# 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_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3))))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3))=>![X2]:s(t_h4s_options_option(t_h4s_nums_num),h4s_whiles_oleast(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2)))))=s(t_h4s_options_option(t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_options_some),s(t_h4s_nums_num,X2)))),file('i/f/while/OLEAST__EQNS_c1', ch4s_whiles_OLEASTu_u_EQNSu_c1)).
fof(42, axiom,![X1]:(![X2]:![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3))))<=>s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2))=>![X2]:s(t_h4s_options_option(t_h4s_nums_num),h4s_whiles_oleast(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X1),s(t_h4s_nums_num,X2)))))=s(t_h4s_options_option(t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_options_option(t_h4s_nums_num)),h4s_options_some),s(t_h4s_nums_num,X2)))),file('i/f/while/OLEAST__EQNS_c1', ah4s_whiles_OLEASTu_u_EQNSu_c0)).
fof(51, axiom,p(s(t_bool,t)),file('i/f/while/OLEAST__EQNS_c1', aHLu_TRUTH)).
fof(56, axiom,![X18]:(s(t_bool,X18)=s(t_bool,t)<=>p(s(t_bool,X18))),file('i/f/while/OLEAST__EQNS_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
