# 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(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))=>![X6]: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(X1),h4s_options_optionu_u_map(s(t_fun(X2,X1),X3),s(t_h4s_options_option(X2),X6)))))),file('i/f/quotient_option/IS__SOME__PRS', ch4s_quotientu_u_options_ISu_u_SOMEu_u_PRS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient_option/IS__SOME__PRS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/quotient_option/IS__SOME__PRS', aHLu_FALSITY)).
fof(4, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/quotient_option/IS__SOME__PRS', aHLu_BOOLu_CASES)).
fof(7, axiom,![X7]:(s(t_bool,t)=s(t_bool,X7)<=>p(s(t_bool,X7))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(8, axiom,![X7]:(s(t_bool,f)=s(t_bool,X7)<=>~(p(s(t_bool,X7)))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(9, axiom,![X1]:![X8]:(s(t_h4s_options_option(X1),X8)=s(t_h4s_options_option(X1),h4s_options_none)|?[X6]:s(t_h4s_options_option(X1),X8)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X6)))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_optionu_u_nchotomy)).
fof(10, axiom,![X1]:![X2]:![X9]:s(t_h4s_options_option(X2),h4s_options_optionu_u_map(s(t_fun(X1,X2),X9),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X2),h4s_options_none),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_OPTIONu_u_MAPu_u_DEFu_c1)).
fof(11, axiom,![X1]:![X6]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X6)))))=s(t_bool,t),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
fof(12, axiom,![X1]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X1),h4s_options_none)))=s(t_bool,f),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_ISu_u_SOMEu_u_DEFu_c1)).
fof(13, axiom,![X2]:![X1]:![X6]:![X9]:s(t_h4s_options_option(X2),h4s_options_optionu_u_map(s(t_fun(X1,X2),X9),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X6)))))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,happ(s(t_fun(X1,X2),X9),s(X1,X6))))),file('i/f/quotient_option/IS__SOME__PRS', ah4s_options_OPTIONu_u_MAPu_u_DEFu_c0)).
# SZS output end CNFRefutation
