# 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_allu_u_distinct(s(t_fun(X1,t_h4s_nums_num),X4))))=>(p(s(t_bool,h4s_bags_bagu_u_inn(s(X1,X3),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),X4))))<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))&p(s(t_bool,h4s_bags_bagu_u_in(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X4)))))))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ch4s_bags_BAGu_u_ALLu_u_DISTINCTu_u_BAGu_u_INN)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X1]:![X3]:![X4]:s(t_bool,h4s_bags_bagu_u_in(s(X1,X3),s(t_fun(X1,t_h4s_nums_num),X4)))=s(t_bool,h4s_bags_bagu_u_inn(s(X1,X3),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))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_bags_BAGu_u_IN0)).
fof(22, axiom,![X2]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_h4s_nums_num,X2))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(26, axiom,![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_numerals_numeralu_u_lteu_c1)).
fof(28, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(29, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X2),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_numerals_numeralu_u_distribu_c1)).
fof(30, axiom,![X1]:![X2]:![X3]:![X4]:s(t_bool,h4s_bags_bagu_u_inn(s(X1,X3),s(t_h4s_nums_num,X2),s(t_fun(X1,t_h4s_nums_num),X4)))=s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X3))),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_bags_BAGu_u_INN0)).
fof(31, axiom,![X1]:![X4]:(p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(X1,t_h4s_nums_num),X4))))<=>![X3]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X3))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_bags_BAGu_u_ALLu_u_DISTINCT0)).
fof(34, axiom,![X2]:![X19]:(~(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,X2))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X2))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X19)))))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(35, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_numerals_numeralu_u_sucu_c0)).
fof(36, axiom,![X2]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_numerals_numeralu_u_addu_c6)).
fof(37, axiom,![X18]:![X2]:![X19]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X18)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(38, axiom,![X2]:![X19]:(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,X2)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X19)))))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(39, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', aHLu_FALSITY)).
fof(46, axiom,![X7]:((p(s(t_bool,X7))=>p(s(t_bool,f)))<=>s(t_bool,X7)=s(t_bool,f)),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(51, axiom,![X2]:![X19]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X19)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X2))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_GREATERu_u_EQ)).
fof(52, axiom,![X2]:![X19]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X2))))),file('i/f/bag/BAG__ALL__DISTINCT__BAG__INN', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
# SZS output end CNFRefutation
