%   ORIGINAL: h4/toto/apcharto__thm
% 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/toto/charto0: h4/toto/charto = h4/toto/TO h4/toto/charOrd
% Assm: h4/toto/charOrd0: !b a. h4/toto/charOrd a b = h4/toto/numOrd (h4/string/ORD a) (h4/string/ORD b)
% 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/bool/TRUTH: T
% Assm: h4/toto/to__bij_c1: !r. h4/toto/TotOrd r <=> h4/toto/apto (h4/toto/TO r) = r
% Assm: h4/toto/toto__equal__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> x = y
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/toto/toto__antisym: !y x c. h4/toto/apto c x y = h4/toto/GREATER <=> h4/toto/apto c y x = h4/toto/LESS
% Assm: h4/toto/totoLGtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/totoELtrans: !z y x c. h4/toto/apto c x y = h4/toto/EQUAL /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__glneq_c0: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm: h4/toto/totoGGtrans: !z y x c. h4/toto/apto c y x = h4/toto/GREATER /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__equal__imp__eq: !y x c. h4/toto/apto c x y = h4/toto/EQUAL ==> x = y
% Assm: h4/toto/totoLEtrans: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/to__bij_c0: !a. h4/toto/TO (h4/toto/apto a) = a
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/toto/toto__glneq_c1: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm: h4/toto/TO__apto__TO__ID: !r. h4/toto/TotOrd r <=> h4/toto/apto (h4/toto/TO r) = r
% Assm: h4/toto/TotOrd0: !c. h4/toto/TotOrd c <=> (!x y. c x y = h4/toto/EQUAL <=> x = y) /\ (!x y. c x y = h4/toto/GREATER <=> c y x = h4/toto/LESS) /\ (!x y z. c x y = h4/toto/LESS /\ c y z = h4/toto/LESS ==> c x z = h4/toto/LESS)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/toto/TotOrd__apto: !c. h4/toto/TotOrd (h4/toto/apto c)
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/toto/toto__refl: !x c. h4/toto/apto c x x = h4/toto/EQUAL
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/toto/toto__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION h4/toto/TotOrd rep
% Assm: h4/toto/toto__equal__sym: !y x c. h4/toto/apto c x y = h4/toto/EQUAL <=> h4/toto/apto c y x = h4/toto/EQUAL
% Assm: h4/toto/totoEEtrans_c1: !z y x c. h4/toto/apto c x y = h4/toto/EQUAL /\ h4/toto/apto c z y = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/EQUAL
% Assm: h4/toto/apnumto__thm: h4/toto/apto h4/toto/numto = h4/toto/numOrd
% Assm: h4/toto/toto__trans__less_c5: !z y x c. h4/toto/apto c x y = h4/toto/EQUAL /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__cpn__eqn_c2: !y x c. h4/toto/apto c x y = h4/toto/GREATER ==> ~(x = y)
% Assm: h4/toto/toto__trans__less_c2: !z y x c. h4/toto/apto c y x = h4/toto/GREATER /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__trans__less_c0: !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/toto/lextoto0: !v c. h4/toto/lextoto c v = h4/toto/TO (h4/toto/lexTO (h4/toto/apto c) (h4/toto/apto v))
% Assm: h4/toto/toto__trans__less_c1: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c z y = h4/toto/GREATER ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/ap__qk__numto__thm: h4/toto/apto h4/toto/qk__numto = h4/toto/qk__numOrd
% Assm: h4/toto/toto__trans__less_c4: !z y x c. h4/toto/apto c x y = h4/toto/LESS /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__cpn__eqn_c1: !y x c. h4/toto/apto c x y = h4/toto/LESS ==> ~(x = y)
% Assm: h4/toto/toto__unequal__imp: !phi cmp. h4/relation/LinearOrder phi /\ cmp = h4/toto/toto__of__LinearOrder phi ==> (!x y. (x = y <=> F) ==> h4/bool/COND (phi x y) (h4/toto/apto cmp x y = h4/toto/LESS) (h4/toto/apto cmp x y = h4/toto/GREATER))
% Assm: h4/toto/toto__cpn__eqn_c0: !y x c. h4/toto/apto c x y = h4/toto/EQUAL ==> x = y
% Assm: h4/toto/TO__apto__TO__IMP: !r. h4/toto/TotOrd r ==> h4/toto/apto (h4/toto/TO r) = r
% Assm: h4/toto/toto__equal__imp: !phi cmp. h4/relation/LinearOrder phi /\ cmp = h4/toto/toto__of__LinearOrder phi ==> (!x y. (x = y <=> T) ==> h4/toto/apto cmp x y = h4/toto/EQUAL)
% Assm: h4/toto/onto__apto: !r. h4/toto/TotOrd r <=> (?a. r = h4/toto/apto a)
% Assm: h4/toto/totoEEtrans_c0: !z y x c. h4/toto/apto c x y = h4/toto/EQUAL /\ h4/toto/apto c y z = h4/toto/EQUAL ==> h4/toto/apto c x z = h4/toto/EQUAL
% Assm: h4/toto/totoGLtrans: !z y x c. h4/toto/apto c y x = h4/toto/GREATER /\ h4/toto/apto c y z = h4/toto/LESS ==> h4/toto/apto c x z = h4/toto/LESS
% Assm: h4/toto/toto__not__less__refl: !h cmp. h4/toto/apto cmp h h = h4/toto/LESS <=> F
% Assm: h4/toto/NOT__EQ__LESS__IMP: !y x cmp. ~(h4/toto/apto cmp x y = h4/toto/LESS) ==> x = y \/ h4/toto/apto cmp y x = h4/toto/LESS
% Assm: h4/toto/TO__apto__ID: !a. h4/toto/TO (h4/toto/apto a) = a
% Assm: h4/toto/toto__swap__cases: !y x c. h4/toto/apto c y x = h4/toto/cpn__CASE (h4/toto/apto c x y) h4/toto/GREATER h4/toto/EQUAL h4/toto/LESS
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/toto/TO__numOrd: h4/toto/TotOrd h4/toto/numOrd
% Assm: h4/toto/numto0: h4/toto/numto = h4/toto/TO h4/toto/numOrd
% Assm: h4/toto/qk__numto0: h4/toto/qk__numto = h4/toto/TO h4/toto/qk__numOrd
% Assm: h4/toto/TO__qk__numOrd: h4/toto/TotOrd h4/toto/qk__numOrd
% Assm: h4/toto/all__cpn__distinct_c0: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm: h4/bool/NOT__CLAUSES_c0: !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__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> 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/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/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/toto/cpn2num__thm_c0: h4/toto/cpn2num h4/toto/LESS = h4/num/0
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/toto/cpn2num__thm_c1: h4/toto/cpn2num h4/toto/EQUAL = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/toto/cpn__EQ__cpn: !a_27 a. a = a_27 <=> h4/toto/cpn2num a = h4/toto/cpn2num a_27
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/toto/TO__of__LinearOrder0: !y x r. h4/toto/TO__of__LinearOrder r x y = h4/bool/COND (x = y) h4/toto/EQUAL (h4/bool/COND (r x y) h4/toto/LESS h4/toto/GREATER)
% Assm: h4/toto/cpn__distinct_c1: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm: h4/toto/cpn__distinct_c2: ~(h4/toto/EQUAL = h4/toto/GREATER)
% Assm: h4/toto/cpn__distinct_c0: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm: h4/toto/toto__of__LinearOrder0: !r. h4/toto/toto__of__LinearOrder r = h4/toto/TO (h4/toto/TO__of__LinearOrder r)
% Assm: h4/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/relation/LinearOrder0: !R. h4/relation/LinearOrder R <=> h4/relation/Order R /\ h4/relation/trichotomous R
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/relation/antisymmetric__def: !R. h4/relation/antisymmetric R <=> (!x y. R x y /\ R y x ==> x = y)
% Assm: h4/relation/Order0: !Z. h4/relation/Order Z <=> h4/relation/antisymmetric Z /\ h4/relation/transitive Z
% Assm: h4/relation/trichotomous0: !R. h4/relation/trichotomous R <=> (!a b. R a b \/ R b a \/ a = b)
% Assm: h4/relation/transitive__def: !R. h4/relation/transitive R <=> (!x y z. R x y /\ R y z ==> R x z)
% 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/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% 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__RATOR: !x g f b. h4/bool/COND b f g x = h4/bool/COND b (f x) (g x)
% 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__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/toto/cpn__nchotomy: !a. a = h4/toto/LESS \/ a = h4/toto/EQUAL \/ a = h4/toto/GREATER
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm: h4/bool/LET__THM: !x f. h4/bool/LET f x = f x
% Assm: h4/toto/cpn__case__def_c1: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/EQUAL v0 v1 v2 = v1
% Assm: h4/toto/cpn__case__def_c2: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/GREATER v0 v1 v2 = v2
% Assm: h4/bool/LET__DEF: h4/bool/LET = (\f x. f x)
% Assm: h4/toto/GREATER__def: h4/toto/GREATER = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm: h4/toto/LESS__def: h4/toto/LESS = h4/toto/num2cpn h4/num/0
% Assm: h4/toto/num2cpn__ONTO: !a. ?r. a = h4/toto/num2cpn r /\ h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm: h4/numeral/iDUB__removal_c0: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm: h4/toto/EQUAL__def: h4/toto/EQUAL = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/numeral/iDUB__removal_c2: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__sub: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/numeral/numeral__lt_c5: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm: h4/numeral/iSUB__THM_c3: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Goal: h4/toto/apto h4/toto/charto = h4/toto/charOrd
%   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_totos_charto0]: h4/toto/charto = h4/toto/TO h4/toto/charOrd
% Assm [h4s_totos_charOrd0]: !b a. happ (happ h4/toto/charOrd a) b = happ (happ h4/toto/numOrd (h4/string/ORD a)) (h4/string/ORD b)
% Assm [h4s_totos_totoLLtrans]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS /\ happ (happ (h4/toto/apto c) y) z = h4/toto/LESS ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_totos_tou_u_biju_c1]: !r. happ h4/toto/TotOrd r <=> h4/toto/apto (h4/toto/TO r) = r
% Assm [h4s_totos_totou_u_equalu_u_eq]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL <=> x = y
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_totos_totou_u_antisym]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/GREATER <=> happ (happ (h4/toto/apto c) y) x = h4/toto/LESS
% Assm [h4s_totos_totoLGtrans]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS /\ happ (happ (h4/toto/apto c) z) y = h4/toto/GREATER ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totoELtrans]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL /\ happ (happ (h4/toto/apto c) y) z = h4/toto/LESS ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totou_u_glnequ_c0]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS ==> ~(x = y)
% Assm [h4s_totos_totoGGtrans]: !z y x c. happ (happ (h4/toto/apto c) y) x = h4/toto/GREATER /\ happ (happ (h4/toto/apto c) z) y = h4/toto/GREATER ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totou_u_equalu_u_impu_u_eq]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL ==> x = y
% Assm [h4s_totos_totoLEtrans]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS /\ happ (happ (h4/toto/apto c) y) z = h4/toto/EQUAL ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_tou_u_biju_c0]: !a. h4/toto/TO (h4/toto/apto a) = a
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_totos_totou_u_glnequ_c1]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/GREATER ==> ~(x = y)
% Assm [h4s_totos_TOu_u_aptou_u_TOu_u_ID]: !r. happ h4/toto/TotOrd r <=> h4/toto/apto (h4/toto/TO r) = r
% Assm [h4s_totos_TotOrd0]: !c. happ h4/toto/TotOrd c <=> (!x y. happ (happ c x) y = h4/toto/EQUAL <=> x = y) /\ (!x y. happ (happ c x) y = h4/toto/GREATER <=> happ (happ c y) x = h4/toto/LESS) /\ (!x y z. happ (happ c x) y = h4/toto/LESS /\ happ (happ c y) z = h4/toto/LESS ==> happ (happ c x) z = h4/toto/LESS)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_totos_TotOrdu_u_apto]: !c. happ h4/toto/TotOrd (h4/toto/apto c)
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_totos_totou_u_refl]: !x c. happ (happ (h4/toto/apto c) x) x = h4/toto/EQUAL
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_totos_totou_u_TYu_u_DEF]: ?rep. h4/bool/TYPE__DEFINITION h4/toto/TotOrd rep
% Assm [h4s_totos_totou_u_equalu_u_sym]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL <=> happ (happ (h4/toto/apto c) y) x = h4/toto/EQUAL
% Assm [h4s_totos_totoEEtransu_c1]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL /\ happ (happ (h4/toto/apto c) z) y = h4/toto/EQUAL ==> happ (happ (h4/toto/apto c) x) z = h4/toto/EQUAL
% Assm [h4s_totos_apnumtou_u_thm]: h4/toto/apto h4/toto/numto = h4/toto/numOrd
% Assm [h4s_totos_totou_u_transu_u_lessu_c5]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL /\ happ (happ (h4/toto/apto c) y) z = h4/toto/LESS ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totou_u_cpnu_u_eqnu_c2]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/GREATER ==> ~(x = y)
% Assm [h4s_totos_totou_u_transu_u_lessu_c2]: !z y x c. happ (happ (h4/toto/apto c) y) x = h4/toto/GREATER /\ happ (happ (h4/toto/apto c) z) y = h4/toto/GREATER ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totou_u_transu_u_lessu_c0]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS /\ happ (happ (h4/toto/apto c) y) z = h4/toto/LESS ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_lextoto0]: !v c. h4/toto/lextoto c v = h4/toto/TO (h4/toto/lexTO (h4/toto/apto c) (h4/toto/apto v))
% Assm [h4s_totos_totou_u_transu_u_lessu_c1]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS /\ happ (happ (h4/toto/apto c) z) y = h4/toto/GREATER ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_apu_u_qku_u_numtou_u_thm]: h4/toto/apto h4/toto/qk__numto = h4/toto/qk__numOrd
% Assm [h4s_totos_totou_u_transu_u_lessu_c4]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS /\ happ (happ (h4/toto/apto c) y) z = h4/toto/EQUAL ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totou_u_cpnu_u_eqnu_c1]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/LESS ==> ~(x = y)
% Assm [h4s_totos_totou_u_unequalu_u_imp]: !phi cmp. h4/relation/LinearOrder phi /\ cmp = h4/toto/toto__of__LinearOrder phi ==> (!x y. (x = y <=> F) ==> (?v. (v <=> happ (happ (h4/toto/apto cmp) x) y = h4/toto/LESS) /\ (?v'. (v' <=> happ (happ (h4/toto/apto cmp) x) y = h4/toto/GREATER) /\ h4/bool/COND (happ (happ phi x) y) v v')))
% Assm [h4s_totos_totou_u_cpnu_u_eqnu_c0]: !y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL ==> x = y
% Assm [h4s_totos_TOu_u_aptou_u_TOu_u_IMP]: !r. happ h4/toto/TotOrd r ==> h4/toto/apto (h4/toto/TO r) = r
% Assm [h4s_totos_totou_u_equalu_u_imp]: !phi cmp. h4/relation/LinearOrder phi /\ cmp = h4/toto/toto__of__LinearOrder phi ==> (!x y. (x = y <=> T) ==> happ (happ (h4/toto/apto cmp) x) y = h4/toto/EQUAL)
% Assm [h4s_totos_ontou_u_apto]: !r. happ h4/toto/TotOrd r <=> (?a. r = h4/toto/apto a)
% Assm [h4s_totos_totoEEtransu_c0]: !z y x c. happ (happ (h4/toto/apto c) x) y = h4/toto/EQUAL /\ happ (happ (h4/toto/apto c) y) z = h4/toto/EQUAL ==> happ (happ (h4/toto/apto c) x) z = h4/toto/EQUAL
% Assm [h4s_totos_totoGLtrans]: !z y x c. happ (happ (h4/toto/apto c) y) x = h4/toto/GREATER /\ happ (happ (h4/toto/apto c) y) z = h4/toto/LESS ==> happ (happ (h4/toto/apto c) x) z = h4/toto/LESS
% Assm [h4s_totos_totou_u_notu_u_lessu_u_refl]: !h cmp. happ (happ (h4/toto/apto cmp) h) h = h4/toto/LESS <=> F
% Assm [h4s_totos_NOTu_u_EQu_u_LESSu_u_IMP]: !y x cmp. ~(happ (happ (h4/toto/apto cmp) x) y = h4/toto/LESS) ==> x = y \/ happ (happ (h4/toto/apto cmp) y) x = h4/toto/LESS
% Assm [h4s_totos_TOu_u_aptou_u_ID]: !a. h4/toto/TO (h4/toto/apto a) = a
% Assm [h4s_totos_totou_u_swapu_u_cases]: !y x c. happ (happ (h4/toto/apto c) y) x = h4/toto/cpn__CASE (happ (happ (h4/toto/apto c) x) y) h4/toto/GREATER h4/toto/EQUAL h4/toto/LESS
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_totos_TOu_u_numOrd]: happ h4/toto/TotOrd h4/toto/numOrd
% Assm [h4s_totos_numto0]: h4/toto/numto = h4/toto/TO h4/toto/numOrd
% Assm [h4s_totos_qku_u_numto0]: h4/toto/qk__numto = h4/toto/TO h4/toto/qk__numOrd
% Assm [h4s_totos_TOu_u_qku_u_numOrd]: happ h4/toto/TotOrd h4/toto/qk__numOrd
% Assm [h4s_totos_allu_u_cpnu_u_distinctu_c0]: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !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_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> 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_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_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_numerals_numeralu_u_equ_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_totos_cpn2numu_u_thmu_c0]: h4/toto/cpn2num h4/toto/LESS = h4/num/0
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_totos_cpn2numu_u_thmu_c1]: h4/toto/cpn2num h4/toto/EQUAL = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_totos_cpnu_u_EQu_u_cpn]: !a_27 a. a = a_27 <=> h4/toto/cpn2num a = h4/toto/cpn2num a_27
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_totos_TOu_u_ofu_u_LinearOrder0]: !y x r. ?v. (v <=> x = y) /\ happ (happ (h4/toto/TO__of__LinearOrder r) x) y = h4/bool/COND v h4/toto/EQUAL (h4/bool/COND (happ (happ r x) y) h4/toto/LESS h4/toto/GREATER)
% Assm [h4s_totos_cpnu_u_distinctu_c1]: ~(h4/toto/LESS = h4/toto/GREATER)
% Assm [h4s_totos_cpnu_u_distinctu_c2]: ~(h4/toto/EQUAL = h4/toto/GREATER)
% Assm [h4s_totos_cpnu_u_distinctu_c0]: ~(h4/toto/LESS = h4/toto/EQUAL)
% Assm [h4s_totos_totou_u_ofu_u_LinearOrder0]: !r. h4/toto/toto__of__LinearOrder r = h4/toto/TO (h4/toto/TO__of__LinearOrder r)
% Assm [h4s_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_relations_LinearOrder0]: !R. h4/relation/LinearOrder R <=> h4/relation/Order R /\ h4/relation/trichotomous R
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_relations_antisymmetricu_u_def]: !R. h4/relation/antisymmetric R <=> (!x y. happ (happ R x) y /\ happ (happ R y) x ==> x = y)
% Assm [h4s_relations_Order0]: !Z. h4/relation/Order Z <=> h4/relation/antisymmetric Z /\ h4/relation/transitive Z
% Assm [h4s_relations_trichotomous0]: !R. h4/relation/trichotomous R <=> (!a b. happ (happ R a) b \/ happ (happ R b) a \/ a = b)
% Assm [h4s_relations_transitiveu_u_def]: !R. h4/relation/transitive R <=> (!x y z. happ (happ R x) y /\ happ (happ R y) z ==> happ (happ R x) z)
% 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_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% 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_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_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_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_totos_cpnu_u_nchotomy]: !a. a = h4/toto/LESS \/ a = h4/toto/EQUAL \/ a = h4/toto/GREATER
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Assm [h4s_bools_LETu_u_THM]: !x f. h4/bool/LET f x = happ f x
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c1]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/EQUAL v0 v1 v2 = v1
% Assm [h4s_totos_cpnu_u_caseu_u_defu_c2]: !v2 v1 v0. h4/toto/cpn__CASE h4/toto/GREATER v0 v1 v2 = v2
% Assm [h4s_bools_LETu_u_DEF]: !x x. h4/bool/LET x x = happ x x
% Assm [h4s_totos_GREATERu_u_def]: h4/toto/GREATER = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))
% Assm [h4s_totos_LESSu_u_def]: h4/toto/LESS = h4/toto/num2cpn h4/num/0
% Assm [h4s_totos_num2cpnu_u_ONTO]: !a. ?r. a = h4/toto/num2cpn r /\ h4/prim__rec/_3C r (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))
% Assm [h4s_numerals_iDUBu_u_removalu_c0]: !n. h4/numeral/iDUB (h4/arithmetic/BIT1 n) = h4/arithmetic/BIT2 (h4/numeral/iDUB n)
% Assm [h4s_totos_EQUALu_u_def]: h4/toto/EQUAL = h4/toto/num2cpn (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_numerals_iDUBu_u_removalu_c2]: h4/numeral/iDUB h4/arithmetic/ZERO = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_sub]: !n m. h4/arithmetic/NUMERAL (h4/arithmetic/_2D n m) = h4/bool/COND (h4/prim__rec/_3C m n) (h4/arithmetic/NUMERAL (h4/numeral/iSUB T n m)) h4/num/0
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_numerals_numeralu_u_ltu_c5]: !n m. h4/prim__rec/_3C (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) <=> ~h4/prim__rec/_3C m n
% Assm [h4s_numerals_iSUBu_u_THMu_c3]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Goal: h4/toto/apto h4/toto/charto = h4/toto/charOrd
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_Q1345744,TV_Q1345740]: ![V_f, V_g]: (![V_x]: s(TV_Q1345740,happ(s(t_fun(TV_Q1345744,TV_Q1345740),V_f),s(TV_Q1345744,V_x))) = s(TV_Q1345740,happ(s(t_fun(TV_Q1345744,TV_Q1345740),V_g),s(TV_Q1345744,V_x))) => s(t_fun(TV_Q1345744,TV_Q1345740),V_f) = s(t_fun(TV_Q1345744,TV_Q1345740),V_g))).
fof(ah4s_totos_charto0, axiom, s(t_h4s_totos_toto(t_h4s_strings_char),h4s_totos_charto) = s(t_h4s_totos_toto(t_h4s_strings_char),h4s_totos_to(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_h4s_totos_cpn)),h4s_totos_charord)))).
fof(ah4s_totos_charOrd0, axiom, ![V_b, V_a]: s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_strings_char,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_h4s_totos_cpn)),h4s_totos_charord),s(t_h4s_strings_char,V_a))),s(t_h4s_strings_char,V_b))) = s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_a))))),s(t_h4s_nums_num,h4s_strings_ord(s(t_h4s_strings_char,V_b)))))).
fof(ah4s_totos_totoLLtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_totos_tou_u_biju_c1, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r)))) <=> s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))).
fof(ah4s_totos_totou_u_equalu_u_eq, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
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_totos_totou_u_antisym, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_greater) <=> s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_less))).
fof(ah4s_totos_totoLGtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totoELtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totou_u_glnequ_c0, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totoGGtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_greater) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totou_u_equalu_u_impu_u_eq, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_totos_totoLEtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_tou_u_biju_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_a))))) = s(t_h4s_totos_toto(TV_u_27a),V_a)).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_totos_totou_u_glnequ_c1, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_greater) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_TOu_u_aptou_u_TOu_u_ID, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r)))) <=> s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))).
fof(ah4s_totos_TotOrd0, axiom, ![TV_u_27a]: ![V_c]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c)))) <=> (![V_x, V_y]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) & (![V_x, V_y]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater) <=> s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_y))),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ![V_x, V_y, V_z]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_c),s(TV_u_27a,V_x))),s(TV_u_27a,V_z))) = s(t_h4s_totos_cpn,h4s_totos_less)))))).
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_totos_TotOrdu_u_apto, axiom, ![TV_u_27a]: ![V_c]: p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))))))).
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_totos_totou_u_refl, axiom, ![TV_u_27a]: ![V_x, V_c]: s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_equal)).
fof(ah4s_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![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) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_totos_totou_u_TYu_u_DEF, axiom, ![TV_u_27a]: ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(t_h4s_totos_toto(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn))),V_rep))))).
fof(ah4s_totos_totou_u_equalu_u_sym, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) <=> s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_equal))).
fof(ah4s_totos_totoEEtransu_c1, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_equal)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal))).
fof(ah4s_totos_apnumtou_u_thm, axiom, s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_nums_num),h4s_totos_numto))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord)).
fof(ah4s_totos_totou_u_transu_u_lessu_c5, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totou_u_cpnu_u_eqnu_c2, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_greater) => ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_transu_u_lessu_c2, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_greater) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totou_u_transu_u_lessu_c0, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_lextoto0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_c]: s(t_h4s_totos_toto(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_lextoto(s(t_h4s_totos_toto(TV_u_27a),V_c),s(t_h4s_totos_toto(TV_u_27b),V_v))) = s(t_h4s_totos_toto(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_totos_to(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_h4s_totos_cpn)),h4s_totos_lexto(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27b),V_v)))))))).
fof(ah4s_totos_totou_u_transu_u_lessu_c1, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_c))),s(TV_u_27a,V_z))),s(TV_u_27a,V_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_apu_u_qku_u_numtou_u_thm, axiom, s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_nums_num),h4s_totos_qku_u_numto))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_qku_u_numord)).
fof(ah4s_totos_totou_u_transu_u_lessu_c4, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totou_u_cpnu_u_eqnu_c1, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_totos_totou_u_unequalu_u_imp, axiom, ![TV_u_27a]: ![V_phi, V_cmp]: ((p(s(t_bool,h4s_relations_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_phi)))) & s(t_h4s_totos_toto(TV_u_27a),V_cmp) = s(t_h4s_totos_toto(TV_u_27a),h4s_totos_totou_u_ofu_u_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_phi)))) => ![V_x, V_y]: ((s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> p(s(t_bool,f))) => ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_y))) = s(t_h4s_totos_cpn,h4s_totos_less)) & ?[V_vi_]: ((p(s(t_bool,V_vi_)) <=> s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_y))) = s(t_h4s_totos_cpn,h4s_totos_greater)) & p(s(t_bool,h4s_bools_cond(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_phi),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))),s(t_bool,V_v),s(t_bool,V_vi_))))))))).
fof(ah4s_totos_totou_u_cpnu_u_eqnu_c0, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_totos_TOu_u_aptou_u_TOu_u_IMP, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r)))) => s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r))).
fof(ah4s_totos_totou_u_equalu_u_imp, axiom, ![TV_u_27a]: ![V_phi, V_cmp]: ((p(s(t_bool,h4s_relations_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_phi)))) & s(t_h4s_totos_toto(TV_u_27a),V_cmp) = s(t_h4s_totos_toto(TV_u_27a),h4s_totos_totou_u_ofu_u_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_phi)))) => ![V_x, V_y]: ((s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> p(s(t_bool,t))) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_y))) = s(t_h4s_totos_cpn,h4s_totos_equal)))).
fof(ah4s_totos_ontou_u_apto, axiom, ![TV_u_27a]: ![V_r]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r)))) <=> ?[V_a]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),V_r) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_a))))).
fof(ah4s_totos_totoEEtransu_c0, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal)) => s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_equal))).
fof(ah4s_totos_totoGLtrans, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_c]: ((s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_greater) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_totos_totou_u_notu_u_lessu_u_refl, axiom, ![TV_u_27a]: ![V_h, V_cmp]: (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_h))),s(TV_u_27a,V_h))) = s(t_h4s_totos_cpn,h4s_totos_less) <=> p(s(t_bool,f)))).
fof(ah4s_totos_NOTu_u_EQu_u_LESSu_u_IMP, axiom, ![TV_u_27a]: ![V_y, V_x, V_cmp]: (~ (s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_y))) = s(t_h4s_totos_cpn,h4s_totos_less)) => (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_cmp))),s(TV_u_27a,V_y))),s(TV_u_27a,V_x))) = s(t_h4s_totos_cpn,h4s_totos_less)))).
fof(ah4s_totos_TOu_u_aptou_u_ID, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(TV_u_27a),V_a))))) = s(t_h4s_totos_toto(TV_u_27a),V_a)).
fof(ah4s_totos_totou_u_swapu_u_cases, axiom, ![TV_u_27a]: ![V_y, V_x, V_c]: s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_x))) = s(t_h4s_totos_cpn,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,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_greater),s(t_h4s_totos_cpn,h4s_totos_equal),s(t_h4s_totos_cpn,h4s_totos_less)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
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_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_totos_TOu_u_numOrd, axiom, p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord))))).
fof(ah4s_totos_numto0, axiom, s(t_h4s_totos_toto(t_h4s_nums_num),h4s_totos_numto) = s(t_h4s_totos_toto(t_h4s_nums_num),h4s_totos_to(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord)))).
fof(ah4s_totos_qku_u_numto0, axiom, s(t_h4s_totos_toto(t_h4s_nums_num),h4s_totos_qku_u_numto) = s(t_h4s_totos_toto(t_h4s_nums_num),h4s_totos_to(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_qku_u_numord)))).
fof(ah4s_totos_TOu_u_qku_u_numOrd, axiom, p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),t_bool),h4s_totos_totord),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_qku_u_numord))))).
fof(ah4s_totos_allu_u_cpnu_u_distinctu_c0, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_equal))).
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_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_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_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
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_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_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_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_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_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = 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_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_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_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_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
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_numerals_numeralu_u_equ_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_totos_cpn2numu_u_thmu_c0, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_less))) = s(t_h4s_nums_num,h4s_nums_0)).
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_totos_cpn2numu_u_thmu_c1, axiom, s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,h4s_totos_equal))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_totos_cpnu_u_EQu_u_cpn, axiom, ![V_au_27, V_a]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,V_au_27) <=> s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_a))) = s(t_h4s_nums_num,h4s_totos_cpn2num(s(t_h4s_totos_cpn,V_au_27))))).
fof(ah4s_numerals_numeralu_u_distribu_c18, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
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_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_totos_TOu_u_ofu_u_LinearOrder0, axiom, ![TV_u_27a]: ![V_y, V_x, V_r]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) & s(t_h4s_totos_cpn,happ(s(t_fun(TV_u_27a,t_h4s_totos_cpn),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(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))) = s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_totos_cpn,h4s_totos_equal),s(t_h4s_totos_cpn,h4s_bools_cond(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))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_greater))))))).
fof(ah4s_totos_cpnu_u_distinctu_c1, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_greater))).
fof(ah4s_totos_cpnu_u_distinctu_c2, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_greater))).
fof(ah4s_totos_cpnu_u_distinctu_c0, axiom, ~ (s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_equal))).
fof(ah4s_totos_totou_u_ofu_u_LinearOrder0, axiom, ![TV_u_27a]: ![V_r]: s(t_h4s_totos_toto(TV_u_27a),h4s_totos_totou_u_ofu_u_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r))) = s(t_h4s_totos_toto(TV_u_27a),h4s_totos_to(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_r)))))).
fof(ah4s_bools_LEFTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) & p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) & (p(s(t_bool,V_A)) | p(s(t_bool,V_C)))))).
fof(ah4s_relations_LinearOrder0, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_linearorder(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_order(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & p(s(t_bool,h4s_relations_trichotomous(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))))))).
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_relations_antisymmetricu_u_def, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),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)),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),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_x))))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))).
fof(ah4s_relations_Order0, axiom, ![TV_u_27g]: ![V_Z]: (p(s(t_bool,h4s_relations_order(s(t_fun(TV_u_27g,t_fun(TV_u_27g,t_bool)),V_Z)))) <=> (p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(TV_u_27g,t_fun(TV_u_27g,t_bool)),V_Z)))) & p(s(t_bool,h4s_relations_transitive(s(t_fun(TV_u_27g,t_fun(TV_u_27g,t_bool)),V_Z))))))).
fof(ah4s_relations_trichotomous0, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_trichotomous(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> ![V_a, V_b]: (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_a))),s(TV_u_27a,V_b)))) | (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_b))),s(TV_u_27a,V_a)))) | s(TV_u_27a,V_a) = s(TV_u_27a,V_b))))).
fof(ah4s_relations_transitiveu_u_def, axiom, ![TV_u_27a]: ![V_R]: (p(s(t_bool,h4s_relations_transitive(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) <=> ![V_x, V_y, V_z]: ((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)))) & 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_y))),s(TV_u_27a,V_z))))) => 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_z))))))).
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_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
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_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_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_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_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = 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_totos_cpnu_u_nchotomy, axiom, ![V_a]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_less) | (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_equal) | s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_greater)))).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
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_totos_cpnu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_equal),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v1)).
fof(ah4s_totos_cpnu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v2, V_v1, V_v0]: s(TV_u_27a,h4s_totos_cpnu_u_case(s(t_h4s_totos_cpn,h4s_totos_greater),s(TV_u_27a,V_v0),s(TV_u_27a,V_v1),s(TV_u_27a,V_v2))) = s(TV_u_27a,V_v2)).
fof(ah4s_bools_LETu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_x0]: s(TV_u_27b,h4s_bools_let(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0)))).
fof(ah4s_totos_GREATERu_u_def, axiom, s(t_h4s_totos_cpn,h4s_totos_greater) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_totos_LESSu_u_def, axiom, s(t_h4s_totos_cpn,h4s_totos_less) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_totos_num2cpnu_u_ONTO, axiom, ![V_a]: ?[V_r]: (s(t_h4s_totos_cpn,V_a) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,V_r))) & p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_r),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))).
fof(ah4s_numerals_iDUBu_u_removalu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_totos_EQUALu_u_def, axiom, s(t_h4s_totos_cpn,h4s_totos_equal) = s(t_h4s_totos_cpn,h4s_totos_num2cpn(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_numerals_iDUBu_u_removalu_c2, axiom, s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_numeralu_u_sub, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_iSUBu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_bools_CONJu_u_ASSOC, 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_numerals_numeralu_u_ltu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m)))))) <=> ~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_iSUBu_u_THMu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ch4s_totos_apchartou_u_thm, conjecture, s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_h4s_totos_cpn)),h4s_totos_apto(s(t_h4s_totos_toto(t_h4s_strings_char),h4s_totos_charto))) = s(t_fun(t_h4s_strings_char,t_fun(t_h4s_strings_char,t_h4s_totos_cpn)),h4s_totos_charord)).
