%   ORIGINAL: h4/enumeral/better__bt__to__ol
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CLAUSES_c3: !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/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/COND__RAND: !y x f b. f (h4/bool/COND b x y) = h4/bool/COND b (f x) (f y)
% 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/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% 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/dc__cond: !s r q p. (p <=> h4/bool/COND q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~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/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND__NIL: !l. h4/list/APPEND l h4/list/NIL = l
% Assm: h4/list/APPEND__ASSOC: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm: h4/list/APPEND__11_c0: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm: h4/list/APPEND__11_c1: !l3 l2 l1. h4/list/APPEND l2 l1 = h4/list/APPEND l3 l1 <=> l2 = l3
% Assm: h4/toto/totoLLtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/enumeral/bt__repfns_c0: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% Assm: h4/enumeral/bt__repfns_c1: !r. (\a0_27. !_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) a0 a1 a2 /\ _27bt_27 a0 /\ _27bt_27 a2) ==> _27bt_27 a0_270) ==> _27bt_27 a0_27) r <=> h4/enumeral/_20_40ind__typeenumeral3 (h4/enumeral/_20_40ind__typeenumeral2 r) = r
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral0____def: h4/enumeral/_20_40ind__typeenumeral0 = h4/enumeral/_20_40ind__typeenumeral2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral1____def: h4/enumeral/_20_40ind__typeenumeral1 = (\a0 a1 a2. h4/enumeral/_20_40ind__typeenumeral2 ((\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) (h4/enumeral/_20_40ind__typeenumeral3 a0) a1 (h4/enumeral/_20_40ind__typeenumeral3 a2)))
% Assm: h4/enumeral/nt0: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm: h4/enumeral/node0: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% Assm: h4/enumeral/bt__to__list0_c0: h4/enumeral/bt__to__list h4/enumeral/nt = h4/list/NIL
% Assm: h4/enumeral/bt__to__list0_c1: !x r l. h4/enumeral/bt__to__list (h4/enumeral/node l x r) = h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__list l) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__list r)
% Assm: h4/enumeral/bt__to__list__thm: !t. h4/enumeral/bt__to__list t = h4/enumeral/bt__to__list__ac t h4/list/NIL
% Assm: h4/enumeral/bt__to__ol__lb__ub0_c0: !ub lb cmp. h4/enumeral/bt__to__ol__lb__ub cmp lb h4/enumeral/nt ub = h4/list/NIL
% Assm: h4/enumeral/bt__to__ol__lb__ub0_c1: !x ub r lb l cmp. h4/enumeral/bt__to__ol__lb__ub cmp lb (h4/enumeral/node l x r) ub = h4/bool/COND (h4/toto/apto cmp lb x = h4/toto/LESS) (h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__lb__ub cmp lb l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb__ub cmp x r ub)) (h4/enumeral/bt__to__ol__lb__ub cmp lb l ub)) (h4/enumeral/bt__to__ol__lb__ub cmp lb r ub)
% Assm: h4/enumeral/bt__to__ol__lb0_c0: !lb cmp. h4/enumeral/bt__to__ol__lb cmp lb h4/enumeral/nt = h4/list/NIL
% Assm: h4/enumeral/bt__to__ol__lb0_c1: !x r lb l cmp. h4/enumeral/bt__to__ol__lb cmp lb (h4/enumeral/node l x r) = h4/bool/COND (h4/toto/apto cmp lb x = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__lb__ub cmp lb l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb cmp x r)) (h4/enumeral/bt__to__ol__lb cmp lb r)
% Assm: h4/enumeral/bt__to__ol__ub0_c0: !ub cmp. h4/enumeral/bt__to__ol__ub cmp h4/enumeral/nt ub = h4/list/NIL
% Assm: h4/enumeral/bt__to__ol__ub0_c1: !x ub r l cmp. h4/enumeral/bt__to__ol__ub cmp (h4/enumeral/node l x r) ub = h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__ub cmp l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb__ub cmp x r ub)) (h4/enumeral/bt__to__ol__ub cmp l ub)
% Assm: h4/enumeral/bt__to__ol0_c0: !cmp. h4/enumeral/bt__to__ol cmp h4/enumeral/nt = h4/list/NIL
% Assm: h4/enumeral/bt__to__ol0_c1: !x r l cmp. h4/enumeral/bt__to__ol cmp (h4/enumeral/node l x r) = h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__ub cmp l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb cmp x r)
% Assm: h4/enumeral/bt__to__ol__lb__ub__ac0_c0: !ub m lb cmp. h4/enumeral/bt__to__ol__lb__ub__ac cmp lb h4/enumeral/nt ub m = m
% Assm: h4/enumeral/bt__to__ol__lb__ub__ac0_c1: !x ub r m lb l cmp. h4/enumeral/bt__to__ol__lb__ub__ac cmp lb (h4/enumeral/node l x r) ub m = h4/bool/COND (h4/toto/apto cmp lb x = h4/toto/LESS) (h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ub__ac cmp x r ub m))) (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb l ub m)) (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb r ub m)
% Assm: h4/enumeral/bt__to__ol__lb__ac0_c0: !m lb cmp. h4/enumeral/bt__to__ol__lb__ac cmp lb h4/enumeral/nt m = m
% Assm: h4/enumeral/bt__to__ol__lb__ac0_c1: !x r m lb l cmp. h4/enumeral/bt__to__ol__lb__ac cmp lb (h4/enumeral/node l x r) m = h4/bool/COND (h4/toto/apto cmp lb x = h4/toto/LESS) (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ac cmp x r m))) (h4/enumeral/bt__to__ol__lb__ac cmp lb r m)
% Assm: h4/enumeral/bt__to__ol__ub__ac0_c0: !ub m cmp. h4/enumeral/bt__to__ol__ub__ac cmp h4/enumeral/nt ub m = m
% Assm: h4/enumeral/bt__to__ol__ub__ac0_c1: !x ub r m l cmp. h4/enumeral/bt__to__ol__ub__ac cmp (h4/enumeral/node l x r) ub m = h4/bool/COND (h4/toto/apto cmp x ub = h4/toto/LESS) (h4/enumeral/bt__to__ol__ub__ac cmp l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ub__ac cmp x r ub m))) (h4/enumeral/bt__to__ol__ub__ac cmp l ub m)
% Assm: h4/enumeral/bt__to__ol__ac0_c0: !m cmp. h4/enumeral/bt__to__ol__ac cmp h4/enumeral/nt m = m
% Assm: h4/enumeral/bt__to__ol__ac0_c1: !x r m l cmp. h4/enumeral/bt__to__ol__ac cmp (h4/enumeral/node l x r) m = h4/enumeral/bt__to__ol__ub__ac cmp l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ac cmp x r m))
% Assm: h4/enumeral/OL__bt__lb__ub0_c0: !ub lb cmp. h4/enumeral/OL__bt__lb__ub cmp lb h4/enumeral/nt ub <=> h4/toto/apto cmp lb ub = h4/toto/LESS
% Assm: h4/enumeral/OL__bt__lb__ub0_c1: !x ub r lb l cmp. h4/enumeral/OL__bt__lb__ub cmp lb (h4/enumeral/node l x r) ub <=> h4/enumeral/OL__bt__lb__ub cmp lb l x /\ h4/enumeral/OL__bt__lb__ub cmp x r ub
% Assm: h4/enumeral/OL__bt__lb0_c0: !lb cmp. h4/enumeral/OL__bt__lb cmp lb h4/enumeral/nt <=> T
% Assm: h4/enumeral/OL__bt__lb0_c1: !x r lb l cmp. h4/enumeral/OL__bt__lb cmp lb (h4/enumeral/node l x r) <=> h4/enumeral/OL__bt__lb__ub cmp lb l x /\ h4/enumeral/OL__bt__lb cmp x r
% Assm: h4/enumeral/OL__bt__ub0_c0: !ub cmp. h4/enumeral/OL__bt__ub cmp h4/enumeral/nt ub <=> T
% Assm: h4/enumeral/OL__bt__ub0_c1: !x ub r l cmp. h4/enumeral/OL__bt__ub cmp (h4/enumeral/node l x r) ub <=> h4/enumeral/OL__bt__ub cmp l x /\ h4/enumeral/OL__bt__lb__ub cmp x r ub
% Assm: h4/enumeral/OL__bt0_c0: !cmp. h4/enumeral/OL__bt cmp h4/enumeral/nt <=> T
% Assm: h4/enumeral/OL__bt0_c1: !x r l cmp. h4/enumeral/OL__bt cmp (h4/enumeral/node l x r) <=> h4/enumeral/OL__bt__ub cmp l x /\ h4/enumeral/OL__bt__lb cmp x r
% Goal: !t cmp. h4/enumeral/bt__to__ol cmp t = h4/bool/COND (h4/enumeral/OL__bt cmp t) (h4/enumeral/bt__to__list__ac t h4/list/NIL) (h4/enumeral/bt__to__ol__ac cmp t h4/list/NIL)
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !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_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_CONDu_u_RAND]: !y x f b. happ f (h4/bool/COND b x y) = h4/bool/COND b (happ f x) (happ f y)
% 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_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% 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_dcu_u_cond]: !s r q p. (p <=> h4/bool/COND q r s) <=> (p \/ q \/ ~s) /\ (p \/ ~r \/ ~q) /\ (p \/ ~r \/ ~s) /\ (~q \/ r \/ ~p) /\ (q \/ s \/ ~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_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPENDu_u_NIL]: !l. h4/list/APPEND l h4/list/NIL = l
% Assm [h4s_lists_APPENDu_u_ASSOC]: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm [h4s_lists_APPENDu_u_11u_c0]: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm [h4s_lists_APPENDu_u_11u_c1]: !l3 l2 l1. h4/list/APPEND l2 l1 = h4/list/APPEND l3 l1 <=> l2 = l3
% Assm [h4s_totos_totoLLtrans]: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm [h4s_enumerals_btu_u_repfnsu_c0]: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% Assm [h4s_enumerals_btu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a2 _0)) /\ happ _27bt_27 a0 /\ happ _27bt_27 a2) ==> happ _27bt_27 a0_270) ==> happ _27bt_27 r) <=> h4/enumeral/_20_40ind__typeenumeral3 (h4/enumeral/_20_40ind__typeenumeral2 r) = r)
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/enumeral/_20_40ind__typeenumeral0 = h4/enumeral/_20_40ind__typeenumeral2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x'. happ (happ (happ h4/enumeral/_20_40ind__typeenumeral1 x) x) x' = h4/enumeral/_20_40ind__typeenumeral2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral3 x) (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral3 x') _0))))
% Assm [h4s_enumerals_nt0]: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm [h4s_enumerals_node0]: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% Assm [h4s_enumerals_btu_u_tou_u_list0u_c0]: h4/enumeral/bt__to__list h4/enumeral/nt = h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_list0u_c1]: !x r l. h4/enumeral/bt__to__list (happ (happ (happ h4/enumeral/node l) x) r) = h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__list l) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__list r)
% Assm [h4s_enumerals_btu_u_tou_u_listu_u_thm]: !t. h4/enumeral/bt__to__list t = h4/enumeral/bt__to__list__ac t h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub0u_c0]: !ub lb cmp. h4/enumeral/bt__to__ol__lb__ub cmp lb h4/enumeral/nt ub = h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub0u_c1]: !x ub r lb l cmp. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ (?v'. (v' <=> h4/toto/apto cmp lb x = h4/toto/LESS) /\ h4/enumeral/bt__to__ol__lb__ub cmp lb (happ (happ (happ h4/enumeral/node l) x) r) ub = h4/bool/COND v' (h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__lb__ub cmp lb l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb__ub cmp x r ub)) (h4/enumeral/bt__to__ol__lb__ub cmp lb l ub)) (h4/enumeral/bt__to__ol__lb__ub cmp lb r ub))
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lb0u_c0]: !lb cmp. h4/enumeral/bt__to__ol__lb cmp lb h4/enumeral/nt = h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lb0u_c1]: !x r lb l cmp. ?v. (v <=> h4/toto/apto cmp lb x = h4/toto/LESS) /\ h4/enumeral/bt__to__ol__lb cmp lb (happ (happ (happ h4/enumeral/node l) x) r) = h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__lb__ub cmp lb l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb cmp x r)) (h4/enumeral/bt__to__ol__lb cmp lb r)
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_ub0u_c0]: !ub cmp. h4/enumeral/bt__to__ol__ub cmp h4/enumeral/nt ub = h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_ub0u_c1]: !x ub r l cmp. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ h4/enumeral/bt__to__ol__ub cmp (happ (happ (happ h4/enumeral/node l) x) r) ub = h4/bool/COND v (h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__ub cmp l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb__ub cmp x r ub)) (h4/enumeral/bt__to__ol__ub cmp l ub)
% Assm [h4s_enumerals_btu_u_tou_u_ol0u_c0]: !cmp. h4/enumeral/bt__to__ol cmp h4/enumeral/nt = h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_ol0u_c1]: !x r l cmp. h4/enumeral/bt__to__ol cmp (happ (happ (happ h4/enumeral/node l) x) r) = h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__ol__ub cmp l x) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__ol__lb cmp x r)
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac0u_c0]: !ub m lb cmp. h4/enumeral/bt__to__ol__lb__ub__ac cmp lb h4/enumeral/nt ub m = m
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac0u_c1]: !x ub r m lb l cmp. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ (?v'. (v' <=> h4/toto/apto cmp lb x = h4/toto/LESS) /\ h4/enumeral/bt__to__ol__lb__ub__ac cmp lb (happ (happ (happ h4/enumeral/node l) x) r) ub m = h4/bool/COND v' (h4/bool/COND v (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ub__ac cmp x r ub m))) (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb l ub m)) (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb r ub m))
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac0u_c0]: !m lb cmp. h4/enumeral/bt__to__ol__lb__ac cmp lb h4/enumeral/nt m = m
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac0u_c1]: !x r m lb l cmp. ?v. (v <=> h4/toto/apto cmp lb x = h4/toto/LESS) /\ h4/enumeral/bt__to__ol__lb__ac cmp lb (happ (happ (happ h4/enumeral/node l) x) r) m = h4/bool/COND v (h4/enumeral/bt__to__ol__lb__ub__ac cmp lb l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ac cmp x r m))) (h4/enumeral/bt__to__ol__lb__ac cmp lb r m)
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac0u_c0]: !ub m cmp. h4/enumeral/bt__to__ol__ub__ac cmp h4/enumeral/nt ub m = m
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac0u_c1]: !x ub r m l cmp. ?v. (v <=> h4/toto/apto cmp x ub = h4/toto/LESS) /\ h4/enumeral/bt__to__ol__ub__ac cmp (happ (happ (happ h4/enumeral/node l) x) r) ub m = h4/bool/COND v (h4/enumeral/bt__to__ol__ub__ac cmp l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ub__ac cmp x r ub m))) (h4/enumeral/bt__to__ol__ub__ac cmp l ub m)
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_ac0u_c0]: !m cmp. h4/enumeral/bt__to__ol__ac cmp h4/enumeral/nt m = m
% Assm [h4s_enumerals_btu_u_tou_u_olu_u_ac0u_c1]: !x r m l cmp. h4/enumeral/bt__to__ol__ac cmp (happ (happ (happ h4/enumeral/node l) x) r) m = h4/enumeral/bt__to__ol__ub__ac cmp l x (h4/list/CONS x (h4/enumeral/bt__to__ol__lb__ac cmp x r m))
% Assm [h4s_enumerals_OLu_u_btu_u_lbu_u_ub0u_c0]: !ub lb cmp. h4/enumeral/OL__bt__lb__ub cmp lb h4/enumeral/nt ub <=> h4/toto/apto cmp lb ub = h4/toto/LESS
% Assm [h4s_enumerals_OLu_u_btu_u_lbu_u_ub0u_c1]: !x ub r lb l cmp. h4/enumeral/OL__bt__lb__ub cmp lb (happ (happ (happ h4/enumeral/node l) x) r) ub <=> h4/enumeral/OL__bt__lb__ub cmp lb l x /\ h4/enumeral/OL__bt__lb__ub cmp x r ub
% Assm [h4s_enumerals_OLu_u_btu_u_lb0u_c0]: !lb cmp. h4/enumeral/OL__bt__lb cmp lb h4/enumeral/nt <=> T
% Assm [h4s_enumerals_OLu_u_btu_u_lb0u_c1]: !x r lb l cmp. h4/enumeral/OL__bt__lb cmp lb (happ (happ (happ h4/enumeral/node l) x) r) <=> h4/enumeral/OL__bt__lb__ub cmp lb l x /\ h4/enumeral/OL__bt__lb cmp x r
% Assm [h4s_enumerals_OLu_u_btu_u_ub0u_c0]: !ub cmp. h4/enumeral/OL__bt__ub cmp h4/enumeral/nt ub <=> T
% Assm [h4s_enumerals_OLu_u_btu_u_ub0u_c1]: !x ub r l cmp. h4/enumeral/OL__bt__ub cmp (happ (happ (happ h4/enumeral/node l) x) r) ub <=> h4/enumeral/OL__bt__ub cmp l x /\ h4/enumeral/OL__bt__lb__ub cmp x r ub
% Assm [h4s_enumerals_OLu_u_bt0u_c0]: !cmp. h4/enumeral/OL__bt cmp h4/enumeral/nt <=> T
% Assm [h4s_enumerals_OLu_u_bt0u_c1]: !x r l cmp. h4/enumeral/OL__bt cmp (happ (happ (happ h4/enumeral/node l) x) r) <=> h4/enumeral/OL__bt__ub cmp l x /\ h4/enumeral/OL__bt__lb cmp x r
% Goal: !t cmp. h4/enumeral/bt__to__ol cmp t = h4/bool/COND (h4/enumeral/OL__bt cmp t) (h4/enumeral/bt__to__list__ac t h4/list/NIL) (h4/enumeral/bt__to__ol__ac cmp t h4/list/NIL)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q334404,TV_Q334400]: ![V_f, V_g]: (![V_x]: s(TV_Q334400,happ(s(t_fun(TV_Q334404,TV_Q334400),V_f),s(TV_Q334404,V_x))) = s(TV_Q334400,happ(s(t_fun(TV_Q334404,TV_Q334400),V_g),s(TV_Q334404,V_x))) => s(t_fun(TV_Q334404,TV_Q334400),V_f) = s(t_fun(TV_Q334404,TV_Q334400),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,t0))).
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_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) => 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,t0))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
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,t0)))).
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,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
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_CONDu_u_RAND, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27a,V_x),s(TV_u_27a,V_y))))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_b),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))))).
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_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (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_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => 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,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
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_dcu_u_cond, axiom, ![V_s, V_r, V_q, V_p]: (s(t_bool,V_p) = s(t_bool,h4s_bools_cond(s(t_bool,V_q),s(t_bool,V_r),s(t_bool,V_s))) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_s))))) & ((p(s(t_bool,V_p)) | (~ (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_s))))) & ((~ (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_s)) | ~ (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_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(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_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = 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),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPENDu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_APPENDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l3))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),V_l3)))).
fof(ah4s_lists_APPENDu_u_11u_c0, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l3))) <=> s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l3))).
fof(ah4s_lists_APPENDu_u_11u_c1, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l3),s(t_h4s_lists_list(TV_u_27a),V_l1))) <=> s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l3))).
fof(ah4s_totos_totoLLtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_less) & s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_y),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)) => s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(TV_u_27a,V_x),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_enumerals_btu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),V_a))))) = s(t_h4s_enumerals_bt(TV_u_27a),V_a)).
fof(ah4s_enumerals_btu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27btu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral0) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0, V_xi_]: s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral1),s(t_h4s_enumerals_bt(TV_u_27a),V_x))),s(TV_u_27a,V_x0))),s(t_h4s_enumerals_bt(TV_u_27a),V_xi_))) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))))).
fof(ah4s_enumerals_nt0, axiom, ![TV_u_27a]: s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral0)).
fof(ah4s_enumerals_node0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node) = s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral1)).
fof(ah4s_enumerals_btu_u_tou_u_list0u_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_enumerals_btu_u_tou_u_list0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),V_r)))))).
fof(ah4s_enumerals_btu_u_tou_u_listu_u_thm, axiom, ![TV_u_27a]: ![V_t]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),V_t))) = s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(TV_u_27a),V_t),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub0u_c0, axiom, ![TV_u_27a]: ![V_ub, V_lb, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub0u_c1, axiom, ![TV_u_27a]: ![V_x, V_ub, V_r, V_lb, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub)))))))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lb0u_c0, axiom, ![TV_u_27a]: ![V_lb, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lb0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_lb, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_ub0u_c0, axiom, ![TV_u_27a]: ![V_ub, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_ub0u_c1, axiom, ![TV_u_27a]: ![V_x, V_ub, V_r, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(TV_u_27a,V_ub))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_ub))))))).
fof(ah4s_enumerals_btu_u_tou_u_ol0u_c0, axiom, ![TV_u_27a]: ![V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_enumerals_btu_u_tou_u_ol0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_l, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r)))))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac0u_c0, axiom, ![TV_u_27a]: ![V_ub, V_m, V_lb, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),V_m)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac0u_c1, axiom, ![TV_u_27a]: ![V_x, V_ub, V_r, V_m, V_lb, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_vi_),s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m)))))))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac0u_c0, axiom, ![TV_u_27a]: ![V_m, V_lb, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),V_m)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_m, V_lb, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(t_h4s_lists_list(TV_u_27a),V_m))))))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac0u_c0, axiom, ![TV_u_27a]: ![V_ub, V_m, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),V_m)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac0u_c1, axiom, ![TV_u_27a]: ![V_x, V_ub, V_r, V_m, V_l, V_cmp]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less)) & s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_ub),s(t_h4s_lists_list(TV_u_27a),V_m))))))).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_ac0u_c0, axiom, ![TV_u_27a]: ![V_m, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),V_m)).
fof(ah4s_enumerals_btu_u_tou_u_olu_u_ac0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_m, V_l, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ubu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_lbu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(t_h4s_lists_list(TV_u_27a),V_m)))))))).
fof(ah4s_enumerals_OLu_u_btu_u_lbu_u_ub0u_c0, axiom, ![TV_u_27a]: ![V_ub, V_lb, V_cmp]: (p(s(t_bool,h4s_enumerals_olu_u_btu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27a,V_ub)))) <=> s(t_h4s_totos_cpn,h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(TV_u_27a,V_ub))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_enumerals_OLu_u_btu_u_lbu_u_ub0u_c1, axiom, ![TV_u_27a]: ![V_x, V_ub, V_r, V_lb, V_l, V_cmp]: (p(s(t_bool,h4s_enumerals_olu_u_btu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(TV_u_27a,V_ub)))) <=> (p(s(t_bool,h4s_enumerals_olu_u_btu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x)))) & p(s(t_bool,h4s_enumerals_olu_u_btu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub))))))).
fof(ah4s_enumerals_OLu_u_btu_u_lb0u_c0, axiom, ![TV_u_27a]: ![V_lb, V_cmp]: s(t_bool,h4s_enumerals_olu_u_btu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_bool,t0)).
fof(ah4s_enumerals_OLu_u_btu_u_lb0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_lb, V_l, V_cmp]: (p(s(t_bool,h4s_enumerals_olu_u_btu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r)))))) <=> (p(s(t_bool,h4s_enumerals_olu_u_btu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_lb),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x)))) & p(s(t_bool,h4s_enumerals_olu_u_btu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))))).
fof(ah4s_enumerals_OLu_u_btu_u_ub0u_c0, axiom, ![TV_u_27a]: ![V_ub, V_cmp]: s(t_bool,h4s_enumerals_olu_u_btu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27a,V_ub))) = s(t_bool,t0)).
fof(ah4s_enumerals_OLu_u_btu_u_ub0u_c1, axiom, ![TV_u_27a]: ![V_x, V_ub, V_r, V_l, V_cmp]: (p(s(t_bool,h4s_enumerals_olu_u_btu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(TV_u_27a,V_ub)))) <=> (p(s(t_bool,h4s_enumerals_olu_u_btu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x)))) & p(s(t_bool,h4s_enumerals_olu_u_btu_u_lbu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(TV_u_27a,V_ub))))))).
fof(ah4s_enumerals_OLu_u_bt0u_c0, axiom, ![TV_u_27a]: ![V_cmp]: s(t_bool,h4s_enumerals_olu_u_bt(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_bool,t0)).
fof(ah4s_enumerals_OLu_u_bt0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_l, V_cmp]: (p(s(t_bool,h4s_enumerals_olu_u_bt(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r)))))) <=> (p(s(t_bool,h4s_enumerals_olu_u_btu_u_ub(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_l),s(TV_u_27a,V_x)))) & p(s(t_bool,h4s_enumerals_olu_u_btu_u_lb(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))))).
fof(ch4s_enumerals_betteru_u_btu_u_tou_u_ol, conjecture, ![TV_u_27a]: ![V_t, V_cmp]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_enumerals_olu_u_bt(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(TV_u_27a),V_t),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_olu_u_ac(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
