# 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),h4s_options_none),s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X3)))))=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(X1,X3)=s(X1,X2))),file('i/f/option/IF__EQUALS__OPTION_c3', ch4s_options_IFu_u_EQUALSu_u_OPTIONu_c3)).
fof(3, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/option/IF__EQUALS__OPTION_c3', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X1]:![X3]:![X4]:(s(t_h4s_options_option(X1),h4s_bools_cond(s(t_bool,X4),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,X3)))))=s(t_h4s_options_option(X1),h4s_options_none)<=>p(s(t_bool,X4))),file('i/f/option/IF__EQUALS__OPTION_c3', ah4s_options_IFu_u_EQUALSu_u_OPTIONu_c1)).
fof(29, axiom,![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,X3)))),file('i/f/option/IF__EQUALS__OPTION_c3', ah4s_options_NOTu_u_NONEu_u_SOME)).
fof(31, axiom,![X1]:![X2]:![X3]:(s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X3)))=s(t_h4s_options_option(X1),happ(s(t_fun(X1,t_h4s_options_option(X1)),h4s_options_some),s(X1,X2)))<=>s(X1,X3)=s(X1,X2)),file('i/f/option/IF__EQUALS__OPTION_c3', ah4s_options_SOMEu_u_11)).
fof(42, axiom,![X1]:![X5]:![X6]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X6),s(X1,X5)))=s(X1,X5),file('i/f/option/IF__EQUALS__OPTION_c3', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(58, axiom,~(p(s(t_bool,f))),file('i/f/option/IF__EQUALS__OPTION_c3', aHLu_FALSITY)).
# SZS output end CNFRefutation
