# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_inter(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))=s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ch4s_extendedu_u_emits_BAGu_u_INTERu_u_EQNSu_c1)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/extended_emit/BAG__INTER__EQNS_c1', aHLu_FALSITY)).
fof(5, axiom,![X4]:![X5]:![X6]:![X7]:(![X8]:s(X5,happ(s(t_fun(X4,X5),X6),s(X4,X8)))=s(X5,happ(s(t_fun(X4,X5),X7),s(X4,X8)))=>s(t_fun(X4,X5),X6)=s(t_fun(X4,X5),X7)),file('i/f/extended_emit/BAG__INTER__EQNS_c1', aHLu_EXT)).
fof(7, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(14, axiom,![X1]:s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X1,t_h4s_nums_num),h4s_combins_k(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ah4s_bags_EMPTYu_u_BAG0)).
fof(15, axiom,![X12]:![X1]:![X11]:![X8]:s(X1,happ(s(t_fun(X12,X1),h4s_combins_k(s(X1,X8))),s(X12,X11)))=s(X1,X8),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ah4s_combins_Ku_u_THM)).
fof(16, axiom,![X1]:![X14]:![X15]:![X8]:s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),h4s_bags_bagu_u_inter(s(t_fun(X1,t_h4s_nums_num),X15),s(t_fun(X1,t_h4s_nums_num),X14))),s(X1,X8)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X15),s(X1,X8))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X14),s(X1,X8))))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X15),s(X1,X8))),s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X14),s(X1,X8))))),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ah4s_bags_BAGu_u_INTER0)).
fof(17, axiom,![X16]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(19, axiom,![X1]:![X9]:![X10]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X10),s(X1,X9)))=s(X1,X9),file('i/f/extended_emit/BAG__INTER__EQNS_c1', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
# SZS output end CNFRefutation
