%   ORIGINAL: h4/quantHeuristics/GUESS__RULES__IMP_c7
% 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/quantHeuristics/GUESSES__NEG__REWRITE_c5: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i (\x. ~P x) <=> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x)
% Assm: h4/quantHeuristics/GUESSES__NEG__REWRITE_c4: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. ~P x) <=> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% 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/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c7: !i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x) /\ h4/quantHeuristics/GUESS__FORALL__POINT i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x \/ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c1: !i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x \/ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c0: !i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x \/ Q x)
% Assm: h4/bool/TRUTH: T
% Assm: h4/quantHeuristics/GUESSES__NEG__DUALITY_c4: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__FORALL__POINT i P
% Assm: h4/quantHeuristics/GUESSES__NEG__DUALITY_c5: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__EXISTS__POINT i P
% Assm: h4/quantHeuristics/GUESSES__NEG__REWRITE_c0: !i P. h4/quantHeuristics/GUESS__EXISTS i (\x. ~P x) <=> h4/quantHeuristics/GUESS__FORALL i (\x. P x)
% Assm: h4/quantHeuristics/GUESSES__NEG__REWRITE_c2: !i P. h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. ~P x) <=> h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x)
% Assm: h4/quantHeuristics/GUESSES__NEG__REWRITE_c3: !i P. h4/quantHeuristics/GUESS__FORALL__GAP i (\x. ~P x) <=> h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x)
% Assm: h4/quantHeuristics/GUESSES__NEG__REWRITE_c1: !i P. h4/quantHeuristics/GUESS__FORALL i (\x. ~P x) <=> h4/quantHeuristics/GUESS__EXISTS i (\x. P x)
% Assm: h4/quantHeuristics/GUESS__RULES__NEG_c5: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. ~P x)
% Assm: h4/quantHeuristics/GUESS__RULES__NEG_c2: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. ~P x)
% Assm: h4/quantHeuristics/GUESS__RULES__IMP_c0: !i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x ==> Q x)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/quantHeuristics/GUESSES__NEG__DUALITY_c2: !i P. h4/quantHeuristics/GUESS__EXISTS__GAP i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__FORALL__GAP i P
% Assm: h4/quantHeuristics/GUESSES__NEG__DUALITY_c3: !i P. h4/quantHeuristics/GUESS__FORALL__GAP i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__EXISTS__GAP i P
% Assm: h4/quantHeuristics/GUESSES__NEG__DUALITY_c0: !i P. h4/quantHeuristics/GUESS__EXISTS i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__FORALL i P
% Assm: h4/quantHeuristics/GUESSES__NEG__DUALITY_c1: !i P. h4/quantHeuristics/GUESS__FORALL i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__EXISTS i P
% Assm: h4/combin/o__DEF: !g f. h4/combin/o f g = (\x. f (g x))
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c1: !i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c0: !i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c7: !i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x) /\ h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__IMP_c1: !i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x ==> Q x)
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/quantHeuristics/GUESS__FORALL__POINT__def: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P <=> (!fv. ~P (i fv))
% Assm: h4/quantHeuristics/GUESS__REWRITES_c3: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P <=> (!fv. ~P (i fv))
% Assm: h4/quantHeuristics/GUESS__REWRITES_c2: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P <=> (!fv. P (i fv))
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c6: !p i Q. h4/quantHeuristics/GUESS__FORALL i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL i (\x. p \/ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c2: !i Q P. h4/quantHeuristics/GUESS__EXISTS i (\x. P x) /\ h4/quantHeuristics/GUESS__EXISTS i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS i (\x. P x \/ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c3: !i Q P. h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x) /\ h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x \/ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c9: !i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x \/ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c5: !q i P. h4/quantHeuristics/GUESS__FORALL i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL i (\x. P x \/ q)
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c8: !i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x \/ Q x)
% Assm: h4/quantHeuristics/GUESS__EXISTS__POINT__def: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P <=> (!fv. P (i fv))
% Assm: h4/quantHeuristics/GUESS__RULES__DISJ_c4: !iK Q P. h4/quantHeuristics/GUESS__FORALL (\xxx. iK) (\x. P x) /\ h4/quantHeuristics/GUESS__FORALL (\xxx. iK) (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL (\xxx. iK) (\x. P x \/ Q x)
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/quantHeuristics/GUESS__REWRITES_c4: !i P. h4/quantHeuristics/GUESS__EXISTS__GAP i P <=> (!v. P v ==> (?fv. v = i fv))
% Assm: h4/quantHeuristics/GUESS__REWRITES_c5: !i P. h4/quantHeuristics/GUESS__FORALL__GAP i P <=> (!v. ~P v ==> (?fv. v = i fv))
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/quantHeuristics/GUESS__REWRITES_c0: !i P. h4/quantHeuristics/GUESS__EXISTS i P <=> (!v. P v ==> (?fv. P (i fv)))
% Assm: h4/quantHeuristics/GUESS__REWRITES_c1: !i P. h4/quantHeuristics/GUESS__FORALL i P <=> (!v. ~P v ==> (?fv. ~P (i fv)))
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> 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/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/bool/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/quantHeuristics/GUESS__POINT__THM_c1: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P ==> ((!v. P v) <=> F)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/quantHeuristics/GUESS__POINT__THM_c0: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P ==> ((?v. P v) <=> T)
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/quantHeuristics/GUESSES__UEXISTS__THM3: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT (\x. i) P ==> (h4/bool/_3F_21 P <=> (!v. P v ==> v = i))
% Assm: h4/quantHeuristics/GUESS__FORALL__POINT__THM: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P ==> ($forall P <=> F)
% Assm: h4/quantHeuristics/GUESSES__WEAKEN__THM_c1: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P ==> h4/quantHeuristics/GUESS__FORALL i P
% Assm: h4/quantHeuristics/GUESS__RULES__EQUATION__FORALL__POINT: !i Q P. (!fv. ~(P (i fv) = Q (i fv))) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x = Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__BOOL_c1: h4/quantHeuristics/GUESS__FORALL__POINT (\ARB. F) (\x. x)
% Assm: h4/quantHeuristics/GUESS__RULES__TRIVIAL__FORALL__POINT: !i P. ~P i ==> h4/quantHeuristics/GUESS__FORALL__POINT (\xxx. i) P
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/quantHeuristics/GUESS__EXISTS__POINT__THM: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P ==> ($exists P <=> T)
% Assm: h4/quantHeuristics/GUESSES__WEAKEN__THM_c2: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P ==> h4/quantHeuristics/GUESS__EXISTS i P
% Assm: h4/quantHeuristics/GUESS__RULES__EQUATION__EXISTS__POINT: !i Q P. P i = Q i ==> h4/quantHeuristics/GUESS__EXISTS__POINT (\xxx. i) (\x. P x = Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__TRIVIAL__EXISTS__POINT: !i P. P i ==> h4/quantHeuristics/GUESS__EXISTS__POINT (\xxx. i) P
% Assm: h4/quantHeuristics/GUESS__RULES__BOOL_c0: h4/quantHeuristics/GUESS__EXISTS__POINT (\ARB. T) (\x. x)
% Assm: h4/quantHeuristics/GUESSES__UEXISTS__THM4: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT (\x. i) P ==> h4/quantHeuristics/GUESS__EXISTS__GAP (\x. i) P ==> (h4/bool/_3F_21 P <=> T)
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/UNWIND__FORALL__THM2: !v f. (!x. x = v ==> f x) <=> f v
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c9: !i Q P. h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__IMP_c2: !i Q P. h4/quantHeuristics/GUESS__FORALL i (\x. P x) /\ h4/quantHeuristics/GUESS__EXISTS i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS i (\x. P x ==> Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__IMP_c5: !q i P. h4/quantHeuristics/GUESS__EXISTS i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL i (\x. P x ==> q)
% Assm: h4/quantHeuristics/GUESS__RULES__NEG_c0: !i P. h4/quantHeuristics/GUESS__EXISTS i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL i (\x. ~P x)
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c6: !p i Q. h4/quantHeuristics/GUESS__EXISTS i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS i (\x. p /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c8: !i Q P. h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__IMP_c3: !i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x) /\ h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. Q x) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x ==> Q x)
% Assm: h4/bool/FORALL__THM: !f. $forall f <=> (!x. f x)
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/LEFT__FORALL__OR__THM: !Q P. (!x. P x \/ Q) <=> (!x. P x) \/ Q
% Assm: h4/bool/NOT__IMP: !B A. ~(A ==> B) <=> A /\ ~B
% Assm: h4/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/EXISTS__UNIQUE__THM: !P. h4/bool/_3F_21 (\x. P x) <=> (?x. P x) /\ (!x y. P x /\ P y ==> x = y)
% 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/quantHeuristics/GUESS__RULES__CONJ_c2: !i Q P. h4/quantHeuristics/GUESS__FORALL i (\x. P x) /\ h4/quantHeuristics/GUESS__FORALL i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__NEG_c3: !i P. h4/quantHeuristics/GUESS__FORALL i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS i (\x. ~P x)
% Assm: h4/quantHeuristics/GUESS__RULES__NEG_c1: !i P. h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. P x) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (\x. ~P x)
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c3: !i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x) /\ h4/quantHeuristics/GUESS__FORALL__GAP i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x /\ Q x)
% Assm: h4/quantHeuristics/GUESS__RULES__CONJ_c5: !q i P. h4/quantHeuristics/GUESS__EXISTS i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS i (\x. P x /\ q)
% Assm: h4/bool/TYPE__DEFINITION0: h4/bool/TYPE__DEFINITION = (\P rep. (!x_27 x_27_27. rep x_27 = rep x_27_27 ==> x_27 = x_27_27) /\ (!x. P x <=> (?x_27. x = rep x_27)))
% Assm: h4/quantHeuristics/GUESS__RULES__NEG_c4: !i P. h4/quantHeuristics/GUESS__FORALL__GAP i (\x. P x) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (\x. ~P x)
% Assm: h4/quantHeuristics/GUESS__RULES__IMP_c6: !p i Q. h4/quantHeuristics/GUESS__FORALL i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL i (\x. p ==> Q x)
% Assm: h4/bool/EXISTS__THM: !f. $exists f <=> (?x. f x)
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/relation/TFL__INDUCTIVE__INVARIANT__ON__WFREC: !x f R P M D. f = h4/relation/WFREC R M /\ h4/relation/WF R /\ h4/relation/INDUCTIVE__INVARIANT__ON R D P M /\ D x ==> P x (f x)
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/relation/INDUCTIVE__INVARIANT__ON__WFREC: !x R P M D. h4/relation/WF R /\ h4/relation/INDUCTIVE__INVARIANT__ON R D P M /\ D x ==> P x (h4/relation/WFREC R M x)
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Goal: !i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. P x) /\ h4/quantHeuristics/GUESS__FORALL__POINT i (\x. Q x) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x ==> Q x)
%   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_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c5]: !_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!i P. h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 P) <=> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _1 P)))
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c4]: !_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 P) <=> h4/quantHeuristics/GUESS__FORALL__POINT i (happ _1 P)))
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% 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_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c7]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 P) /\ h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c1]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c0]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c4]: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__FORALL__POINT i P
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c5]: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__EXISTS__POINT i P
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c0]: !_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS i (happ _0 P) <=> h4/quantHeuristics/GUESS__FORALL i (happ _1 P)))
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c2]: !_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 P) <=> h4/quantHeuristics/GUESS__FORALL__GAP i (happ _1 P)))
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c3]: !_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!i P. h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 P) <=> h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _1 P)))
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c1]: !_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!i P. h4/quantHeuristics/GUESS__FORALL i (happ _0 P) <=> h4/quantHeuristics/GUESS__EXISTS i (happ _1 P)))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c5]: !_1. (!P x. happ (happ _1 P) x <=> ~happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i P. h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 (happ _1 P))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c2]: !_1. (!P x. happ (happ _1 P) x <=> ~happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 (happ _1 P))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c0]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x ==> happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c2]: !i P. h4/quantHeuristics/GUESS__EXISTS__GAP i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__FORALL__GAP i P
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c3]: !i P. h4/quantHeuristics/GUESS__FORALL__GAP i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__EXISTS__GAP i P
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c0]: !i P. h4/quantHeuristics/GUESS__EXISTS i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__FORALL i P
% Assm [h4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c1]: !i P. h4/quantHeuristics/GUESS__FORALL i (h4/combin/o $not P) <=> h4/quantHeuristics/GUESS__EXISTS i P
% Assm [h4s_combins_ou_u_DEF]: !g f x. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c1]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c0]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c7]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 P) /\ h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c1]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x ==> happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_quantHeuristicss_GUESSu_u_FORALLu_u_POINTu_u_def]: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P <=> (!fv. ~happ P (happ i fv))
% Assm [h4s_quantHeuristicss_GUESSu_u_REWRITESu_c3]: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P <=> (!fv. ~happ P (happ i fv))
% Assm [h4s_quantHeuristicss_GUESSu_u_REWRITESu_c2]: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P <=> (!fv. happ P (happ i fv))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c6]: !_1. (!p Q x. happ (happ (happ _1 p) Q) x <=> p \/ happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!p i Q. h4/quantHeuristics/GUESS__FORALL i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL i (happ _0 (happ (happ _1 p) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c2]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS i (happ _0 P) /\ h4/quantHeuristics/GUESS__EXISTS i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c3]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 P) /\ h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c9]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c5]: !_1. (!P q x. happ (happ (happ _1 P) q) x <=> happ P x \/ q) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!q i P. h4/quantHeuristics/GUESS__FORALL i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL i (happ _0 (happ (happ _1 P) q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c8]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x \/ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_EXISTSu_u_POINTu_u_def]: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P <=> (!fv. happ P (happ i fv))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c4]: !_2. (!P Q x. happ (happ (happ _2 P) Q) x <=> happ P x \/ happ Q x) ==> (!_1. (!P x. happ (happ _1 P) x <=> happ P x) ==> (!_0. (!iK xxx. happ (happ _0 iK) xxx = iK) ==> (!iK Q P. h4/quantHeuristics/GUESS__FORALL (happ _0 iK) (happ _1 P) /\ h4/quantHeuristics/GUESS__FORALL (happ _0 iK) (happ _1 Q) ==> h4/quantHeuristics/GUESS__FORALL (happ _0 iK) (happ _1 (happ (happ _2 P) Q)))))
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_quantHeuristicss_GUESSu_u_REWRITESu_c4]: !i P. h4/quantHeuristics/GUESS__EXISTS__GAP i P <=> (!v. happ P v ==> (?fv. v = happ i fv))
% Assm [h4s_quantHeuristicss_GUESSu_u_REWRITESu_c5]: !i P. h4/quantHeuristics/GUESS__FORALL__GAP i P <=> (!v. ~happ P v ==> (?fv. v = happ i fv))
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_quantHeuristicss_GUESSu_u_REWRITESu_c0]: !i P. h4/quantHeuristics/GUESS__EXISTS i P <=> (!v. happ P v ==> (?fv. happ P (happ i fv)))
% Assm [h4s_quantHeuristicss_GUESSu_u_REWRITESu_c1]: !i P. h4/quantHeuristics/GUESS__FORALL i P <=> (!v. ~happ P v ==> (?fv. ~happ P (happ i fv)))
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 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_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> 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_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_bools_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_quantHeuristicss_GUESSu_u_POINTu_u_THMu_c1]: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P ==> ((!v. happ P v) <=> F)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_quantHeuristicss_GUESSu_u_POINTu_u_THMu_c0]: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P ==> ((?v. happ P v) <=> T)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_quantHeuristicss_GUESSESu_u_UEXISTSu_u_THM3]: !_0. (!i x. happ (happ _0 i) x = i) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS__POINT (happ _0 i) P ==> (h4/bool/_3F_21 P <=> (!v. happ P v ==> v = i)))
% Assm [h4s_quantHeuristicss_GUESSu_u_FORALLu_u_POINTu_u_THM]: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P ==> ($forall P <=> F)
% Assm [h4s_quantHeuristicss_GUESSESu_u_WEAKENu_u_THMu_c1]: !i P. h4/quantHeuristics/GUESS__FORALL__POINT i P ==> h4/quantHeuristics/GUESS__FORALL i P
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_EQUATIONu_u_FORALLu_u_POINT]: !_0. (!P Q x. happ (happ (happ _0 P) Q) x <=> happ P x = happ Q x) ==> (!i Q P. (!fv. ~(happ P (happ i fv) = happ Q (happ i fv))) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (happ (happ _0 P) Q))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_BOOLu_c1]: !_1. (!x. happ _1 x <=> x) ==> (!_0. (!ARB. happ _0 ARB <=> F) ==> h4/quantHeuristics/GUESS__FORALL__POINT _0 _1)
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_TRIVIALu_u_FORALLu_u_POINT]: !_0. (!i xxx. happ (happ _0 i) xxx = i) ==> (!i P. ~happ P i ==> h4/quantHeuristics/GUESS__FORALL__POINT (happ _0 i) P)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_quantHeuristicss_GUESSu_u_EXISTSu_u_POINTu_u_THM]: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P ==> ($exists P <=> T)
% Assm [h4s_quantHeuristicss_GUESSESu_u_WEAKENu_u_THMu_c2]: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i P ==> h4/quantHeuristics/GUESS__EXISTS i P
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_EQUATIONu_u_EXISTSu_u_POINT]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x = happ Q x) ==> (!_0. (!i xxx. happ (happ _0 i) xxx = i) ==> (!i Q P. happ P i = happ Q i ==> h4/quantHeuristics/GUESS__EXISTS__POINT (happ _0 i) (happ (happ _1 P) Q)))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_TRIVIALu_u_EXISTSu_u_POINT]: !_0. (!i xxx. happ (happ _0 i) xxx = i) ==> (!i P. happ P i ==> h4/quantHeuristics/GUESS__EXISTS__POINT (happ _0 i) P)
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_BOOLu_c0]: !_1. (!x. happ _1 x <=> x) ==> (!_0. (!ARB. happ _0 ARB <=> T) ==> h4/quantHeuristics/GUESS__EXISTS__POINT _0 _1)
% Assm [h4s_quantHeuristicss_GUESSESu_u_UEXISTSu_u_THM4]: !_1. (!i x. happ (happ _1 i) x = i) ==> (!_0. (!i x. happ (happ _0 i) x = i) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS__POINT (happ _0 i) P ==> h4/quantHeuristics/GUESS__EXISTS__GAP (happ _1 i) P ==> (h4/bool/_3F_21 P <=> T)))
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_UNWINDu_u_FORALLu_u_THM2]: !v f. (!x. x = v ==> happ f x) <=> happ f v
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c9]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c2]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x ==> happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL i (happ _0 P) /\ h4/quantHeuristics/GUESS__EXISTS i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c5]: !_1. (!P q x. happ (happ (happ _1 P) q) x <=> happ P x ==> q) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!q i P. h4/quantHeuristics/GUESS__EXISTS i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL i (happ _0 (happ (happ _1 P) q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c0]: !_1. (!P x. happ (happ _1 P) x <=> ~happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL i (happ _0 (happ _1 P))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c6]: !_1. (!p Q x. happ (happ (happ _1 p) Q) x <=> p /\ happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!p i Q. h4/quantHeuristics/GUESS__EXISTS i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS i (happ _0 (happ (happ _1 p) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c8]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c3]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x ==> happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 P) /\ h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 Q) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_bools_FORALLu_u_THM]: !f. $forall f <=> (!x. happ f x)
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. happ P x \/ Q) <=> (!x. happ P x) \/ Q
% Assm [h4s_bools_NOTu_u_IMP]: !B A. ~(A ==> B) <=> A /\ ~B
% Assm [h4s_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_EXISTSu_u_UNIQUEu_u_THM]: !_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!P. h4/bool/_3F_21 (happ _0 P) <=> (?x. happ P x) /\ (!x y. happ P x /\ happ P y ==> x = y))
% 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_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c2]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL i (happ _0 P) /\ h4/quantHeuristics/GUESS__FORALL i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c3]: !_1. (!P x. happ (happ _1 P) x <=> ~happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i P. h4/quantHeuristics/GUESS__FORALL i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS i (happ _0 (happ _1 P))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c1]: !_1. (!P x. happ (happ _1 P) x <=> ~happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i P. h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 P) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 (happ _1 P))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c3]: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x /\ happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 P) /\ h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 (happ (happ _1 P) Q))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c5]: !_1. (!P q x. happ (happ (happ _1 P) q) x <=> happ P x /\ q) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!q i P. h4/quantHeuristics/GUESS__EXISTS i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS i (happ _0 (happ (happ _1 P) q))))
% Assm [h4s_bools_TYPEu_u_DEFINITION0]: !x x. h4/bool/TYPE__DEFINITION x x <=> (!x_27 x_27_27. happ x x_27 = happ x x_27_27 ==> x_27 = x_27_27) /\ (!x. happ x x <=> (?x_27. x = happ x x_27))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c4]: !_1. (!P x. happ (happ _1 P) x <=> ~happ P x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i P. h4/quantHeuristics/GUESS__FORALL__GAP i (happ _0 P) ==> h4/quantHeuristics/GUESS__EXISTS__GAP i (happ _0 (happ _1 P))))
% Assm [h4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c6]: !_1. (!p Q x. happ (happ (happ _1 p) Q) x <=> p ==> happ Q x) ==> (!_0. (!Q x. happ (happ _0 Q) x <=> happ Q x) ==> (!p i Q. h4/quantHeuristics/GUESS__FORALL i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL i (happ _0 (happ (happ _1 p) Q))))
% Assm [h4s_bools_EXISTSu_u_THM]: !f. $exists f <=> (?x. happ f x)
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_relations_TFLu_u_INDUCTIVEu_u_INVARIANTu_u_ONu_u_WFREC]: !x f R P M D. f = h4/relation/WFREC R M /\ h4/relation/WF R /\ h4/relation/INDUCTIVE__INVARIANT__ON R D P M /\ happ D x ==> happ (happ P x) (happ f x)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_relations_INDUCTIVEu_u_INVARIANTu_u_ONu_u_WFREC]: !x R P M D. h4/relation/WF R /\ h4/relation/INDUCTIVE__INVARIANT__ON R D P M /\ happ D x ==> happ (happ P x) (happ (h4/relation/WFREC R M) x)
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Goal: !_1. (!P Q x. happ (happ (happ _1 P) Q) x <=> happ P x ==> happ Q x) ==> (!_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!i Q P. h4/quantHeuristics/GUESS__EXISTS__POINT i (happ _0 P) /\ h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 Q) ==> h4/quantHeuristics/GUESS__FORALL__POINT i (happ _0 (happ (happ _1 P) 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_Q1096904,TV_Q1096900]: ![V_f, V_g]: (![V_x]: s(TV_Q1096900,happ(s(t_fun(TV_Q1096904,TV_Q1096900),V_f),s(TV_Q1096904,V_x))) = s(TV_Q1096900,happ(s(t_fun(TV_Q1096904,TV_Q1096900),V_g),s(TV_Q1096904,V_x))) => s(t_fun(TV_Q1096904,TV_Q1096900),V_f) = s(t_fun(TV_Q1096904,TV_Q1096900),V_g))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c5, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c4, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))).
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_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_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_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c7, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c4, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c5, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_REWRITEu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c5, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
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_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))).
fof(ah4s_quantHeuristicss_GUESSESu_u_NEGu_u_DUALITYu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27b,t_bool),V_P))))) = s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))).
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_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c7, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
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_quantHeuristicss_GUESSu_u_FORALLu_u_POINTu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_fv]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_REWRITESu_c3, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_fv]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_REWRITESu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_fv]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv)))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c6, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_p, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_bool,V_p))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,V_p)) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_p, V_i, V_Q]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_bool,V_p))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c9, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c5, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_bool,V_q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,V_q)))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_q, V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_bool,V_q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c8, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_EXISTSu_u_POINTu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_fv]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv)))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_DISJu_c4, axiom, ![TV_u_27b]: ![V_uu_2]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_2),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_1]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_iK, V_xxx]: s(TV_u_27b,happ(s(t_fun(t_h4s_ones_one,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_ones_one,TV_u_27b)),V_uu_0),s(TV_u_27b,V_iK))),s(t_h4s_ones_one,V_xxx))) = s(TV_u_27b,V_iK) => ![V_iK, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(t_h4s_ones_one,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_ones_one,TV_u_27b)),V_uu_0),s(TV_u_27b,V_iK))),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(t_h4s_ones_one,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_ones_one,TV_u_27b)),V_uu_0),s(TV_u_27b,V_iK))),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(t_h4s_ones_one,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_ones_one,TV_u_27b)),V_uu_0),s(TV_u_27b,V_iK))),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_2),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))))))))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, 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_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_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_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_quantHeuristicss_GUESSu_u_REWRITESu_c4, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_v]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_v)))) => ?[V_fv]: s(TV_u_27b,V_v) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv)))))).
fof(ah4s_quantHeuristicss_GUESSu_u_REWRITESu_c5, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_v]: (~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_v))))) => ?[V_fv]: s(TV_u_27b,V_v) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_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_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_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_quantHeuristicss_GUESSu_u_REWRITESu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_v]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_v)))) => ?[V_fv]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_REWRITESu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) <=> ![V_v]: (~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_v))))) => ?[V_fv]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv)))))))))).
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_FALSITY, axiom, ![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_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_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_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_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_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_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_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_quantHeuristicss_GUESSu_u_POINTu_u_THMu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) => (![V_v]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_v)))) <=> p(s(t_bool,f))))).
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_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_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_quantHeuristicss_GUESSu_u_POINTu_u_THMu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) => (?[V_v]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_v)))) <=> p(s(t_bool,t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_quantHeuristicss_GUESSESu_u_UEXISTSu_u_THM3, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_i, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(TV_u_27b,V_x))) = s(TV_u_27a,V_i) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_fun(TV_u_27a,t_bool),V_P)))) => (p(s(t_bool,h4s_bools_u_3fu_21(s(t_fun(TV_u_27a,t_bool),V_P)))) <=> ![V_v]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_v)))) => s(TV_u_27a,V_v) = s(TV_u_27a,V_i)))))).
fof(ah4s_quantHeuristicss_GUESSu_u_FORALLu_u_POINTu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) => s(t_bool,d_forall(s(t_fun(TV_u_27b,t_bool),V_P))) = s(t_bool,f))).
fof(ah4s_quantHeuristicss_GUESSESu_u_WEAKENu_u_THMu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_EQUATIONu_u_FORALLu_u_POINT, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_uu_0]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27b,TV_u_27c),V_P))),s(t_fun(TV_u_27b,TV_u_27c),V_Q))),s(TV_u_27b,V_x)))) <=> s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),V_P),s(TV_u_27b,V_x))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),V_Q),s(TV_u_27b,V_x)))) => ![V_i, V_Q, V_P]: (![V_fv]: ~ (s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),V_P),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),V_Q),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(TV_u_27a,V_fv)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27b,TV_u_27c),V_P))),s(t_fun(TV_u_27b,TV_u_27c),V_Q))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_BOOLu_c1, axiom, ![V_uu_1]: (![V_x]: s(t_bool,happ(s(t_fun(t_bool,t_bool),V_uu_1),s(t_bool,V_x))) = s(t_bool,V_x) => ![V_uu_0]: (![V_ARB]: s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),V_uu_0),s(t_h4s_ones_one,V_ARB))) = s(t_bool,f) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(t_h4s_ones_one,t_bool),V_uu_0),s(t_fun(t_bool,t_bool),V_uu_1))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_TRIVIALu_u_FORALLu_u_POINT, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_i, V_xxx]: s(TV_u_27a,happ(s(t_fun(t_h4s_ones_one,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_ones_one,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_h4s_ones_one,V_xxx))) = s(TV_u_27a,V_i) => ![V_i, V_P]: (~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_i))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(t_h4s_ones_one,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_ones_one,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_fun(TV_u_27a,t_bool),V_P))))))).
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_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_quantHeuristicss_GUESSu_u_EXISTSu_u_POINTu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) => s(t_bool,d_exists(s(t_fun(TV_u_27b,t_bool),V_P))) = s(t_bool,t))).
fof(ah4s_quantHeuristicss_GUESSESu_u_WEAKENu_u_THMu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),V_P)))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_EQUATIONu_u_EXISTSu_u_POINT, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,TV_u_27b),V_P))),s(t_fun(TV_u_27a,TV_u_27b),V_Q))),s(TV_u_27a,V_x)))) <=> s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_P),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_Q),s(TV_u_27a,V_x)))) => ![V_uu_0]: (![V_i, V_xxx]: s(TV_u_27a,happ(s(t_fun(t_h4s_ones_one,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_ones_one,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_h4s_ones_one,V_xxx))) = s(TV_u_27a,V_i) => ![V_i, V_Q, V_P]: (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_P),s(TV_u_27a,V_i))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_Q),s(TV_u_27a,V_i))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(t_h4s_ones_one,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_ones_one,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_bool))),V_uu_1),s(t_fun(TV_u_27a,TV_u_27b),V_P))),s(t_fun(TV_u_27a,TV_u_27b),V_Q)))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_TRIVIALu_u_EXISTSu_u_POINT, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_i, V_xxx]: s(TV_u_27a,happ(s(t_fun(t_h4s_ones_one,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_ones_one,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_h4s_ones_one,V_xxx))) = s(TV_u_27a,V_i) => ![V_i, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_i)))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(t_h4s_ones_one,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_ones_one,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_fun(TV_u_27a,t_bool),V_P))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_BOOLu_c0, axiom, ![V_uu_1]: (![V_x]: s(t_bool,happ(s(t_fun(t_bool,t_bool),V_uu_1),s(t_bool,V_x))) = s(t_bool,V_x) => ![V_uu_0]: (![V_ARB]: s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),V_uu_0),s(t_h4s_ones_one,V_ARB))) = s(t_bool,t) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(t_h4s_ones_one,t_bool),V_uu_0),s(t_fun(t_bool,t_bool),V_uu_1))))))).
fof(ah4s_quantHeuristicss_GUESSESu_u_UEXISTSu_u_THM4, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_1]: (![V_i, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a)),V_uu_1),s(TV_u_27a,V_i))),s(TV_u_27c,V_x))) = s(TV_u_27a,V_i) => ![V_uu_0]: (![V_i, V_x]: s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(TV_u_27b,V_x))) = s(TV_u_27a,V_i) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_uu_0),s(TV_u_27a,V_i))),s(t_fun(TV_u_27a,t_bool),V_P)))) => (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,TV_u_27a)),V_uu_1),s(TV_u_27a,V_i))),s(t_fun(TV_u_27a,t_bool),V_P)))) => s(t_bool,h4s_bools_u_3fu_21(s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,t)))))).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![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))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
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_UNWINDu_u_FORALLu_u_THM2, axiom, ![TV_u_27a]: ![V_v, V_f]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_v) => 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_v)))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c9, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c5, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_bool,V_q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) => p(s(t_bool,V_q)))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_q, V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_bool,V_q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c6, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_p, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_bool,V_p))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,V_p)) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_p, V_i, V_Q]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_bool,V_p))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c8, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_bools_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_f]: (p(s(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_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_bools_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_bools_LEFTu_u_FORALLu_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,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_bools_NOTu_u_IMP, 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_LEFTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) & p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) & (p(s(t_bool,V_A)) | p(s(t_bool,V_C)))))).
fof(ah4s_bools_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_EXISTSu_u_UNIQUEu_u_THM, 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]: (p(s(t_bool,h4s_bools_u_3fu_21(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)))))) <=> (?[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, V_y]: ((p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y))))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))))).
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_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_CONJu_c5, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_bool,V_q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) & p(s(t_bool,V_q)))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_q, V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_exists(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_bool,V_q)))))))))))).
fof(ah4s_bools_TYPEu_u_DEFINITION0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_x0]: (p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27b,TV_u_27a),V_x0)))) <=> (![V_xu_27, V_xu_27u_27]: (s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27u_27))) => s(TV_u_27b,V_xu_27) = s(TV_u_27b,V_xu_27u_27)) & ![V_x1]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x1)))) <=> ?[V_xu_27]: s(TV_u_27a,V_x1) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_NEGu_c4, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_P]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_gap(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P)))))))))))).
fof(ah4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c6, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_p, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_bool,V_p))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,V_p)) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_Q, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x))) => ![V_p, V_i, V_Q]: (p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q)))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forall(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_bool,V_p))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
fof(ah4s_bools_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_f]: (p(s(t_bool,d_exists(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_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_relations_TFLu_u_INDUCTIVEu_u_INVARIANTu_u_ONu_u_WFREC, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_f, V_R, V_P, V_M, V_D]: ((s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) & (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & (p(s(t_bool,h4s_relations_inductiveu_u_invariantu_u_on(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_D),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_D),s(TV_u_27a,V_x))))))) => 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,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_relations_INDUCTIVEu_u_INVARIANTu_u_ONu_u_WFREC, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_R, V_P, V_M, V_D]: ((p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) & (p(s(t_bool,h4s_relations_inductiveu_u_invariantu_u_on(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_D),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_D),s(TV_u_27a,V_x)))))) => 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,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))),s(TV_u_27a,V_x)))))))).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ch4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c7, conjecture, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_P, V_Q, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q))),s(TV_u_27b,V_x)))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_Q),s(TV_u_27b,V_x)))))) => ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P))),s(TV_u_27b,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),V_P),s(TV_u_27b,V_x))) => ![V_i, V_Q, V_P]: ((p(s(t_bool,h4s_quantheuristicss_guessu_u_existsu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_P)))))) & p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),V_Q))))))) => p(s(t_bool,h4s_quantheuristicss_guessu_u_forallu_u_point(s(t_fun(TV_u_27a,TV_u_27b),V_i),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),V_uu_0),s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27b,t_bool),t_fun(t_fun(TV_u_27b,t_bool),t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27b,t_bool),V_P))),s(t_fun(TV_u_27b,t_bool),V_Q)))))))))))).
