%   ORIGINAL: h4/patricia/EMPTY__IS__PTREE
% 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/patricia/IS__PTREE__def_c0: h4/patricia/IS__PTREE h4/patricia/Empty <=> T
% Goal: h4/patricia/IS__PTREE h4/patricia/Empty
%   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_patricias_ISu_u_PTREEu_u_defu_c0]: h4/patricia/IS__PTREE h4/patricia/Empty <=> T
% Goal: h4/patricia/IS__PTREE h4/patricia/Empty
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_Q285964,TV_Q285960]: ![V_f, V_g]: (![V_x]: s(TV_Q285960,happ(s(t_fun(TV_Q285964,TV_Q285960),V_f),s(TV_Q285964,V_x))) = s(TV_Q285960,happ(s(t_fun(TV_Q285964,TV_Q285960),V_g),s(TV_Q285964,V_x))) => s(t_fun(TV_Q285964,TV_Q285960),V_f) = s(t_fun(TV_Q285964,TV_Q285960),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_patricias_ISu_u_PTREEu_u_defu_c0, axiom, ![TV_u_27a]: s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty))) = s(t_bool,t)).
fof(ch4s_patricias_EMPTYu_u_ISu_u_PTREE, conjecture, ![TV_u_27a]: p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty))))).
