%   ORIGINAL: h4/patricia/SIZE0_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/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/patricia/TRAVERSE__def_c1: !j d. h4/patricia/TRAVERSE (h4/patricia/Leaf j d) = h4/list/CONS j h4/list/NIL
% Assm: h4/patricia/SIZE__def: !t. h4/patricia/SIZE t = h4/list/LENGTH (h4/patricia/TRAVERSE t)
% Goal: !k d. h4/patricia/SIZE (h4/patricia/Leaf k d) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
%   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_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_patricias_TRAVERSEu_u_defu_c1]: !j d. h4/patricia/TRAVERSE (h4/patricia/Leaf j d) = h4/list/CONS j h4/list/NIL
% Assm [h4s_patricias_SIZEu_u_def]: !t. h4/patricia/SIZE t = h4/list/LENGTH (h4/patricia/TRAVERSE t)
% Goal: !k d. h4/patricia/SIZE (h4/patricia/Leaf k d) = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
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_Q288031,TV_Q288027]: ![V_f, V_g]: (![V_x]: s(TV_Q288027,happ(s(t_fun(TV_Q288031,TV_Q288027),V_f),s(TV_Q288031,V_x))) = s(TV_Q288027,happ(s(t_fun(TV_Q288031,TV_Q288027),V_g),s(TV_Q288031,V_x))) => s(t_fun(TV_Q288031,TV_Q288027),V_f) = s(t_fun(TV_Q288031,TV_Q288027),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_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_lists_LENGTH0u_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_patricias_TRAVERSEu_u_defu_c1, axiom, ![TV_u_27a]: ![V_j, V_d]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_j),s(TV_u_27a,V_d))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,V_j),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil)))).
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_c1, conjecture, ![TV_u_27a]: ![V_k, V_d]: s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_d))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
