# 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,f))),file('i/f/bag/BAG__DELETE__BAG__IN__down', 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__down', 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__down', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(31, axiom,(p(s(t_bool,f))<=>![X6]:p(s(t_bool,X6))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ah4s_bools_Fu_u_DEF)).
fof(46, 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(54, axiom,![X1]:![X21]:![X4]:![X5]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X21),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,X21),s(t_fun(X1,t_h4s_nums_num),X5)))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ah4s_bags_BAGu_u_DELETE0)).
fof(76, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/bag/BAG__DELETE__BAG__IN__down', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
