# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X4),s(t_h4s_options_option(X1),X3),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X2)))<=>(p(s(t_bool,X4))&s(t_h4s_options_option(X1),X3)=s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X2))))),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ch4s_options_IFu_u_NONEu_u_EQUALSu_u_OPTIONu_c2)).
fof(9, axiom,![X1]:![X2]:~(s(t_h4s_options_option(X1),h4s_options_none)=s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X2)))),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ah4s_options_NOTu_u_NONEu_u_SOME)).
fof(22, axiom,![X17]:![X18]:((p(s(t_bool,X18))=>p(s(t_bool,X17)))=>((p(s(t_bool,X17))=>p(s(t_bool,X18)))=>s(t_bool,X18)=s(t_bool,X17))),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(43, axiom,![X1]:![X17]:![X18]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X18),s(X1,X17)))=s(X1,X18),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(44, axiom,![X1]:![X17]:![X18]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X18),s(X1,X17)))=s(X1,X17),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(53, axiom,p(s(t_bool,t)),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', aHLu_TRUTH)).
fof(57, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(58, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)<=>p(s(t_bool,X12))),file('i/f/option/IF__NONE__EQUALS__OPTION_c2', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
