# 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))))=>p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X3))))),file('i/f/bag/BAG__DELETE__BAG__IN', ch4s_bags_BAGu_u_DELETEu_u_BAGu_u_IN)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__DELETE__BAG__IN', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__DELETE__BAG__IN', aHLu_FALSITY)).
fof(5, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/bag/BAG__DELETE__BAG__IN', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(18, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/bag/BAG__DELETE__BAG__IN', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(43, axiom,(p(s(t_bool,f))<=>![X5]:p(s(t_bool,X5))),file('i/f/bag/BAG__DELETE__BAG__IN', ah4s_bools_Fu_u_DEF)).
fof(61, axiom,![X1]:![X23]:![X24]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X24),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X23),s(t_fun(X1,t_h4s_nums_num),X4))))))<=>(s(X1,X24)=s(X1,X23)|p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X24),s(t_fun(X1,t_h4s_nums_num),X4)))))),file('i/f/bag/BAG__DELETE__BAG__IN', ah4s_bags_BAGu_u_INu_u_BAGu_u_INSERT)).
fof(70, 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', ah4s_bags_BAGu_u_DELETE0)).
# SZS output end CNFRefutation
