# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),X3))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_none))))&![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))))))),file('i/f/option/FORALL__OPTION', ch4s_options_FORALLu_u_OPTION)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/option/FORALL__OPTION', aHLu_FALSITY)).
fof(22, axiom,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_none))))&![X19]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X19)))))))=>![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),X4))))),file('i/f/option/FORALL__OPTION', ah4s_options_optionu_u_induction)).
fof(23, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/option/FORALL__OPTION', aHLu_BOOLu_CASES)).
fof(25, axiom,p(s(t_bool,t)),file('i/f/option/FORALL__OPTION', aHLu_TRUTH)).
fof(27, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/option/FORALL__OPTION', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
