# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:s(X2,happ(s(t_fun(t_fun(X1,X2),X2),happ(s(t_fun(X1,t_fun(t_fun(X1,X2),X2)),X3),s(X1,X4))),s(t_fun(X1,X2),X5)))=s(X2,happ(s(t_fun(X1,X2),X5),s(X1,X4)))=>![X4]:![X6]:s(t_h4s_options_option(X2),h4s_options_optionu_u_apply(s(t_h4s_options_option(t_fun(X1,X2)),X6),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))))=s(t_h4s_options_option(X2),h4s_options_optionu_u_apply(s(t_h4s_options_option(t_fun(t_fun(X1,X2),X2)),h4s_options_some(s(t_fun(t_fun(X1,X2),X2),happ(s(t_fun(X1,t_fun(t_fun(X1,X2),X2)),X3),s(X1,X4))))),s(t_h4s_options_option(t_fun(X1,X2)),X6)))),file('i/f/option/SOME__APPLY__PERMUTE', ch4s_options_SOMEu_u_APPLYu_u_PERMUTE)).
fof(2, axiom,![X2]:![X1]:![X4]:s(t_h4s_options_option(X1),h4s_options_optionu_u_apply(s(t_h4s_options_option(t_fun(X2,X1)),h4s_options_none),s(t_h4s_options_option(X2),X4)))=s(t_h4s_options_option(X1),h4s_options_none),file('i/f/option/SOME__APPLY__PERMUTE', ah4s_options_OPTIONu_u_APPLYu_u_defu_c0)).
fof(3, axiom,![X1]:![X2]:![X4]:![X6]:s(t_h4s_options_option(X1),h4s_options_optionu_u_apply(s(t_h4s_options_option(t_fun(X2,X1)),h4s_options_some(s(t_fun(X2,X1),X6))),s(t_h4s_options_option(X2),X4)))=s(t_h4s_options_option(X1),h4s_options_optionu_u_map(s(t_fun(X2,X1),X6),s(t_h4s_options_option(X2),X4))),file('i/f/option/SOME__APPLY__PERMUTE', ah4s_options_OPTIONu_u_APPLYu_u_defu_c1)).
fof(6, axiom,![X2]:![X1]:![X4]:![X6]:s(t_h4s_options_option(X2),h4s_options_optionu_u_map(s(t_fun(X1,X2),X6),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))))=s(t_h4s_options_option(X2),h4s_options_some(s(X2,happ(s(t_fun(X1,X2),X6),s(X1,X4))))),file('i/f/option/SOME__APPLY__PERMUTE', ah4s_options_OPTIONu_u_MAPu_u_DEFu_c0)).
fof(7, axiom,![X1]:![X11]:(s(t_h4s_options_option(X1),X11)=s(t_h4s_options_option(X1),h4s_options_none)|?[X4]:s(t_h4s_options_option(X1),X11)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))),file('i/f/option/SOME__APPLY__PERMUTE', ah4s_options_optionu_u_nchotomy)).
fof(8, axiom,![X1]:![X2]:![X6]:s(t_h4s_options_option(X2),h4s_options_optionu_u_map(s(t_fun(X1,X2),X6),s(t_h4s_options_option(X1),h4s_options_none)))=s(t_h4s_options_option(X2),h4s_options_none),file('i/f/option/SOME__APPLY__PERMUTE', ah4s_options_OPTIONu_u_MAPu_u_DEFu_c1)).
# SZS output end CNFRefutation
