%   ORIGINAL: h4/basis__emit/i2w__itself__ind
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/ITSELF__UNIQUE: !i. i = h4/bool/the__value
% Assm: h4/bool/TYPE__DEFINITION0: h4/bool/TYPE__DEFINITION = (\P rep. (!x_27 x_27_27. rep x_27 = rep x_27_27 ==> x_27 = x_27_27) /\ (!x. P x <=> (?x_27. x = rep x_27)))
% Assm: h4/bool/itself__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION ($equals h4/bool/ARB) rep
% Assm: h4/bool/itself__induction: !P. P h4/bool/the__value ==> (!i. P i)
% Assm: h4/words/n2w__itself__ind: !P. (!n. P (h4/pair/_2C n h4/bool/the__value)) ==> (!v v1. P (h4/pair/_2C v v1))
% Assm: h4/basis__emit/fromNum__ind: !P. (!n. P (h4/pair/_2C n h4/bool/the__value)) ==> (!v v1. P (h4/pair/_2C v v1))
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/bool/FALSITY: !t. F ==> t
% 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/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/TRUTH: T
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/relation/WF__INDUCTION__THM: !R. h4/relation/WF R ==> (!P. (!x. (!y. R y x ==> P y) ==> P x) ==> (!x. P x))
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/words/word__rrx__def: !w c. h4/words/word__rrx (h4/pair/_2C c w) = h4/pair/_2C (h4/words/word__lsb w) (h4/fcp/FCP (\i. h4/bool/COND (i = h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) c (h4/fcp/fcp__index (h4/words/word__lsr w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i)))
% Assm: h4/words/word__rrx__n2w: !c a. h4/words/word__rrx (h4/pair/_2C c (h4/words/n2w a)) = h4/pair/_2C (h4/arithmetic/ODD a) (h4/words/n2w (h4/arithmetic/_2B (h4/bit/BITS (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) (h4/bit/SBIT c (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))
% Assm: h4/basis__emit/FCPi__def: !f. h4/basis__emit/FCPi (h4/pair/_2C f h4/bool/the__value) = h4/fcp/FCP f
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/words/nzcv__def: !b a. h4/words/nzcv a b = h4/bool/LET (\q. h4/bool/LET (\r. h4/pair/_2C (h4/words/word__msb r) (h4/pair/_2C (r = h4/words/n2w h4/num/0) (h4/pair/_2C (h4/bit/BIT (h4/fcp/dimindex h4/bool/the__value) q \/ b = h4/words/n2w h4/num/0) (~(h4/words/word__msb a <=> h4/words/word__msb b) /\ ~(h4/words/word__msb r <=> h4/words/word__msb a))))) (h4/words/n2w q)) (h4/arithmetic/_2B (h4/words/w2n a) (h4/words/w2n (h4/words/word__2comp b)))
% Assm: h4/basis__emit/fromNum__primitive__def: h4/basis__emit/fromNum = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\fromNum a. h4/pair/pair__CASE a (\n v1. h4/combin/I (h4/words/n2w__itself (h4/pair/_2C (h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)) h4/bool/the__value))))
% Assm: h4/words/n2w__itself__def: !n. h4/words/n2w__itself (h4/pair/_2C n h4/bool/the__value) = h4/words/n2w n
% Assm: h4/basis__emit/FCPi__primitive__def: h4/basis__emit/FCPi = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\FCPi a. h4/pair/pair__CASE a (\f v1. h4/combin/I (h4/fcp/FCP f)))
% Assm: h4/words/n2w__itself__primitive__def: h4/words/n2w__itself = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\n2w__itself a. h4/pair/pair__CASE a (\n v1. h4/combin/I (h4/words/n2w n)))
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/words/EXISTS__HB: ?m. h4/fcp/dimindex h4/bool/the__value = h4/num/SUC m
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/fcp/FCP__BETA: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = g i
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bit/BITS__SUM: !l h b a. h4/prim__rec/_3C b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l) ==> h4/bit/BITS h l (h4/arithmetic/_2B (h4/arithmetic/_2A a (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)) b) = h4/bit/BITS h l (h4/arithmetic/_2A a (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l))
% Assm: h4/words/word__lsr__def: !w n. h4/words/word__lsr w n = h4/fcp/FCP (\i. h4/prim__rec/_3C (h4/arithmetic/_2B i n) (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w (h4/arithmetic/_2B i n))
% Assm: h4/bit/BIT__OF__BITS__THM: !n l h a. h4/arithmetic/_3C_3D (h4/arithmetic/_2B l n) h ==> (h4/bit/BIT n (h4/bit/BITS h l a) <=> h4/bit/BIT (h4/arithmetic/_2B l n) a)
% Assm: h4/bit/BITS__COMP__THM2: !n l2 l1 h2 h1. h4/bit/BITS h2 l2 (h4/bit/BITS h1 l1 n) = h4/bit/BITS (h4/arithmetic/MIN h1 (h4/arithmetic/_2B h2 l1)) (h4/arithmetic/_2B l2 l1) n
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/numeral/numeral__eq_c1: !n. 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_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/arithmetic/SUB__LEFT__EQ: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/SUB__LEFT__LESS__EQ: !p n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2D n p) <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B m p) n \/ h4/arithmetic/_3C_3D m h4/num/0
% 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/bit/BITS__ZERO: !n l h. h4/prim__rec/_3C h l ==> h4/bit/BITS h l n = h4/num/0
% 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/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/EXP__ADD: !q p n. h4/arithmetic/EXP n (h4/arithmetic/_2B p q) = h4/arithmetic/_2A (h4/arithmetic/EXP n p) (h4/arithmetic/EXP n q)
% Assm: h4/words/DIMINDEX__GT__0: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/words/n2w__def: !n. h4/words/n2w n = h4/fcp/FCP (\i. h4/bit/BIT i n)
% Assm: h4/words/word__lsb__def: !w. h4/words/word__lsb w <=> h4/fcp/fcp__index w h4/num/0
% Assm: h4/fcp/CART__EQ: !y x. x = y <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index x i = h4/fcp/fcp__index y i)
% Assm: h4/bit/BITS__SUM2: !l h b a. h4/bit/BITS h l (h4/arithmetic/_2B (h4/arithmetic/_2A a (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h))) b) = h4/bit/BITS h l b
% Assm: h4/bit/BIT0__ODD: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm: h4/bit/BIT__B: !b. h4/bit/BIT b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) b)
% Assm: h4/arithmetic/ADD1: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/bit/SBIT__def: !n b. h4/bit/SBIT b n = h4/bool/COND b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) h4/num/0
% Assm: h4/numeral/numeral__lt_c0: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm: h4/bit/BIT__def: !n b. h4/bit/BIT b n <=> h4/bit/BITS b b n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% 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__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/bit/BITSLT__THM: !n l h. h4/prim__rec/_3C (h4/bit/BITS h l n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/num/SUC h) l))
% Assm: h4/arithmetic/MIN__DEF: !n m. h4/arithmetic/MIN m n = h4/bool/COND (h4/prim__rec/_3C m n) m n
% Assm: h4/arithmetic/MIN__LT_c0: !p n m. h4/prim__rec/_3C (h4/arithmetic/MIN m n) p <=> h4/prim__rec/_3C m p \/ h4/prim__rec/_3C n p
% 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/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = 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/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/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/SUC__SUB1: !m. h4/arithmetic/_2D (h4/num/SUC m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm: h4/arithmetic/MULT__LEFT__1: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__MONO__ADD__EQ: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2B m p) (h4/arithmetic/_2B n p) <=> h4/prim__rec/_3C m n
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/prim__rec/LESS__0: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm: h4/prim__rec/LESS__REFL: !n. ~h4/prim__rec/_3C n n
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/COND__RAND: !y x f b. f (h4/bool/COND b x y) = h4/bool/COND b (f x) (f y)
% Assm: h4/bool/COND__EXPAND: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/arithmetic/LESS__ADD__1: !n m. h4/prim__rec/_3C n m ==> (?p. m = h4/arithmetic/_2B n (h4/arithmetic/_2B p (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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/COND__RATOR: !x g f b. h4/bool/COND b f g x = h4/bool/COND b (f x) (g x)
% Goal: !P. (!i. P (h4/pair/_2C i h4/bool/the__value)) ==> (!v v1. P (h4/pair/_2C v v1))
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_ITSELFu_u_UNIQUE]: !i. i = h4/bool/the__value
% Assm [h4s_bools_TYPEu_u_DEFINITION0]: !x x. h4/bool/TYPE__DEFINITION x x <=> (!x_27 x_27_27. happ x x_27 = happ x x_27_27 ==> x_27 = x_27_27) /\ (!x. happ x x <=> (?x_27. x = happ x x_27))
% Assm [h4s_bools_itselfu_u_TYu_u_DEF]: ?rep. h4/bool/TYPE__DEFINITION ($equals h4/bool/ARB) rep
% Assm [h4s_bools_itselfu_u_induction]: !P. happ P h4/bool/the__value ==> (!i. happ P i)
% Assm [h4s_wordss_n2wu_u_itselfu_u_ind]: !P. (!n. happ P (h4/pair/_2C n h4/bool/the__value)) ==> (!v v1. happ P (h4/pair/_2C v v1))
% Assm [h4s_basisu_u_emits_fromNumu_u_ind]: !P. (!n. happ P (h4/pair/_2C n h4/bool/the__value)) ==> (!v v1. happ P (h4/pair/_2C v v1))
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% 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_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_relations_WFu_u_INDUCTIONu_u_THM]: !R. h4/relation/WF R ==> (!P. (!x. (!y. happ (happ R y) x ==> happ P y) ==> happ P x) ==> (!x. happ P x))
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_wordss_wordu_u_rrxu_u_def]: !_0. (!c w i. ?v. (v <=> i = h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) /\ (happ (happ (happ _0 c) w) i <=> h4/bool/COND v c (h4/fcp/fcp__index (h4/words/word__lsr w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) i))) ==> (!w c. h4/words/word__rrx (h4/pair/_2C c w) = h4/pair/_2C (h4/words/word__lsb w) (h4/fcp/FCP (happ (happ _0 c) w)))
% Assm [h4s_wordss_wordu_u_rrxu_u_n2w]: !c a. h4/words/word__rrx (h4/pair/_2C c (h4/words/n2w a)) = h4/pair/_2C (happ h4/arithmetic/ODD a) (h4/words/n2w (h4/arithmetic/_2B (h4/bit/BITS (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) a) (h4/bit/SBIT c (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))
% Assm [h4s_basisu_u_emits_FCPiu_u_def]: !f. happ h4/basis__emit/FCPi (h4/pair/_2C f h4/bool/the__value) = h4/fcp/FCP f
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_wordss_nzcvu_u_def]: !_1. (!q b a r. ?v. (v <=> ~(h4/words/word__msb a <=> h4/words/word__msb b) /\ ~(h4/words/word__msb r <=> h4/words/word__msb a)) /\ (?v'. (v' <=> happ (h4/bit/BIT (h4/fcp/dimindex h4/bool/the__value)) q \/ b = h4/words/n2w h4/num/0) /\ (?v''. (v'' <=> r = h4/words/n2w h4/num/0) /\ happ (happ (happ (happ _1 q) b) a) r = h4/pair/_2C (h4/words/word__msb r) (h4/pair/_2C v'' (h4/pair/_2C v' v))))) ==> (!_0. (!b a q. happ (happ (happ _0 b) a) q = h4/bool/LET (happ (happ (happ _1 q) b) a) (h4/words/n2w q)) ==> (!b a. h4/words/nzcv a b = h4/bool/LET (happ (happ _0 b) a) (h4/arithmetic/_2B (h4/words/w2n a) (h4/words/w2n (h4/words/word__2comp b)))))
% Assm [h4s_basisu_u_emits_fromNumu_u_primitiveu_u_def]: !_4. (!n v1. happ (happ _4 n) v1 = h4/combin/I (happ h4/words/n2w__itself (h4/pair/_2C (h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)) h4/bool/the__value))) ==> (!_3. (!n. happ _3 n = happ _4 n) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!fromNum. happ _1 fromNum = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/basis__emit/fromNum = h4/relation/WFREC (h4/min/_40 _0) _1))))
% Assm [h4s_wordss_n2wu_u_itselfu_u_def]: !n. happ h4/words/n2w__itself (h4/pair/_2C n h4/bool/the__value) = h4/words/n2w n
% Assm [h4s_basisu_u_emits_FCPiu_u_primitiveu_u_def]: !_4. (!f v1. happ (happ _4 f) v1 = h4/combin/I (h4/fcp/FCP f)) ==> (!_3. (!f. happ _3 f = happ _4 f) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!FCPi. happ _1 FCPi = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/basis__emit/FCPi = h4/relation/WFREC (h4/min/_40 _0) _1))))
% Assm [h4s_wordss_n2wu_u_itselfu_u_primitiveu_u_def]: !_4. (!n v1. happ (happ _4 n) v1 = h4/combin/I (h4/words/n2w n)) ==> (!_3. (!n. happ _3 n = happ _4 n) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!n2w__itself. happ _1 n2w__itself = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/words/n2w__itself = h4/relation/WFREC (h4/min/_40 _0) _1))))
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_wordss_EXISTSu_u_HB]: ?m. h4/fcp/dimindex h4/bool/the__value = h4/num/SUC m
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_fcps_FCPu_u_BETA]: !i g. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index (h4/fcp/FCP g) i = happ g i
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bits_BITSu_u_SUM]: !l h b a. h4/prim__rec/_3C b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l) ==> h4/bit/BITS h l (h4/arithmetic/_2B (h4/arithmetic/_2A a (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)) b) = h4/bit/BITS h l (h4/arithmetic/_2A a (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l))
% Assm [h4s_wordss_wordu_u_lsru_u_def]: !_0. (!w n i. happ (happ (happ _0 w) n) i <=> h4/prim__rec/_3C (h4/arithmetic/_2B i n) (h4/fcp/dimindex h4/bool/the__value) /\ h4/fcp/fcp__index w (h4/arithmetic/_2B i n)) ==> (!w n. h4/words/word__lsr w n = h4/fcp/FCP (happ (happ _0 w) n))
% Assm [h4s_bits_BITu_u_OFu_u_BITSu_u_THM]: !n l h a. h4/arithmetic/_3C_3D (h4/arithmetic/_2B l n) h ==> (happ (h4/bit/BIT n) (h4/bit/BITS h l a) <=> happ (h4/bit/BIT (h4/arithmetic/_2B l n)) a)
% Assm [h4s_bits_BITSu_u_COMPu_u_THM2]: !n l2 l1 h2 h1. h4/bit/BITS h2 l2 (h4/bit/BITS h1 l1 n) = h4/bit/BITS (h4/arithmetic/MIN h1 (h4/arithmetic/_2B h2 l1)) (h4/arithmetic/_2B l2 l1) n
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. 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_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_EQ]: !p n m. m = h4/arithmetic/_2D n p <=> h4/arithmetic/_2B m p = n \/ h4/arithmetic/_3C_3D m h4/num/0 /\ h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_SUBu_u_LEFTu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2D n p) <=> h4/arithmetic/_3C_3D (h4/arithmetic/_2B m p) n \/ h4/arithmetic/_3C_3D m h4/num/0
% 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_bits_BITSu_u_ZERO]: !n l h. h4/prim__rec/_3C h l ==> h4/bit/BITS h l n = h4/num/0
% 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_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_EXPu_u_ADD]: !q p n. h4/arithmetic/EXP n (h4/arithmetic/_2B p q) = h4/arithmetic/_2A (h4/arithmetic/EXP n p) (h4/arithmetic/EXP n q)
% Assm [h4s_wordss_DIMINDEXu_u_GTu_u_0]: h4/prim__rec/_3C h4/num/0 (h4/fcp/dimindex h4/bool/the__value)
% Assm [h4s_wordss_n2wu_u_def]: !_0. (!n i. happ (happ _0 n) i <=> happ (h4/bit/BIT i) n) ==> (!n. h4/words/n2w n = h4/fcp/FCP (happ _0 n))
% Assm [h4s_wordss_wordu_u_lsbu_u_def]: !w. h4/words/word__lsb w <=> h4/fcp/fcp__index w h4/num/0
% Assm [h4s_fcps_CARTu_u_EQ]: !y x. x = y <=> (!i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> h4/fcp/fcp__index x i = h4/fcp/fcp__index y i)
% Assm [h4s_bits_BITSu_u_SUM2]: !l h b a. h4/bit/BITS h l (h4/arithmetic/_2B (h4/arithmetic/_2A a (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h))) b) = h4/bit/BITS h l b
% Assm [h4s_bits_BIT0u_u_ODD]: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm [h4s_bits_BITu_u_B]: !b. happ (h4/bit/BIT b) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) b)
% Assm [h4s_arithmetics_ADD1]: !m. h4/num/SUC m = h4/arithmetic/_2B m (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_bits_SBITu_u_def]: !n b. h4/bit/SBIT b n = h4/bool/COND b (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) h4/num/0
% Assm [h4s_numerals_numeralu_u_ltu_c0]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT1 n) <=> T
% Assm [h4s_bits_BITu_u_def]: !n b. happ (h4/bit/BIT b) n <=> h4/bit/BITS b b n = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% 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_distribu_c21]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_bits_BITSLTu_u_THM]: !n l h. h4/prim__rec/_3C (h4/bit/BITS h l n) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/num/SUC h) l))
% Assm [h4s_arithmetics_MINu_u_DEF]: !n m. h4/arithmetic/MIN m n = h4/bool/COND (h4/prim__rec/_3C m n) m n
% Assm [h4s_arithmetics_MINu_u_LTu_c0]: !p n m. h4/prim__rec/_3C (h4/arithmetic/MIN m n) p <=> h4/prim__rec/_3C m p \/ h4/prim__rec/_3C n p
% 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_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = 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_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_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_SUCu_u_SUB1]: !m. h4/arithmetic/_2D (h4/num/SUC m) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = m
% Assm [h4s_arithmetics_MULTu_u_LEFTu_u_1]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ]: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2B m p) (h4/arithmetic/_2B n p) <=> h4/prim__rec/_3C m n
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_primu_u_recs_LESSu_u_0]: !n. h4/prim__rec/_3C h4/num/0 (h4/num/SUC n)
% Assm [h4s_primu_u_recs_LESSu_u_REFL]: !n. ~h4/prim__rec/_3C n n
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_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_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_CONDu_u_RAND]: !y x f b. happ f (h4/bool/COND b x y) = h4/bool/COND b (happ f x) (happ f y)
% Assm [h4s_bools_CONDu_u_EXPAND]: !t2 t1 b. h4/bool/COND b t1 t2 <=> (~b \/ t1) /\ (b \/ t2)
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_arithmetics_LESSu_u_ADDu_u_1]: !n m. h4/prim__rec/_3C n m ==> (?p. m = h4/arithmetic/_2B n (h4/arithmetic/_2B p (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% 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_CONDu_u_RATOR]: !x g f b. happ (h4/bool/COND b f g) x = h4/bool/COND b (happ f x) (happ g x)
% Goal: !P. (!i. happ P (h4/pair/_2C i h4/bool/the__value)) ==> (!v v1. happ P (h4/pair/_2C v v1))
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_Q1309922,TV_Q1309918]: ![V_f, V_g]: (![V_x]: s(TV_Q1309918,happ(s(t_fun(TV_Q1309922,TV_Q1309918),V_f),s(TV_Q1309922,V_x))) = s(TV_Q1309918,happ(s(t_fun(TV_Q1309922,TV_Q1309918),V_g),s(TV_Q1309922,V_x))) => s(t_fun(TV_Q1309922,TV_Q1309918),V_f) = s(t_fun(TV_Q1309922,TV_Q1309918),V_g))).
fof(ah4s_bools_ITSELFu_u_UNIQUE, axiom, ![TV_u_27a]: ![V_i]: s(t_h4s_bools_itself(TV_u_27a),V_i) = s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)).
fof(ah4s_bools_TYPEu_u_DEFINITION0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_x0]: (p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27b,TV_u_27a),V_x0)))) <=> (![V_xu_27, V_xu_27u_27]: (s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27u_27))) => s(TV_u_27b,V_xu_27) = s(TV_u_27b,V_xu_27u_27)) & ![V_x1]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x1)))) <=> ?[V_xu_27]: s(TV_u_27a,V_x1) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27))))))).
fof(ah4s_bools_itselfu_u_TYu_u_DEF, axiom, ![TV_u_27a]: ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),d_equals(s(TV_u_27a,h4s_bools_arb))),s(t_fun(t_h4s_bools_itself(TV_u_27a),TV_u_27a),V_rep))))).
fof(ah4s_bools_itselfu_u_induction, axiom, ![TV_u_27a]: ![V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_bools_itself(TV_u_27a),t_bool),V_P),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))) => ![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_bools_itself(TV_u_27a),t_bool),V_P),s(t_h4s_bools_itself(TV_u_27a),V_i)))))).
fof(ah4s_wordss_n2wu_u_itselfu_u_ind, axiom, ![TV_u_27a]: ![V_P]: (![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_v),s(t_h4s_bools_itself(TV_u_27a),V_v1)))))))).
fof(ah4s_basisu_u_emits_fromNumu_u_ind, axiom, ![TV_u_27a]: ![V_P]: (![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_v),s(t_h4s_bools_itself(TV_u_27a),V_v1)))))))).
fof(ah4s_relations_WFu_u_EMPTYu_u_REL, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_relations_WFu_u_INDUCTIONu_u_THM, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_P]: (![V_x]: (![V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_q),s(TV_u_27b,V_r)))).
fof(ah4s_bools_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_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_wordss_wordu_u_rrxu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_c, V_w, V_i]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_i) = s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_bool,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_bool,V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bools_cond(s(t_bool,V_v),s(t_bool,V_c),s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),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_i)))))) => ![V_w, V_c]: s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_rrx(s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_pairs_u_2c(s(t_bool,V_c),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_pairs_u_2c(s(t_bool,h4s_wordss_wordu_u_lsb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_bool,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_bool,V_c))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))))).
fof(ah4s_wordss_wordu_u_rrxu_u_n2w, axiom, ![TV_u_27a]: ![V_c, V_a]: s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_rrx(s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_pairs_u_2c(s(t_bool,V_c),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_a))))))) = s(t_h4s_pairs_prod(t_bool,t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_pairs_u_2c(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd),s(t_h4s_nums_num,V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,V_c),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))).
fof(ah4s_basisu_u_emits_FCPiu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_basisu_u_emits_fcpi),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_wordss_nzcvu_u_def, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_q, V_b, V_a, V_r]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (~ (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & ~ (s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r))) = s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_h4s_nums_num,V_q)))) | s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) & ?[V_vi_i_]: ((p(s(t_bool,V_vi_i_)) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) & s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))))),V_uu_1),s(t_h4s_nums_num,V_q))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r))) = s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_pairs_u_2c(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_r))),s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),h4s_pairs_u_2c(s(t_bool,V_vi_i_),s(t_h4s_pairs_prod(t_bool,t_bool),h4s_pairs_u_2c(s(t_bool,V_vi_),s(t_bool,V_v)))))))))) => ![V_uu_0]: (![V_b, V_a, V_q]: s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,V_q))) = s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_bools_let(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))))),V_uu_1),s(t_h4s_nums_num,V_q))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_q))))) => ![V_b, V_a]: s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_wordss_nzcv(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),h4s_bools_let(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)))))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))))))))).
fof(ah4s_basisu_u_emits_fromNumu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_4]: (![V_n, V_v1]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_4),s(t_h4s_nums_num,V_n))),s(t_h4s_bools_itself(TV_u_27a),V_v1))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_combins_i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_n2wu_u_itself),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))) => ![V_uu_3]: (![V_n]: s(t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_3),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_4),s(t_h4s_nums_num,V_n))) => ![V_uu_2]: (![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),V_uu_2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),V_a),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_3))) => ![V_uu_1]: (![V_fromNum]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),V_fromNum))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_basisu_u_emits_fromnum) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_1))))))))).
fof(ah4s_wordss_n2wu_u_itselfu_u_def, axiom, ![TV_u_27a]: ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_n2wu_u_itself),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n)))).
fof(ah4s_basisu_u_emits_FCPiu_u_primitiveu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_4]: (![V_f, V_v1]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b))),V_uu_4),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_bools_itself(TV_u_27b),V_v1))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_combins_i(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))))) => ![V_uu_3]: (![V_f]: s(t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b))),V_uu_3),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))) = s(t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b))),V_uu_4),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))) => ![V_uu_2]: (![V_a]: s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),V_uu_2),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),V_a))) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),V_a),s(t_fun(t_fun(t_h4s_nums_num,TV_u_27a),t_fun(t_h4s_bools_itself(TV_u_27b),t_h4s_fcps_cart(TV_u_27a,TV_u_27b))),V_uu_3))) => ![V_uu_1]: (![V_FCPi]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),V_FCPi))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_basisu_u_emits_fcpi) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,TV_u_27a),t_h4s_bools_itself(TV_u_27b)),t_h4s_fcps_cart(TV_u_27a,TV_u_27b))),V_uu_1))))))))).
fof(ah4s_wordss_n2wu_u_itselfu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_4]: (![V_n, V_v1]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_4),s(t_h4s_nums_num,V_n))),s(t_h4s_bools_itself(TV_u_27a),V_v1))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_combins_i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) => ![V_uu_3]: (![V_n]: s(t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_3),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_4),s(t_h4s_nums_num,V_n))) => ![V_uu_2]: (![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),V_uu_2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),V_a),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_bools_itself(TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_3))) => ![V_uu_1]: (![V_n2wu_u_itself]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),V_n2wu_u_itself))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_n2wu_u_itself) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_bools_itself(TV_u_27a)),t_h4s_fcps_cart(t_bool,TV_u_27a))),V_uu_1))))))))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_wordss_EXISTSu_u_HB, axiom, ![TV_u_27a]: ?[V_m]: s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_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_fcps_FCPu_u_BETA, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_g]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g))),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_g),s(t_h4s_nums_num,V_i))))).
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_bits_BITSu_u_SUM, axiom, ![V_l, V_h, V_b, V_a]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_arithmetics_exp(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_l)))))) => s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_exp(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_l))))),s(t_h4s_nums_num,V_b))))) = s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_exp(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_l))))))))).
fof(ah4s_wordss_wordu_u_lsru_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_n, V_i]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i)))) <=> (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_i),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) & p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n)))))))) => ![V_w, V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_lsr(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_bits_BITu_u_OFu_u_BITSu_u_THM, axiom, ![V_n, V_l, V_h, V_a]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_h)))) => s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_a))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_a))))).
fof(ah4s_bits_BITSu_u_COMPu_u_THM2, axiom, ![V_n, V_l2, V_l1, V_h2, V_h1]: s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h2),s(t_h4s_nums_num,V_l2),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h1),s(t_h4s_nums_num,V_l1),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_h2),s(t_h4s_nums_num,V_l1))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_l2),s(t_h4s_nums_num,V_l1))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = 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_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_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_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_distribu_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_c18, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
fof(ah4s_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_SUBu_u_LEFTu_u_EQ, axiom, ![V_p, V_n, V_m]: (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_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,V_n) | (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0)))) & 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_SUBu_u_LEFTu_u_LESSu_u_EQ, 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,h4s_arithmetics_u_2d(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,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)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))))))).
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_bits_BITSu_u_ZERO, axiom, ![V_n, V_l, V_h]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l)))) => s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
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_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_EQu_u_LESSu_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,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_arithmetics_EXPu_u_ADD, axiom, ![V_q, V_p, V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_q))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_q)))))).
fof(ah4s_wordss_DIMINDEXu_u_GTu_u_0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_wordss_n2wu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_i))),s(t_h4s_nums_num,V_n))) => ![V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_fcps_fcp(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_wordu_u_lsbu_u_def, axiom, ![TV_u_27a]: ![V_w]: s(t_bool,h4s_wordss_wordu_u_lsb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_fcps_CARTu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: (s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_y) <=> ![V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27b),h4s_bools_theu_u_value)))))) => s(TV_u_27a,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_x),s(t_h4s_nums_num,V_i))) = s(TV_u_27a,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(TV_u_27a,TV_u_27b),V_y),s(t_h4s_nums_num,V_i)))))).
fof(ah4s_bits_BITSu_u_SUM2, axiom, ![V_l, V_h, V_b, V_a]: s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_exp(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,h4s_nums_suc(s(t_h4s_nums_num,V_h))))))),s(t_h4s_nums_num,V_b))))) = s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_b)))).
fof(ah4s_bits_BIT0u_u_ODD, axiom, s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,h4s_nums_0))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd)).
fof(ah4s_bits_BITu_u_B, axiom, ![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,h4s_arithmetics_exp(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_b))))))).
fof(ah4s_arithmetics_ADD1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_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_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, 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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,V_p)))).
fof(ah4s_bits_SBITu_u_def, axiom, ![V_n, V_b]: s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,V_b),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_exp(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_nums_0)))).
fof(ah4s_numerals_numeralu_u_ltu_c0, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_bits_BITu_u_def, axiom, ![V_n, V_b]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_bits_bit(s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,V_n)))) <=> s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_numerals_numeralu_u_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_distribu_c21, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
fof(ah4s_bits_BITSLTu_u_THM, axiom, ![V_n, V_l, V_h]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_exp(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,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_h))),s(t_h4s_nums_num,V_l))))))))).
fof(ah4s_arithmetics_MINu_u_DEF, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MINu_u_LTu_c0, axiom, ![V_p, V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_min(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,V_p)))) | p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))))).
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_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_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_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_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_SUCu_u_SUB1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_MULTu_u_LEFTu_u_1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQ, axiom, ![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,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: 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,h4s_arithmetics_u_2b(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,V_m),s(t_h4s_nums_num,V_n)))).
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_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_primu_u_recs_LESSu_u_0, axiom, ![V_n]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))))).
fof(ah4s_primu_u_recs_LESSu_u_REFL, axiom, ![V_n]: ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_n)))))).
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_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_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_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_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_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_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(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_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_ORu_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_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_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_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_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_CONDu_u_RAND, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27a,V_x),s(TV_u_27a,V_y))))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))))).
fof(ah4s_bools_CONDu_u_EXPAND, axiom, ![V_t2, V_t1, V_b]: (p(s(t_bool,h4s_bools_cond(s(t_bool,V_b),s(t_bool,V_t1),s(t_bool,V_t2)))) <=> ((~ (p(s(t_bool,V_b))) | p(s(t_bool,V_t1))) & (p(s(t_bool,V_b)) | p(s(t_bool,V_t2)))))).
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_arithmetics_LESSu_u_ADDu_u_1, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))) => ?[V_p]: 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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))).
fof(ah4s_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_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_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_CONDu_u_RATOR, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_g, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_bools_cond(s(t_bool,V_b),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),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(ch4s_basisu_u_emits_i2wu_u_itselfu_u_ind, conjecture, ![TV_u_27a]: ![V_P]: (![V_i]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_bools_itself(TV_u_27a)),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_integers_int,V_i),s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))) => ![V_v, V_v1]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_bools_itself(TV_u_27a)),t_bool),V_P),s(t_h4s_pairs_prod(t_h4s_integers_int,t_h4s_bools_itself(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_integers_int,V_v),s(t_h4s_bools_itself(TV_u_27a),V_v1)))))))).
