%   ORIGINAL: h4/patricia/UNION__PTREE__EMPTY_c0
% 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/patricia/UNION__PTREE__def: !t2 t1. h4/patricia/UNION__PTREE t1 t2 = h4/patricia/PTREE__OF__NUMSET t1 (h4/patricia/NUMSET__OF__PTREE t2)
% Assm: h4/patricia/NUMSET__OF__PTREE__EMPTY: h4/patricia/NUMSET__OF__PTREE h4/patricia/Empty = h4/pred__set/EMPTY
% Assm: h4/patricia/PTREE__OF__NUMSET__EMPTY: !t. h4/patricia/PTREE__OF__NUMSET t h4/pred__set/EMPTY = t
% Goal: !t. h4/patricia/UNION__PTREE t h4/patricia/Empty = 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_patricias_UNIONu_u_PTREEu_u_def]: !t2 t1. h4/patricia/UNION__PTREE t1 t2 = h4/patricia/PTREE__OF__NUMSET t1 (h4/patricia/NUMSET__OF__PTREE t2)
% Assm [h4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_EMPTY]: h4/patricia/NUMSET__OF__PTREE h4/patricia/Empty = h4/pred__set/EMPTY
% Assm [h4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_EMPTY]: !t. h4/patricia/PTREE__OF__NUMSET t h4/pred__set/EMPTY = t
% Goal: !t. h4/patricia/UNION__PTREE t h4/patricia/Empty = 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_Q287503,TV_Q287499]: ![V_f, V_g]: (![V_x]: s(TV_Q287499,happ(s(t_fun(TV_Q287503,TV_Q287499),V_f),s(TV_Q287503,V_x))) = s(TV_Q287499,happ(s(t_fun(TV_Q287503,TV_Q287499),V_g),s(TV_Q287503,V_x))) => s(t_fun(TV_Q287503,TV_Q287499),V_f) = s(t_fun(TV_Q287503,TV_Q287499),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_patricias_UNIONu_u_PTREEu_u_def, axiom, ![V_t2, V_t1]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_unionu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t1),s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t2))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t1),s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t2)))))).
fof(ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_EMPTY, axiom, s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_EMPTY, axiom, ![V_t]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t)).
fof(ch4s_patricias_UNIONu_u_PTREEu_u_EMPTYu_c0, conjecture, ![V_t]: s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_unionu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t),s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty))) = s(t_h4s_patricias_ptree(t_h4s_ones_one),V_t)).
