%   ORIGINAL: h4/quantHeuristics/GUESS__RULES__IMP_c4
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% 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_c1: !i P. h4/quantHeuristics/GUESS__FORALL i (\x. ~P x) <=> h4/quantHeuristics/GUESS__EXISTS 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_c4: !i P. h4/quantHeuristics/GUESS__EXISTS__POINT i (\x. ~P x) <=> h4/quantHeuristics/GUESS__FORALL__POINT i (\x. P x)
% 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/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/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_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_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/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_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_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_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__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)
% Goal: !iK Q P. h4/quantHeuristics/GUESS__EXISTS (\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)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_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_combins_ou_u_THM]: !x g f. h4/combin/o f g x = happ f (happ g x)
% 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_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_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_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_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_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_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_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_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_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_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_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_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_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))))
% Goal: !_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__EXISTS (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)))))
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_Q21570,TV_Q21566]: ![V_f, V_g]: (![V_x]: s(TV_Q21566,happ(s(t_fun(TV_Q21570,TV_Q21566),V_f),s(TV_Q21570,V_x))) = s(TV_Q21566,happ(s(t_fun(TV_Q21570,TV_Q21566),V_g),s(TV_Q21570,V_x))) => s(t_fun(TV_Q21570,TV_Q21566),V_f) = s(t_fun(TV_Q21570,TV_Q21566),V_g))).
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_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_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(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_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_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_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_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_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_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_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_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_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_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_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_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_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_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(ch4s_quantHeuristicss_GUESSu_u_RULESu_u_IMPu_c4, conjecture, ![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_exists(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))))))))))))).
