%   ORIGINAL: h4/bag/BAG__DISJOINT__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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/pred__set/DISJOINT__EMPTY_c0: !s. h4/pred__set/DISJOINT h4/pred__set/EMPTY s
% Assm: h4/pred__set/DISJOINT__EMPTY_c1: !s. h4/pred__set/DISJOINT s h4/pred__set/EMPTY
% Assm: h4/bag/BAG__OF__EMPTY: h4/bag/SET__OF__BAG h4/bag/EMPTY__BAG = h4/pred__set/EMPTY
% Assm: h4/bag/BAG__DISJOINT0: !b2 b1. h4/bag/BAG__DISJOINT b1 b2 <=> h4/pred__set/DISJOINT (h4/bag/SET__OF__BAG b1) (h4/bag/SET__OF__BAG b2)
% Goal: !b. h4/bag/BAG__DISJOINT b h4/bag/EMPTY__BAG
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_predu_u_sets_DISJOINTu_u_EMPTYu_c0]: !s. h4/pred__set/DISJOINT h4/pred__set/EMPTY s
% Assm [h4s_predu_u_sets_DISJOINTu_u_EMPTYu_c1]: !s. h4/pred__set/DISJOINT s h4/pred__set/EMPTY
% Assm [h4s_bags_BAGu_u_OFu_u_EMPTY]: h4/bag/SET__OF__BAG h4/bag/EMPTY__BAG = h4/pred__set/EMPTY
% Assm [h4s_bags_BAGu_u_DISJOINT0]: !b2 b1. h4/bag/BAG__DISJOINT b1 b2 <=> h4/pred__set/DISJOINT (h4/bag/SET__OF__BAG b1) (h4/bag/SET__OF__BAG b2)
% Goal: !b. h4/bag/BAG__DISJOINT b h4/bag/EMPTY__BAG
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_Q230258,TV_Q230254]: ![V_f, V_g]: (![V_x]: s(TV_Q230254,happ(s(t_fun(TV_Q230258,TV_Q230254),V_f),s(TV_Q230258,V_x))) = s(TV_Q230254,happ(s(t_fun(TV_Q230258,TV_Q230254),V_g),s(TV_Q230258,V_x))) => s(t_fun(TV_Q230258,TV_Q230254),V_f) = s(t_fun(TV_Q230258,TV_Q230254),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_predu_u_sets_DISJOINTu_u_EMPTYu_c0, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_predu_u_sets_DISJOINTu_u_EMPTYu_c1, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))))).
fof(ah4s_bags_BAGu_u_OFu_u_EMPTY, axiom, ![TV_u_27a]: 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_emptyu_u_bag))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_bags_BAGu_u_DISJOINT0, axiom, ![TV_u_27a]: ![V_b2, V_b1]: s(t_bool,h4s_bags_bagu_u_disjoint(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2))) = s(t_bool,h4s_predu_u_sets_disjoint(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_b1))),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_b2)))))).
fof(ch4s_bags_BAGu_u_DISJOINTu_u_EMPTYu_c0, conjecture, ![TV_u_27a]: ![V_b]: p(s(t_bool,h4s_bags_bagu_u_disjoint(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))).
