%   ORIGINAL: h4/bool/MONO__NOT__EQ
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EXCLUDED__MIDDLE0: !t. t \/ ~t
% Assm: h4/bool/MONO__NOT: !y x. (y ==> x) ==> ~x ==> ~y
% Goal: !y x. y ==> x <=> ~x ==> ~y
%   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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE0]: !t. t \/ ~t
% Assm [h4s_bools_MONOu_u_NOT]: !y x. (y ==> x) ==> ~x ==> ~y
% Goal: !y x. y ==> x <=> ~x ==> ~y
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_Q293264,TV_Q293260]: ![V_f, V_g]: (![V_x]: s(TV_Q293260,happ(s(t_fun(TV_Q293264,TV_Q293260),V_f),s(TV_Q293264,V_x))) = s(TV_Q293260,happ(s(t_fun(TV_Q293264,TV_Q293260),V_g),s(TV_Q293264,V_x))) => s(t_fun(TV_Q293264,TV_Q293260),V_f) = s(t_fun(TV_Q293264,TV_Q293260),V_g))).
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_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE0, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_MONOu_u_NOT, axiom, ![V_y, V_x]: ((p(s(t_bool,V_y)) => p(s(t_bool,V_x))) => (~ (p(s(t_bool,V_x))) => ~ (p(s(t_bool,V_y)))))).
fof(ch4s_bools_MONOu_u_NOTu_u_EQ, conjecture, ![V_y, V_x]: ((p(s(t_bool,V_y)) => p(s(t_bool,V_x))) <=> (~ (p(s(t_bool,V_x))) => ~ (p(s(t_bool,V_y)))))).
