# 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,p(s(t_bool,t)),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', aHLu_FALSITY)).
fof(14, axiom,![X6]:(s(t_bool,t)=s(t_bool,X6)<=>p(s(t_bool,X6))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(16, axiom,![X6]:(s(t_bool,f)=s(t_bool,X6)<=>~(p(s(t_bool,X6)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(26, axiom,![X1]:![X7]:![X3]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X3),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X7))),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(32, axiom,![X1]:![X17]:(s(t_h4s_options_option(X1),X17)=s(t_h4s_options_option(X1),h4s_options_none)|?[X7]:s(t_h4s_options_option(X1),X17)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X7)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_optionu_u_nchotomy)).
fof(35, axiom,![X1]:![X7]:s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X7)))))=s(t_bool,f),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_options_ISu_u_NONEu_u_DEFu_c0)).
fof(36, 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(38, axiom,![X1]:![X6]:![X18]:s(X1,h4s_bools_cond(s(t_bool,X18),s(X1,X6),s(X1,X6)))=s(X1,X6),file('i/f/option/IF__NONE__EQUALS__OPTION_c0', ah4s_bools_CONDu_u_ID)).
# SZS output end CNFRefutation
