# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,X2))))<=>(p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,t))))&p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,f)))))),file('i/f/bool/FORALL__BOOL', ch4s_bools_FORALLu_u_BOOL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bool/FORALL__BOOL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bool/FORALL__BOOL', aHLu_FALSITY)).
fof(4, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/bool/FORALL__BOOL', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(5, axiom,![X1]:((p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,t))))&p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,f)))))=>![X2]:p(s(t_bool,happ(s(t_fun(t_bool,t_bool),X1),s(t_bool,X2))))),file('i/f/bool/FORALL__BOOL', ah4s_bools_boolu_u_INDUCT)).
fof(6, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/bool/FORALL__BOOL', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
