%   ORIGINAL: h4/pred__set/NOT__UNIV__PSUBSET
% 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/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/pred__set/UNIV__SUBSET: !s. h4/pred__set/SUBSET h4/pred__set/UNIV s <=> s = h4/pred__set/UNIV
% Assm: h4/pred__set/PSUBSET__DEF: !t s. h4/pred__set/PSUBSET s t <=> h4/pred__set/SUBSET s t /\ ~(s = t)
% Goal: !s. ~h4/pred__set/PSUBSET h4/pred__set/UNIV s
%   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_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_predu_u_sets_UNIVu_u_SUBSET]: !s. h4/pred__set/SUBSET h4/pred__set/UNIV s <=> s = h4/pred__set/UNIV
% Assm [h4s_predu_u_sets_PSUBSETu_u_DEF]: !t s. h4/pred__set/PSUBSET s t <=> h4/pred__set/SUBSET s t /\ ~(s = t)
% Goal: !s. ~h4/pred__set/PSUBSET h4/pred__set/UNIV s
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_Q147221,TV_Q147217]: ![V_f, V_g]: (![V_x]: s(TV_Q147217,happ(s(t_fun(TV_Q147221,TV_Q147217),V_f),s(TV_Q147221,V_x))) = s(TV_Q147217,happ(s(t_fun(TV_Q147221,TV_Q147217),V_g),s(TV_Q147221,V_x))) => s(t_fun(TV_Q147221,TV_Q147217),V_f) = s(t_fun(TV_Q147221,TV_Q147217),V_g))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (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_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_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
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_predu_u_sets_UNIVu_u_SUBSET, axiom, ![TV_u_27a]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ),s(t_fun(TV_u_27a,t_bool),V_s)))) <=> s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))).
fof(ah4s_predu_u_sets_PSUBSETu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) & ~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),V_t))))).
fof(ch4s_predu_u_sets_NOTu_u_UNIVu_u_PSUBSET, conjecture, ![TV_u_27a]: ![V_s]: ~ (p(s(t_bool,h4s_predu_u_sets_psubset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ),s(t_fun(TV_u_27a,t_bool),V_s)))))).
