# 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_some(s(X1,X3))),s(t_h4s_options_option(X1),h4s_options_none)))=s(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_c2', ch4s_options_IFu_u_EQUALSu_u_OPTIONu_c2)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/option/IF__EQUALS__OPTION_c2', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/option/IF__EQUALS__OPTION_c2', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/option/IF__EQUALS__OPTION_c2', aHLu_BOOLu_CASES)).
fof(14, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/option/IF__EQUALS__OPTION_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(15, axiom,![X1]:![X2]:![X3]:(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X3)))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X2)))<=>s(X1,X3)=s(X1,X2)),file('i/f/option/IF__EQUALS__OPTION_c2', ah4s_options_SOMEu_u_11)).
fof(16, axiom,![X1]:![X3]:~(s(t_h4s_options_option(X1),h4s_options_none)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X3)))),file('i/f/option/IF__EQUALS__OPTION_c2', ah4s_options_NOTu_u_NONEu_u_SOME)).
fof(17, axiom,![X1]:![X6]:![X7]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X7),s(X1,X6)))=s(X1,X7),file('i/f/option/IF__EQUALS__OPTION_c2', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(18, axiom,![X1]:![X6]:![X7]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X7),s(X1,X6)))=s(X1,X6),file('i/f/option/IF__EQUALS__OPTION_c2', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
