# 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,happ(s(t_fun(t_h4s_options_option(X2),t_bool),happ(s(t_fun(t_h4s_options_option(X2),t_fun(t_h4s_options_option(X2),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_none(s(t_h4s_options_option(X2),X6)))=s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X2),X7))))),file('i/f/quotient_option/IS__NONE__RSP', ch4s_quotientu_u_options_ISu_u_NONEu_u_RSP)).
fof(3, axiom,![X12]:![X13]:((p(s(t_bool,X13))=>p(s(t_bool,X12)))=>((p(s(t_bool,X12))=>p(s(t_bool,X13)))=>s(t_bool,X13)=s(t_bool,X12))),file('i/f/quotient_option/IS__NONE__RSP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(29, axiom,![X2]:![X6]:(p(s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X2),X6))))<=>s(t_h4s_options_option(X2),X6)=s(t_h4s_options_option(X2),h4s_options_none)),file('i/f/quotient_option/IS__NONE__RSP', ah4s_options_ISu_u_NONEu_u_EQu_u_NONE)).
fof(30, axiom,![X2]:![X6]:s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X2),h4s_options_some(s(X2,X6)))))=s(t_bool,f),file('i/f/quotient_option/IS__NONE__RSP', ah4s_options_ISu_u_NONEu_u_DEFu_c0)).
fof(31, axiom,![X2]:s(t_bool,h4s_options_isu_u_none(s(t_h4s_options_option(X2),h4s_options_none)))=s(t_bool,t),file('i/f/quotient_option/IS__NONE__RSP', ah4s_options_ISu_u_NONEu_u_DEFu_c1)).
fof(35, axiom,![X1]:![X2]:![X10]:![X27]:?[X29]:(s(X1,happ(s(t_fun(t_h4s_options_option(X2),X1),X29),s(t_h4s_options_option(X2),h4s_options_none)))=s(X1,X27)&![X6]:s(X1,happ(s(t_fun(t_h4s_options_option(X2),X1),X29),s(t_h4s_options_option(X2),h4s_options_some(s(X2,X6)))))=s(X1,happ(s(t_fun(X2,X1),X10),s(X2,X6)))),file('i/f/quotient_option/IS__NONE__RSP', ah4s_options_optionu_u_Axiom)).
fof(40, axiom,![X1]:![X2]:![X6]:![X10]:s(t_h4s_options_option(X1),happ(s(t_fun(t_h4s_options_option(X2),t_h4s_options_option(X1)),h4s_options_optionu_u_map(s(t_fun(X2,X1),X10))),s(t_h4s_options_option(X2),h4s_options_some(s(X2,X6)))))=s(t_h4s_options_option(X1),h4s_options_some(s(X1,happ(s(t_fun(X2,X1),X10),s(X2,X6))))),file('i/f/quotient_option/IS__NONE__RSP', ah4s_options_OPTIONu_u_MAPu_u_DEFu_c0)).
fof(43, axiom,![X2]:![X1]:![X7]:![X6]:![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),happ(s(t_fun(t_h4s_options_option(X2),t_fun(t_h4s_options_option(X1),t_bool)),h4s_options_optrel(s(t_fun(X2,t_fun(X1,t_bool)),X5))),s(t_h4s_options_option(X2),X6))),s(t_h4s_options_option(X1),X7))))<=>((s(t_h4s_options_option(X2),X6)=s(t_h4s_options_option(X2),h4s_options_none)&s(t_h4s_options_option(X1),X7)=s(t_h4s_options_option(X1),h4s_options_none))|?[X31]:?[X32]:(s(t_h4s_options_option(X2),X6)=s(t_h4s_options_option(X2),h4s_options_some(s(X2,X31)))&(s(t_h4s_options_option(X1),X7)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X32)))&p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X2,t_fun(X1,t_bool)),X5),s(X2,X31))),s(X1,X32)))))))),file('i/f/quotient_option/IS__NONE__RSP', ah4s_options_OPTRELu_u_def)).
fof(64, axiom,~(p(s(t_bool,f))),file('i/f/quotient_option/IS__NONE__RSP', aHLu_FALSITY)).
fof(65, axiom,![X14]:(s(t_bool,f)=s(t_bool,X14)<=>~(p(s(t_bool,X14)))),file('i/f/quotient_option/IS__NONE__RSP', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
