# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:~(s(t_h4s_options_option(X1),h4s_options_none)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X2)))),file('i/f/option/NOT__NONE__SOME', ch4s_options_NOTu_u_NONEu_u_SOME)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/option/NOT__NONE__SOME', aHLu_FALSITY)).
fof(4, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/option/NOT__NONE__SOME', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X7]:![X8]:![X9]:((p(s(t_bool,X9))<=>s(t_bool,X8)=s(t_bool,X7))<=>((p(s(t_bool,X9))|(p(s(t_bool,X8))|p(s(t_bool,X7))))&((p(s(t_bool,X9))|(~(p(s(t_bool,X7)))|~(p(s(t_bool,X8)))))&((p(s(t_bool,X8))|(~(p(s(t_bool,X7)))|~(p(s(t_bool,X9)))))&(p(s(t_bool,X7))|(~(p(s(t_bool,X8)))|~(p(s(t_bool,X9))))))))),file('i/f/option/NOT__NONE__SOME', ah4s_sats_dcu_u_eq)).
fof(30, axiom,(p(s(t_bool,f))<=>![X3]:p(s(t_bool,X3))),file('i/f/option/NOT__NONE__SOME', ah4s_bools_Fu_u_DEF)).
fof(32, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/option/NOT__NONE__SOME', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(60, axiom,![X12]:![X1]:![X2]:![X26]:![X21]:s(X12,h4s_options_optionu_u_case(s(t_h4s_options_option(X1),h4s_options_some(s(X1,X2))),s(X12,X26),s(t_fun(X1,X12),X21)))=s(X12,happ(s(t_fun(X1,X12),X21),s(X1,X2))),file('i/f/option/NOT__NONE__SOME', ah4s_options_optionu_u_caseu_u_defu_c1)).
fof(62, axiom,![X1]:![X12]:![X26]:![X21]:s(X12,h4s_options_optionu_u_case(s(t_h4s_options_option(X1),h4s_options_none),s(X12,X26),s(t_fun(X1,X12),X21)))=s(X12,X26),file('i/f/option/NOT__NONE__SOME', ah4s_options_optionu_u_caseu_u_defu_c0)).
fof(63, axiom,p(s(t_bool,t)),file('i/f/option/NOT__NONE__SOME', aHLu_TRUTH)).
fof(65, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/option/NOT__NONE__SOME', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
