%   ORIGINAL: h4/bag/BAG__REST__SING
% 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/EL__BAG0: !e. h4/bag/EL__BAG e = h4/bag/BAG__INSERT e h4/bag/EMPTY__BAG
% Assm: h4/bag/BAG__DIFF__EMPTY__simple_c2: !b. h4/bag/BAG__DIFF h4/bag/EMPTY__BAG b = h4/bag/EMPTY__BAG
% Assm: h4/bag/BAG__DIFF__INSERT__same: !x b2 b1. h4/bag/BAG__DIFF (h4/bag/BAG__INSERT x b1) (h4/bag/BAG__INSERT x b2) = h4/bag/BAG__DIFF b1 b2
% Assm: h4/bag/BAG__REST__DEF: !b. h4/bag/BAG__REST b = h4/bag/BAG__DIFF b (h4/bag/EL__BAG (h4/bag/BAG__CHOICE b))
% Assm: h4/bag/BAG__CHOICE__SING: !x. h4/bag/BAG__CHOICE (h4/bag/BAG__INSERT x h4/bag/EMPTY__BAG) = x
% Goal: !x. h4/bag/BAG__REST (h4/bag/BAG__INSERT x h4/bag/EMPTY__BAG) = 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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bags_ELu_u_BAG0]: !e. h4/bag/EL__BAG e = h4/bag/BAG__INSERT e h4/bag/EMPTY__BAG
% Assm [h4s_bags_BAGu_u_DIFFu_u_EMPTYu_u_simpleu_c2]: !b. h4/bag/BAG__DIFF h4/bag/EMPTY__BAG b = h4/bag/EMPTY__BAG
% Assm [h4s_bags_BAGu_u_DIFFu_u_INSERTu_u_same]: !x b2 b1. h4/bag/BAG__DIFF (h4/bag/BAG__INSERT x b1) (h4/bag/BAG__INSERT x b2) = h4/bag/BAG__DIFF b1 b2
% Assm [h4s_bags_BAGu_u_RESTu_u_DEF]: !b. h4/bag/BAG__REST b = h4/bag/BAG__DIFF b (h4/bag/EL__BAG (h4/bag/BAG__CHOICE b))
% Assm [h4s_bags_BAGu_u_CHOICEu_u_SING]: !x. h4/bag/BAG__CHOICE (h4/bag/BAG__INSERT x h4/bag/EMPTY__BAG) = x
% Goal: !x. h4/bag/BAG__REST (h4/bag/BAG__INSERT x h4/bag/EMPTY__BAG) = 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_Q231438,TV_Q231434]: ![V_f, V_g]: (![V_x]: s(TV_Q231434,happ(s(t_fun(TV_Q231438,TV_Q231434),V_f),s(TV_Q231438,V_x))) = s(TV_Q231434,happ(s(t_fun(TV_Q231438,TV_Q231434),V_g),s(TV_Q231438,V_x))) => s(t_fun(TV_Q231438,TV_Q231434),V_f) = s(t_fun(TV_Q231438,TV_Q231434),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_ELu_u_BAG0, axiom, ![TV_u_27a]: ![V_e]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_elu_u_bag(s(TV_u_27a,V_e))) = 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)))).
fof(ah4s_bags_BAGu_u_DIFFu_u_EMPTYu_u_simpleu_c2, axiom, ![TV_u_27c]: ![V_b]: s(t_fun(TV_u_27c,t_h4s_nums_num),h4s_bags_bagu_u_diff(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_b))) = s(t_fun(TV_u_27c,t_h4s_nums_num),h4s_bags_emptyu_u_bag)).
fof(ah4s_bags_BAGu_u_DIFFu_u_INSERTu_u_same, axiom, ![TV_u_27a]: ![V_x, V_b2, V_b1]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_diff(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_b1))),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_b2))))) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_diff(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b1),s(t_fun(TV_u_27a,t_h4s_nums_num),V_b2)))).
fof(ah4s_bags_BAGu_u_RESTu_u_DEF, axiom, ![TV_u_27a]: ![V_b]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_rest(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_diff(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b),s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_elu_u_bag(s(TV_u_27a,h4s_bags_bagu_u_choice(s(t_fun(TV_u_27a,t_h4s_nums_num),V_b)))))))).
fof(ah4s_bags_BAGu_u_CHOICEu_u_SING, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_bags_bagu_u_choice(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),h4s_bags_emptyu_u_bag))))) = s(TV_u_27a,V_x)).
fof(ch4s_bags_BAGu_u_RESTu_u_SING, conjecture, ![TV_u_27a]: ![V_x]: s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_bagu_u_rest(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),h4s_bags_emptyu_u_bag))))) = s(t_fun(TV_u_27a,t_h4s_nums_num),h4s_bags_emptyu_u_bag)).
