# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X1))))=>s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty),s(t_fun(t_h4s_nums_num,t_bool),X1)))))=s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(t_h4s_nums_num,t_bool),X1)))),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ch4s_patricias_SIZEu_u_PTREEu_u_OFu_u_NUMSETu_u_EMPTY)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', aHLu_TRUTH)).
fof(7, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X2]:![X1]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X1))))=>((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))))&p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_append(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_setu_u_tou_u_list(s(t_fun(t_h4s_nums_num,t_bool),X1)))))))))=>s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_ptreeu_u_ofu_u_numset(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2),s(t_fun(t_h4s_nums_num,t_bool),X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(t_h4s_nums_num,t_bool),X1))))))),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_SIZEu_u_PTREEu_u_OFu_u_NUMSET)).
fof(12, axiom,![X3]:![X1]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X3,t_bool),X1))))=>p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(X3),h4s_lists_setu_u_tou_u_list(s(t_fun(X3,t_bool),X1))))))),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_lists_ALLu_u_DISTINCTu_u_SETu_u_TOu_u_LIST)).
fof(13, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X15),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_arithmetics_ADDu_u_0)).
fof(14, axiom,![X16]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15))),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_arithmetics_ADDu_u_SYM)).
fof(15, axiom,![X3]:s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X3),h4s_patricias_empty)))=s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_TRAVERSEu_u_defu_c0)).
fof(16, axiom,![X3]:s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(X3),h4s_patricias_empty)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_SIZE0u_c0)).
fof(17, axiom,![X3]:p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X3),h4s_patricias_empty)))),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_EMPTYu_u_ISu_u_PTREE)).
fof(19, axiom,![X3]:![X17]:s(t_h4s_lists_list(X3),h4s_lists_append(s(t_h4s_lists_list(X3),h4s_lists_nil),s(t_h4s_lists_list(X3),X17)))=s(t_h4s_lists_list(X3),X17),file('i/f/patricia/SIZE__PTREE__OF__NUMSET__EMPTY', ah4s_lists_APPEND0u_c0)).
# SZS output end CNFRefutation
