# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))=>![X6]:![X7]:(p(s(t_bool,h4s_options_optrel(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_h4s_options_option(X2),X6),s(t_h4s_options_option(X2),X7))))=>s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X2),X6)))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X2),X7))))),file('i/f/quotient_option/IS__SOME__RSP', ch4s_quotientu_u_options_ISu_u_SOMEu_u_RSP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient_option/IS__SOME__RSP', aHLu_TRUTH)).
fof(11, axiom,![X8]:(s(t_bool,t)=s(t_bool,X8)<=>p(s(t_bool,X8))),file('i/f/quotient_option/IS__SOME__RSP', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(12, axiom,![X8]:(s(t_bool,f)=s(t_bool,X8)<=>~(p(s(t_bool,X8)))),file('i/f/quotient_option/IS__SOME__RSP', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(13, axiom,![X2]:![X9]:(s(t_h4s_options_option(X2),X9)=s(t_h4s_options_option(X2),h4s_options_none)|?[X6]:s(t_h4s_options_option(X2),X9)=s(t_h4s_options_option(X2),h4s_options_some(s(X2,X6)))),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_optionu_u_nchotomy)).
fof(15, axiom,![X2]:![X6]:![X5]:s(t_bool,h4s_options_optrel(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_h4s_options_option(X2),h4s_options_some(s(X2,X6))),s(t_h4s_options_option(X2),h4s_options_none)))=s(t_bool,f),file('i/f/quotient_option/IS__SOME__RSP', ah4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c1)).
fof(16, axiom,![X2]:![X7]:![X5]:s(t_bool,h4s_options_optrel(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_h4s_options_option(X2),h4s_options_none),s(t_h4s_options_option(X2),h4s_options_some(s(X2,X7)))))=s(t_bool,f),file('i/f/quotient_option/IS__SOME__RSP', ah4s_quotientu_u_options_OPTIONu_u_RELu_u_defu_c2)).
fof(17, axiom,![X2]:![X6]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X2),h4s_options_some(s(X2,X6)))))=s(t_bool,t),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
# SZS output end CNFRefutation
