# 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_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(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_fun(t_h4s_nums_num,t_bool),X1)),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ch4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_PTREEu_u_OFu_u_NUMSETu_u_EMPTY)).
fof(5, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(32, axiom,![X10]:![X1]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X10))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X1)))))=>s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(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),X10),s(t_fun(t_h4s_nums_num,t_bool),X1)))))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_union(s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X10))),s(t_fun(t_h4s_nums_num,t_bool),X1)))),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_PTREEu_u_OFu_u_NUMSET)).
fof(34, axiom,s(t_fun(t_h4s_nums_num,t_bool),h4s_patricias_numsetu_u_ofu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty)))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_EMPTY)).
fof(43, axiom,![X9]:p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X9),h4s_patricias_empty)))),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_EMPTYu_u_ISu_u_PTREE)).
fof(45, axiom,![X9]:s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X9),h4s_patricias_empty)))=s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_TRAVERSEu_u_defu_c0)).
fof(64, axiom,![X9]:![X10]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X9),X10))))=>p(s(t_bool,h4s_lists_allu_u_distinct(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X9),X10))))))),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_ALLu_u_DISTINCTu_u_TRAVERSE)).
fof(66, axiom,![X9]:![X1]:s(t_fun(X9,t_bool),h4s_predu_u_sets_union(s(t_fun(X9,t_bool),X1),s(t_fun(X9,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X9,t_bool),X1),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_predu_u_sets_UNIONu_u_EMPTYu_c1)).
fof(69, axiom,![X9]:![X10]:![X1]:s(t_fun(X9,t_bool),h4s_predu_u_sets_union(s(t_fun(X9,t_bool),X1),s(t_fun(X9,t_bool),X10)))=s(t_fun(X9,t_bool),h4s_predu_u_sets_union(s(t_fun(X9,t_bool),X10),s(t_fun(X9,t_bool),X1))),file('i/f/patricia/NUMSET__OF__PTREE__PTREE__OF__NUMSET__EMPTY', ah4s_predu_u_sets_UNIONu_u_COMM)).
# SZS output end CNFRefutation
