# 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),h4s_options_none),s(t_h4s_options_option(X1),X2)))=s(t_h4s_options_option(X1),h4s_options_none)<=>(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X2))))=>p(s(t_bool,X3)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ch4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c1)).
fof(24, axiom,![X1]:![X14]:(~(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),X14)))))<=>s(t_h4s_options_option(X1),X14)=s(t_h4s_options_option(X1),h4s_options_none)),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE)).
fof(25, axiom,![X1]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),h4s_options_none)))=s(t_bool,f),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_options_ISu_u_SOMEu_u_DEFu_c1)).
fof(42, 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_c1', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(43, 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_c1', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(58, axiom,~(p(s(t_bool,f))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', aHLu_FALSITY)).
fof(59, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', aHLu_BOOLu_CASES)).
fof(61, axiom,![X9]:((p(s(t_bool,f))=>p(s(t_bool,X9)))<=>p(s(t_bool,t))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_bools_IMPu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
