# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:(p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(X7,t_h4s_nums_num),X8))))<=>![X9]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,happ(s(t_fun(X7,t_h4s_nums_num),X8),s(X7,X9))),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(6, axiom,![X7]:s(t_fun(X7,t_h4s_nums_num),h4s_bags_emptyu_u_bag)=s(t_fun(X7,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(9, axiom,![X7]:![X8]:(p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X7,t_h4s_nums_num),X8))))=>(s(t_h4s_nums_num,h4s_bags_bagu_u_card(s(t_fun(X7,t_h4s_nums_num),X8)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_fun(X7,t_h4s_nums_num),X8)=s(t_fun(X7,t_h4s_nums_num),h4s_bags_emptyu_u_bag))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_bags_BCARDu_u_0)).
fof(18, axiom,![X14]:![X7]:![X15]:![X6]:s(X7,happ(s(t_fun(X14,X7),h4s_combins_k(s(X7,X6))),s(X14,X15)))=s(X7,X6),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_combins_Ku_u_THM)).
fof(21, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(57, axiom,![X7]:p(s(t_bool,h4s_bags_finiteu_u_bag(s(t_fun(X7,t_h4s_nums_num),h4s_bags_emptyu_u_bag)))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_bags_FINITEu_u_BAGu_u_THMu_c0)).
fof(67, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(80, axiom,![X27]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X27)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X27),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_arithmetics_ADD1)).
fof(105, axiom,![X29]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X29)))),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(132, axiom,![X27]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X27)))=s(t_h4s_nums_num,X27),file('i/f/bag/BAG__ALL__DISTINCT__THM_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(133, conjecture,![X7]:p(s(t_bool,h4s_bags_bagu_u_allu_u_distinct(s(t_fun(X7,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)).
# SZS output end CNFRefutation
