# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),X3))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_none))))&![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))))))),file('i/f/option/FORALL__OPTION', ch4s_options_FORALLu_u_OPTION)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/option/FORALL__OPTION', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/option/FORALL__OPTION', aHLu_FALSITY)).
fof(7, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/option/FORALL__OPTION', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/option/FORALL__OPTION', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(17, axiom,(p(s(t_bool,f))<=>![X5]:p(s(t_bool,X5))),file('i/f/option/FORALL__OPTION', ah4s_bools_Fu_u_DEF)).
fof(18, axiom,![X1]:![X12]:![X10]:(![X4]:(s(X1,X12)=s(X1,X4)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X10),s(X1,X4)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X10),s(X1,X12))))),file('i/f/option/FORALL__OPTION', ah4s_bools_UNWINDu_u_FORALLu_u_THM1)).
fof(61, axiom,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_none))))&![X13]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),h4s_options_some(s(X1,X13)))))))=>![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_options_option(X1),t_bool),X2),s(t_h4s_options_option(X1),X4))))),file('i/f/option/FORALL__OPTION', ah4s_options_optionu_u_induction)).
# SZS output end CNFRefutation
