%   ORIGINAL: h4/numeral__bit/BIT__REVERSE__EVAL
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% 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/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/arithmetic/EXP0_c0: !m. h4/arithmetic/EXP m h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/arithmetic/EXP0_c1: !n m. h4/arithmetic/EXP m (h4/num/SUC n) = h4/arithmetic/_2A m (h4/arithmetic/EXP m n)
% Assm: h4/arithmetic/FUNPOW0_c0: !x f. h4/arithmetic/FUNPOW f h4/num/0 x = x
% Assm: h4/arithmetic/FUNPOW0_c1: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = h4/arithmetic/FUNPOW f n (f x)
% Assm: h4/arithmetic/TWO: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/MULT__COMM: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm: h4/arithmetic/EQ__MONO__ADD__EQ: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm: h4/arithmetic/ZERO__LESS__EXP: !n m. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/num/SUC n) m)
% Assm: h4/arithmetic/DIV__1: !q. h4/arithmetic/DIV q (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = q
% Assm: h4/arithmetic/DIV__DIV__DIV__MULT: !n m. h4/prim__rec/_3C h4/num/0 m /\ h4/prim__rec/_3C h4/num/0 n ==> (!x. h4/arithmetic/DIV (h4/arithmetic/DIV x m) n = h4/arithmetic/DIV x (h4/arithmetic/_2A m n))
% Assm: h4/arithmetic/EXP__1_c1: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm: h4/arithmetic/FUNPOW__SUC: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = f (h4/arithmetic/FUNPOW f n x)
% Assm: h4/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/numeral/numeral__distrib_c21: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm: h4/numeral/numeral__lt_c1: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm: h4/numeral/numeral__pre_c1: h4/prim__rec/PRE (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__texp__help_c0: !acc. h4/numeral/texp__help h4/arithmetic/ZERO acc = h4/arithmetic/BIT2 acc
% Assm: h4/numeral/TWO__EXP__THM_c0: h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/numeral/TWO__EXP__THM_c1: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = h4/arithmetic/NUMERAL (h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) h4/arithmetic/ZERO)
% 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/bit/BIT__REVERSE__def_c0: !x. h4/bit/BIT__REVERSE h4/num/0 x = h4/num/0
% Assm: h4/bit/BIT__REVERSE__def_c1: !x n. h4/bit/BIT__REVERSE (h4/num/SUC n) x = h4/arithmetic/_2B (h4/arithmetic/_2A (h4/bit/BIT__REVERSE n x) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/bit/SBIT (h4/bit/BIT n x) h4/num/0)
% Assm: h4/bit/SUC__SUB: !a. h4/arithmetic/_2D (h4/num/SUC a) a = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/bit/BITS__THM: !n l h. h4/bit/BITS h l n = h4/arithmetic/MOD (h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/num/SUC h) l))
% Assm: h4/bit/BIT0__ODD: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm: h4/numeral__bit/BIT__REV__def_c0: !y x. h4/numeral__bit/BIT__REV h4/num/0 x y = y
% Assm: h4/numeral__bit/BIT__REV__def_c1: !y x n. h4/numeral__bit/BIT__REV (h4/num/SUC n) x y = h4/numeral__bit/BIT__REV n (h4/arithmetic/DIV x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) y) (h4/bit/SBIT (h4/arithmetic/ODD x) h4/num/0))
% Goal: !n m. h4/bit/BIT__REVERSE m n = h4/numeral__bit/BIT__REV m n h4/num/0
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% 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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% 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_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% 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_arithmetics_EXP0u_c0]: !m. h4/arithmetic/EXP m h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_arithmetics_EXP0u_c1]: !n m. h4/arithmetic/EXP m (h4/num/SUC n) = h4/arithmetic/_2A m (h4/arithmetic/EXP m n)
% Assm [h4s_arithmetics_FUNPOW0u_c0]: !x f. h4/arithmetic/FUNPOW f h4/num/0 x = x
% Assm [h4s_arithmetics_FUNPOW0u_c1]: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = h4/arithmetic/FUNPOW f n (happ f x)
% Assm [h4s_arithmetics_TWO]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_MULTu_u_COMM]: !n m. h4/arithmetic/_2A m n = h4/arithmetic/_2A n m
% Assm [h4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ]: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EXP]: !n m. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/num/SUC n) m)
% Assm [h4s_arithmetics_DIVu_u_1]: !q. h4/arithmetic/DIV q (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = q
% Assm [h4s_arithmetics_DIVu_u_DIVu_u_DIVu_u_MULT]: !n m. h4/prim__rec/_3C h4/num/0 m /\ h4/prim__rec/_3C h4/num/0 n ==> (!x. h4/arithmetic/DIV (h4/arithmetic/DIV x m) n = h4/arithmetic/DIV x (h4/arithmetic/_2A m n))
% Assm [h4s_arithmetics_EXPu_u_1u_c1]: !n. h4/arithmetic/EXP n (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = n
% Assm [h4s_arithmetics_FUNPOWu_u_SUC]: !x n f. h4/arithmetic/FUNPOW f (h4/num/SUC n) x = happ f (h4/arithmetic/FUNPOW f n x)
% Assm [h4s_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_numerals_numeralu_u_distribu_c21]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/NUMERAL n) <=> h4/prim__rec/_3C h4/arithmetic/ZERO n
% Assm [h4s_numerals_numeralu_u_ltu_c1]: !n. h4/prim__rec/_3C h4/arithmetic/ZERO (h4/arithmetic/BIT2 n) <=> T
% Assm [h4s_numerals_numeralu_u_preu_c1]: h4/prim__rec/PRE (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c0]: !acc. h4/numeral/texp__help h4/arithmetic/ZERO acc = h4/arithmetic/BIT2 acc
% Assm [h4s_numerals_TWOu_u_EXPu_u_THMu_c0]: h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_numerals_TWOu_u_EXPu_u_THMu_c1]: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)) = h4/arithmetic/NUMERAL (h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) h4/arithmetic/ZERO)
% 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_bits_BITu_u_REVERSEu_u_defu_c0]: !x. h4/bit/BIT__REVERSE h4/num/0 x = h4/num/0
% Assm [h4s_bits_BITu_u_REVERSEu_u_defu_c1]: !x n. h4/bit/BIT__REVERSE (h4/num/SUC n) x = h4/arithmetic/_2B (h4/arithmetic/_2A (h4/bit/BIT__REVERSE n x) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/bit/SBIT (happ (h4/bit/BIT n) x) h4/num/0)
% Assm [h4s_bits_SUCu_u_SUB]: !a. h4/arithmetic/_2D (h4/num/SUC a) a = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_bits_BITSu_u_THM]: !n l h. h4/bit/BITS h l n = h4/arithmetic/MOD (h4/arithmetic/DIV n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) l)) (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/_2D (h4/num/SUC h) l))
% Assm [h4s_bits_BIT0u_u_ODD]: h4/bit/BIT h4/num/0 = h4/arithmetic/ODD
% Assm [h4s_numeralu_u_bits_BITu_u_REVu_u_defu_c0]: !y x. h4/numeral__bit/BIT__REV h4/num/0 x y = y
% Assm [h4s_numeralu_u_bits_BITu_u_REVu_u_defu_c1]: !y x n. h4/numeral__bit/BIT__REV (h4/num/SUC n) x y = h4/numeral__bit/BIT__REV n (h4/arithmetic/DIV x (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) (h4/arithmetic/_2B (h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) y) (h4/bit/SBIT (happ h4/arithmetic/ODD x) h4/num/0))
% Goal: !n m. h4/bit/BIT__REVERSE m n = h4/numeral__bit/BIT__REV m n h4/num/0
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_Q15627,TV_Q15623]: ![V_f, V_g]: (![V_x]: s(TV_Q15623,happ(s(t_fun(TV_Q15627,TV_Q15623),V_f),s(TV_Q15627,V_x))) = s(TV_Q15623,happ(s(t_fun(TV_Q15627,TV_Q15623),V_g),s(TV_Q15627,V_x))) => s(t_fun(TV_Q15627,TV_Q15623),V_f) = s(t_fun(TV_Q15627,TV_Q15623),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_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_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_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
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_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_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_arithmetics_EXP0u_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = 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_EXP0u_c1, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_FUNPOW0u_c0, axiom, ![TV_u_27a]: ![V_x, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_arithmetics_FUNPOW0u_c1, axiom, ![TV_u_27a]: ![V_x, V_n, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_x))) = s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,V_n),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_x)))))).
fof(ah4s_arithmetics_TWO, axiom, 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,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_arithmetics_MULTu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ, 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,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_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EXP, axiom, ![V_n, V_m]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(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_DIVu_u_1, axiom, ![V_q]: s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_q),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_q)).
fof(ah4s_arithmetics_DIVu_u_DIVu_u_DIVu_u_MULT, axiom, ![V_n, V_m]: ((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m)))) & 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))))) => ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_arithmetics_EXPu_u_1u_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_FUNPOWu_u_SUC, axiom, ![TV_u_27a]: ![V_x, V_n, V_f]: s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(TV_u_27a,V_x))) = s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,h4s_arithmetics_funpow(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(t_h4s_nums_num,V_n),s(TV_u_27a,V_x)))))).
fof(ah4s_numerals_numeralu_u_distribu_c13, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))) = 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_numerals_numeralu_u_distribu_c21, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_numeralu_u_ltu_c1, axiom, ![V_n]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_preu_c1, axiom, s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c0, axiom, ![V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_acc)))).
fof(ah4s_numerals_TWOu_u_EXPu_u_THMu_c0, axiom, 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_0))) = 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_numerals_TWOu_u_EXPu_u_THMu_c1, axiom, ![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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
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_bits_BITu_u_REVERSEu_u_defu_c0, axiom, ![V_x]: s(t_h4s_nums_num,h4s_bits_bitu_u_reverse(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bits_BITu_u_REVERSEu_u_defu_c1, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_bitu_u_reverse(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_bits_bitu_u_reverse(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_bits_sbit(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,V_x))),s(t_h4s_nums_num,h4s_nums_0)))))).
fof(ah4s_bits_SUCu_u_SUB, axiom, ![V_a]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_a))) = 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_bits_BITSu_u_THM, axiom, ![V_n, V_l, V_h]: 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_mod(s(t_h4s_nums_num,h4s_arithmetics_div(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_l))))),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_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_numeralu_u_bits_BITu_u_REVu_u_defu_c0, axiom, ![V_y, V_x]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,V_y)).
fof(ah4s_numeralu_u_bits_BITu_u_REVu_u_defu_c1, axiom, ![V_y, V_x, V_n]: s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,V_y))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,V_x),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_y))),s(t_h4s_nums_num,h4s_bits_sbit(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ch4s_numeralu_u_bits_BITu_u_REVERSEu_u_EVAL, conjecture, ![V_n, V_m]: s(t_h4s_nums_num,h4s_bits_bitu_u_reverse(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_rev(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0)))).
