/state__transformer/MMAP f) (h4/state__transformer/MMAP g)
% Assm: h4/state__transformer/MMAP__ID: h4/state__transformer/MMAP h4/combin/I = h4/combin/I
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/state__transformer/FOR__primitive__def: h4/state__transformer/FOR = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!a j i. ~(i = j) ==> R (h4/pair/_2C (h4/bool/COND (h4/prim__rec/_3C i j) (h4/arithmetic/_2B i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C j a)) (h4/pair/_2C i (h4/pair/_2C j a))))) (\FOR a_27. h4/pair/pair__CASE a_27 (\i v1. h4/pair/pair__CASE v1 (\j a. h4/combin/I (h4/bool/COND (i = j) (a i) (h4/state__transformer/BIND (a i) (\u. FOR (h4/pair/_2C (h4/bool/COND (h4/prim__rec/_3C i j) (h4/arithmetic/_2B i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C j a))))))))
% Assm: h4/state__transformer/MWHILE__DEF: !g b. h4/state__transformer/MWHILE g b = h4/state__transformer/BIND g (\gv. h4/bool/COND gv (h4/state__transformer/IGNORE__BIND b (h4/state__transformer/MWHILE g b)) (h4/state__transformer/UNIT h4/one/one0))
% Assm: h4/state__transformer/sequence__def: h4/state__transformer/sequence = h4/list/FOLDR (\m ms. h4/state__transformer/BIND m (\x. h4/state__transformer/BIND ms (\xs. h4/state__transformer/UNIT (h4/list/CONS x xs)))) (h4/state__transformer/UNIT h4/list/NIL)
% Assm: h4/state__transformer/FOR__def: !j i a. h4/state__transformer/FOR (h4/pair/_2C i (h4/pair/_2C j a)) = h4/bool/COND (i = j) (a i) (h4/state__transformer/BIND (a i) (\u. h4/state__transformer/FOR (h4/pair/_2C (h4/bool/COND (h4/prim__rec/_3C i j) (h4/arithmetic/_2B i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C j a))))
% Assm: h4/combin/K__DEF: h4/combin/K = (\x y. x)
% Assm: h4/combin/S__DEF: h4/combin/S = (\f g x. f x (g x))
% Assm: h4/combin/I__DEF: h4/combin/I = h4/combin/S h4/combin/K h4/combin/K
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/state__transformer/UNIT__UNCURRY: !s. h4/pair/UNCURRY h4/state__transformer/UNIT s = s
% Assm: h4/state__transformer/UNIT__DEF: !x. h4/state__transformer/UNIT x = (\s. h4/pair/_2C x s)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% 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/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% 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/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> 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/FALSITY: !t. F ==> t
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/while/LEAST__ELIM: !Q P. (?n. P n) /\ (!n. (!m. h4/prim__rec/_3C m n ==> ~P m) /\ P n ==> Q n) ==> Q (h4/while/LEAST P)
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/bool/SKOLEM__THM: !P. (!x. ?y. P x y) <=> (?f. !x. P x (f x))
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/arithmetic/FUNPOW__0: !x f. h4/arithmetic/FUNPOW f h4/num/0 x = x
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/arithmetic/num__CASES: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Assm: h4/arithmetic/LESS__MONO__EQ: !n m. h4/prim__rec/_3C (h4/num/SUC m) (h4/num/SUC n) <=> h4/prim__rec/_3C m n
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/arithmetic/FUNPOW0_c1: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = h4/arithmetic/FUNPOW f n (f x)
% Assm: h4/prim__rec/INV__SUC__EQ: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/combin/GEN__LET__RAND: !v f P. P (h4/bool/LET f v) = h4/bool/LET (h4/combin/o P f) v
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/combin/C__ABS__L: !y f. h4/combin/C (\x. f x) y = (\x. f x y)
% Assm: h4/combin/C__THM: !y x f. h4/combin/C f x y = f y x
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/combin/S__ABS__R: !g f. h4/combin/S f (\x. g x) = (\x. f x (g x))
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/combin/GEN__LET__RATOR: !x v f. h4/bool/LET f v x = h4/bool/LET (h4/combin/C f x) v
% Assm: h4/combin/LET__FORALL__ELIM: !v f. h4/bool/LET f v <=> $forall (h4/combin/S (h4/combin/o $imply (h4/combin/o h4/marker/Abbrev (h4/combin/C $equals v))) f)
% Assm: h4/bool/NOT__IMP: !B A. ~(A ==> B) <=> A /\ ~B
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/combin/o__ABS__R: !g f. h4/combin/o f (\x. g x) = (\x. f (g x))
% Assm: h4/bool/EXISTS__REFL: !a. ?x. x = a
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/marker/Cong__def: !x. h4/marker/Cong x <=> x
% Assm: h4/pair/pair__CASES: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/numeral/numeral__add_c6: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm: h4/numeral/numeral__add_c4: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__add_c3: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__suc_c0: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm: h4/arithmetic/SUB__RIGHT__LESS: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm: h4/arithmetic/SUB__LEFT__LESS: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/SUB__LEFT__SUB: !p n m. h4/arithmetic/_2D m (h4/arithmetic/_2D n p) = h4/bool/COND (h4/arithmetic/_3C_3D n p) m (h4/arithmetic/_2D (h4/arithmetic/_2B m p) n)
% Assm: h4/arithmetic/SUB__RIGHT__SUB: !p n m. h4/arithmetic/_2D (h4/arithmetic/_2D m n) p = h4/arithmetic/_2D m (h4/arithmetic/_2B n p)
% Assm: h4/arithmetic/SUB__RIGHT__ADD: !p n m. h4/arithmetic/_2B (h4/arithmetic/_2D m n) p = h4/bool/COND (h4/arithmetic/_3C_3D m n) p (h4/arithmetic/_2D (h4/arithmetic/_2B m p) n)
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/TIMES2: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm: h4/arithmetic/MULT__ASSOC: !p n m. h4/arithmetic/_2A m (h4/arithmetic/_2A n p) = h4/arithmetic/_2A (h4/arithmetic/_2A m n) p
% Assm: h4/arithmetic/LEFT__ADD__DISTRIB: !p n m. h4/arithmetic/_2A p (h4/arithmetic/_2B m n) = h4/arithmetic/_2B (h4/arithmetic/_2A p m) (h4/arithmetic/_2A p n)
% Goal: !m k. h4/state__transformer/BIND k m = h4/state__transformer/JOIN (h4/state__transformer/MMAP m k)
%   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_stateu_u_transformers_BINDu_u_DEF]: !g f. h4/state__transformer/BIND g f = h4/combin/o (h4/pair/UNCURRY f) g
% Assm [h4s_stateu_u_transformers_MMAPu_u_DEF]: !m f. happ (h4/state__transformer/MMAP f) m = h4/state__transformer/BIND m (h4/combin/o h4/state__transformer/UNIT f)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_stateu_u_transformers_JOINu_u_DEF]: !z. happ h4/state__transformer/JOIN z = h4/state__transformer/BIND z h4/combin/I
% Assm [h4s_stateu_u_transformers_BINDu_u_LEFTu_u_UNIT]: !x k. h4/state__transformer/BIND (happ h4/state__transformer/UNIT x) k = happ k x
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_EXT]: !g f. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_stateu_u_transformers_IGNOREu_u_BINDu_u_DEF]: !_0. (!g x. happ (happ _0 g) x = g) ==> (!g f. h4/state__transformer/IGNORE__BIND f g = h4/state__transformer/BIND f (happ _0 g))
% Assm [h4s_stateu_u_transformers_JOINu_u_MAPu_u_JOIN]: h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP h4/state__transformer/JOIN) = h4/combin/o h4/state__transformer/JOIN h4/state__transformer/JOIN
% Assm [h4s_stateu_u_transformers_MMAPu_u_JOIN]: !f. h4/combin/o (h4/state__transformer/MMAP f) h4/state__transformer/JOIN = h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP (h4/state__transformer/MMAP f))
% Assm [h4s_stateu_u_transformers_JOINu_u_MMAPu_u_UNIT]: h4/combin/o h4/state__transformer/JOIN (h4/state__transformer/MMAP h4/state__transformer/UNIT) = h4/combin/I
% Assm [h4s_stateu_u_transformers_WIDENu_u_def]: !_3. (!r s1 s3. happ (happ (happ _3 r) s1) s3 = h4/pair/_2C r (h4/pair/_2C s1 s3)) ==> (!_2. (!s1 r. happ (happ _2 s1) r = happ (happ _3 r) s1) ==> (!_1. (!s1 f s2. happ (happ (happ _1 s1) f) s2 = h4/bool/LET (h4/pair/UNCURRY (happ _2 s1)) (happ f s2)) ==> (!_0. (!f s1. happ (happ _0 f) s1 = happ (happ _1 s1) f) ==> (!f. h4/state__transformer/WIDEN f = h4/pair/UNCURRY (happ _0 f)))))
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_combins_Iu_u_THM]: !x. happ h4/combin/I x = x
% Assm [h4s_stateu_u_transformers_BINDu_u_ASSOC]: !_0. (!m n a. happ (happ (happ _0 m) n) a = h4/state__transformer/BIND (happ m a) n) ==> (!n m k. h4/state__transformer/BIND k (happ (happ _0 m) n) = h4/state__transformer/BIND (h4/state__transformer/BIND k m) n)
% Assm [h4s_stateu_u_transformers_JOINu_u_UNIT]: h4/combin/o h4/state__transformer/JOIN h4/state__transformer/UNIT = h4/combin/I
% Assm [h4s_stateu_u_transformers_BINDu_u_RIGHTu_u_UNIT]: !k. h4/state__transformer/BIND k h4/state__transformer/UNIT = k
% Assm [h4s_stateu_u_transformers_MMAPu_u_UNIT]: !f. h4/combin/o (h4/state__transformer/MMAP f) h4/state__transformer/UNIT = h4/combin/o h4/state__transformer/UNIT f
% Assm [h4s_stateu_u_transformers_MMAPu_u_COMP]: !g f. h4/state__transformer/MMAP (h4/combin/o f g) = h4/combin/o (h4/state__transformer/MMAP f) (h4/state__transformer/MMAP g)
% Assm [h4s_stateu_u_transformers_MMAPu_u_ID]: h4/state__transformer/MMAP h4/combin/I = h4/combin/I
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_stateu_u_transformers_FORu_u_primitiveu_u_def]: !_7. (!FOR i j a u. happ (happ (happ (happ (happ _7 FOR) i) j) a) u = happ FOR (h4/pair/_2C (h4/bool/COND (h4/prim__rec/_3C i j) (h4/arithmetic/_2B i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C j a))) ==> (!_6. (!FOR i j a. ?v. (v <=> i = j) /\ happ (happ (happ (happ _6 FOR) i) j) a = happ h4/combin/I (h4/bool/COND v (happ a i) (h4/state__transformer/BIND (happ a i) (happ (happ (happ (happ _7 FOR) i) j) a)))) ==> (!_5. (!FOR i j. happ (happ (happ _5 FOR) i) j = happ (happ (happ _6 FOR) i) j) ==> (!_4. (!FOR i v1. happ (happ (happ _4 FOR) i) v1 = h4/pair/pair__CASE v1 (happ (happ _5 FOR) i)) ==> (!_3. (!FOR i. happ (happ _3 FOR) i = happ (happ _4 FOR) i) ==> (!_2. (!FOR a_27. happ (happ _2 FOR) a_27 = h4/pair/pair__CASE a_27 (happ _3 FOR)) ==> (!_1. (!FOR. happ _1 FOR = happ _2 FOR) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!a j i. ~(i = j) ==> happ (happ R (h4/pair/_2C (h4/bool/COND (h4/prim__rec/_3C i j) (h4/arithmetic/_2B i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C j a))) (h4/pair/_2C i (h4/pair/_2C j a)))) ==> h4/state__transformer/FOR = h4/relation/WFREC (h4/min/_40 _0) _1)))))))
% Assm [h4s_stateu_u_transformers_MWHILEu_u_DEF]: !_0. (!g b gv. happ (happ (happ _0 g) b) gv = h4/bool/COND gv (h4/state__transformer/IGNORE__BIND b (h4/state__transformer/MWHILE g b)) (happ h4/state__transformer/UNIT h4/one/one0)) ==> (!g b. h4/state__transformer/MWHILE g b = h4/state__transformer/BIND g (happ (happ _0 g) b))
% Assm [h4s_stateu_u_transformers_sequenceu_u_def]: !_3. (!x xs. happ (happ _3 x) xs = happ h4/state__transformer/UNIT (h4/list/CONS x xs)) ==> (!_2. (!ms x. happ (happ _2 ms) x = h4/state__transformer/BIND ms (happ _3 x)) ==> (!_1. (!m ms. happ (happ _1 m) ms = h4/state__transformer/BIND m (happ _2 ms)) ==> (!_0. (!m. happ _0 m = happ _1 m) ==> h4/state__transformer/sequence = h4/list/FOLDR _0 (happ h4/state__transformer/UNIT h4/list/NIL))))
% Assm [h4s_stateu_u_transformers_FORu_u_def]: !_0. (!i j a u. happ (happ (happ (happ _0 i) j) a) u = happ h4/state__transformer/FOR (h4/pair/_2C (h4/bool/COND (h4/prim__rec/_3C i j) (h4/arithmetic/_2B i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/_2D i (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C j a))) ==> (!j i a. ?v. (v <=> i = j) /\ happ h4/state__transformer/FOR (h4/pair/_2C i (h4/pair/_2C j a)) = h4/bool/COND v (happ a i) (h4/state__transformer/BIND (happ a i) (happ (happ (happ _0 i) j) a)))
% Assm [h4s_combins_Ku_u_DEF]: !x x. happ (happ h4/combin/K x) x = x
% Assm [h4s_combins_Su_u_DEF]: !x x x. happ (h4/combin/S x x) x = happ (happ x x) (happ x x)
% Assm [h4s_combins_Iu_u_DEF]: h4/combin/I = h4/combin/S h4/combin/K h4/combin/K
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_stateu_u_transformers_UNITu_u_UNCURRY]: !s. happ (h4/pair/UNCURRY h4/state__transformer/UNIT) s = s
% Assm [h4s_stateu_u_transformers_UNITu_u_DEF]: !x x. happ (happ h4/state__transformer/UNIT x) x = h4/pair/_2C x x
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% 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_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% 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_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% 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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% 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_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> 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_FALSITY]: !t. F ==> t
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% 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_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_whiles_LEASTu_u_ELIM]: !Q P. (?n. happ P n) /\ (!n. (!m. h4/prim__rec/_3C m n ==> ~happ P m) /\ happ P n ==> happ Q n) ==> happ Q (h4/while/LEAST P)
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_bools_SKOLEMu_u_THM]: !P. (!x. ?y. happ (happ P x) y) <=> (?f. !x. happ (happ P x) (happ f x))
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_arithmetics_FUNPOWu_u_0]: !x f. h4/arithmetic/FUNPOW f h4/num/0 x = x
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_arithmetics_numu_u_CASES]: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_EQ]: !n m. h4/prim__rec/_3C (h4/num/SUC m) (h4/num/SUC n) <=> h4/prim__rec/_3C m n
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_arithmetics_FUNPOW0u_c1]: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = h4/arithmetic/FUNPOW f n (happ f x)
% Assm [h4s_primu_u_recs_INVu_u_SUCu_u_EQ]: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_combins_GENu_u_LETu_u_RAND]: !v f P. happ P (h4/bool/LET f v) = h4/bool/LET (h4/combin/o P f) v
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_combins_Cu_u_ABSu_u_L]: !_0. (!f x. happ (happ _0 f) x = happ f x) ==> (!y f x. happ (h4/combin/C (happ _0 f) y) x = happ (happ f x) y)
% Assm [h4s_combins_Cu_u_THM]: !y x f. happ (h4/combin/C f x) y = happ (happ f y) x
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_combins_Su_u_ABSu_u_R]: !_0. (!g x. happ (happ _0 g) x = happ g x) ==> (!g f x. happ (h4/combin/S f (happ _0 g)) x = happ (happ f x) (happ g x))
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_combins_GENu_u_LETu_u_RATOR]: !x v f. happ (h4/bool/LET f v) x = h4/bool/LET (h4/combin/C f x) v
% Assm [h4s_combins_LETu_u_FORALLu_u_ELIM]: !v f. h4/bool/LET f v <=> $forall (h4/combin/S (h4/combin/o $imply (h4/combin/o h4/marker/Abbrev (h4/combin/C $equals v))) f)
% Assm [h4s_bools_NOTu_u_IMP]: !B A. ~(A ==> B) <=> A /\ ~B
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_combins_ou_u_ABSu_u_R]: !_0. (!g x. happ (happ _0 g) x = happ g x) ==> (!g f x. happ (h4/combin/o f (happ _0 g)) x = happ f (happ g x))
% Assm [h4s_bools_EXISTSu_u_REFL]: !a. ?x. x = a
% Assm [h4s_markers_Abbrevu_u_def]: !x. happ h4/marker/Abbrev x <=> x
% Assm [h4s_markers_Congu_u_def]: !x. h4/marker/Cong x <=> x
% Assm [h4s_pairs_pairu_u_CASES]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_numerals_numeralu_u_addu_c6]: !n. h4/num/SUC (h4/arithmetic/_2B h4/arithmetic/ZERO n) = h4/num/SUC n
% Assm [h4s_numerals_numeralu_u_addu_c4]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_addu_c3]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m)) = h4/arithmetic/BIT1 (h4/num/SUC (h4/arithmetic/_2B n m))
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_sucu_c0]: h4/num/SUC h4/arithmetic/ZERO = h4/arithmetic/BIT1 h4/arithmetic/ZERO
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESS]: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2D m n) p <=> h4/prim__rec/_3C m (h4/arithmetic/_2B n p) /\ h4/prim__rec/_3C h4/num/0 p
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESS]: !p n m. h4/prim__rec/_3C m (h4/arithmetic/_2D n p) <=> h4/prim__rec/_3C (h4/arithmetic/_2B m p) n
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_SUB]: !p n m. h4/arithmetic/_2D m (h4/arithmetic/_2D n p) = h4/bool/COND (h4/arithmetic/_3C_3D n p) m (h4/arithmetic/_2D (h4/arithmetic/_2B m p) n)
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_SUB]: !p n m. h4/arithmetic/_2D (h4/arithmetic/_2D m n) p = h4/arithmetic/_2D m (h4/arithmetic/_2B n p)
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_ADD]: !p n m. h4/arithmetic/_2B (h4/arithmetic/_2D m n) p = h4/bool/COND (h4/arithmetic/_3C_3D m n) p (h4/arithmetic/_2D (h4/arithmetic/_2B m p) n)
% Assm [h4s_arithmetics_NOTu_u_LEQ]: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_TIMES2]: !n. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n = h4/arithmetic/_2B n n
% Assm [h4s_arithmetics_MULTu_u_ASSOC]: !p n m. h4/arithmetic/_2A m (h4/arithmetic/_2A n p) = h4/arithmetic/_2A (h4/arithmetic/_2A m n) p
% Assm [h4s_arithmetics_LEFTu_u_ADDu_u_DISTRIB]: !p n m. h4/arithmetic/_2A p (h4/arithmetic/_2B m n) = h4/arithmetic/_2B (h4/arithmetic/_2A p m) (h4/arithmetic/_2A p n)
% Goal: !m k. h4/state__transformer/BIND k m = happ h4/state__transformer/JOIN (happ (h4/state__transformer/MMAP m) k)
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_Q1448488,TV_Q1448484]: ![V_f, V_g]: (![V_x]: s(TV_Q1448484,happ(s(t_fun(TV_Q1448488,TV_Q1448484),V_f),s(TV_Q1448488,V_x))) = s(TV_Q1448484,happ(s(t_fun(TV_Q1448488,TV_Q1448484),V_g),s(TV_Q1448488,V_x))) => s(t_fun(TV_Q1448488,TV_Q1448484),V_f) = s(t_fun(TV_Q1448488,TV_Q1448484),V_g))).
fof(ah4s_stateu_u_transformers_BINDu_u_DEF, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_g, V_f]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_f))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_combins_o(s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_pairs_uncurry(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_f))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g)))).
fof(ah4s_stateu_u_transformers_MMAPu_u_DEF, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_m, V_f]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),V_m))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),V_m),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_o(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_unit),s(t_fun(TV_u_27c,TV_u_27b),V_f)))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_combins_ou_u_DEF, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x)))))).
fof(ah4s_stateu_u_transformers_JOINu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_z]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),V_z))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),V_z),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_i)))).
fof(ah4s_stateu_u_transformers_BINDu_u_LEFTu_u_UNIT, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_x, V_k]: s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_stateu_u_transformers_unit),s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_k))) = s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27c,TV_u_27b))),V_k),s(TV_u_27a,V_x)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_EXT, axiom, ![TV_u_27a,TV_u_27b]: ![V_g, V_f]: (![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),V_g),s(TV_u_27a,V_x))) => s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g))).
fof(ah4s_stateu_u_transformers_IGNOREu_u_BINDu_u_DEF, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_g, V_x]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g))),s(TV_u_27c,V_x))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g) => ![V_g, V_f]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_ignoreu_u_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),V_f),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),V_f),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_g))))))).
fof(ah4s_stateu_u_transformers_JOINu_u_MAPu_u_JOIN, axiom, ![TV_u_27b,TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join))))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_join)))).
fof(ah4s_stateu_u_transformers_MMAPu_u_JOIN, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_f]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,TV_u_27c),V_f))),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,TV_u_27c),V_f)))))))).
fof(ah4s_stateu_u_transformers_JOINu_u_MMAPu_u_UNIT, axiom, ![TV_u_27b,TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_unit))))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_i)).
fof(ah4s_stateu_u_transformers_WIDENu_u_def, axiom, ![TV_u_27b,TV_u_27a,TV_u_27state]: ![V_uu_3]: (![V_r, V_s1, V_s3]: s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)),happ(s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_3),s(TV_u_27a,V_r))),s(TV_u_27b,V_s1))),s(TV_u_27state,V_s3))) = s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)),h4s_pairs_u_2c(s(TV_u_27a,V_r),s(t_h4s_pairs_prod(TV_u_27b,TV_u_27state),h4s_pairs_u_2c(s(TV_u_27b,V_s1),s(TV_u_27state,V_s3))))) => ![V_uu_2]: (![V_s1, V_r]: s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_2),s(TV_u_27b,V_s1))),s(TV_u_27a,V_r))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_3),s(TV_u_27a,V_r))),s(TV_u_27b,V_s1))) => ![V_uu_1]: (![V_s1, V_f, V_s2]: s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)),happ(s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),happ(s(t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_1),s(TV_u_27b,V_s1))),s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),V_f))),s(TV_u_27state,V_s2))) = s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27state),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_2),s(TV_u_27b,V_s1))))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27state),happ(s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),V_f),s(TV_u_27state,V_s2))))) => ![V_uu_0]: (![V_f, V_s1]: s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_0),s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),V_f))),s(TV_u_27b,V_s1))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),happ(s(t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(TV_u_27b,t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_1),s(TV_u_27b,V_s1))),s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),V_f))) => ![V_f]: s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27state),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),h4s_stateu_u_transformers_widen(s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),V_f))) = s(t_fun(t_h4s_pairs_prod(TV_u_27b,TV_u_27state),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))),h4s_pairs_uncurry(s(t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state)))),happ(s(t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),t_fun(TV_u_27b,t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27state))))),V_uu_0),s(t_fun(TV_u_27state,t_h4s_pairs_prod(TV_u_27a,TV_u_27state)),V_f)))))))))).
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_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_stateu_u_transformers_BINDu_u_ASSOC, axiom, ![TV_u_27b,TV_u_27c,TV_u_27d,TV_u_27a]: ![V_uu_0]: (![V_m, V_n, V_a]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))))),V_uu_0),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))),s(TV_u_27b,V_a))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m),s(TV_u_27b,V_a))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))) => ![V_n, V_m, V_k]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),t_fun(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))))),V_uu_0),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),V_n))))).
fof(ah4s_stateu_u_transformers_JOINu_u_UNIT, axiom, ![TV_u_27b,TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_unit))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_i)).
fof(ah4s_stateu_u_transformers_BINDu_u_RIGHTu_u_UNIT, axiom, ![TV_u_27b,TV_u_27a]: ![V_k]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_unit))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k)).
fof(ah4s_stateu_u_transformers_MMAPu_u_UNIT, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_f]: s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,TV_u_27c),V_f))),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_unit))) = s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_combins_o(s(t_fun(TV_u_27c,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_unit),s(t_fun(TV_u_27b,TV_u_27c),V_f)))).
fof(ah4s_stateu_u_transformers_MMAPu_u_COMP, axiom, ![TV_u_27d,TV_u_27a,TV_u_27b,TV_u_27c]: ![V_g, V_f]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,TV_u_27d),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27d),V_f),s(t_fun(TV_u_27b,TV_u_27c),V_g))))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),h4s_combins_o(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27d,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27c,TV_u_27d),V_f))),s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,TV_u_27c),V_g)))))).
fof(ah4s_stateu_u_transformers_MMAPu_u_ID, axiom, ![TV_u_27b,TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,TV_u_27b),h4s_combins_i))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_combins_i)).
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_stateu_u_transformers_FORu_u_primitiveu_u_def, axiom, ![TV_u_27state]: ![V_uu_7]: (![V_FOR, V_i, V_j, V_a, V_u]: s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))),s(t_h4s_ones_one,V_u))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_j))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),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_arithmetics_u_2d(s(t_h4s_nums_num,V_i),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_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_j),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))))))) => ![V_uu_6]: (![V_FOR, V_i, V_j, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_i) = s(t_h4s_nums_num,V_j)) & s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),h4s_combins_i),s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),h4s_bools_cond(s(t_bool,V_v),s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a),s(t_h4s_nums_num,V_i))),s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a),s(t_h4s_nums_num,V_i))),s(t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a)))))))))) => ![V_uu_5]: (![V_FOR, V_i, V_j]: s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))) = s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))) => ![V_uu_4]: (![V_FOR, V_i, V_v1]: s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),V_v1))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),V_v1),s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))))) => ![V_uu_3]: (![V_FOR, V_i]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_nums_num,V_i))) => ![V_uu_2]: (![V_FOR, V_au_27]: s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),V_au_27))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),V_au_27),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))))) => ![V_uu_1]: (![V_FOR]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_FOR))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool)),V_R)))) & ![V_a, V_j, V_i]: (~ (s(t_h4s_nums_num,V_i) = s(t_h4s_nums_num,V_j)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_j))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),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_arithmetics_u_2d(s(t_h4s_nums_num,V_i),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_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_j),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_j),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),h4s_stateu_u_transformers_for) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),V_uu_1)))))))))))).
fof(ah4s_stateu_u_transformers_MWHILEu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_g, V_b, V_gv]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_bool,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_bool,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a))))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),V_g))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_b))),s(t_bool,V_gv))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),h4s_bools_cond(s(t_bool,V_gv),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),h4s_stateu_u_transformers_ignoreu_u_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_b),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),h4s_stateu_u_transformers_mwhile(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),V_g),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_b))))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),happ(s(t_fun(t_h4s_ones_one,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a))),h4s_stateu_u_transformers_unit),s(t_h4s_ones_one,h4s_ones_one0))))) => ![V_g, V_b]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),h4s_stateu_u_transformers_mwhile(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),V_g),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_b))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),V_g),s(t_fun(t_bool,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_bool,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a)))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_bool,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27a))))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_bool,TV_u_27a)),V_g))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_b))))))).
fof(ah4s_stateu_u_transformers_sequenceu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_3]: (![V_x, V_xs]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_3),s(TV_u_27b,V_x))),s(t_h4s_lists_list(TV_u_27b),V_xs))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),h4s_stateu_u_transformers_unit),s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,V_x),s(t_h4s_lists_list(TV_u_27b),V_xs))))) => ![V_uu_2]: (![V_ms, V_x]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_2),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms))),s(TV_u_27b,V_x))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms),s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_3),s(TV_u_27b,V_x))))) => ![V_uu_1]: (![V_m, V_ms]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_2),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),V_ms))))) => ![V_uu_0]: (![V_m]: s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m))) = s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_m))) => s(t_fun(t_h4s_lists_list(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),h4s_stateu_u_transformers_sequence) = s(t_fun(t_h4s_lists_list(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),h4s_lists_foldr(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),TV_u_27a))),h4s_stateu_u_transformers_unit),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))))))))).
fof(ah4s_stateu_u_transformers_FORu_u_def, axiom, ![TV_u_27state]: ![V_uu_0]: (![V_i, V_j, V_a, V_u]: s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),V_uu_0),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))),s(t_h4s_ones_one,V_u))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),h4s_stateu_u_transformers_for),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_j))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),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_arithmetics_u_2d(s(t_h4s_nums_num,V_i),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_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_j),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))))))) => ![V_j, V_i, V_a]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_i) = s(t_h4s_nums_num,V_j)) & s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),h4s_stateu_u_transformers_for),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_i),s(t_h4s_pairs_prod(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_j),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a))))))) = s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),h4s_bools_cond(s(t_bool,V_v),s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a),s(t_h4s_nums_num,V_i))),s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a),s(t_h4s_nums_num,V_i))),s(t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),t_fun(t_h4s_ones_one,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state)))))),V_uu_0),s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_j))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27state,t_h4s_pairs_prod(t_h4s_ones_one,TV_u_27state))),V_a)))))))))).
fof(ah4s_combins_Ku_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),h4s_combins_k),s(TV_u_27a,V_x))),s(TV_u_27b,V_x0))) = s(TV_u_27a,V_x)).
fof(ah4s_combins_Su_u_DEF, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_x, V_x0, V_x1]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_x),s(t_fun(TV_u_27a,TV_u_27b),V_x0))),s(TV_u_27a,V_x1))) = 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_x),s(TV_u_27a,V_x1))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x0),s(TV_u_27a,V_x1)))))).
fof(ah4s_combins_Iu_u_DEF, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i) = s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27a),TV_u_27a)),h4s_combins_k),s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27a)),h4s_combins_k)))).
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,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),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_stateu_u_transformers_UNITu_u_UNCURRY, axiom, ![TV_u_27a,TV_u_27b]: ![V_s]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_stateu_u_transformers_unit))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_s))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_s)).
fof(ah4s_stateu_u_transformers_UNITu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a))),h4s_stateu_u_transformers_unit),s(TV_u_27b,V_x))),s(TV_u_27a,V_x0))) = s(t_h4s_pairs_prod(TV_u_27b,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27a,V_x0)))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_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_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_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_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_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, 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_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_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (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,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
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_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_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_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
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_bools_CONJu_u_ASSOC, 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_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_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_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(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_27b,V_y)).
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_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_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_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_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_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> 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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_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_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_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_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_whiles_LEASTu_u_ELIM, axiom, ![V_Q, V_P]: ((?[V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) & ![V_n]: ((![V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) => ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_m)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_Q),s(t_h4s_nums_num,V_n)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_Q),s(t_h4s_nums_num,h4s_whiles_least(s(t_fun(t_h4s_nums_num,t_bool),V_P)))))))).
fof(ah4s_bools_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![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),V_g),s(TV_u_27a,V_x))))).
fof(ah4s_bools_SKOLEMu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (![V_x]: ?[V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))) <=> ?[V_f]: ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),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_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_FUNPOWu_u_0, axiom, ![TV_u_27a]: ![V_x, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_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_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_arithmetics_numu_u_CASES, axiom, ![V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0) | ?[V_n]: s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_LESSu_u_MONOu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_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_arithmetics_FUNPOW0u_c1, axiom, ![TV_u_27a]: ![V_x, V_n, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_x))) = s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,V_n),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_x)))))).
fof(ah4s_primu_u_recs_INVu_u_SUCu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
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_combins_GENu_u_LETu_u_RAND, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_v, V_f, V_P]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_P),s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,V_v))))) = s(TV_u_27a,h4s_bools_let(s(t_fun(TV_u_27c,TV_u_27a),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27a),V_P),s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(TV_u_27c,V_v)))).
fof(ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_combins_Cu_u_ABSu_u_L, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_uu_0]: (![V_f, V_x]: s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(TV_u_27a,V_x))) => ![V_y, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f))),s(TV_u_27c,V_y))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27c,V_y))))).
fof(ah4s_combins_Cu_u_THM, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27b,V_x))),s(TV_u_27a,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_y))),s(TV_u_27b,V_x)))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_combins_Su_u_ABSu_u_R, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_0]: (![V_g, V_x]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))) => ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_bools_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_combins_GENu_u_LETu_u_RATOR, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_x, V_v, V_f]: s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),h4s_bools_let(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_v))),s(TV_u_27c,V_x))) = s(TV_u_27a,h4s_bools_let(s(t_fun(TV_u_27b,TV_u_27a),h4s_combins_c(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27c,V_x))),s(TV_u_27b,V_v)))).
fof(ah4s_combins_LETu_u_FORALLu_u_ELIM, axiom, ![TV_u_27a]: ![V_v, V_f]: s(t_bool,h4s_bools_let(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_v))) = s(t_bool,d_forall(s(t_fun(TV_u_27a,t_bool),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),h4s_combins_o(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_imply),s(t_fun(TV_u_27a,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),h4s_markers_abbrev),s(t_fun(TV_u_27a,t_bool),h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),d_equals),s(TV_u_27a,V_v))))))),s(t_fun(TV_u_27a,t_bool),V_f)))))).
fof(ah4s_bools_NOTu_u_IMP, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) => p(s(t_bool,V_B)))) <=> (p(s(t_bool,V_A)) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_combins_ou_u_ABSu_u_R, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_0]: (![V_g, V_x]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))) => ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_EXISTSu_u_REFL, axiom, ![TV_u_27a]: ![V_a]: ?[V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_a)).
fof(ah4s_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,happ(s(t_fun(t_bool,t_bool),h4s_markers_abbrev),s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_markers_Congu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_cong(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_pairs_pairu_u_CASES, 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_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_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_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_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_numerals_numeralu_u_addu_c6, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_addu_c4, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(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_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_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_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_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(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_numerals_numeralu_u_addu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_nums_suc(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_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_sucu_c0, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESS, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))) <=> (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_p))))))).
fof(ah4s_arithmetics_SUBu_u_LEFTu_u_LESS, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_primu_u_recs_u_3c(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_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(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_SUBu_u_LEFTu_u_SUB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_SUB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_ADD, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_NOTu_u_LEQ, axiom, ![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,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_TIMES2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(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_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MULTu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_LEFTu_u_ADDu_u_DISTRIB, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_p),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,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_n)))))).
fof(ch4s_stateu_u_transformers_JOINu_u_MAP, conjecture, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_m, V_k]: s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),h4s_stateu_u_transformers_bind(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))) = s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),h4s_stateu_u_transformers_join),s(t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),t_fun(TV_u_27a,t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a)),TV_u_27a))),h4s_stateu_u_transformers_mmap(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27c,TV_u_27a))),V_m))),s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27b,TV_u_27a)),V_k)))))).
