%   ORIGINAL: h4/Encode/wf__pred__bnum__total
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/ZERO__LESS__EXP: !n m. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/num/SUC n) m)
% Assm: h4/Encode/wf__pred__def: !p. h4/Encode/wf__pred p <=> (?x. p x)
% Assm: h4/Encode/wf__pred__bnum__def: !p m. h4/Encode/wf__pred__bnum m p <=> h4/Encode/wf__pred p /\ (!x. p x ==> h4/prim__rec/_3C x (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m))
% Goal: !m. h4/Encode/wf__pred__bnum m (\x. h4/prim__rec/_3C x (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m))
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% 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_ZEROu_u_LESSu_u_EXP]: !n m. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/num/SUC n) m)
% Assm [h4s_Encodes_wfu_u_predu_u_def]: !p. h4/Encode/wf__pred p <=> (?x. happ p x)
% Assm [h4s_Encodes_wfu_u_predu_u_bnumu_u_def]: !p m. h4/Encode/wf__pred__bnum m p <=> h4/Encode/wf__pred p /\ (!x. happ p x ==> h4/prim__rec/_3C x (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m))
% Goal: !_0. (!m x. happ (happ _0 m) x <=> h4/prim__rec/_3C x (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) m)) ==> (!m. h4/Encode/wf__pred__bnum m (happ _0 m))
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_Q204285,TV_Q204281]: ![V_f, V_g]: (![V_x]: s(TV_Q204281,happ(s(t_fun(TV_Q204285,TV_Q204281),V_f),s(TV_Q204285,V_x))) = s(TV_Q204281,happ(s(t_fun(TV_Q204285,TV_Q204281),V_g),s(TV_Q204285,V_x))) => s(t_fun(TV_Q204285,TV_Q204281),V_f) = s(t_fun(TV_Q204285,TV_Q204281),V_g))).
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_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_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_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_Encodes_wfu_u_predu_u_def, axiom, ![TV_u_27a]: ![V_p]: (p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(TV_u_27a,t_bool),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)))))).
fof(ah4s_Encodes_wfu_u_predu_u_bnumu_u_def, axiom, ![V_p, V_m]: (p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,V_m),s(t_fun(t_h4s_nums_num,t_bool),V_p)))) <=> (p(s(t_bool,h4s_encodes_wfu_u_pred(s(t_fun(t_h4s_nums_num,t_bool),V_p)))) & ![V_x]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_p),s(t_h4s_nums_num,V_x)))) => 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_m)))))))))).
fof(ch4s_Encodes_wfu_u_predu_u_bnumu_u_total, conjecture, ![V_uu_0]: (![V_m, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_x))) = 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_m))))) => ![V_m]: p(s(t_bool,h4s_encodes_wfu_u_predu_u_bnum(s(t_h4s_nums_num,V_m),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_m)))))))).
