%   ORIGINAL: h4/quotient/FORALL__REGULAR
% 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/FORALL__THM: !f. $forall f <=> (!x. f x)
% Assm: h4/quotient/EQUIV__RES__FORALL: !P E. h4/quotient/EQUIV E ==> (h4/bool/RES__FORALL (h4/quotient/respects E) P <=> $forall P)
% Assm: h4/res__quan/RES__FORALL__UNIV: !p. h4/bool/RES__FORALL h4/pred__set/UNIV p <=> $forall p
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/res__quan/RES__FORALL: !f P. h4/bool/RES__FORALL P f <=> (!x. h4/bool/IN x P ==> f x)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/FORALL__DEF: $forall = (\P. P = (\x. T))
% Assm: h4/pair/FORALL__UNCURRY: !f. $forall (h4/pair/UNCURRY f) <=> $forall (h4/combin/o $forall f)
% Assm: h4/pred__set/SPECIFICATION: !x P. h4/bool/IN x P <=> P x
% Assm: h4/pair/PFORALL__THM: !P. (!x y. P x y) <=> $forall (h4/pair/UNCURRY (\x y. P x y))
% Assm: h4/quotient/RESPECTS: !x R. h4/quotient/respects R x <=> R x x
% Assm: h4/quotient/EQUIV__def: !E. h4/quotient/EQUIV E <=> (!x y. E x y <=> E x = E y)
% 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/pred__set/IN__UNIV: !x. h4/bool/IN x h4/pred__set/UNIV
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% 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/combin/literal__case__FORALL__ELIM: !v f. h4/bool/literal__case f v <=> $forall (h4/combin/S (h4/combin/o $imply (h4/combin/o h4/marker/Abbrev (h4/combin/C $equals v))) f)
% Assm: h4/quotient/FORALL__PRS: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!f. $forall f <=> h4/bool/RES__FORALL (h4/quotient/respects R) (h4/quotient/_2D_2D_3E abs h4/combin/I f))
% Assm: h4/pair/ELIM__PFORALL__EVAL: !P. $forall (h4/pair/UNCURRY (\x. P x)) <=> (!x. $forall (P x))
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/pair/ELIM__PFORALL: !P. (!p. P (h4/pair/FST p) (h4/pair/SND p)) <=> (!p1 p2. P p1 p2)
% Assm: h4/pair/ELIM__UNCURRY: !f. h4/pair/UNCURRY f = (\x. f (h4/pair/FST x) (h4/pair/SND x))
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/combin/S__DEF: h4/combin/S = (\f g x. f x (g x))
% Assm: h4/combin/C__DEF: h4/combin/C = (\f x y. f y x)
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/bool/FUN__EQ__THM: !g f. f = g <=> (!x. f x = g x)
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/pair/UNCURRY0: !v f. h4/pair/UNCURRY f v = f (h4/pair/FST v) (h4/pair/SND v)
% Assm: h4/pair/FORALL__PROD: !P. (!p. P p) <=> (!p__1 p__2. P (h4/pair/_2C p__1 p__2))
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/bool/ETA__THM: !M. (\x. M x) = M
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/bool/literal__case__THM: !x f. h4/bool/literal__case f x = f x
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/quotient/FUN__MAP__THM: !x h g f. h4/quotient/_2D_2D_3E f g h x = g (h (f x))
% Assm: h4/quotient/QUOTIENT__REP__REFL: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!a. R (rep a) (rep a))
% Assm: h4/quotient/QUOTIENT__ABS__REP: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!a. abs (rep a) = a)
% Assm: h4/quotient/respects__def: h4/quotient/respects = h4/combin/W
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/combin/W__THM: !x f. h4/combin/W f x = f x x
% Assm: h4/quotient/RES__EXISTS__EQUIV__DEF: h4/quotient/RES__EXISTS__EQUIV = (\R P. h4/bool/RES__EXISTS (h4/quotient/respects R) (\x. P x) /\ h4/bool/RES__FORALL (h4/quotient/respects R) (\x. h4/bool/RES__FORALL (h4/quotient/respects R) (\y. P x /\ P y ==> R x y)))
% Assm: h4/bool/RES__EXISTS__UNIQUE__DEF: h4/bool/RES__EXISTS__UNIQUE = (\p m. h4/bool/RES__EXISTS p (\x. m x) /\ h4/bool/RES__FORALL p (\x. h4/bool/RES__FORALL p (\y. m x /\ m y ==> x = y)))
% Assm: h4/bool/RES__SELECT__DEF: h4/bool/RES__SELECT = (\p m. h4/min/_40 (\x. h4/bool/IN x p /\ m x))
% Assm: h4/bool/RES__EXISTS__DEF: h4/bool/RES__EXISTS = (\p m. ?x. h4/bool/IN x p /\ m x)
% Assm: h4/quotient/RES__EXISTS__EQUIV0: !m R. h4/quotient/RES__EXISTS__EQUIV R m <=> h4/bool/RES__EXISTS (h4/quotient/respects R) (\x. m x) /\ h4/bool/RES__FORALL (h4/quotient/respects R) (\x. h4/bool/RES__FORALL (h4/quotient/respects R) (\y. m x /\ m y ==> R x y))
% Assm: h4/bool/RES__EXISTS__UNIQUE__THM: !f P. h4/bool/RES__EXISTS__UNIQUE P f <=> h4/bool/RES__EXISTS P (\x. f x) /\ h4/bool/RES__FORALL P (\x. h4/bool/RES__FORALL P (\y. f x /\ f y ==> x = y))
% Assm: h4/bool/RES__EXISTS__CONG: !g f Q P. P = Q ==> (!x. h4/bool/IN x Q ==> (f x <=> g x)) ==> (h4/bool/RES__EXISTS P f <=> h4/bool/RES__EXISTS Q g)
% Assm: h4/list/EVERY__FILTER: !l P2 P1. h4/list/EVERY P1 (h4/list/FILTER P2 l) <=> h4/list/EVERY (\x. P2 x ==> P1 x) l
% Assm: h4/res__quan/RES__SELECT: !f P. h4/bool/RES__SELECT P f = h4/min/_40 (\x. h4/bool/IN x P /\ f x)
% Assm: h4/option/some__elim: !Q P. Q (h4/option/some P) ==> (?x. P x /\ Q (h4/option/SOME x)) \/ (!x. ~P x) /\ Q h4/option/NONE
% Assm: h4/res__quan/RES__EXISTS__DISJ__DIST: !R Q P. h4/bool/RES__EXISTS P (\i. Q i \/ R i) <=> h4/bool/RES__EXISTS P (\i. Q i) \/ h4/bool/RES__EXISTS P (\i. R i)
% Assm: h4/list/EXISTS__CONG: !l2 l1 P_27 P. l1 = l2 /\ (!x. h4/bool/IN x (h4/list/LIST__TO__SET l2) ==> (P x <=> P_27 x)) ==> (h4/list/EXISTS P l1 <=> h4/list/EXISTS P_27 l2)
% Assm: h4/list/FILTER__EQ__CONS: !lr l h P. h4/list/FILTER P l = h4/list/CONS h lr <=> (?l1 l2. l = h4/list/APPEND (h4/list/APPEND l1 (h4/list/CONS h h4/list/NIL)) l2 /\ h4/list/FILTER P l1 = h4/list/NIL /\ h4/list/FILTER P l2 = lr /\ P h)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/FALSITY: !t. F ==> 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/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/res__quan/RES__EXISTS: !f P. h4/bool/RES__EXISTS P f <=> (?x. h4/bool/IN x P /\ f x)
% Assm: h4/bool/CONJ__SYM: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/RIGHT__AND__OVER__OR: !C B A. (B \/ C) /\ A <=> B /\ A \/ C /\ A
% Assm: h4/list/FILTER0_c1: !t h P. h4/list/FILTER P (h4/list/CONS h t) = h4/bool/COND (P h) (h4/list/CONS h (h4/list/FILTER P t)) (h4/list/FILTER P t)
% Assm: h4/list/FILTER0_c0: !P. h4/list/FILTER P h4/list/NIL = h4/list/NIL
% 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/COND__RAND: !y x f b. f (h4/bool/COND b x y) = h4/bool/COND b (f x) (f y)
% Assm: h4/bool/COND__RATOR: !x g f b. h4/bool/COND b f g x = h4/bool/COND b (f x) (g x)
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/list/EVERY__DEF_c1: !t h P. h4/list/EVERY P (h4/list/CONS h t) <=> P h /\ h4/list/EVERY P t
% Assm: h4/list/EVERY__DEF_c0: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/T__DEF: T <=> (\x. x) = (\x. x)
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% 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/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/option/some__def: !P. h4/option/some P = h4/bool/COND (?x. P x) (h4/option/SOME (h4/min/_40 (\x. P x))) h4/option/NONE
% Assm: h4/bool/RIGHT__FORALL__OR__THM: !Q P. (!x. P \/ Q x) <=> P \/ (!x. Q x)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% 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/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% 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/bool/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/list/MEM_c1: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/CONS h t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm: h4/list/EXISTS__DEF_c1: !t h P. h4/list/EXISTS P (h4/list/CONS h t) <=> P h \/ h4/list/EXISTS P t
% Assm: h4/list/EXISTS__DEF_c0: !P. h4/list/EXISTS P h4/list/NIL <=> F
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/list/APPEND__eq__NIL_c0: !l2 l1. h4/list/NIL = h4/list/APPEND l1 l2 <=> l1 = h4/list/NIL /\ l2 = h4/list/NIL
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% 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/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/list/NOT__CONS__NIL: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/F__DEF: F <=> (!t. t)
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Goal: !Q P. (!x. P x ==> Q x) ==> $forall P ==> $forall Q
%   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_FORALLu_u_THM]: !f. happ $forall f <=> (!x. happ f x)
% Assm [h4s_quotients_EQUIVu_u_RESu_u_FORALL]: !P E. h4/quotient/EQUIV E ==> (h4/bool/RES__FORALL (happ h4/quotient/respects E) P <=> happ $forall P)
% Assm [h4s_resu_u_quans_RESu_u_FORALLu_u_UNIV]: !p. h4/bool/RES__FORALL h4/pred__set/UNIV p <=> happ $forall p
% Assm [h4s_bools_TRUTH]: T
% 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_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_resu_u_quans_RESu_u_FORALL]: !f P. h4/bool/RES__FORALL P f <=> (!x. h4/bool/IN x P ==> happ f x)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_FORALLu_u_DEF]: !x. happ $forall x <=> (!x. happ x x <=> T)
% Assm [h4s_pairs_FORALLu_u_UNCURRY]: !f. happ $forall (h4/pair/UNCURRY f) <=> happ $forall (h4/combin/o $forall f)
% Assm [h4s_predu_u_sets_SPECIFICATION]: !x P. h4/bool/IN x P <=> happ P x
% Assm [h4s_pairs_PFORALLu_u_THM]: !_1. (!P x y. happ (happ (happ _1 P) x) y <=> happ (happ P x) y) ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!P. (!x y. happ (happ P x) y) <=> happ $forall (h4/pair/UNCURRY (happ _0 P))))
% Assm [h4s_quotients_RESPECTS]: !x R. happ (happ h4/quotient/respects R) x <=> happ (happ R x) x
% Assm [h4s_quotients_EQUIVu_u_def]: !E. h4/quotient/EQUIV E <=> (!x y. happ (happ E x) y <=> happ E x = happ E y)
% 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_predu_u_sets_INu_u_UNIV]: !x. h4/bool/IN x h4/pred__set/UNIV
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_combins_LETu_u_FORALLu_u_ELIM]: !v f. h4/bool/LET f v <=> happ $forall (h4/combin/S (h4/combin/o $imply (h4/combin/o h4/marker/Abbrev (h4/combin/C $equals v))) f)
% Assm [h4s_combins_literalu_u_caseu_u_FORALLu_u_ELIM]: !v f. h4/bool/literal__case f v <=> happ $forall (h4/combin/S (h4/combin/o $imply (h4/combin/o h4/marker/Abbrev (h4/combin/C $equals v))) f)
% Assm [h4s_quotients_FORALLu_u_PRS]: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!f. happ $forall f <=> h4/bool/RES__FORALL (happ h4/quotient/respects R) (h4/quotient/_2D_2D_3E abs h4/combin/I f))
% Assm [h4s_pairs_ELIMu_u_PFORALLu_u_EVAL]: !_0. (!P x. happ (happ _0 P) x = happ P x) ==> (!P. happ $forall (h4/pair/UNCURRY (happ _0 P)) <=> (!x. happ $forall (happ P x)))
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_pairs_ELIMu_u_PFORALL]: !P. (!p. happ (happ P (h4/pair/FST p)) (h4/pair/SND p)) <=> (!p1 p2. happ (happ P p1) p2)
% Assm [h4s_pairs_ELIMu_u_UNCURRY]: !f x. happ (h4/pair/UNCURRY f) x = happ (happ f (h4/pair/FST x)) (h4/pair/SND x)
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_combins_Su_u_DEF]: !x x x. happ (h4/combin/S x x) x = happ (happ x x) (happ x x)
% Assm [h4s_combins_Cu_u_DEF]: !x x x. happ (h4/combin/C x x) x = happ (happ x x) x
% Assm [h4s_markers_Abbrevu_u_def]: !x. happ h4/marker/Abbrev x <=> x
% Assm [h4s_bools_FUNu_u_EQu_u_THM]: !g f. f = g <=> (!x. happ f x = happ g x)
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_pairs_UNCURRY0]: !v f. happ (h4/pair/UNCURRY f) v = happ (happ f (h4/pair/FST v)) (h4/pair/SND v)
% Assm [h4s_pairs_FORALLu_u_PROD]: !P. (!p. happ P p) <=> (!p__1 p__2. happ P (h4/pair/_2C p__1 p__2))
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_bools_ETAu_u_THM]: !M x. happ M x = happ M x
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_bools_literalu_u_caseu_u_THM]: !x f. h4/bool/literal__case f x = happ f x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_quotients_FUNu_u_MAPu_u_THM]: !x h g f. happ (h4/quotient/_2D_2D_3E f g h) x = happ g (happ h (happ f x))
% Assm [h4s_quotients_QUOTIENTu_u_REPu_u_REFL]: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!a. happ (happ R (happ rep a)) (happ rep a))
% Assm [h4s_quotients_QUOTIENTu_u_ABSu_u_REP]: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!a. happ abs (happ rep a) = a)
% Assm [h4s_quotients_respectsu_u_def]: h4/quotient/respects = h4/combin/W
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_combins_Iu_u_THM]: !x. happ h4/combin/I x = x
% Assm [h4s_combins_Wu_u_THM]: !x f. happ (happ h4/combin/W f) x = happ (happ f x) x
% Assm [h4s_quotients_RESu_u_EXISTSu_u_EQUIVu_u_DEF]: !_2. (!x x x y. happ (happ (happ (happ _2 x) x) x) y <=> happ x x /\ happ x y ==> happ (happ x x) y) ==> (!_1. (!x x x. happ (happ (happ _1 x) x) x <=> h4/bool/RES__FORALL (happ h4/quotient/respects x) (happ (happ (happ _2 x) x) x)) ==> (!_0. (!x x. happ (happ _0 x) x <=> happ x x) ==> (!x x. h4/quotient/RES__EXISTS__EQUIV x x <=> h4/bool/RES__EXISTS (happ h4/quotient/respects x) (happ _0 x) /\ h4/bool/RES__FORALL (happ h4/quotient/respects x) (happ _0 (happ (happ _1 x) x)))))
% Assm [h4s_bools_RESu_u_EXISTSu_u_UNIQUEu_u_DEF]: !_2. (!x' x y. happ (happ (happ _2 x') x) y <=> happ x' x /\ happ x' y ==> x = y) ==> (!_1. (!x x' x. happ (happ (happ _1 x) x') x <=> h4/bool/RES__FORALL x (happ (happ _2 x') x)) ==> (!_0. (!x' x. happ (happ _0 x') x <=> happ x' x) ==> (!x x'. h4/bool/RES__EXISTS__UNIQUE x x' <=> h4/bool/RES__EXISTS x (happ _0 x') /\ h4/bool/RES__FORALL x (happ _0 (happ (happ _1 x) x')))))
% Assm [h4s_bools_RESu_u_SELECTu_u_DEF]: !_0. (!x x' x. happ (happ (happ _0 x) x') x <=> h4/bool/IN x x /\ happ x' x) ==> (!x x'. h4/bool/RES__SELECT x x' = h4/min/_40 (happ (happ _0 x) x'))
% Assm [h4s_bools_RESu_u_EXISTSu_u_DEF]: !x x'. h4/bool/RES__EXISTS x x' <=> (?x. h4/bool/IN x x /\ happ x' x)
% Assm [h4s_quotients_RESu_u_EXISTSu_u_EQUIV0]: !_2. (!m R x y. happ (happ (happ (happ _2 m) R) x) y <=> happ m x /\ happ m y ==> happ (happ R x) y) ==> (!_1. (!m R x. happ (happ (happ _1 m) R) x <=> h4/bool/RES__FORALL (happ h4/quotient/respects R) (happ (happ (happ _2 m) R) x)) ==> (!_0. (!m x. happ (happ _0 m) x <=> happ m x) ==> (!m R. h4/quotient/RES__EXISTS__EQUIV R m <=> h4/bool/RES__EXISTS (happ h4/quotient/respects R) (happ _0 m) /\ h4/bool/RES__FORALL (happ h4/quotient/respects R) (happ _0 (happ (happ _1 m) R)))))
% Assm [h4s_bools_RESu_u_EXISTSu_u_UNIQUEu_u_THM]: !_2. (!f x y. happ (happ (happ _2 f) x) y <=> happ f x /\ happ f y ==> x = y) ==> (!_1. (!P f x. happ (happ (happ _1 P) f) x <=> h4/bool/RES__FORALL P (happ (happ _2 f) x)) ==> (!_0. (!f x. happ (happ _0 f) x <=> happ f x) ==> (!f P. h4/bool/RES__EXISTS__UNIQUE P f <=> h4/bool/RES__EXISTS P (happ _0 f) /\ h4/bool/RES__FORALL P (happ _0 (happ (happ _1 P) f)))))
% Assm [h4s_bools_RESu_u_EXISTSu_u_CONG]: !g f Q P. P = Q ==> (!x. h4/bool/IN x Q ==> (happ f x <=> happ g x)) ==> (h4/bool/RES__EXISTS P f <=> h4/bool/RES__EXISTS Q g)
% Assm [h4s_lists_EVERYu_u_FILTER]: !_0. (!P2 P1 x. happ (happ (happ _0 P2) P1) x <=> happ P2 x ==> happ P1 x) ==> (!l P2 P1. h4/list/EVERY P1 (h4/list/FILTER P2 l) <=> h4/list/EVERY (happ (happ _0 P2) P1) l)
% Assm [h4s_resu_u_quans_RESu_u_SELECT]: !_0. (!P f x. happ (happ (happ _0 P) f) x <=> h4/bool/IN x P /\ happ f x) ==> (!f P. h4/bool/RES__SELECT P f = h4/min/_40 (happ (happ _0 P) f))
% Assm [h4s_options_someu_u_elim]: !Q P. happ Q (h4/option/some P) ==> (?x. happ P x /\ happ Q (h4/option/SOME x)) \/ (!x. ~happ P x) /\ happ Q h4/option/NONE
% Assm [h4s_resu_u_quans_RESu_u_EXISTSu_u_DISJu_u_DIST]: !_1. (!Q i. happ (happ _1 Q) i <=> happ Q i) ==> (!_0. (!Q R i. happ (happ (happ _0 Q) R) i <=> happ Q i \/ happ R i) ==> (!R Q P. h4/bool/RES__EXISTS P (happ (happ _0 Q) R) <=> h4/bool/RES__EXISTS P (happ _1 Q) \/ h4/bool/RES__EXISTS P (happ _1 R)))
% Assm [h4s_lists_EXISTSu_u_CONG]: !l2 l1 P_27 P. l1 = l2 /\ (!x. h4/bool/IN x (h4/list/LIST__TO__SET l2) ==> (happ P x <=> happ P_27 x)) ==> (h4/list/EXISTS P l1 <=> h4/list/EXISTS P_27 l2)
% Assm [h4s_lists_FILTERu_u_EQu_u_CONS]: !lr l h P. h4/list/FILTER P l = happ (happ h4/list/CONS h) lr <=> (?l1 l2. l = h4/list/APPEND (h4/list/APPEND l1 (happ (happ h4/list/CONS h) h4/list/NIL)) l2 /\ h4/list/FILTER P l1 = h4/list/NIL /\ h4/list/FILTER P l2 = lr /\ happ P h)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% 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_FALSITY]: !t. F ==> 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_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_resu_u_quans_RESu_u_EXISTS]: !f P. h4/bool/RES__EXISTS P f <=> (?x. h4/bool/IN x P /\ happ f x)
% Assm [h4s_bools_CONJu_u_SYM]: !t2 t1. t1 /\ t2 <=> t2 /\ t1
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_ANDu_u_OVERu_u_OR]: !C B A. (B \/ C) /\ A <=> B /\ A \/ C /\ A
% Assm [h4s_lists_FILTER0u_c1]: !t h P. h4/list/FILTER P (happ (happ h4/list/CONS h) t) = h4/bool/COND (happ P h) (happ (happ h4/list/CONS h) (h4/list/FILTER P t)) (h4/list/FILTER P t)
% Assm [h4s_lists_FILTER0u_c0]: !P. h4/list/FILTER P h4/list/NIL = h4/list/NIL
% 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_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_CONDu_u_RATOR]: !x g f b. happ (h4/bool/COND b f g) x = h4/bool/COND b (happ f x) (happ g x)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_lists_EVERYu_u_DEFu_c1]: !t h P. h4/list/EVERY P (happ (happ h4/list/CONS h) t) <=> happ P h /\ h4/list/EVERY P t
% Assm [h4s_lists_EVERYu_u_DEFu_c0]: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_Tu_u_DEF]: T <=> (!x. x <=> x)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% 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_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% Assm [h4s_options_someu_u_def]: !_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!P. ?v. (v <=> (?x. happ P x)) /\ h4/option/some P = h4/bool/COND v (h4/option/SOME (h4/min/_40 (happ _0 P))) h4/option/NONE)
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. P \/ happ Q x) <=> P \/ (!x. happ Q x)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% 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_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% 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_bools_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_lists_MEMu_c1]: !x t h. h4/bool/IN x (h4/list/LIST__TO__SET (happ (happ h4/list/CONS h) t)) <=> x = h \/ h4/bool/IN x (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_EXISTSu_u_DEFu_c1]: !t h P. h4/list/EXISTS P (happ (happ h4/list/CONS h) t) <=> happ P h \/ h4/list/EXISTS P t
% Assm [h4s_lists_EXISTSu_u_DEFu_c0]: !P. h4/list/EXISTS P h4/list/NIL <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_lists_APPENDu_u_equ_u_NILu_c0]: !l2 l1. h4/list/NIL = h4/list/APPEND l1 l2 <=> l1 = h4/list/NIL /\ l2 = h4/list/NIL
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. happ (happ h4/list/CONS a0) a1 = happ (happ h4/list/CONS a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_lists_NOTu_u_CONSu_u_NIL]: !a1 a0. ~(happ (happ h4/list/CONS a0) a1 = h4/list/NIL)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_Fu_u_DEF]: F <=> (!t. t)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% 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_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Goal: !Q P. (!x. happ P x ==> happ Q x) ==> happ $forall P ==> happ $forall Q
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_Q1318689,TV_Q1318685]: ![V_f, V_g]: (![V_x]: s(TV_Q1318685,happ(s(t_fun(TV_Q1318689,TV_Q1318685),V_f),s(TV_Q1318689,V_x))) = s(TV_Q1318685,happ(s(t_fun(TV_Q1318689,TV_Q1318685),V_g),s(TV_Q1318689,V_x))) => s(t_fun(TV_Q1318689,TV_Q1318685),V_f) = s(t_fun(TV_Q1318689,TV_Q1318685),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_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_f]: (p(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),V_f)))) <=> ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x)))))).
fof(ah4s_quotients_EQUIVu_u_RESu_u_FORALL, axiom, ![TV_u_27a]: ![V_P, V_E]: (p(s(t_bool,h4s_quotients_equiv(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_E)))) => s(t_bool,h4s_bools_resu_u_forall(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_E))),s(t_fun(TV_u_27a,t_bool),V_P))) = 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),V_P))))).
fof(ah4s_resu_u_quans_RESu_u_FORALLu_u_UNIV, axiom, ![TV_u_27a]: ![V_p]: s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ),s(t_fun(TV_u_27a,t_bool),V_p))) = 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),V_p)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_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_IMPu_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_resu_u_quans_RESu_u_FORALL, axiom, ![TV_u_27a]: ![V_f, V_P]: (p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),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_FORALLu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: (p(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),V_x)))) <=> ![V_x0]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x0))) = s(t_bool,t))).
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),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_predu_u_sets_SPECIFICATION, axiom, ![TV_u_27a]: ![V_x, V_P]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))).
fof(ah4s_pairs_PFORALLu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x, V_y]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) => ![V_uu_0]: (![V_P, V_x]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))) => ![V_P]: (![V_x, V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))) <=> p(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)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P)))))))))))).
fof(ah4s_quotients_RESPECTS, axiom, ![TV_u_27a]: ![V_x, V_R]: s(t_bool,happ(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_x)))).
fof(ah4s_quotients_EQUIVu_u_def, axiom, ![TV_u_27a]: ![V_E]: (p(s(t_bool,h4s_quotients_equiv(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_E)))) <=> ![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_E),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_E),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_E),s(TV_u_27a,V_y)))))).
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_predu_u_sets_INu_u_UNIV, axiom, ![TV_u_27a]: ![V_x]: p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_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),h4s_combins_s(s(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),h4s_combins_o(s(t_fun(t_bool,t_bool),h4s_markers_abbrev),s(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_combins_literalu_u_caseu_u_FORALLu_u_ELIM, axiom, ![TV_u_27a]: ![V_v, V_f]: s(t_bool,h4s_bools_literalu_u_case(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),h4s_combins_s(s(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),h4s_combins_o(s(t_fun(t_bool,t_bool),h4s_markers_abbrev),s(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_quotients_FORALLu_u_PRS, axiom, ![TV_u_27a,TV_u_27b]: ![V_rep, V_abs, V_R]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ![V_f]: s(t_bool,happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_bool),d_forall),s(t_fun(TV_u_27b,t_bool),V_f))) = s(t_bool,h4s_bools_resu_u_forall(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(TV_u_27a,t_bool),h4s_quotients_u_2du_2du_3e(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(t_bool,t_bool),h4s_combins_i),s(t_fun(TV_u_27b,t_bool),V_f))))))).
fof(ah4s_pairs_ELIMu_u_PFORALLu_u_EVAL, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))) => ![V_P]: (p(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)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P)))))))) <=> ![V_x]: p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_bool),d_forall),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))))))))).
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_pairs_ELIMu_u_PFORALL, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: (![V_p]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p)))))) <=> ![V_p1, V_p2]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_p1))),s(TV_u_27b,V_p2)))))).
fof(ah4s_pairs_ELIMu_u_UNCURRY, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_f, V_x]: s(TV_u_27c,happ(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)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))) = 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,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)))))).
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),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_Su_u_DEF, axiom, ![TV_u_27c,TV_u_27b,TV_u_27a]: ![V_x, V_x0, V_x1]: s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),h4s_combins_s(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_x),s(t_fun(TV_u_27a,TV_u_27b),V_x0))),s(TV_u_27a,V_x1))) = 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_x),s(TV_u_27a,V_x1))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x0),s(TV_u_27a,V_x1)))))).
fof(ah4s_combins_Cu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_x, V_x0, V_x1]: s(TV_u_27c,happ(s(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_x),s(TV_u_27b,V_x0))),s(TV_u_27a,V_x1))) = 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_x),s(TV_u_27a,V_x1))),s(TV_u_27b,V_x0)))).
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_bools_FUNu_u_EQu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),V_g) <=> ![V_x]: 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_g),s(TV_u_27a,V_x))))).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(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(TV_u_27b,V_y)).
fof(ah4s_combins_ou_u_DEF, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_g, V_f, V_x]: s(TV_u_27b,happ(s(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),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_pairs_UNCURRY0, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27c,happ(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)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))) = 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,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v))))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_v)))))).
fof(ah4s_pairs_FORALLu_u_PROD, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: (![V_p]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p)))) <=> ![V_pu_u_1, V_pu_u_2]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_pu_u_1),s(TV_u_27b,V_pu_u_2)))))))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(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(TV_u_27a,V_x)).
fof(ah4s_bools_ETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_M, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_M),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_M),s(TV_u_27a,V_x)))).
fof(ah4s_bools_LETu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_let(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_x)))).
fof(ah4s_bools_literalu_u_caseu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,h4s_bools_literalu_u_case(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_x)))).
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,t)))).
fof(ah4s_quotients_FUNu_u_MAPu_u_THM, axiom, ![TV_u_27d,TV_u_27b,TV_u_27c,TV_u_27a]: ![V_x, V_h, V_g, V_f]: s(TV_u_27d,happ(s(t_fun(TV_u_27a,TV_u_27d),h4s_quotients_u_2du_2du_3e(s(t_fun(TV_u_27a,TV_u_27c),V_f),s(t_fun(TV_u_27b,TV_u_27d),V_g),s(t_fun(TV_u_27c,TV_u_27b),V_h))),s(TV_u_27a,V_x))) = s(TV_u_27d,happ(s(t_fun(TV_u_27b,TV_u_27d),V_g),s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_h),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_f),s(TV_u_27a,V_x)))))))).
fof(ah4s_quotients_QUOTIENTu_u_REPu_u_REFL, axiom, ![TV_u_27a,TV_u_27b]: ![V_rep, V_abs, V_R]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ![V_a]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a)))))))).
fof(ah4s_quotients_QUOTIENTu_u_ABSu_u_REP, axiom, ![TV_u_27a,TV_u_27b]: ![V_rep, V_abs, V_R]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a))).
fof(ah4s_quotients_respectsu_u_def, axiom, ![TV_u_27a,TV_u_27b]: s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,TV_u_27b)),h4s_quotients_respects) = s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,TV_u_27b)),h4s_combins_w)).
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_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),h4s_combins_i),s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_combins_Wu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,TV_u_27b)),h4s_combins_w),s(t_fun(TV_u_27a,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),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,V_x)))).
fof(ah4s_quotients_RESu_u_EXISTSu_u_EQUIVu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_2]: (![V_x, V_x0, V_x1, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),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))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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)))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x0))),s(TV_u_27a,V_x1))),s(TV_u_27a,V_y)))) <=> ((p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x1)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x0),s(TV_u_27a,V_x1))),s(TV_u_27a,V_y)))))) => ![V_uu_1]: (![V_x, V_x0, V_x1]: s(t_bool,happ(s(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_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x0))),s(TV_u_27a,V_x1))) = s(t_bool,h4s_bools_resu_u_forall(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x0))),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))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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)))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x0))),s(TV_u_27a,V_x1))))) => ![V_uu_0]: (![V_x, V_x0]: s(t_bool,happ(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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_x))),s(TV_u_27a,V_x0))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x0))) => ![V_x, V_x0]: (p(s(t_bool,h4s_quotients_resu_u_existsu_u_equiv(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x),s(t_fun(TV_u_27a,t_bool),V_x0)))) <=> (p(s(t_bool,h4s_bools_resu_u_exists(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x))),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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_x0)))))) & p(s(t_bool,h4s_bools_resu_u_forall(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x))),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)),V_uu_0),s(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_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_x0))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_x)))))))))))))).
fof(ah4s_bools_RESu_u_EXISTSu_u_UNIQUEu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_2]: (![V_xi_, V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_xi_))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> ((p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_xi_),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_xi_),s(TV_u_27a,V_y))))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y))) => ![V_uu_1]: (![V_x, V_xi_, V_x0]: s(t_bool,happ(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_bool),V_xi_))),s(TV_u_27a,V_x0))) = s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),V_x),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_bool),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_xi_))),s(TV_u_27a,V_x0))))) => ![V_uu_0]: (![V_xi_, V_x]: s(t_bool,happ(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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_xi_))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_xi_),s(TV_u_27a,V_x))) => ![V_x, V_xi_]: (p(s(t_bool,h4s_bools_resu_u_existsu_u_unique(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27a,t_bool),V_xi_)))) <=> (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_x),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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_xi_)))))) & p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),V_x),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)),V_uu_0),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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_bool),V_xi_)))))))))))))).
fof(ah4s_bools_RESu_u_SELECTu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_xi_, V_x0]: (p(s(t_bool,happ(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_bool),V_xi_))),s(TV_u_27a,V_x0)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x0),s(t_fun(TV_u_27a,t_bool),V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_xi_),s(TV_u_27a,V_x0)))))) => ![V_x, V_xi_]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27a,t_bool),V_xi_))) = s(TV_u_27a,h4s_mins_u_40(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_x))),s(t_fun(TV_u_27a,t_bool),V_xi_))))))).
fof(ah4s_bools_RESu_u_EXISTSu_u_DEF, axiom, ![TV_u_27a]: ![V_x, V_xi_]: (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27a,t_bool),V_xi_)))) <=> ?[V_x0]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x0),s(t_fun(TV_u_27a,t_bool),V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_xi_),s(TV_u_27a,V_x0))))))).
fof(ah4s_quotients_RESu_u_EXISTSu_u_EQUIV0, axiom, ![TV_u_27a]: ![V_uu_2]: (![V_m, V_R, V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),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))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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)))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_m))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> ((p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_m),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_m),s(TV_u_27a,V_y))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))))) => ![V_uu_1]: (![V_m, V_R, V_x]: s(t_bool,happ(s(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_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_m))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))) = s(t_bool,h4s_bools_resu_u_forall(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),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))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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)))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_m))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(TV_u_27a,V_x))))) => ![V_uu_0]: (![V_m, V_x]: s(t_bool,happ(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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_m))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_m),s(TV_u_27a,V_x))) => ![V_m, V_R]: (p(s(t_bool,h4s_quotients_resu_u_existsu_u_equiv(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_m)))) <=> (p(s(t_bool,h4s_bools_resu_u_exists(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_m)))))) & p(s(t_bool,h4s_bools_resu_u_forall(s(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_bool)),h4s_quotients_respects),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),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)),V_uu_0),s(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_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_m))),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))))))))))))).
fof(ah4s_bools_RESu_u_EXISTSu_u_UNIQUEu_u_THM, axiom, ![TV_u_27a]: ![V_uu_2]: (![V_f, V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> ((p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_y))))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y))) => ![V_uu_1]: (![V_P, V_f, V_x]: s(t_bool,happ(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x))) = s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),V_P),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_bool),t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),V_uu_2),s(t_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x))))) => ![V_uu_0]: (![V_f, V_x]: s(t_bool,happ(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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))) => ![V_f, V_P]: (p(s(t_bool,h4s_bools_resu_u_existsu_u_unique(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f)))) <=> (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_f)))))) & p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(TV_u_27a,t_bool),V_P),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)),V_uu_0),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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_fun(TV_u_27a,t_bool),V_f)))))))))))))).
fof(ah4s_bools_RESu_u_EXISTSu_u_CONG, axiom, ![TV_u_27a]: ![V_g, V_f, V_Q, V_P]: (s(t_fun(TV_u_27a,t_bool),V_P) = s(t_fun(TV_u_27a,t_bool),V_Q) => (![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_Q)))) => s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_g),s(TV_u_27a,V_x)))) => s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f))) = s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_Q),s(t_fun(TV_u_27a,t_bool),V_g)))))).
fof(ah4s_lists_EVERYu_u_FILTER, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P2, V_P1, V_x]: (p(s(t_bool,happ(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P2))),s(t_fun(TV_u_27a,t_bool),V_P1))),s(TV_u_27a,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P2),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P1),s(TV_u_27a,V_x)))))) => ![V_l, V_P2, V_P1]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P2),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_bool,h4s_lists_every(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P2))),s(t_fun(TV_u_27a,t_bool),V_P1))),s(t_h4s_lists_list(TV_u_27a),V_l))))).
fof(ah4s_resu_u_quans_RESu_u_SELECT, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_f, V_x]: (p(s(t_bool,happ(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x)))))) => ![V_f, V_P]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f))) = s(TV_u_27a,h4s_mins_u_40(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_fun(TV_u_27a,t_bool),V_f))))))).
fof(ah4s_options_someu_u_elim, axiom, ![TV_u_27a]: ![V_Q, V_P]: (p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),V_Q),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(t_fun(TV_u_27a,t_bool),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(t_h4s_options_option(TV_u_27a),t_bool),V_Q),s(t_h4s_options_option(TV_u_27a),h4s_options_some0(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))))) & p(s(t_bool,happ(s(t_fun(t_h4s_options_option(TV_u_27a),t_bool),V_Q),s(t_h4s_options_option(TV_u_27a),h4s_options_none)))))))).
fof(ah4s_resu_u_quans_RESu_u_EXISTSu_u_DISJu_u_DIST, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_Q, V_i]: s(t_bool,happ(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)),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_Q))),s(TV_u_27a,V_i))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_i))) => ![V_uu_0]: (![V_Q, V_R, V_i]: (p(s(t_bool,happ(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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_Q))),s(t_fun(TV_u_27a,t_bool),V_R))),s(TV_u_27a,V_i)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_i)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_R),s(TV_u_27a,V_i)))))) => ![V_R, V_Q, V_P]: (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),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_bool),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_Q))),s(t_fun(TV_u_27a,t_bool),V_R)))))) <=> (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),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)),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_Q)))))) | p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),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)),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_R))))))))))).
fof(ah4s_lists_EXISTSu_u_CONG, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_Pu_27, V_P]: ((s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),V_l2) & ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l2)))))) => s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Pu_27),s(TV_u_27a,V_x))))) => s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_Pu_27),s(t_h4s_lists_list(TV_u_27a),V_l2))))).
fof(ah4s_lists_FILTERu_u_EQu_u_CONS, axiom, ![TV_u_27a]: ![V_lr, V_l, V_h, V_P]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_lr))) <=> ?[V_l1, V_l2]: (s(t_h4s_lists_list(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_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_nil))))),s(t_h4s_lists_list(TV_u_27a),V_l2))) & (s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & (s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),V_lr) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h))))))))).
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_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => 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,t),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_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_resu_u_quans_RESu_u_EXISTS, axiom, ![TV_u_27a]: ![V_f, V_P]: (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f)))) <=> ?[V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_CONJu_u_SYM, 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))))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, 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_RIGHTu_u_ANDu_u_OVERu_u_OR, 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_lists_FILTER0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_FILTER0u_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
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_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_CONDu_u_RATOR, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_g, V_f, V_b]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_bools_cond(s(t_bool,V_b),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_g))),s(TV_u_27a,V_x))) = 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_g),s(TV_u_27a,V_x)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_EVERYu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) & p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_EVERYu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = 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_Tu_u_DEF, axiom, (p(s(t_bool,t)) <=> ![V_x]: s(t_bool,V_x) = s(t_bool,V_x))).
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_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_bools_LEFTu_u_ANDu_u_FORALLu_u_THM, 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,V_Q))) <=> ![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,V_Q))))).
fof(ah4s_options_someu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))) => ![V_P]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) & s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_options_option(TV_u_27a),h4s_options_some0(s(TV_u_27a,h4s_mins_u_40(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)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))))))),s(t_h4s_options_option(TV_u_27a),h4s_options_none)))))).
fof(ah4s_bools_RIGHTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![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))))) <=> (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))))))).
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_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_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_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_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_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_MEMu_c1, axiom, ![TV_u_27a]: ![V_x, V_t, V_h]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_h) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_t))))))))).
fof(ah4s_lists_EXISTSu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) | p(s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_EXISTSu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,f)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
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_lists_APPENDu_u_equ_u_NILu_c0, axiom, ![TV_u_27a]: ![V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = 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_l1) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0u_27))),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),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_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_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]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(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_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_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_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_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(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_lists_NOTu_u_CONSu_u_NIL, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
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_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_listu_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_27listu_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]: (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_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_a1),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_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_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_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(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_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
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_Fu_u_DEF, axiom, (p(s(t_bool,f)) <=> ![V_t]: p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_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_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_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_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(ch4s_quotients_FORALLu_u_REGULAR, conjecture, ![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))))) => (p(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),V_P)))) => p(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),V_Q))))))).
