# 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/EXISTS__OPTION', ch4s_options_EXISTSu_u_OPTION)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/option/EXISTS__OPTION', aHLu_FALSITY)).
fof(23, axiom,![X1]:![X4]:s(t_bool,d_exists(s(t_fun(X1,t_bool),X4)))=s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,h4s_mins_u_40(s(t_fun(X1,t_bool),X4))))),file('i/f/option/EXISTS__OPTION', ah4s_bools_EXISTSu_u_DEF)).
fof(24, axiom,![X1]:![X4]:![X2]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,X4))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,h4s_mins_u_40(s(t_fun(X1,t_bool),X2))))))),file('i/f/option/EXISTS__OPTION', ah4s_bools_SELECTu_u_AX)).
fof(25, axiom,![X1]:![X3]:(s(t_h4s_options_option(X1),X3)=s(t_h4s_options_option(X1),h4s_options_none)|?[X4]:s(t_h4s_options_option(X1),X3)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X4)))),file('i/f/option/EXISTS__OPTION', ah4s_options_optionu_u_nchotomy)).
fof(26, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/option/EXISTS__OPTION', aHLu_BOOLu_CASES)).
fof(27, axiom,p(s(t_bool,t)),file('i/f/option/EXISTS__OPTION', aHLu_TRUTH)).
fof(29, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/option/EXISTS__OPTION', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
