# 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(9, axiom,![X1]:![X10]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X10)))))=s(t_bool,t),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
fof(10, 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(11, axiom,![X1]:![X15]:(s(t_h4s_options_option(X1),X15)=s(t_h4s_options_option(X1),h4s_options_none)|?[X10]:s(t_h4s_options_option(X1),X15)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X10)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_options_optionu_u_nchotomy)).
fof(15, axiom,![X1]:![X10]:![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),h4s_options_some(s(X1,X10)))))=s(t_h4s_options_option(X1),h4s_options_none)<=>p(s(t_bool,X3))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c1)).
fof(18, axiom,![X1]:![X11]:![X16]:s(X1,h4s_bools_cond(s(t_bool,X16),s(X1,X11),s(X1,X11)))=s(X1,X11),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_bools_CONDu_u_ID)).
fof(19, axiom,p(s(t_bool,t)),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', aHLu_TRUTH)).
fof(27, axiom,![X11]:(s(t_bool,t)=s(t_bool,X11)<=>p(s(t_bool,X11))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(29, axiom,~(p(s(t_bool,f))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', aHLu_FALSITY)).
fof(33, axiom,![X11]:(s(t_bool,f)=s(t_bool,X11)<=>~(p(s(t_bool,X11)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c1', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
