# 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_psubu_u_bag(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_h4s_nums_num),X3))))),file('i/f/bag/BAG__DELETE__PSUB__BAG', ch4s_bags_BAGu_u_DELETEu_u_PSUBu_u_BAG)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__DELETE__PSUB__BAG', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__DELETE__PSUB__BAG', aHLu_FALSITY)).
fof(12, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/bag/BAG__DELETE__PSUB__BAG', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(16, axiom,![X1]:![X13]:![X14]:(p(s(t_bool,h4s_bags_psubu_u_bag(s(t_fun(X1,t_h4s_nums_num),X14),s(t_fun(X1,t_h4s_nums_num),X13))))<=>(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X14),s(t_fun(X1,t_h4s_nums_num),X13))))&~(s(t_fun(X1,t_h4s_nums_num),X14)=s(t_fun(X1,t_h4s_nums_num),X13)))),file('i/f/bag/BAG__DELETE__PSUB__BAG', ah4s_bags_PSUBu_u_BAG0)).
fof(17, axiom,![X1]:![X13]:![X14]:(p(s(t_bool,h4s_bags_subu_u_bag(s(t_fun(X1,t_h4s_nums_num),X14),s(t_fun(X1,t_h4s_nums_num),X13))))<=>![X8]:![X15]:(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X8),s(t_h4s_nums_num,X15),s(t_fun(X1,t_h4s_nums_num),X14))))=>p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X8),s(t_h4s_nums_num,X15),s(t_fun(X1,t_h4s_nums_num),X13)))))),file('i/f/bag/BAG__DELETE__PSUB__BAG', ah4s_bags_SUBu_u_BAG0)).
fof(18, axiom,![X1]:![X8]:![X4]:~(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X8),s(t_fun(X1,t_h4s_nums_num),X4)))=s(t_fun(X1,t_h4s_nums_num),X4)),file('i/f/bag/BAG__DELETE__PSUB__BAG', ah4s_bags_BAGu_u_INSERTu_u_DIFF)).
fof(19, 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__PSUB__BAG', ah4s_bags_BAGu_u_DELETE0)).
fof(20, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/bag/BAG__DELETE__PSUB__BAG', aHLu_BOOLu_CASES)).
fof(21, axiom,![X1]:![X15]:![X16]:![X17]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X17),s(t_h4s_nums_num,X15),s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_insert(s(X1,X16),s(t_fun(X1,t_h4s_nums_num),X4))))))<=>((p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X17),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_fun(X1,t_h4s_nums_num),X4))))&s(X1,X17)=s(X1,X16))|p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X17),s(t_h4s_nums_num,X15),s(t_fun(X1,t_h4s_nums_num),X4)))))),file('i/f/bag/BAG__DELETE__PSUB__BAG', ah4s_bags_BAGu_u_INNu_u_BAGu_u_INSERT)).
# SZS output end CNFRefutation
