%   ORIGINAL: h4/numposrep/l2n__pow2__compute_c1
% 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/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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/bit/MOD__2EXP__def: !x n. h4/bit/MOD__2EXP x n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm: h4/bit/TIMES__2EXP__def: !x n. h4/bit/TIMES__2EXP x n = h4/arithmetic/_2A n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm: h4/numposrep/l2n__def_c1: !t h b. h4/numposrep/l2n b (h4/list/CONS h t) = h4/arithmetic/_2B (h4/arithmetic/MOD h b) (h4/arithmetic/_2A b (h4/numposrep/l2n b t))
% Goal: !t p h. h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p) (h4/list/CONS h t) = h4/arithmetic/_2B (h4/bit/MOD__2EXP p h) (h4/bit/TIMES__2EXP p (h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p) t))
%   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_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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_bits_MODu_u_2EXPu_u_def]: !x n. h4/bit/MOD__2EXP x n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_bits_TIMESu_u_2EXPu_u_def]: !x n. h4/bit/TIMES__2EXP x n = h4/arithmetic/_2A n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) x)
% Assm [h4s_numposreps_l2nu_u_defu_c1]: !t h b. h4/numposrep/l2n b (h4/list/CONS h t) = h4/arithmetic/_2B (h4/arithmetic/MOD h b) (h4/arithmetic/_2A b (h4/numposrep/l2n b t))
% Goal: !t p h. h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p) (h4/list/CONS h t) = h4/arithmetic/_2B (h4/bit/MOD__2EXP p h) (h4/bit/TIMES__2EXP p (h4/numposrep/l2n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) p) t))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q210139,TV_Q210135]: ![V_f, V_g]: (![V_x]: s(TV_Q210135,happ(s(t_fun(TV_Q210139,TV_Q210135),V_f),s(TV_Q210139,V_x))) = s(TV_Q210135,happ(s(t_fun(TV_Q210139,TV_Q210135),V_g),s(TV_Q210139,V_x))) => s(t_fun(TV_Q210139,TV_Q210135),V_f) = s(t_fun(TV_Q210139,TV_Q210135),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
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,t0)))).
fof(ah4s_arithmetics_ADDu_u_COMM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_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_bits_MODu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_x),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_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_x)))))).
fof(ah4s_bits_TIMESu_u_2EXPu_u_def, axiom, ![V_x, V_n]: s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_x),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,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_x)))))).
fof(ah4s_numposreps_l2nu_u_defu_c1, axiom, ![V_t, V_h, V_b]: s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,V_h),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_b))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_numposreps_l2n(s(t_h4s_nums_num,V_b),s(t_h4s_lists_list(t_h4s_nums_num),V_t)))))))).
fof(ch4s_numposreps_l2nu_u_pow2u_u_computeu_c1, conjecture, ![V_t, V_p, V_h]: s(t_h4s_nums_num,h4s_numposreps_l2n(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_p))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,V_h),s(t_h4s_lists_list(t_h4s_nums_num),V_t))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_bits_modu_u_2exp(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_h))),s(t_h4s_nums_num,h4s_bits_timesu_u_2exp(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,h4s_numposreps_l2n(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_p))),s(t_h4s_lists_list(t_h4s_nums_num),V_t)))))))).
