# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X3),s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X4))))=>![X5]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X5),s(t_fun(X1,t_h4s_nums_num),X4))))=>p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X5),s(t_fun(X1,t_h4s_nums_num),X3)))))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ch4s_bags_BAGu_u_DELETEu_u_BAGu_u_INu_u_up)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__DELETE__BAG__IN__up', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__DELETE__BAG__IN__up', aHLu_FALSITY)).
fof(6, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:![X7]:![X8]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X8),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X7),s(t_fun(X1,t_h4s_nums_num),X4))))))<=>(s(X1,X8)=s(X1,X7)|p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X8),s(t_fun(X1,t_h4s_nums_num),X4)))))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bags_BAGu_u_INu_u_BAGu_u_INSERT)).
fof(8, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X3),s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X4))))<=>s(t_fun(X1,t_h4s_nums_num),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),X4)))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bags_BAGu_u_DELETE0)).
fof(9, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/bag/BAG__DELETE__BAG__IN__up', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
