%   ORIGINAL: h4/patricia/SIZE0_c2
% 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/EQ__MONO__ADD__EQ: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm: h4/list/LENGTH__APPEND: !l2 l1. h4/list/LENGTH (h4/list/APPEND l1 l2) = h4/arithmetic/_2B (h4/list/LENGTH l1) (h4/list/LENGTH l2)
% Assm: h4/patricia/TRAVERSE__def_c2: !r p m l. h4/patricia/TRAVERSE (h4/patricia/Branch p m l r) = h4/list/APPEND (h4/patricia/TRAVERSE l) (h4/patricia/TRAVERSE r)
% Assm: h4/patricia/SIZE__def: !t. h4/patricia/SIZE t = h4/list/LENGTH (h4/patricia/TRAVERSE t)
% Goal: !r p m l. h4/patricia/SIZE (h4/patricia/Branch p m l r) = h4/arithmetic/_2B (h4/patricia/SIZE l) (h4/patricia/SIZE r)
%   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_EQu_u_MONOu_u_ADDu_u_EQ]: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm [h4s_lists_LENGTHu_u_APPEND]: !l2 l1. h4/list/LENGTH (h4/list/APPEND l1 l2) = h4/arithmetic/_2B (h4/list/LENGTH l1) (h4/list/LENGTH l2)
% Assm [h4s_patricias_TRAVERSEu_u_defu_c2]: !r p m l. h4/patricia/TRAVERSE (h4/patricia/Branch p m l r) = h4/list/APPEND (h4/patricia/TRAVERSE l) (h4/patricia/TRAVERSE r)
% Assm [h4s_patricias_SIZEu_u_def]: !t. h4/patricia/SIZE t = h4/list/LENGTH (h4/patricia/TRAVERSE t)
% Goal: !r p m l. h4/patricia/SIZE (h4/patricia/Branch p m l r) = h4/arithmetic/_2B (h4/patricia/SIZE l) (h4/patricia/SIZE r)
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_Q288056,TV_Q288052]: ![V_f, V_g]: (![V_x]: s(TV_Q288052,happ(s(t_fun(TV_Q288056,TV_Q288052),V_f),s(TV_Q288056,V_x))) = s(TV_Q288052,happ(s(t_fun(TV_Q288056,TV_Q288052),V_g),s(TV_Q288056,V_x))) => s(t_fun(TV_Q288056,TV_Q288052),V_f) = s(t_fun(TV_Q288056,TV_Q288052),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_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_lists_LENGTHu_u_APPEND, axiom, ![TV_u_27a]: ![V_l2, V_l1]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_patricias_TRAVERSEu_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_p, V_m, V_l]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_m),s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_patricias_ptree(TV_u_27a),V_r))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_append(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_r)))))).
fof(ah4s_patricias_SIZEu_u_def, axiom, ![TV_u_27a]: ![V_t]: s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(TV_u_27a),V_t))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_t)))))).
fof(ch4s_patricias_SIZE0u_c2, conjecture, ![TV_u_27a]: ![V_r, V_p, V_m, V_l]: s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_m),s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_patricias_ptree(TV_u_27a),V_r))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(TV_u_27a),V_r)))))).
