%   ORIGINAL: h4/Past__Temporal__Logic/WHEN__EXPRESSIVE_c3
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/Temporal__Logic/ALWAYS__AS__WHEN: !a. h4/Temporal__Logic/ALWAYS a = h4/Temporal__Logic/WHEN (\t. F) (\t. ~a t)
% Assm: h4/Temporal__Logic/EVENTUAL__AS__WHEN: !a. h4/Temporal__Logic/EVENTUAL a = (\t. ~h4/Temporal__Logic/WHEN (\t0. F) a t)
% Assm: h4/Temporal__Logic/UNTIL__AS__WHEN: !b a. h4/Temporal__Logic/UNTIL a b = h4/Temporal__Logic/WHEN b (\t. a t ==> b t)
% Assm: h4/Temporal__Logic/BEFORE__AS__WHEN: !b a. h4/Temporal__Logic/BEFORE a b = h4/Temporal__Logic/WHEN (\t. ~b t) (\t. a t \/ b t)
% Assm: h4/Temporal__Logic/SWHEN__AS__NOT__WHEN: !t0 b a. h4/Temporal__Logic/SWHEN a b t0 <=> ~h4/Temporal__Logic/WHEN (\t. ~a t) b t0
% Assm: h4/Temporal__Logic/SUNTIL__AS__SWHEN: !b a. h4/Temporal__Logic/SUNTIL a b = h4/Temporal__Logic/SWHEN b (\t. a t ==> b t)
% Assm: h4/Temporal__Logic/SBEFORE__AS__SWHEN: !b a. h4/Temporal__Logic/SBEFORE a b = h4/Temporal__Logic/SWHEN (\t. ~b t) (\t. a t \/ b t)
% Assm: h4/Temporal__Logic/NOT__WHEN: !t0 b a. ~h4/Temporal__Logic/WHEN a b t0 <=> h4/Temporal__Logic/SWHEN (\t. ~a t) b t0
% Goal: !b a. h4/Temporal__Logic/UNTIL a b = (\t. h4/Temporal__Logic/WHEN b (\t0. a t0 ==> b t0) t)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_Temporalu_u_Logics_ALWAYSu_u_ASu_u_WHEN]: !_1. (!a t. happ (happ _1 a) t <=> ~happ a t) ==> (!_0. (!t. happ _0 t <=> F) ==> (!a. h4/Temporal__Logic/ALWAYS a = h4/Temporal__Logic/WHEN _0 (happ _1 a)))
% Assm [h4s_Temporalu_u_Logics_EVENTUALu_u_ASu_u_WHEN]: !_0. (!t0. happ _0 t0 <=> F) ==> (!a x. h4/Temporal__Logic/EVENTUAL a x <=> ~happ (h4/Temporal__Logic/WHEN _0 a) x)
% Assm [h4s_Temporalu_u_Logics_UNTILu_u_ASu_u_WHEN]: !_0. (!a b t. happ (happ (happ _0 a) b) t <=> happ a t ==> happ b t) ==> (!b a. h4/Temporal__Logic/UNTIL a b = h4/Temporal__Logic/WHEN b (happ (happ _0 a) b))
% Assm [h4s_Temporalu_u_Logics_BEFOREu_u_ASu_u_WHEN]: !_1. (!a b t. happ (happ (happ _1 a) b) t <=> happ a t \/ happ b t) ==> (!_0. (!b t. happ (happ _0 b) t <=> ~happ b t) ==> (!b a. h4/Temporal__Logic/BEFORE a b = h4/Temporal__Logic/WHEN (happ _0 b) (happ (happ _1 a) b)))
% Assm [h4s_Temporalu_u_Logics_SWHENu_u_ASu_u_NOTu_u_WHEN]: !_0. (!a t. happ (happ _0 a) t <=> ~happ a t) ==> (!t0 b a. happ (h4/Temporal__Logic/SWHEN a b) t0 <=> ~happ (h4/Temporal__Logic/WHEN (happ _0 a) b) t0)
% Assm [h4s_Temporalu_u_Logics_SUNTILu_u_ASu_u_SWHEN]: !_0. (!a b t. happ (happ (happ _0 a) b) t <=> happ a t ==> happ b t) ==> (!b a. h4/Temporal__Logic/SUNTIL a b = h4/Temporal__Logic/SWHEN b (happ (happ _0 a) b))
% Assm [h4s_Temporalu_u_Logics_SBEFOREu_u_ASu_u_SWHEN]: !_1. (!a b t. happ (happ (happ _1 a) b) t <=> happ a t \/ happ b t) ==> (!_0. (!b t. happ (happ _0 b) t <=> ~happ b t) ==> (!b a. h4/Temporal__Logic/SBEFORE a b = h4/Temporal__Logic/SWHEN (happ _0 b) (happ (happ _1 a) b)))
% Assm [h4s_Temporalu_u_Logics_NOTu_u_WHEN]: !_0. (!a t. happ (happ _0 a) t <=> ~happ a t) ==> (!t0 b a. ~happ (h4/Temporal__Logic/WHEN a b) t0 <=> happ (h4/Temporal__Logic/SWHEN (happ _0 a) b) t0)
% Goal: !_0. (!a b t0. happ (happ (happ _0 a) b) t0 <=> happ a t0 ==> happ b t0) ==> (!b a x. happ (h4/Temporal__Logic/UNTIL a b) x <=> happ (h4/Temporal__Logic/WHEN b (happ (happ _0 a) b)) x)
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_Q319739,TV_Q319735]: ![V_f, V_g]: (![V_x]: s(TV_Q319735,happ(s(t_fun(TV_Q319739,TV_Q319735),V_f),s(TV_Q319739,V_x))) = s(TV_Q319735,happ(s(t_fun(TV_Q319739,TV_Q319735),V_g),s(TV_Q319739,V_x))) => s(t_fun(TV_Q319739,TV_Q319735),V_f) = s(t_fun(TV_Q319739,TV_Q319735),V_g))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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_Temporalu_u_Logics_ALWAYSu_u_ASu_u_WHEN, axiom, ![V_uu_1]: (![V_a, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))))) => ![V_uu_0]: (![V_t]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t))) = s(t_bool,f) => ![V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_always(s(t_fun(t_h4s_nums_num,t_bool),V_a))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_a)))))))).
fof(ah4s_Temporalu_u_Logics_EVENTUALu_u_ASu_u_WHEN, axiom, ![V_uu_0]: (![V_t0]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_h4s_nums_num,V_t0))) = s(t_bool,f) => ![V_a, V_x]: (p(s(t_bool,h4s_temporalu_u_logics_eventual(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_x)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_x)))))))).
fof(ah4s_Temporalu_u_Logics_UNTILu_u_ASu_u_WHEN, axiom, ![V_uu_0]: (![V_a, V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_b, V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))))))).
fof(ah4s_Temporalu_u_Logics_BEFOREu_u_ASu_u_WHEN, axiom, ![V_uu_1]: (![V_a, V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))) | p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_uu_0]: (![V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_b, V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_before(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b)))))))).
fof(ah4s_Temporalu_u_Logics_SWHENu_u_ASu_u_NOTu_u_WHEN, axiom, ![V_uu_0]: (![V_a, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))))) => ![V_t0, V_b, V_a]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))))))).
fof(ah4s_Temporalu_u_Logics_SUNTILu_u_ASu_u_SWHEN, axiom, ![V_uu_0]: (![V_a, V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_b, V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_suntil(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))))))).
fof(ah4s_Temporalu_u_Logics_SBEFOREu_u_ASu_u_SWHEN, axiom, ![V_uu_1]: (![V_a, V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))) | p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_uu_0]: (![V_b, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t)))))) => ![V_b, V_a]: s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_sbefore(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))) = s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_1),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b)))))))).
fof(ah4s_Temporalu_u_Logics_NOTu_u_WHEN, axiom, ![V_uu_0]: (![V_a, V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_h4s_nums_num,V_t)))) <=> ~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t)))))) => ![V_t0, V_b, V_a]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0))))) <=> p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_swhen(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0))))))).
fof(ch4s_Pastu_u_Temporalu_u_Logics_WHENu_u_EXPRESSIVEu_c3, conjecture, ![V_uu_0]: (![V_a, V_b, V_t0]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_t0)))) <=> (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_h4s_nums_num,V_t0)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_h4s_nums_num,V_t0)))))) => ![V_b, V_a, V_x]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_until(s(t_fun(t_h4s_nums_num,t_bool),V_a),s(t_fun(t_h4s_nums_num,t_bool),V_b))),s(t_h4s_nums_num,V_x))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_temporalu_u_logics_when(s(t_fun(t_h4s_nums_num,t_bool),V_b),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),V_uu_0),s(t_fun(t_h4s_nums_num,t_bool),V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_b))))),s(t_h4s_nums_num,V_x))))).
