# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X3),s(t_h4s_options_option(X1),X2),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_none)<=>(p(s(t_bool,X3))=>p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X1),X2)))))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ch4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c0)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(24, axiom,![X1]:![X10]:(p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X1),X10))))<=>s(t_h4s_options_option(X1),X10)=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_ISu_u_NONEu_u_EQu_u_NONE)).
fof(27, axiom,![X1]:s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X1),h4s_options_none)))=s(t_bool,t),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_ISu_u_NONEu_u_DEFu_c1)).
fof(28, axiom,![X1]:![X10]:s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X10)))))=s(t_bool,f),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_ISu_u_NONEu_u_DEFu_c0)).
fof(32, axiom,![X1]:![X10]:~(s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X10)))=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_NOTu_u_SOMEu_u_NONE)).
fof(39, axiom,![X1]:![X10]:![X3]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X3),s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X10))),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),h4s_options_none)<=>~(p(s(t_bool,X3)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c0)).
fof(41, axiom,![X1]:![X4]:![X5]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X5),s(X1,X4)))=s(X1,X5),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(42, axiom,![X1]:![X4]:![X5]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X5),s(X1,X4)))=s(X1,X4),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
