# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X5))))&(~(s(X1,X3)=s(X1,X2))&p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X4))))))=>p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X5))))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ch4s_bags_BAGu_u_DELETEu_u_BAGu_u_INu_u_down)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__DELETE__BAG__IN__down', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__DELETE__BAG__IN__down', aHLu_FALSITY)).
fof(13, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(22, axiom,![X1]:![X2]:![X3]:![X5]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X5))))))<=>(s(X1,X3)=s(X1,X2)|p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X5)))))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ah4s_bags_BAGu_u_INu_u_BAGu_u_INSERT)).
fof(25, axiom,![X1]:![X25]:![X4]:![X5]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X25),s(t_fun(X1,t_h4s_nums_num),X5))))<=>s(t_fun(X1,t_h4s_nums_num),X4)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X25),s(t_fun(X1,t_h4s_nums_num),X5)))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ah4s_bags_BAGu_u_DELETE0)).
fof(26, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/bag/BAG__DELETE__BAG__IN__down', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
