# 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,f))),file('i/f/bag/BAG__DELETE__BAG__IN__up', aHLu_FALSITY)).
fof(4, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(8, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(33, axiom,(p(s(t_bool,f))<=>![X6]:p(s(t_bool,X6))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bools_Fu_u_DEF)).
fof(50, axiom,![X1]:![X25]:![X26]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X26),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X25),s(t_fun(X1,t_h4s_nums_num),X4))))))<=>(s(X1,X26)=s(X1,X25)|p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X26),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(54, 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(71, 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)).
fof(72, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/bag/BAG__DELETE__BAG__IN__up', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
