%   ORIGINAL: h4/tc/REMPTY__RRESTR
% 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/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/relation/EMPTY__REL__DEF: !y x. h4/relation/EMPTY__REL x y <=> F
% Assm: h4/tc/RRESTR: !s b a R. h4/tc/_7C_5E R s a b <=> h4/bool/IN b s /\ R a b
% Goal: !s. h4/tc/_7C_5E h4/relation/EMPTY__REL s = h4/relation/EMPTY__REL
%   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_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_relations_EMPTYu_u_RELu_u_DEF]: !y x. happ (happ h4/relation/EMPTY__REL x) y <=> F
% Assm [h4s_tcs_RRESTR]: !s b a R. happ (happ (h4/tc/_7C_5E R s) a) b <=> h4/bool/IN b s /\ happ (happ R a) b
% Goal: !s. h4/tc/_7C_5E h4/relation/EMPTY__REL s = h4/relation/EMPTY__REL
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_Q189373,TV_Q189369]: ![V_f, V_g]: (![V_x]: s(TV_Q189369,happ(s(t_fun(TV_Q189373,TV_Q189369),V_f),s(TV_Q189373,V_x))) = s(TV_Q189369,happ(s(t_fun(TV_Q189373,TV_Q189369),V_g),s(TV_Q189373,V_x))) => s(t_fun(TV_Q189373,TV_Q189369),V_f) = s(t_fun(TV_Q189373,TV_Q189369),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_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_relations_EMPTYu_u_RELu_u_DEF, axiom, ![TV_u_27a]: ![V_y, V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))) = s(t_bool,f)).
fof(ah4s_tcs_RRESTR, axiom, ![TV_u_27a]: ![V_s, V_b, V_a, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_u_7cu_5e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27a,V_a))),s(TV_u_27a,V_b)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_b),s(t_fun(TV_u_27a,t_bool),V_s)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_a))),s(TV_u_27a,V_b))))))).
fof(ch4s_tcs_REMPTYu_u_RRESTR, conjecture, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_tcs_u_7cu_5e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel)).
