# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/quotient_option/IS__SOME__RSP', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/quotient_option/IS__SOME__RSP', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/quotient_option/IS__SOME__RSP', aHLu_BOOLu_CASES)).
fof(6, axiom,![X7]:![X6]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X7),happ(s(t_fun(X7,t_h4s_options_option(X7)),h4s_options_some),s(X7,X6)))))=s(t_bool,t),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
fof(7, axiom,![X7]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X7),h4s_options_none)))=s(t_bool,f),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_ISu_u_SOMEu_u_DEFu_c1)).
fof(13, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/quotient_option/IS__SOME__RSP', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(18, axiom,![X7]:![X6]:(~(p(s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X7),X6)))))<=>s(t_h4s_options_option(X7),X6)=s(t_h4s_options_option(X7),h4s_options_none)),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_NOTu_u_ISu_u_SOMEu_u_EQu_u_NONE)).
fof(23, axiom,![X7]:![X8]:![X17]:![X6]:![X11]:(p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X8),t_bool),happ(s(t_fun(t_h4s_options_option(X7),t_fun(t_h4s_options_option(X8),t_bool)),h4s_options_optrel(s(t_fun(X7,t_fun(X8,t_bool)),X11))),s(t_h4s_options_option(X7),X6))),s(t_h4s_options_option(X8),X17))))<=>((s(t_h4s_options_option(X7),X6)=s(t_h4s_options_option(X7),h4s_options_none)&s(t_h4s_options_option(X8),X17)=s(t_h4s_options_option(X8),h4s_options_none))|?[X23]:?[X24]:(s(t_h4s_options_option(X7),X6)=s(t_h4s_options_option(X7),happ(s(t_fun(X7,t_h4s_options_option(X7)),h4s_options_some),s(X7,X23)))&(s(t_h4s_options_option(X8),X17)=s(t_h4s_options_option(X8),happ(s(t_fun(X8,t_h4s_options_option(X8)),h4s_options_some),s(X8,X24)))&p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X7,t_fun(X8,t_bool)),X11),s(X7,X23))),s(X8,X24)))))))),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_OPTRELu_u_def)).
fof(24, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/quotient_option/IS__SOME__RSP', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(46, axiom,![X7]:![X6]:~(s(t_h4s_options_option(X7),happ(s(t_fun(X7,t_h4s_options_option(X7)),h4s_options_some),s(X7,X6)))=s(t_h4s_options_option(X7),h4s_options_none)),file('i/f/quotient_option/IS__SOME__RSP', ah4s_options_optionu_u_CLAUSESu_c3)).
fof(133, conjecture,![X8]:![X7]:![X9]:![X10]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X7,t_fun(X7,t_bool)),X11),s(t_fun(X7,X8),X10),s(t_fun(X8,X7),X9))))=>![X6]:![X17]:(p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X7),t_bool),happ(s(t_fun(t_h4s_options_option(X7),t_fun(t_h4s_options_option(X7),t_bool)),h4s_options_optrel(s(t_fun(X7,t_fun(X7,t_bool)),X11))),s(t_h4s_options_option(X7),X6))),s(t_h4s_options_option(X7),X17))))=>s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X7),X6)))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X7),X17))))),file('i/f/quotient_option/IS__SOME__RSP', ch4s_quotientu_u_options_ISu_u_SOMEu_u_RSP)).
# SZS output end CNFRefutation
