# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X2)))))=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),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),X1),s(t_fun(t_h4s_nums_num,t_bool),X2))))))<=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))|p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X3),s(t_fun(t_h4s_nums_num,t_bool),X2))))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ch4s_patricias_INu_u_PTREEu_u_OFu_u_NUMSET)).
fof(5, axiom,![X11]:![X10]:![X1]:![X2]:(p(s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),h4s_predu_u_sets_union(s(t_fun(X11,t_bool),X2),s(t_fun(X11,t_bool),X1))))))<=>(p(s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),X2))))|p(s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),X1)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_predu_u_sets_INu_u_UNION)).
fof(6, axiom,![X11]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X11,t_bool),X2))))=>![X10]:s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),X2)))=s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X11),h4s_lists_setu_u_tou_u_list(s(t_fun(X11,t_bool),X2)))))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_lists_SETu_u_TOu_u_LISTu_u_INu_u_MEM)).
fof(7, axiom,![X1]:![X12]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X12),s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1)))))))=s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X12),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),X1)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_MEMu_u_TRAVERSE)).
fof(8, axiom,![X1]:![X3]:s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1)))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(t_h4s_ones_one),h4s_patricias_peek(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1),s(t_h4s_nums_num,X3))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_INu_u_PTREEu_u_def)).
fof(9, axiom,![X1]:![X2]: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),X1),s(t_fun(t_h4s_nums_num,t_bool),X2)))=s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_lists_foldl(s(t_fun(t_h4s_patricias_ptree(t_h4s_ones_one),t_fun(t_h4s_nums_num,t_h4s_patricias_ptree(t_h4s_ones_one))),h4s_combins_c(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(t_h4s_ones_one),t_h4s_patricias_ptree(t_h4s_ones_one))),h4s_patricias_insertu_u_ptree))),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1),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),X2))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_def)).
fof(10, axiom,![X1]:![X2]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))=>p(s(t_bool,h4s_patricias_isu_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),X1),s(t_fun(t_h4s_nums_num,t_bool),X2))))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_ISu_u_PTREE)).
fof(11, axiom,![X11]:![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X11,t_bool),h4s_predu_u_sets_union(s(t_fun(X11,t_bool),X2),s(t_fun(X11,t_bool),X1))))))<=>(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X11,t_bool),X2))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X11,t_bool),X1)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_predu_u_sets_FINITEu_u_UNION)).
fof(12, axiom,![X1]:p(s(t_bool,h4s_predu_u_sets_finite(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),X1)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_FINITEu_u_NUMSETu_u_OFu_u_PTREE)).
fof(13, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X2))))=>(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_lists_foldl(s(t_fun(t_h4s_patricias_ptree(t_h4s_ones_one),t_fun(t_h4s_nums_num,t_h4s_patricias_ptree(t_h4s_ones_one))),h4s_combins_c(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(t_h4s_ones_one),t_h4s_patricias_ptree(t_h4s_ones_one))),h4s_patricias_insertu_u_ptree))),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1),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),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),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),X1))),s(t_fun(t_h4s_nums_num,t_bool),X2)))))))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_PERMu_u_INSERTu_u_PTREE)).
fof(14, axiom,![X11]:![X13]:![X14]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X11),X14),s(t_h4s_lists_list(X11),X13))))=>![X10]:s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X11),X14)))))=s(t_bool,h4s_bools_in(s(X11,X10),s(t_fun(X11,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X11),X13)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_sortings_PERMu_u_MEMu_u_EQ)).
fof(15, axiom,![X11]:![X1]:![X12]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X11),X1))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X12),s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X11),X1)))))))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X11),h4s_patricias_peek(s(t_h4s_patricias_ptree(X11),X1),s(t_h4s_nums_num,X12)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET', ah4s_patricias_MEMu_u_TRAVERSEu_u_PEEK)).
# SZS output end CNFRefutation
