%   ORIGINAL: h4/pred__set/DISJOINT__EMPTY__REFL__RWT
% 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/pred__set/DISJOINT__EMPTY__REFL: !s. s = h4/pred__set/EMPTY <=> h4/pred__set/DISJOINT s s
% Goal: !s. h4/pred__set/DISJOINT s s <=> s = h4/pred__set/EMPTY
%   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_predu_u_sets_DISJOINTu_u_EMPTYu_u_REFL]: !s. s = h4/pred__set/EMPTY <=> h4/pred__set/DISJOINT s s
% Goal: !s. h4/pred__set/DISJOINT s s <=> s = h4/pred__set/EMPTY
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_Q148123,TV_Q148119]: ![V_f, V_g]: (![V_x]: s(TV_Q148119,happ(s(t_fun(TV_Q148123,TV_Q148119),V_f),s(TV_Q148123,V_x))) = s(TV_Q148119,happ(s(t_fun(TV_Q148123,TV_Q148119),V_g),s(TV_Q148123,V_x))) => s(t_fun(TV_Q148123,TV_Q148119),V_f) = s(t_fun(TV_Q148123,TV_Q148119),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_predu_u_sets_DISJOINTu_u_EMPTYu_u_REFL, axiom, ![TV_u_27a]: ![V_s]: (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty) <=> p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ch4s_predu_u_sets_DISJOINTu_u_EMPTYu_u_REFLu_u_RWT, conjecture, ![TV_u_27a]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_disjoint(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),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))).
