# 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),X2))))=>(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X1),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),h4s_patricias_insertu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))))))))))<=>(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,X3)|(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,X3))&p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X1),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),X2)))))))))))),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ch4s_patricias_MEMu_u_TRAVERSEu_u_INSERTu_u_PTREE)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', aHLu_FALSITY)).
fof(16, axiom,![X2]:(s(t_bool,t0)=s(t_bool,X2)<=>p(s(t_bool,X2))),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(20, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)|s(t_bool,X2)=s(t_bool,f)),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', aHLu_BOOLu_CASES)).
fof(22, axiom,![X6]:![X2]:![X11]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X6),X2))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X11),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(X6),X2)))))))=s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X6),h4s_patricias_peek(s(t_h4s_patricias_ptree(X6),X2),s(t_h4s_nums_num,X11)))))),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_patricias_MEMu_u_TRAVERSEu_u_PEEK)).
fof(23, axiom,![X1]:![X2]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))))=>p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_insertu_u_ptree(s(t_h4s_nums_num,X1),s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))))))),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_patricias_INSERTu_u_PTREEu_u_ISu_u_PTREE)).
fof(24, axiom,![X2]:![X11]:![X12]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))))=>?[X13]:((p(s(t_bool,X13))<=>s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,X12))&s(t_h4s_options_option(t_h4s_ones_one),h4s_patricias_peek(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_insertu_u_ptree(s(t_h4s_nums_num,X11),s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))),s(t_h4s_nums_num,X12)))=s(t_h4s_options_option(t_h4s_ones_one),h4s_bools_cond(s(t_bool,X13),s(t_h4s_options_option(t_h4s_ones_one),h4s_options_some(s(t_h4s_ones_one,h4s_ones_one0))),s(t_h4s_options_option(t_h4s_ones_one),h4s_patricias_peek(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2),s(t_h4s_nums_num,X12))))))),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_patricias_PEEKu_u_INSERTu_u_PTREE)).
fof(26, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,t0),s(X6,X5),s(X6,X4)))=s(X6,X5),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(27, axiom,![X6]:![X4]:![X5]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X5),s(X6,X4)))=s(X6,X4),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(28, axiom,![X6]:![X1]:s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(X6),h4s_options_some(s(X6,X1)))))=s(t_bool,t0),file('i/f/patricia/MEM__TRAVERSE__INSERT__PTREE', ah4s_options_ISu_u_SOMEu_u_DEFu_c0)).
# SZS output end CNFRefutation
