%   ORIGINAL: h4/words/WORD__0__LS
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/words/WORD__LS: !b a. h4/words/word__ls a b <=> h4/arithmetic/_3C_3D (h4/words/w2n a) (h4/words/w2n b)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/words/WORD__LOWER__OR__EQ: !b a. h4/words/word__ls a b <=> h4/words/word__lo a b \/ a = b
% Assm: h4/words/WORD__NOT__LOWER: !b a. ~h4/words/word__lo a b <=> h4/words/word__ls b a
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/words/WORD__LOWER__EQ__CASES: !b a. h4/words/word__ls a b \/ h4/words/word__ls b a
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/words/word__ls__def: !b a. h4/words/word__ls a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. ~c \/ z)))) (h4/words/nzcv a b)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/words/WORD__LOWER__EQ__REFL: !a. h4/words/word__ls a a
% Assm: h4/words/WORD__LOWER__LOWER__EQ__TRANS: !c b a. h4/words/word__lo a b /\ h4/words/word__ls b c ==> h4/words/word__lo a c
% Assm: h4/words/WORD__LOWER__EQ__TRANS: !c b a. h4/words/word__ls a b /\ h4/words/word__ls b c ==> h4/words/word__ls a c
% Assm: h4/words/WORD__LOWER__CASES: !b a. h4/words/word__lo a b \/ h4/words/word__ls b a
% Assm: h4/words/WORD__LOWER__EQ__LOWER__TRANS: !c b a. h4/words/word__ls a b /\ h4/words/word__lo b c ==> h4/words/word__lo a c
% Assm: h4/words/WORD__HIGHER__EQ: !b a. h4/words/word__hs a b <=> h4/words/word__ls b a
% Assm: h4/words/WORD__LOWER__EQ__ANTISYM: !b a. ~(h4/words/word__lo a b /\ h4/words/word__ls b a)
% Assm: h4/words/WORD__LOWER__IMP__LOWER__OR__EQ: !b a. h4/words/word__lo a b ==> h4/words/word__ls a b
% Assm: h4/words/WORD__NOT__HIGHER: !b a. ~h4/words/word__hi a b <=> h4/words/word__ls a b
% Assm: h4/words/WORD__LOWER__EQUAL__ANTISYM: !b a. h4/words/word__ls a b /\ h4/words/word__ls b a ==> a = b
% Assm: h4/words/WORD__NOT__LOWER__EQUAL: !b a. ~h4/words/word__ls a b <=> h4/words/word__lo b a
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/words/WORD__LO: !b a. h4/words/word__lo a b <=> h4/prim__rec/_3C (h4/words/w2n a) (h4/words/w2n b)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/arithmetic/LESS__EQ__CASES: !n m. h4/arithmetic/_3C_3D m n \/ h4/arithmetic/_3C_3D n m
% 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/words/w2n__11: !w v. h4/words/w2n v = h4/words/w2n w <=> v = w
% Assm: h4/arithmetic/LESS__OR__EQ: !n m. h4/arithmetic/_3C_3D m n <=> h4/prim__rec/_3C m n \/ m = n
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% 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/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/bool/EXCLUDED__MIDDLE: !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/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/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/words/w2n__eq__0: !w. h4/words/w2n w = h4/num/0 <=> w = h4/words/n2w h4/num/0
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/arithmetic/NOT__LEQ: !n m. ~h4/arithmetic/_3C_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/words/WORD__AND__COMP: !a. h4/words/word__and a (h4/words/word__1comp a) = h4/words/n2w h4/num/0
% Assm: h4/words/LOG2__w2n__lt: !w. ~(w = h4/words/n2w h4/num/0) ==> h4/prim__rec/_3C (h4/bit/LOG2 (h4/words/w2n w)) (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/words/WORD__SLICE__ZERO: !w l h. h4/prim__rec/_3C h l ==> h4/words/word__slice h l w = h4/words/n2w h4/num/0
% Assm: h4/arithmetic/LESS__LESS__EQ__TRANS: !p n m. h4/prim__rec/_3C m n /\ h4/arithmetic/_3C_3D n p ==> h4/prim__rec/_3C m p
% Assm: h4/words/WORD__EXTRACT__ZERO3: !w l h. h4/arithmetic/_3C_3D (h4/fcp/dimindex h4/bool/the__value) l ==> h4/words/word__extract h l w = h4/words/n2w h4/num/0
% Assm: h4/words/LEAST__BIT__LT: !w. ~(w = h4/words/n2w h4/num/0) ==> h4/prim__rec/_3C (h4/while/LEAST (\i. h4/fcp/fcp__index w i)) (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/arithmetic/LESS__EQ__LESS__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/prim__rec/_3C n p ==> h4/prim__rec/_3C m p
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n 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/words/WORD__HIGHER: !b a. h4/words/word__hi a b <=> h4/words/word__lo b a
% 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/words/WORD__HS: !b a. h4/words/word__hs a b <=> h4/arithmetic/_3E_3D (h4/words/w2n a) (h4/words/w2n b)
% Assm: h4/arithmetic/NOT__GREATER__EQ: !n m. ~h4/arithmetic/_3E_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/GREATER__EQ: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/words/WORD__LCANCEL__SUB: !x w v. h4/words/word__sub v w = h4/words/word__sub x w <=> v = x
% Assm: h4/words/WORD__SUB__REFL: !w. h4/words/word__sub w w = h4/words/n2w h4/num/0
% Assm: h4/words/word__add__n2w: !n m. h4/words/word__add (h4/words/n2w m) (h4/words/n2w n) = h4/words/n2w (h4/arithmetic/_2B m n)
% Assm: h4/words/n2w__w2n: !w. h4/words/n2w (h4/words/w2n w) = w
% Assm: h4/words/word__lo__def: !b a. h4/words/word__lo a b <=> h4/bool/LET (h4/pair/UNCURRY (\n. h4/pair/UNCURRY (\z. h4/pair/UNCURRY (\c v. ~c)))) (h4/words/nzcv a b)
% Assm: h4/words/word__sub__def: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% 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/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/words/n2w__11: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm: h4/words/WORD__LOWER__ANTISYM: !b a. ~(h4/words/word__lo a b /\ h4/words/word__lo b a)
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/words/ZERO__LT__dimword: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm: h4/arithmetic/ZERO__MOD: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm: h4/words/dimword__def: h4/words/dimword h4/bool/the__value = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)
% Assm: h4/words/word__nchotomy: !w. ?n. w = h4/words/n2w n
% Assm: h4/words/w2n__n2w: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/words/w2n__lt: !w. h4/prim__rec/_3C (h4/words/w2n w) (h4/words/dimword h4/bool/the__value)
% Assm: h4/bit/LT__TWOEXP: !x n. h4/prim__rec/_3C x (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) <=> x = h4/num/0 \/ h4/prim__rec/_3C (h4/bit/LOG2 x) n
% Assm: h4/words/w2w__0: h4/words/w2w (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Assm: h4/words/WORD__BITS__ZERO3: !w l h. h4/arithmetic/_3C_3D (h4/fcp/dimindex h4/bool/the__value) l ==> h4/words/word__bits h l w = h4/words/n2w h4/num/0
% Assm: h4/words/word__extract__def: !l h. h4/words/word__extract h l = h4/combin/o h4/words/w2w (h4/words/word__bits h l)
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/words/word__and__def: !w v. h4/words/word__and v w = h4/fcp/FCP (\i. h4/fcp/fcp__index v i /\ h4/fcp/fcp__index w i)
% Assm: h4/words/word__1comp__def: !w. h4/words/word__1comp w = h4/fcp/FCP (\i. ~h4/fcp/fcp__index w i)
% Assm: h4/words/word__0: !i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> ~h4/fcp/fcp__index (h4/words/n2w h4/num/0) i
% 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/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/bool/NOT__AND: !t. ~(t /\ ~t)
% Assm: h4/words/ranged__word__nchotomy: !w. ?n. w = h4/words/n2w n /\ h4/prim__rec/_3C n (h4/words/dimword h4/bool/the__value)
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/words/word__slice__n2w: !n l h. h4/words/word__slice h l (h4/words/n2w n) = h4/words/n2w (h4/bit/SLICE (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) l n)
% Assm: h4/bit/SLICE__ZERO: !n l h. h4/prim__rec/_3C h l ==> h4/bit/SLICE h l n = h4/num/0
% 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/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/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/words/word__index: !n i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/n2w n) i <=> h4/bit/BIT i n)
% Assm: h4/bit/EXISTS__BIT__LT: !n b. ~(n = h4/num/0) /\ h4/prim__rec/_3C n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) b) ==> (?i. h4/prim__rec/_3C i b /\ h4/bit/BIT i n)
% Goal: !w. h4/words/word__ls (h4/words/n2w h4/num/0) w
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_wordss_WORDu_u_LS]: !b a. h4/words/word__ls a b <=> h4/arithmetic/_3C_3D (h4/words/w2n a) (h4/words/w2n b)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_wordss_WORDu_u_LOWERu_u_ORu_u_EQ]: !b a. h4/words/word__ls a b <=> h4/words/word__lo a b \/ a = b
% Assm [h4s_wordss_WORDu_u_NOTu_u_LOWER]: !b a. ~h4/words/word__lo a b <=> h4/words/word__ls b a
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% 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_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_wordss_WORDu_u_LOWERu_u_EQu_u_CASES]: !b a. h4/words/word__ls a b \/ h4/words/word__ls b a
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_wordss_wordu_u_lsu_u_def]: !_3. (!c z v. happ (happ (happ _3 c) z) v <=> ~c \/ z) ==> (!_2. (!z c. happ (happ _2 z) c = happ (happ _3 c) z) ==> (!_1. (!z. happ _1 z = h4/pair/UNCURRY (happ _2 z)) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY _1) ==> (!b a. h4/words/word__ls a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_wordss_WORDu_u_LOWERu_u_EQu_u_REFL]: !a. h4/words/word__ls a a
% Assm [h4s_wordss_WORDu_u_LOWERu_u_LOWERu_u_EQu_u_TRANS]: !c b a. h4/words/word__lo a b /\ h4/words/word__ls b c ==> h4/words/word__lo a c
% Assm [h4s_wordss_WORDu_u_LOWERu_u_EQu_u_TRANS]: !c b a. h4/words/word__ls a b /\ h4/words/word__ls b c ==> h4/words/word__ls a c
% Assm [h4s_wordss_WORDu_u_LOWERu_u_CASES]: !b a. h4/words/word__lo a b \/ h4/words/word__ls b a
% Assm [h4s_wordss_WORDu_u_LOWERu_u_EQu_u_LOWERu_u_TRANS]: !c b a. h4/words/word__ls a b /\ h4/words/word__lo b c ==> h4/words/word__lo a c
% Assm [h4s_wordss_WORDu_u_HIGHERu_u_EQ]: !b a. h4/words/word__hs a b <=> h4/words/word__ls b a
% Assm [h4s_wordss_WORDu_u_LOWERu_u_EQu_u_ANTISYM]: !b a. ~(h4/words/word__lo a b /\ h4/words/word__ls b a)
% Assm [h4s_wordss_WORDu_u_LOWERu_u_IMPu_u_LOWERu_u_ORu_u_EQ]: !b a. h4/words/word__lo a b ==> h4/words/word__ls a b
% Assm [h4s_wordss_WORDu_u_NOTu_u_HIGHER]: !b a. ~h4/words/word__hi a b <=> h4/words/word__ls a b
% Assm [h4s_wordss_WORDu_u_LOWERu_u_EQUALu_u_ANTISYM]: !b a. h4/words/word__ls a b /\ h4/words/word__ls b a ==> a = b
% Assm [h4s_wordss_WORDu_u_NOTu_u_LOWERu_u_EQUAL]: !b a. ~h4/words/word__ls a b <=> h4/words/word__lo b a
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_wordss_WORDu_u_LO]: !b a. h4/words/word__lo a b <=> h4/prim__rec/_3C (h4/words/w2n a) (h4/words/w2n b)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_arithmetics_LESSu_u_EQu_u_CASES]: !n m. h4/arithmetic/_3C_3D m n \/ h4/arithmetic/_3C_3D n m
% 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_wordss_w2nu_u_11]: !w v. h4/words/w2n v = h4/words/w2n w <=> v = w
% Assm [h4s_arithmetics_LESSu_u_ORu_u_EQ]: !n m. h4/arithmetic/_3C_3D m n <=> h4/prim__rec/_3C m n \/ m = n
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% 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_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !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_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_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% 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_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_wordss_w2nu_u_equ_u_0]: !w. h4/words/w2n w = h4/num/0 <=> w = h4/words/n2w h4/num/0
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% 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_wordss_WORDu_u_ANDu_u_COMP]: !a. h4/words/word__and a (h4/words/word__1comp a) = h4/words/n2w h4/num/0
% Assm [h4s_wordss_LOG2u_u_w2nu_u_lt]: !w. ~(w = h4/words/n2w h4/num/0) ==> h4/prim__rec/_3C (h4/bit/LOG2 (h4/words/w2n w)) (h4/fcp/dimindex h4/bool/the__value)
% Assm [h4s_wordss_WORDu_u_SLICEu_u_ZERO]: !w l h. h4/prim__rec/_3C h l ==> h4/words/word__slice h l w = h4/words/n2w h4/num/0
% Assm [h4s_arithmetics_LESSu_u_LESSu_u_EQu_u_TRANS]: !p n m. h4/prim__rec/_3C m n /\ h4/arithmetic/_3C_3D n p ==> h4/prim__rec/_3C m p
% Assm [h4s_wordss_WORDu_u_EXTRACTu_u_ZERO3]: !w l h. h4/arithmetic/_3C_3D (h4/fcp/dimindex h4/bool/the__value) l ==> happ (h4/words/word__extract h l) w = h4/words/n2w h4/num/0
% Assm [h4s_wordss_LEASTu_u_BITu_u_LT]: !_0. (!w i. happ (happ _0 w) i <=> h4/fcp/fcp__index w i) ==> (!w. ~(w = h4/words/n2w h4/num/0) ==> h4/prim__rec/_3C (h4/while/LEAST (happ _0 w)) (h4/fcp/dimindex h4/bool/the__value))
% Assm [h4s_arithmetics_LESSu_u_EQu_u_LESSu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/prim__rec/_3C n p ==> h4/prim__rec/_3C m p
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n 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_wordss_WORDu_u_HIGHER]: !b a. h4/words/word__hi a b <=> h4/words/word__lo b a
% 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_wordss_WORDu_u_HS]: !b a. h4/words/word__hs a b <=> h4/arithmetic/_3E_3D (h4/words/w2n a) (h4/words/w2n b)
% Assm [h4s_arithmetics_NOTu_u_GREATERu_u_EQ]: !n m. ~h4/arithmetic/_3E_3D m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_GREATERu_u_EQ]: !n m. h4/arithmetic/_3E_3D n m <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_wordss_WORDu_u_LCANCELu_u_SUB]: !x w v. h4/words/word__sub v w = h4/words/word__sub x w <=> v = x
% Assm [h4s_wordss_WORDu_u_SUBu_u_REFL]: !w. h4/words/word__sub w w = h4/words/n2w h4/num/0
% Assm [h4s_wordss_wordu_u_addu_u_n2w]: !n m. h4/words/word__add (h4/words/n2w m) (h4/words/n2w n) = h4/words/n2w (h4/arithmetic/_2B m n)
% Assm [h4s_wordss_n2wu_u_w2n]: !w. h4/words/n2w (h4/words/w2n w) = w
% Assm [h4s_wordss_wordu_u_lou_u_def]: !_3. (!c v. happ (happ _3 c) v <=> ~c) ==> (!_2. (!c. happ _2 c = happ _3 c) ==> (!_1. (!z. happ _1 z = h4/pair/UNCURRY _2) ==> (!_0. (!n. happ _0 n = h4/pair/UNCURRY _1) ==> (!b a. h4/words/word__lo a b <=> h4/bool/LET (h4/pair/UNCURRY _0) (h4/words/nzcv a b)))))
% Assm [h4s_wordss_wordu_u_subu_u_def]: !w v. h4/words/word__sub v w = h4/words/word__add v (h4/words/word__2comp w)
% 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' <=> 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_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_wordss_n2wu_u_11]: !n m. h4/words/n2w m = h4/words/n2w n <=> h4/arithmetic/MOD m (h4/words/dimword h4/bool/the__value) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_wordss_WORDu_u_LOWERu_u_ANTISYM]: !b a. ~(h4/words/word__lo a b /\ h4/words/word__lo b a)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_wordss_ZEROu_u_LTu_u_dimword]: h4/prim__rec/_3C h4/num/0 (h4/words/dimword h4/bool/the__value)
% Assm [h4s_arithmetics_ZEROu_u_MOD]: !n. h4/prim__rec/_3C h4/num/0 n ==> h4/arithmetic/MOD h4/num/0 n = h4/num/0
% Assm [h4s_wordss_dimwordu_u_def]: h4/words/dimword h4/bool/the__value = h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/fcp/dimindex h4/bool/the__value)
% Assm [h4s_wordss_wordu_u_nchotomy]: !w. ?n. w = h4/words/n2w n
% Assm [h4s_wordss_w2nu_u_n2w]: !n. h4/words/w2n (h4/words/n2w n) = h4/arithmetic/MOD n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_wordss_w2nu_u_lt]: !w. h4/prim__rec/_3C (h4/words/w2n w) (h4/words/dimword h4/bool/the__value)
% Assm [h4s_bits_LTu_u_TWOEXP]: !x n. h4/prim__rec/_3C x (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n) <=> x = h4/num/0 \/ h4/prim__rec/_3C (h4/bit/LOG2 x) n
% Assm [h4s_wordss_w2wu_u_0]: happ h4/words/w2w (h4/words/n2w h4/num/0) = h4/words/n2w h4/num/0
% Assm [h4s_wordss_WORDu_u_BITSu_u_ZERO3]: !w l h. h4/arithmetic/_3C_3D (h4/fcp/dimindex h4/bool/the__value) l ==> happ (h4/words/word__bits h l) w = h4/words/n2w h4/num/0
% Assm [h4s_wordss_wordu_u_extractu_u_def]: !l h. h4/words/word__extract h l = h4/combin/o h4/words/w2w (h4/words/word__bits h l)
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_wordss_wordu_u_andu_u_def]: !_0. (!v w i. happ (happ (happ _0 v) w) i <=> h4/fcp/fcp__index v i /\ h4/fcp/fcp__index w i) ==> (!w v. h4/words/word__and v w = h4/fcp/FCP (happ (happ _0 v) w))
% Assm [h4s_wordss_wordu_u_1compu_u_def]: !_0. (!w i. happ (happ _0 w) i <=> ~h4/fcp/fcp__index w i) ==> (!w. h4/words/word__1comp w = h4/fcp/FCP (happ _0 w))
% Assm [h4s_wordss_wordu_u_0]: !i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> ~h4/fcp/fcp__index (h4/words/n2w h4/num/0) i
% 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_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_bools_NOTu_u_AND]: !t. ~(t /\ ~t)
% Assm [h4s_wordss_rangedu_u_wordu_u_nchotomy]: !w. ?n. w = h4/words/n2w n /\ h4/prim__rec/_3C n (h4/words/dimword h4/bool/the__value)
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_wordss_wordu_u_sliceu_u_n2w]: !n l h. h4/words/word__slice h l (h4/words/n2w n) = h4/words/n2w (h4/bit/SLICE (h4/arithmetic/MIN h (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) l n)
% Assm [h4s_bits_SLICEu_u_ZERO]: !n l h. h4/prim__rec/_3C h l ==> h4/bit/SLICE h l n = h4/num/0
% 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_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_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_wordss_wordu_u_index]: !n i. h4/prim__rec/_3C i (h4/fcp/dimindex h4/bool/the__value) ==> (h4/fcp/fcp__index (h4/words/n2w n) i <=> h4/bit/BIT i n)
% Assm [h4s_bits_EXISTSu_u_BITu_u_LT]: !n b. ~(n = h4/num/0) /\ h4/prim__rec/_3C n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) b) ==> (?i. h4/prim__rec/_3C i b /\ h4/bit/BIT i n)
% Goal: !w. h4/words/word__ls (h4/words/n2w h4/num/0) w
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_Q1212351,TV_Q1212347]: ![V_f, V_g]: (![V_x]: s(TV_Q1212347,happ(s(t_fun(TV_Q1212351,TV_Q1212347),V_f),s(TV_Q1212351,V_x))) = s(TV_Q1212347,happ(s(t_fun(TV_Q1212351,TV_Q1212347),V_g),s(TV_Q1212351,V_x))) => s(t_fun(TV_Q1212351,TV_Q1212347),V_f) = s(t_fun(TV_Q1212351,TV_Q1212347),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_wordss_WORDu_u_LS, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_ls(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_bool,h4s_arithmetics_u_3cu_3d(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),V_b)))))).
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_wordss_WORDu_u_LOWERu_u_ORu_u_EQ, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) <=> (p(s(t_bool,h4s_wordss_wordu_u_lo(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_fcps_cart(t_bool,TV_u_27a),V_a) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))).
fof(ah4s_wordss_WORDu_u_NOTu_u_LOWER, axiom, ![TV_u_27a]: ![V_b, V_a]: (~ (p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) <=> p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_wordss_WORDu_u_LOWERu_u_EQu_u_CASES, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) | p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
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_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_wordss_wordu_u_lsu_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_c, V_z, V_v]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_c))),s(t_bool,V_z))),s(t_bool,V_v)))) <=> (~ (p(s(t_bool,V_c))) | p(s(t_bool,V_z)))) => ![V_uu_2]: (![V_z, V_c]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_z))),s(t_bool,V_c))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_3),s(t_bool,V_c))),s(t_bool,V_z))) => ![V_uu_1]: (![V_z]: s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1),s(t_bool,V_z))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_bool,t_fun(t_bool,t_fun(t_bool,t_bool))),V_uu_2),s(t_bool,V_z))))) => ![V_uu_0]: (![V_n]: s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0),s(t_bool,V_n))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1))) => ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_ls(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_bool,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0))),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)))))))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_a]: p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_LOWERu_u_EQu_u_TRANS, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: ((p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c))))) => p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c)))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_EQu_u_TRANS, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: ((p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c))))) => p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c)))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_CASES, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) | p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_EQu_u_LOWERu_u_TRANS, axiom, ![TV_u_27a]: ![V_c, V_b, V_a]: ((p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c))))) => p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_c)))))).
fof(ah4s_wordss_WORDu_u_HIGHERu_u_EQ, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_hs(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_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_EQu_u_ANTISYM, axiom, ![TV_u_27a]: ![V_b, V_a]: ~ ((p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_IMPu_u_LOWERu_u_ORu_u_EQ, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) => p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_wordss_WORDu_u_NOTu_u_HIGHER, axiom, ![TV_u_27a]: ![V_b, V_a]: (~ (p(s(t_bool,h4s_wordss_wordu_u_hi(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) <=> p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_EQUALu_u_ANTISYM, axiom, ![TV_u_27a]: ![V_b, V_a]: ((p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & p(s(t_bool,h4s_wordss_wordu_u_ls(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_a) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))).
fof(ah4s_wordss_WORDu_u_NOTu_u_LOWERu_u_EQUAL, axiom, ![TV_u_27a]: ![V_b, V_a]: (~ (p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))) <=> p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
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_wordss_WORDu_u_LO, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_lo(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_bool,h4s_primu_u_recs_u_3c(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),V_b)))))).
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_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_arithmetics_LESSu_u_EQu_u_CASES, 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,V_n),s(t_h4s_nums_num,V_m)))))).
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_wordss_w2nu_u_11, axiom, ![TV_u_27a]: ![V_w, V_v]: (s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))) = s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))).
fof(ah4s_arithmetics_LESSu_u_ORu_u_EQ, 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_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_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
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_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_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_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_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_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
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_bools_EXCLUDEDu_u_MIDDLE, 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_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_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_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_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_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_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_wordss_w2nu_u_equ_u_0, axiom, ![TV_u_27a]: ![V_w]: (s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_nums_num,h4s_nums_0) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
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_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_wordss_WORDu_u_ANDu_u_COMP, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(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,h4s_nums_0)))).
fof(ah4s_wordss_LOG2u_u_w2nu_u_lt, axiom, ![TV_u_27a]: ![V_w]: (~ (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) => p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))))).
fof(ah4s_wordss_WORDu_u_SLICEu_u_ZERO, axiom, ![TV_u_27a]: ![V_w, 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_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_arithmetics_LESSu_u_LESSu_u_EQu_u_TRANS, axiom, ![V_p, 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_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)))))).
fof(ah4s_wordss_WORDu_u_EXTRACTu_u_ZERO3, axiom, ![TV_u_27a,TV_u_27b]: ![V_w, V_l, V_h]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_l)))) => s(t_h4s_fcps_cart(t_bool,TV_u_27b),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_wordss_LEASTu_u_BITu_u_LT, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_i]: 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)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i))) = 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,V_i))) => ![V_w]: (~ (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))) => p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_whiles_least(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)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))),s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_LESSu_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_primu_u_recs_u_3c(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)))))).
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_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_wordss_WORDu_u_HIGHER, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_hi(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_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
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_wordss_WORDu_u_HS, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_hs(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_bool,h4s_arithmetics_u_3eu_3d(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),V_b)))))).
fof(ah4s_arithmetics_NOTu_u_GREATERu_u_EQ, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_arithmetics_u_3eu_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_m))),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_GREATERu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
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_wordss_WORDu_u_LCANCELu_u_SUB, axiom, ![TV_u_27a]: ![V_x, V_w, V_v]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) <=> s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))).
fof(ah4s_wordss_WORDu_u_SUBu_u_REFL, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_wordu_u_addu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))),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_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_wordss_n2wu_u_w2n, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)).
fof(ah4s_wordss_wordu_u_lou_u_def, axiom, ![TV_u_27a]: ![V_uu_3]: (![V_c, V_v]: (p(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_3),s(t_bool,V_c))),s(t_bool,V_v)))) <=> ~ (p(s(t_bool,V_c)))) => ![V_uu_2]: (![V_c]: s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_2),s(t_bool,V_c))) = s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_3),s(t_bool,V_c))) => ![V_uu_1]: (![V_z]: s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1),s(t_bool,V_z))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_uu_2))) => ![V_uu_0]: (![V_n]: s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),happ(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0),s(t_bool,V_n))) = s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_bool),t_bool)),V_uu_1))) => ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_lo(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_bool,h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool))),t_bool),h4s_pairs_uncurry(s(t_fun(t_bool,t_fun(t_h4s_pairs_prod(t_bool,t_h4s_pairs_prod(t_bool,t_bool)),t_bool)),V_uu_0))),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)))))))))).
fof(ah4s_wordss_wordu_u_subu_u_def, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_sub(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),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_w)))))).
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,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_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_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_n2wu_u_11, axiom, ![TV_u_27a]: ![V_n, V_m]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))) = 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))))))).
fof(ah4s_wordss_WORDu_u_LOWERu_u_ANTISYM, axiom, ![TV_u_27a]: ![V_b, V_a]: ~ ((p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) & p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))))))).
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_wordss_ZEROu_u_LTu_u_dimword, 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_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_arithmetics_ZEROu_u_MOD, 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,V_n)))) => s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_wordss_dimwordu_u_def, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))) = 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_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value)))))).
fof(ah4s_wordss_wordu_u_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_n]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n)))).
fof(ah4s_wordss_w2nu_u_n2w, axiom, ![TV_u_27a]: ![V_n]: s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = 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)))))).
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_wordss_w2nu_u_lt, axiom, ![TV_u_27a]: ![V_w]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))).
fof(ah4s_bits_LTu_u_TWOEXP, axiom, ![V_x, V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_x),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,V_x) = s(t_h4s_nums_num,h4s_nums_0) | p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_bits_log2(s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_wordss_w2wu_u_0, axiom, ![TV_u_27b,TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27b),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_w2w),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_wordss_WORDu_u_BITSu_u_ZERO3, axiom, ![TV_u_27a]: ![V_w, V_l, V_h]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(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_l)))) => s(t_h4s_fcps_cart(t_bool,TV_u_27a),happ(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ah4s_wordss_wordu_u_extractu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_l, V_h]: s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l))) = s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_combins_o(s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27b)),h4s_wordss_w2w),s(t_fun(t_h4s_fcps_cart(t_bool,TV_u_27a),t_h4s_fcps_cart(t_bool,TV_u_27a)),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l)))))).
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_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_wordss_wordu_u_andu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_v, V_w, V_i]: (p(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_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_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> (p(s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_nums_num,V_i)))) & 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,V_i)))))) => ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_and(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),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_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_bool))),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_wordu_u_1compu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_w, V_i]: (p(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)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_nums_num,V_i)))) <=> ~ (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,V_i)))))) => ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_1comp(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)),V_uu_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))))).
fof(ah4s_wordss_wordu_u_0, axiom, ![TV_u_27a]: ![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_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),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,V_i))))))).
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_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_bools_NOTu_u_AND, axiom, ![V_t]: ~ ((p(s(t_bool,V_t)) & ~ (p(s(t_bool,V_t)))))).
fof(ah4s_wordss_rangedu_u_wordu_u_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_n]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))) & p(s(t_bool,h4s_primu_u_recs_u_3c(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)))))))).
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_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_wordss_wordu_u_sliceu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_slice(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),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_wordss_n2w(s(t_h4s_nums_num,h4s_bits_slice(s(t_h4s_nums_num,h4s_arithmetics_min(s(t_h4s_nums_num,V_h),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,V_l),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_bits_SLICEu_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_slice(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_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_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_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
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_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_wordss_wordu_u_index, axiom, ![TV_u_27a]: ![V_n, 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_27a),h4s_bools_theu_u_value)))))) => s(t_bool,h4s_fcps_fcpu_u_index(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))).
fof(ah4s_bits_EXISTSu_u_BITu_u_LT, axiom, ![V_n, V_b]: ((~ (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0)) & p(s(t_bool,h4s_primu_u_recs_u_3c(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,V_b))))))) => ?[V_i]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_b)))) & p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_i),s(t_h4s_nums_num,V_n))))))).
fof(ch4s_wordss_WORDu_u_0u_u_LS, conjecture, ![TV_u_27a]: ![V_w]: p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))).
