%   ORIGINAL: h4/list/ZIP__UNZIP
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/ZIP0_c0: h4/list/ZIP (h4/pair/_2C h4/list/NIL h4/list/NIL) = h4/list/NIL
% Assm: h4/list/ZIP0_c1: !x2 x1 l2 l1. h4/list/ZIP (h4/pair/_2C (h4/list/CONS x1 l1) (h4/list/CONS x2 l2)) = h4/list/CONS (h4/pair/_2C x1 x2) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm: h4/list/UNZIP0_c0: h4/list/UNZIP h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm: h4/list/UNZIP0_c1: !x l. h4/list/UNZIP (h4/list/CONS x l) = h4/pair/_2C (h4/list/CONS (h4/pair/FST x) (h4/pair/FST (h4/list/UNZIP l))) (h4/list/CONS (h4/pair/SND x) (h4/pair/SND (h4/list/UNZIP l)))
% Goal: !l. h4/list/ZIP (h4/list/UNZIP l) = l
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_ZIP0u_c0]: h4/list/ZIP (h4/pair/_2C h4/list/NIL h4/list/NIL) = h4/list/NIL
% Assm [h4s_lists_ZIP0u_c1]: !x2 x1 l2 l1. h4/list/ZIP (h4/pair/_2C (h4/list/CONS x1 l1) (h4/list/CONS x2 l2)) = h4/list/CONS (h4/pair/_2C x1 x2) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm [h4s_lists_UNZIP0u_c0]: h4/list/UNZIP h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm [h4s_lists_UNZIP0u_c1]: !x l. h4/list/UNZIP (h4/list/CONS x l) = h4/pair/_2C (h4/list/CONS (h4/pair/FST x) (h4/pair/FST (h4/list/UNZIP l))) (h4/list/CONS (h4/pair/SND x) (h4/pair/SND (h4/list/UNZIP l)))
% Goal: !l. h4/list/ZIP (h4/list/UNZIP l) = l
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_Q242854,TV_Q242850]: ![V_f, V_g]: (![V_x]: s(TV_Q242850,happ(s(t_fun(TV_Q242854,TV_Q242850),V_f),s(TV_Q242854,V_x))) = s(TV_Q242850,happ(s(t_fun(TV_Q242854,TV_Q242850),V_g),s(TV_Q242854,V_x))) => s(t_fun(TV_Q242854,TV_Q242850),V_f) = s(t_fun(TV_Q242854,TV_Q242850),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
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_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_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_ZIP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil)).
fof(ah4s_lists_ZIP0u_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_x2, V_x1, V_l2, V_l1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x1),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,V_x2),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(TV_u_27b,V_x2))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))))))).
fof(ah4s_lists_UNZIP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))).
fof(ah4s_lists_UNZIP0u_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_l]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_cons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_lists_list(TV_u_27b),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))))))).
fof(ch4s_lists_ZIPu_u_UNZIP, conjecture, ![TV_u_27a,TV_u_27b]: ![V_l]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)).
