%   ORIGINAL: h4/bag/BAG__ALL__DISTINCT__BAG__OF__SET
% 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/bag/SET__BAG__I: !s. h4/bag/SET__OF__BAG (h4/bag/BAG__OF__SET s) = s
% Assm: h4/bag/BAG__ALL__DISTINCT__SET: !b. h4/bag/BAG__ALL__DISTINCT b <=> h4/bag/BAG__OF__SET (h4/bag/SET__OF__BAG b) = b
% Goal: !s. h4/bag/BAG__ALL__DISTINCT (h4/bag/BAG__OF__SET s)
%   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_bags_SETu_u_BAGu_u_I]: !s. h4/bag/SET__OF__BAG (h4/bag/BAG__OF__SET s) = s
% Assm [h4s_bags_BAGu_u_ALLu_u_DISTINCTu_u_SET]: !b. h4/bag/BAG__ALL__DISTINCT b <=> h4/bag/BAG__OF__SET (h4/bag/SET__OF__BAG b) = b
% Goal: !s. h4/bag/BAG__ALL__DISTINCT (h4/bag/BAG__OF__SET s)
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_Q232400,TV_Q232396]: ![V_f, V_g]: (![V_x]: s(TV_Q232396,happ(s(t_fun(TV_Q232400,TV_Q232396),V_f),s(TV_Q232400,V_x))) = s(TV_Q232396,happ(s(t_fun(TV_Q232400,TV_Q232396),V_g),s(TV_Q232400,V_x))) => s(t_fun(TV_Q232400,TV_Q232396),V_f) = s(t_fun(TV_Q232400,TV_Q232396),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_bags_SETu_u_BAGu_u_I, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_bags_BAGu_u_ALLu_u_DISTINCTu_u_SET, axiom, ![TV_u_27a]: ![V_b]: (p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))) <=> s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(TV_u_27a,t_bool),h4s_bags_setu_u_ofu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))))) = s(t_fun(TV_u_27a,t_h4s_nums_num),V_b))).
fof(ch4s_bags_BAGu_u_ALLu_u_DISTINCTu_u_BAGu_u_OFu_u_SET, conjecture, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_ofu_u_set(s(t_fun(TV_u_27a,t_bool),V_s))))))).
