# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(X1,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ch4s_bags_BAGu_u_ALLu_u_DISTINCTu_u_THMu_c0)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', aHLu_FALSITY)).
fof(17, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(39, axiom,![X19]:![X20]:(s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,X19)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20)))))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(42, axiom,![X1]:![X21]:(p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(X1,t_h4s_nums_num),X21))))<=>![X22]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X21),s(X1,X22))),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__THM_c0', ah4s_bags_BAGu_u_ALLu_u_DISTINCT0)).
fof(43, 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/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_bags_EMPTYu_u_BAG0)).
fof(51, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', aHLu_BOOLu_CASES)).
fof(53, axiom,![X19]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19)))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(58, axiom,![X19]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_numerals_numeralu_u_distribu_c27)).
fof(62, axiom,![X19]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X19)))))=s(t_h4s_nums_num,X19),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_numerals_numeralu_u_addu_c0)).
fof(64, axiom,![X27]:![X1]:![X14]:![X5]:s(X1,happ(s(t_fun(X27,X1),h4s_combins_k(s(X1,X5))),s(X27,X14)))=s(X1,X5),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_combins_Ku_u_THM)).
fof(66, axiom,![X20]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X20),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_arithmetics_ADDu_u_0)).
fof(71, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', aHLu_TRUTH)).
# SZS output end CNFRefutation
