# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),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))))),file('i/f/bag/BAG__IN__BAG__DELETE', ch4s_bags_BAGu_u_INu_u_BAGu_u_DELETE)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__IN__BAG__DELETE', aHLu_FALSITY)).
fof(5, 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__IN__BAG__DELETE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, 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__IN__BAG__DELETE', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(16, axiom,(p(s(t_bool,f))<=>![X5]:p(s(t_bool,X5))),file('i/f/bag/BAG__IN__BAG__DELETE', ah4s_bools_Fu_u_DEF)).
fof(42, axiom,![X1]:![X2]:![X24]:![X3]:(p(s(t_bool,h4s_bags_bagu_u_delete(s(t_fun(X1,t_h4s_nums_num),X24),s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X3))))<=>s(t_fun(X1,t_h4s_nums_num),X24)=s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X3)))),file('i/f/bag/BAG__IN__BAG__DELETE', ah4s_bags_BAGu_u_DELETE0)).
fof(62, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X2),s(t_fun(X1,t_h4s_nums_num),X3))))=>?[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__IN__BAG__DELETE', ah4s_bags_BAGu_u_DECOMPOSE)).
fof(66, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/bag/BAG__IN__BAG__DELETE', aHLu_BOOLu_CASES)).
fof(67, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/bag/BAG__IN__BAG__DELETE', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
