%   ORIGINAL: h4/bag/BAG__NOT__LESS__EMPTY
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bag/BAG__INSERT__NOT__EMPTY: !x b. ~(h4/bag/BAG__INSERT x b = h4/bag/EMPTY__BAG)
% Assm: h4/bag/BAG__UNION__EMPTY_c2: !b2 b1. h4/bag/BAG__UNION b1 b2 = h4/bag/EMPTY__BAG <=> b1 = h4/bag/EMPTY__BAG /\ b2 = h4/bag/EMPTY__BAG
% Assm: h4/bag/FINITE__BAG__THM_c0: h4/bag/FINITE__BAG h4/bag/EMPTY__BAG
% Assm: h4/bag/mlt1__def: !r b2 b1. h4/bag/mlt1 r b1 b2 <=> h4/bag/FINITE__BAG b1 /\ h4/bag/FINITE__BAG b2 /\ (?e rep res. b1 = h4/bag/BAG__UNION rep res /\ b2 = h4/bag/BAG__UNION res (h4/bag/BAG__INSERT e h4/bag/EMPTY__BAG) /\ (!e_27. h4/bag/BAG__IN e_27 rep ==> r e_27 e))
% Goal: !r b. ~h4/bag/mlt1 r 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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bags_BAGu_u_INSERTu_u_NOTu_u_EMPTY]: !x b. ~(h4/bag/BAG__INSERT x b = h4/bag/EMPTY__BAG)
% Assm [h4s_bags_BAGu_u_UNIONu_u_EMPTYu_c2]: !b2 b1. h4/bag/BAG__UNION b1 b2 = h4/bag/EMPTY__BAG <=> b1 = h4/bag/EMPTY__BAG /\ b2 = h4/bag/EMPTY__BAG
% Assm [h4s_bags_FINITEu_u_BAGu_u_THMu_c0]: h4/bag/FINITE__BAG h4/bag/EMPTY__BAG
% Assm [h4s_bags_mlt1u_u_def]: !r b2 b1. h4/bag/mlt1 r b1 b2 <=> h4/bag/FINITE__BAG b1 /\ h4/bag/FINITE__BAG b2 /\ (?e rep res. b1 = h4/bag/BAG__UNION rep res /\ b2 = h4/bag/BAG__UNION res (h4/bag/BAG__INSERT e h4/bag/EMPTY__BAG) /\ (!e_27. h4/bag/BAG__IN e_27 rep ==> happ (happ r e_27) e))
% Goal: !r b. ~h4/bag/mlt1 r 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_Q232877,TV_Q232873]: ![V_f, V_g]: (![V_x]: s(TV_Q232873,happ(s(t_fun(TV_Q232877,TV_Q232873),V_f),s(TV_Q232877,V_x))) = s(TV_Q232873,happ(s(t_fun(TV_Q232877,TV_Q232873),V_g),s(TV_Q232877,V_x))) => s(t_fun(TV_Q232877,TV_Q232873),V_f) = s(t_fun(TV_Q232877,TV_Q232873),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXISTSu_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_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
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_bags_BAGu_u_INSERTu_u_NOTu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x, V_b]: ~ (s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_x),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))).
fof(ah4s_bags_BAGu_u_UNIONu_u_EMPTYu_c2, axiom, ![TV_u_27c]: ![V_b2, V_b1]: (s(t_fun(TV_u_27c,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27c,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27c,t_h4s_nums_num),V_b2))) = s(t_fun(TV_u_27c,t_h4s_nums_num),h4s_bags_emptyu_u_bag) <=> (s(t_fun(TV_u_27c,t_h4s_nums_num),V_b1) = s(t_fun(TV_u_27c,t_h4s_nums_num),h4s_bags_emptyu_u_bag) & s(t_fun(TV_u_27c,t_h4s_nums_num),V_b2) = s(t_fun(TV_u_27c,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))).
fof(ah4s_bags_FINITEu_u_BAGu_u_THMu_c0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))).
fof(ah4s_bags_mlt1u_u_def, axiom, ![TV_u_27a]: ![V_r, V_b2, V_b1]: (p(s(t_bool,h4s_bags_mlt1(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2)))) <=> (p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1)))) & (p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2)))) & ?[V_e, V_rep, V_res]: (s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_rep),s(t_fun(TV_u_27a,t_h4s_nums_num),V_res))) & (s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_union(s(t_fun(TV_u_27a,t_h4s_nums_num),V_res),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag))))) & ![V_eu_27]: (p(s(t_bool,h4s_bags_bagu_u_in(s(TV_u_27a,V_eu_27),s(t_fun(TV_u_27a,t_h4s_nums_num),V_rep)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r),s(TV_u_27a,V_eu_27))),s(TV_u_27a,V_e))))))))))).
fof(ch4s_bags_BAGu_u_NOTu_u_LESSu_u_EMPTY, conjecture, ![TV_u_27a]: ![V_r, V_b]: ~ (p(s(t_bool,h4s_bags_mlt1(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r),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)))))).
