%   ORIGINAL: h4/llist/LZIP__LUNZIP
% 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/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% 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_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> 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/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/bool/RIGHT__OR__OVER__AND: !C B A. B /\ C \/ A <=> (B \/ A) /\ (C \/ A)
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/EXISTS__REFL: !a. ?x. x = a
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/marker/Cong__def: !x. h4/marker/Cong x <=> x
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/combin/o__ABS__R: !g f. h4/combin/o f (\x. g x) = (\x. f (g x))
% Assm: h4/combin/S__ABS__R: !g f. h4/combin/S f (\x. g x) = (\x. f x (g x))
% Assm: h4/combin/C__THM: !y x f. h4/combin/C f x y = f y x
% Assm: h4/combin/C__ABS__L: !y f. h4/combin/C (\x. f x) y = (\x. f x y)
% Assm: h4/combin/GEN__LET__RAND: !v f P. P (h4/bool/LET f v) = h4/bool/LET (h4/combin/o P f) v
% Assm: h4/combin/GEN__LET__RATOR: !x v f. h4/bool/LET f v x = h4/bool/LET (h4/combin/C f x) v
% Assm: h4/combin/LET__FORALL__ELIM: !v f. h4/bool/LET f v <=> $forall (h4/combin/S (h4/combin/o $imply (h4/combin/o h4/marker/Abbrev (h4/combin/C $equals v))) f)
% Assm: h4/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/pair/o__UNCURRY__R: !g f. h4/combin/o f (h4/pair/UNCURRY g) = h4/pair/UNCURRY (h4/combin/o (h4/combin/o f) g)
% Assm: h4/pair/C__UNCURRY__L: !x f. h4/combin/C (h4/pair/UNCURRY f) x = h4/pair/UNCURRY (h4/combin/C (h4/combin/o h4/combin/C f) x)
% Assm: h4/pair/S__UNCURRY__R: !g f. h4/combin/S f (h4/pair/UNCURRY g) = h4/pair/UNCURRY (h4/combin/S (h4/combin/o h4/combin/S (h4/combin/o (h4/combin/o f) h4/pair/_2C)) g)
% Assm: h4/pair/FORALL__UNCURRY: !f. $forall (h4/pair/UNCURRY f) <=> $forall (h4/combin/o $forall f)
% Assm: h4/llist/llist__CASES: !l. l = h4/llist/LNIL \/ (?h t. l = h4/llist/LCONS h t)
% Assm: h4/llist/LCONS__NOT__NIL_c0: !t h. ~(h4/llist/LCONS h t = h4/llist/LNIL)
% Assm: h4/llist/LCONS__11: !t2 t1 h2 h1. h4/llist/LCONS h1 t1 = h4/llist/LCONS h2 t2 <=> h1 = h2 /\ t1 = t2
% Assm: h4/llist/LLIST__BISIMULATION0: !ll2 ll1. ll1 = ll2 <=> (?R. R ll1 ll2 /\ (!ll3 ll4. R ll3 ll4 ==> ll3 = h4/llist/LNIL /\ ll4 = h4/llist/LNIL \/ (?h t1 t2. ll3 = h4/llist/LCONS h t1 /\ ll4 = h4/llist/LCONS h t2 /\ R t1 t2)))
% Assm: h4/llist/LZIP__THM_c1: !l2. h4/llist/LZIP (h4/pair/_2C h4/llist/LNIL l2) = h4/llist/LNIL
% Assm: h4/llist/LZIP__THM_c2: !t2 t1 h2 h1. h4/llist/LZIP (h4/pair/_2C (h4/llist/LCONS h1 t1) (h4/llist/LCONS h2 t2)) = h4/llist/LCONS (h4/pair/_2C h1 h2) (h4/llist/LZIP (h4/pair/_2C t1 t2))
% Assm: h4/llist/LUNZIP__THM_c0: h4/llist/LUNZIP h4/llist/LNIL = h4/pair/_2C h4/llist/LNIL h4/llist/LNIL
% Assm: h4/llist/LUNZIP__THM_c1: !y x t. h4/llist/LUNZIP (h4/llist/LCONS (h4/pair/_2C x y) t) = h4/bool/LET (h4/pair/UNCURRY (\ll1 ll2. h4/pair/_2C (h4/llist/LCONS x ll1) (h4/llist/LCONS y ll2))) (h4/llist/LUNZIP t)
% Goal: !ll. h4/llist/LZIP (h4/llist/LUNZIP ll) = ll
%   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_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% 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_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> 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_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_bools_RIGHTu_u_ORu_u_OVERu_u_AND]: !C B A. B /\ C \/ A <=> (B \/ A) /\ (C \/ A)
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_EXISTSu_u_REFL]: !a. ?x. x = a
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_markers_Abbrevu_u_def]: !x. happ h4/marker/Abbrev x <=> x
% Assm [h4s_markers_Congu_u_def]: !x. h4/marker/Cong x <=> x
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (happ (h4/combin/o f) g) x = happ f (happ g x)
% Assm [h4s_combins_ou_u_ABSu_u_R]: !_0. (!g x. happ (happ _0 g) x = happ g x) ==> (!g f x. happ (happ (h4/combin/o f) (happ _0 g)) x = happ f (happ g x))
% Assm [h4s_combins_Su_u_ABSu_u_R]: !_0. (!g x. happ (happ _0 g) x = happ g x) ==> (!g f x. happ (happ (happ h4/combin/S f) (happ _0 g)) x = happ (happ f x) (happ g x))
% Assm [h4s_combins_Cu_u_THM]: !y x f. happ (happ (happ h4/combin/C f) x) y = happ (happ f y) x
% Assm [h4s_combins_Cu_u_ABSu_u_L]: !_0. (!f x. happ (happ _0 f) x = happ f x) ==> (!y f x. happ (happ (happ h4/combin/C (happ _0 f)) y) x = happ (happ f x) y)
% Assm [h4s_combins_GENu_u_LETu_u_RAND]: !v f P. happ P (h4/bool/LET f v) = h4/bool/LET (happ (h4/combin/o P) f) v
% Assm [h4s_combins_GENu_u_LETu_u_RATOR]: !x v f. happ (h4/bool/LET f v) x = h4/bool/LET (happ (happ h4/combin/C f) x) v
% Assm [h4s_combins_LETu_u_FORALLu_u_ELIM]: !v f. h4/bool/LET f v <=> happ $forall (happ (happ h4/combin/S (happ (h4/combin/o $imply) (happ (h4/combin/o h4/marker/Abbrev) (happ (happ h4/combin/C $equals) v)))) f)
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. happ (happ h4/pair/_2C x) y = happ (happ h4/pair/_2C a) b <=> x = a /\ y = b
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = happ (happ h4/pair/_2C q) r
% Assm [h4s_pairs_ou_u_UNCURRYu_u_R]: !g f. happ (h4/combin/o f) (h4/pair/UNCURRY g) = h4/pair/UNCURRY (happ (h4/combin/o (h4/combin/o f)) g)
% Assm [h4s_pairs_Cu_u_UNCURRYu_u_L]: !x f. happ (happ h4/combin/C (h4/pair/UNCURRY f)) x = h4/pair/UNCURRY (happ (happ h4/combin/C (happ (h4/combin/o h4/combin/C) f)) x)
% Assm [h4s_pairs_Su_u_UNCURRYu_u_R]: !g f. happ (happ h4/combin/S f) (h4/pair/UNCURRY g) = h4/pair/UNCURRY (happ (happ h4/combin/S (happ (h4/combin/o h4/combin/S) (happ (h4/combin/o (h4/combin/o f)) h4/pair/_2C))) g)
% Assm [h4s_pairs_FORALLu_u_UNCURRY]: !f. happ $forall (h4/pair/UNCURRY f) <=> happ $forall (happ (h4/combin/o $forall) f)
% Assm [h4s_llists_llistu_u_CASES]: !l. l = h4/llist/LNIL \/ (?h t. l = h4/llist/LCONS h t)
% Assm [h4s_llists_LCONSu_u_NOTu_u_NILu_c0]: !t h. ~(h4/llist/LCONS h t = h4/llist/LNIL)
% Assm [h4s_llists_LCONSu_u_11]: !t2 t1 h2 h1. h4/llist/LCONS h1 t1 = h4/llist/LCONS h2 t2 <=> h1 = h2 /\ t1 = t2
% Assm [h4s_llists_LLISTu_u_BISIMULATION0]: !ll2 ll1. ll1 = ll2 <=> (?R. happ (happ R ll1) ll2 /\ (!ll3 ll4. happ (happ R ll3) ll4 ==> ll3 = h4/llist/LNIL /\ ll4 = h4/llist/LNIL \/ (?h t1 t2. ll3 = h4/llist/LCONS h t1 /\ ll4 = h4/llist/LCONS h t2 /\ happ (happ R t1) t2)))
% Assm [h4s_llists_LZIPu_u_THMu_c1]: !l2. h4/llist/LZIP (happ (happ h4/pair/_2C h4/llist/LNIL) l2) = h4/llist/LNIL
% Assm [h4s_llists_LZIPu_u_THMu_c2]: !t2 t1 h2 h1. h4/llist/LZIP (happ (happ h4/pair/_2C (h4/llist/LCONS h1 t1)) (h4/llist/LCONS h2 t2)) = h4/llist/LCONS (happ (happ h4/pair/_2C h1) h2) (h4/llist/LZIP (happ (happ h4/pair/_2C t1) t2))
% Assm [h4s_llists_LUNZIPu_u_THMu_c0]: h4/llist/LUNZIP h4/llist/LNIL = happ (happ h4/pair/_2C h4/llist/LNIL) h4/llist/LNIL
% Assm [h4s_llists_LUNZIPu_u_THMu_c1]: !_1. (!x ll1 y ll2. happ (happ (happ (happ _1 x) ll1) y) ll2 = happ (happ h4/pair/_2C (h4/llist/LCONS x ll1)) (h4/llist/LCONS y ll2)) ==> (!_0. (!x y ll1. happ (happ (happ _0 x) y) ll1 = happ (happ (happ _1 x) ll1) y) ==> (!y x t. h4/llist/LUNZIP (h4/llist/LCONS (happ (happ h4/pair/_2C x) y) t) = h4/bool/LET (h4/pair/UNCURRY (happ (happ _0 x) y)) (h4/llist/LUNZIP t)))
% Goal: !ll. h4/llist/LZIP (h4/llist/LUNZIP ll) = ll
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_Q171707,TV_Q171703]: ![V_f, V_g]: (![V_x]: s(TV_Q171703,happ(s(t_fun(TV_Q171707,TV_Q171703),V_f),s(TV_Q171707,V_x))) = s(TV_Q171703,happ(s(t_fun(TV_Q171707,TV_Q171703),V_g),s(TV_Q171707,V_x))) => s(t_fun(TV_Q171707,TV_Q171703),V_f) = s(t_fun(TV_Q171707,TV_Q171703),V_g))).
fof(ah4s_bools_EXISTSu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_x)))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
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_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,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_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
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_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_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) & p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) & (p(s(t_bool,V_A)) | p(s(t_bool,V_C)))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: (((p(s(t_bool,V_B)) & p(s(t_bool,V_C))) | p(s(t_bool,V_A))) <=> ((p(s(t_bool,V_B)) | p(s(t_bool,V_A))) & (p(s(t_bool,V_C)) | p(s(t_bool,V_A)))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_EXISTSu_u_REFL, axiom, ![TV_u_27a]: ![V_a]: ?[V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_a)).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,happ(s(t_fun(t_bool,t_bool),h4s_markers_abbrev),s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_markers_Congu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_cong(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27a),t_fun(TV_u_27c,TV_u_27b)),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_combins_ou_u_ABSu_u_R, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_0]: (![V_g, V_x]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))) => ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27b)),h4s_combins_o(s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))))))).
fof(ah4s_combins_Su_u_ABSu_u_R, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_0]: (![V_g, V_x]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))),s(TV_u_27a,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))) => ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27b))),h4s_combins_s),s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27c),t_fun(TV_u_27a,TV_u_27c)),V_uu_0),s(t_fun(TV_u_27a,TV_u_27c),V_g))))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_g),s(TV_u_27a,V_x))))))).
fof(ah4s_combins_Cu_u_THM, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27c))),h4s_combins_c),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(TV_u_27b,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_x)))).
fof(ah4s_combins_Cu_u_ABSu_u_L, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_uu_0]: (![V_f, V_x]: s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(TV_u_27a,V_x))) => ![V_y, V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),t_fun(TV_u_27c,t_fun(TV_u_27a,TV_u_27b))),h4s_combins_c),s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f))))),s(TV_u_27c,V_y))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27c,V_y))))).
fof(ah4s_combins_GENu_u_LETu_u_RAND, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_v, V_f, V_P]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_P),s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,V_v))))) = s(TV_u_27a,h4s_bools_let(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,TV_u_27a)),h4s_combins_o(s(t_fun(TV_u_27b,TV_u_27a),V_P))),s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(TV_u_27c,V_v)))).
fof(ah4s_combins_GENu_u_LETu_u_RATOR, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_x, V_v, V_f]: s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),h4s_bools_let(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_v))),s(TV_u_27c,V_x))) = s(TV_u_27a,h4s_bools_let(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27b,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),t_fun(TV_u_27c,t_fun(TV_u_27b,TV_u_27a))),h4s_combins_c),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))),s(TV_u_27c,V_x))),s(TV_u_27b,V_v)))).
fof(ah4s_combins_LETu_u_FORALLu_u_ELIM, axiom, ![TV_u_27a]: ![V_v, V_f]: s(t_bool,h4s_bools_let(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_v))) = s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),d_forall),s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),h4s_combins_s),s(t_fun(TV_u_27a,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_bool,t_bool))),h4s_combins_o(s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_imply))),s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),h4s_combins_o(s(t_fun(t_bool,t_bool),h4s_markers_abbrev))),s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),h4s_combins_c),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),d_equals))),s(TV_u_27a,V_v))))))))),s(t_fun(TV_u_27a,t_bool),V_f)))))).
fof(ah4s_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c),s(TV_u_27a,V_q))),s(TV_u_27b,V_r)))).
fof(ah4s_pairs_ou_u_UNCURRYu_u_R, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b,TV_u_27d]: ![V_g, V_f]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27d),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c)),h4s_combins_o(s(t_fun(TV_u_27d,TV_u_27c),V_f))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27d),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),V_g))))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),h4s_combins_o(s(t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(TV_u_27b,TV_u_27c)),h4s_combins_o(s(t_fun(TV_u_27d,TV_u_27c),V_f))))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),V_g)))))).
fof(ah4s_pairs_Cu_u_UNCURRYu_u_L, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c,TV_u_27d]: ![V_x, V_f]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),happ(s(t_fun(TV_u_27d,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27d,TV_u_27c)),t_fun(TV_u_27d,t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c))),h4s_combins_c),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27d,TV_u_27c)),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c))),V_f))))),s(TV_u_27d,V_x))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(TV_u_27d,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27d,t_fun(TV_u_27b,TV_u_27c))),t_fun(TV_u_27d,t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)))),h4s_combins_c),s(t_fun(TV_u_27a,t_fun(TV_u_27d,t_fun(TV_u_27b,TV_u_27c))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c))),t_fun(TV_u_27a,t_fun(TV_u_27d,t_fun(TV_u_27b,TV_u_27c)))),h4s_combins_o(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c)),t_fun(TV_u_27d,t_fun(TV_u_27b,TV_u_27c))),h4s_combins_c))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c))),V_f))))),s(TV_u_27d,V_x)))))).
fof(ah4s_pairs_Su_u_UNCURRYu_u_R, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b,TV_u_27d]: ![V_g, V_f]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27d),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27d,TV_u_27c)),t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27d),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c))),h4s_combins_s),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27d,TV_u_27c)),V_f))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27d),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),V_g))))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(TV_u_27b,TV_u_27c))),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)))),h4s_combins_s),s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(TV_u_27b,TV_u_27c))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c))),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(TV_u_27b,TV_u_27c)))),h4s_combins_o(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c)),t_fun(t_fun(TV_u_27b,TV_u_27d),t_fun(TV_u_27b,TV_u_27c))),h4s_combins_s))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c)))),h4s_combins_o(s(t_fun(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_fun(TV_u_27b,t_fun(TV_u_27d,TV_u_27c))),h4s_combins_o(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27d,TV_u_27c)),V_f))))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c))))))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27d)),V_g)))))).
fof(ah4s_pairs_FORALLu_u_UNCURRY, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),t_bool),d_forall),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_f))))) = s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),d_forall),s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_bool)),h4s_combins_o(s(t_fun(t_fun(TV_u_27b,t_bool),t_bool),d_forall))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_f)))))).
fof(ah4s_llists_llistu_u_CASES, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_llists_llist(TV_u_27a),V_l) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil) | ?[V_h, V_t]: s(t_h4s_llists_llist(TV_u_27a),V_l) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h),s(t_h4s_llists_llist(TV_u_27a),V_t))))).
fof(ah4s_llists_LCONSu_u_NOTu_u_NILu_c0, axiom, ![TV_u_27a]: ![V_t, V_h]: ~ (s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h),s(t_h4s_llists_llist(TV_u_27a),V_t))) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil))).
fof(ah4s_llists_LCONSu_u_11, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_h2, V_h1]: (s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h1),s(t_h4s_llists_llist(TV_u_27a),V_t1))) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h2),s(t_h4s_llists_llist(TV_u_27a),V_t2))) <=> (s(TV_u_27a,V_h1) = s(TV_u_27a,V_h2) & s(t_h4s_llists_llist(TV_u_27a),V_t1) = s(t_h4s_llists_llist(TV_u_27a),V_t2)))).
fof(ah4s_llists_LLISTu_u_BISIMULATION0, axiom, ![TV_u_27a]: ![V_ll2, V_ll1]: (s(t_h4s_llists_llist(TV_u_27a),V_ll1) = s(t_h4s_llists_llist(TV_u_27a),V_ll2) <=> ?[V_R]: (p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27a),t_bool)),V_R),s(t_h4s_llists_llist(TV_u_27a),V_ll1))),s(t_h4s_llists_llist(TV_u_27a),V_ll2)))) & ![V_ll3, V_ll4]: (p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27a),t_bool)),V_R),s(t_h4s_llists_llist(TV_u_27a),V_ll3))),s(t_h4s_llists_llist(TV_u_27a),V_ll4)))) => ((s(t_h4s_llists_llist(TV_u_27a),V_ll3) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil) & s(t_h4s_llists_llist(TV_u_27a),V_ll4) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil)) | ?[V_h, V_t1, V_t2]: (s(t_h4s_llists_llist(TV_u_27a),V_ll3) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h),s(t_h4s_llists_llist(TV_u_27a),V_t1))) & (s(t_h4s_llists_llist(TV_u_27a),V_ll4) = s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h),s(t_h4s_llists_llist(TV_u_27a),V_t2))) & p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_bool),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27a),t_bool)),V_R),s(t_h4s_llists_llist(TV_u_27a),V_t1))),s(t_h4s_llists_llist(TV_u_27a),V_t2))))))))))).
fof(ah4s_llists_LZIPu_u_THMu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_l2]: s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lzip(s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),happ(s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),h4s_pairs_u_2c),s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil))),s(t_h4s_llists_llist(TV_u_27b),V_l2))))) = s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lnil)).
fof(ah4s_llists_LZIPu_u_THMu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_t2, V_t1, V_h2, V_h1]: s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lzip(s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),happ(s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),h4s_pairs_u_2c),s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_h1),s(t_h4s_llists_llist(TV_u_27a),V_t1))))),s(t_h4s_llists_llist(TV_u_27b),h4s_llists_lcons(s(TV_u_27b,V_h2),s(t_h4s_llists_llist(TV_u_27b),V_t2))))))) = s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lcons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c),s(TV_u_27a,V_h1))),s(TV_u_27b,V_h2))),s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lzip(s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),happ(s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),h4s_pairs_u_2c),s(t_h4s_llists_llist(TV_u_27a),V_t1))),s(t_h4s_llists_llist(TV_u_27b),V_t2)))))))).
fof(ah4s_llists_LUNZIPu_u_THMu_c0, axiom, ![TV_u_27a,TV_u_27b]: s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),h4s_llists_lunzip(s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lnil))) = s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),happ(s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),h4s_pairs_u_2c),s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lnil))),s(t_h4s_llists_llist(TV_u_27b),h4s_llists_lnil)))).
fof(ah4s_llists_LUNZIPu_u_THMu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_x, V_ll1, V_y, V_ll2]: s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),happ(s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))))),V_uu_1),s(TV_u_27a,V_x))),s(t_h4s_llists_llist(TV_u_27a),V_ll1))),s(TV_u_27b,V_y))),s(t_h4s_llists_llist(TV_u_27b),V_ll2))) = s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),happ(s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),h4s_pairs_u_2c),s(t_h4s_llists_llist(TV_u_27a),h4s_llists_lcons(s(TV_u_27a,V_x),s(t_h4s_llists_llist(TV_u_27a),V_ll1))))),s(t_h4s_llists_llist(TV_u_27b),h4s_llists_lcons(s(TV_u_27b,V_y),s(t_h4s_llists_llist(TV_u_27b),V_ll2))))) => ![V_uu_0]: (![V_x, V_y, V_ll1]: s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))))),V_uu_0),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))),s(t_h4s_llists_llist(TV_u_27a),V_ll1))) = s(t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),happ(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))))),V_uu_1),s(TV_u_27a,V_x))),s(t_h4s_llists_llist(TV_u_27a),V_ll1))),s(TV_u_27b,V_y))) => ![V_y, V_x, V_t]: s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),h4s_llists_lunzip(s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lcons(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),h4s_pairs_u_2c),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))),s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_t))))) = s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))),h4s_pairs_uncurry(s(t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b))))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_llists_llist(TV_u_27a),t_fun(t_h4s_llists_llist(TV_u_27b),t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)))))),V_uu_0),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))))),s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),h4s_llists_lunzip(s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_t)))))))).
fof(ch4s_llists_LZIPu_u_LUNZIP, conjecture, ![TV_u_27a,TV_u_27b]: ![V_ll]: s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_llists_lzip(s(t_h4s_pairs_prod(t_h4s_llists_llist(TV_u_27a),t_h4s_llists_llist(TV_u_27b)),h4s_llists_lunzip(s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_ll))))) = s(t_h4s_llists_llist(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_ll)).
