# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4))))<=>~(s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,X3)))=>![X5]:![X3]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X1),X5))))&p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X3),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(X1),X5)))))))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),h4s_patricias_remove(s(t_h4s_patricias_ptree(X1),X5),s(t_h4s_nums_num,X3))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_filter(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_nums_num,X3))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),X5)))))))))),file('i/f/patricia/PERM__REMOVE', ch4s_patricias_PERMu_u_REMOVE)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/patricia/PERM__REMOVE', aHLu_TRUTH)).
fof(7, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)<=>p(s(t_bool,X5))),file('i/f/patricia/PERM__REMOVE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X2]:(![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X4))))<=>~(s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,X3)))=>![X5]:![X3]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X5))))&p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X3),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),X5)))))))))=>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_patricias_remove(s(t_h4s_patricias_ptree(t_h4s_ones_one),X5),s(t_h4s_nums_num,X3))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_filter(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_nums_num,X3))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(t_h4s_ones_one),X5)))))))))),file('i/f/patricia/PERM__REMOVE', ah4s_patricias_PERMu_u_DELETEu_u_PTREE)).
fof(12, axiom,![X12]:![X1]:![X5]:![X13]:s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X12),h4s_patricias_transform(s(t_fun(X1,X12),X13),s(t_h4s_patricias_ptree(X1),X5)))))=s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),X5))),file('i/f/patricia/PERM__REMOVE', ah4s_patricias_TRAVERSEu_u_TRANSFORM)).
fof(13, axiom,![X12]:![X1]:![X5]:![X13]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X1),X5))))=>p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X12),h4s_patricias_transform(s(t_fun(X1,X12),X13),s(t_h4s_patricias_ptree(X1),X5))))))),file('i/f/patricia/PERM__REMOVE', ah4s_patricias_TRANSFORMu_u_ISu_u_PTREE)).
fof(14, axiom,![X12]:![X1]:![X5]:![X3]:![X13]:s(t_h4s_patricias_ptree(X12),h4s_patricias_transform(s(t_fun(X1,X12),X13),s(t_h4s_patricias_ptree(X1),h4s_patricias_remove(s(t_h4s_patricias_ptree(X1),X5),s(t_h4s_nums_num,X3)))))=s(t_h4s_patricias_ptree(X12),h4s_patricias_remove(s(t_h4s_patricias_ptree(X12),h4s_patricias_transform(s(t_fun(X1,X12),X13),s(t_h4s_patricias_ptree(X1),X5))),s(t_h4s_nums_num,X3))),file('i/f/patricia/PERM__REMOVE', ah4s_patricias_REMOVEu_u_TRANSFORM)).
# SZS output end CNFRefutation
