# 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))))=>?[X4]:((p(s(t_bool,X4))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3))&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,X2),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))),s(t_h4s_nums_num,X3)))=s(t_h4s_options_option(t_h4s_ones_one),h4s_bools_cond(s(t_bool,X4),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),X1),s(t_h4s_nums_num,X3))))))),file('i/f/patricia/PEEK__INSERT__PTREE', ch4s_patricias_PEEKu_u_INSERTu_u_PTREE)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/patricia/PEEK__INSERT__PTREE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/patricia/PEEK__INSERT__PTREE', aHLu_FALSITY)).
fof(4, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t0)|s(t_bool,X1)=s(t_bool,f)),file('i/f/patricia/PEEK__INSERT__PTREE', aHLu_BOOLu_CASES)).
fof(5, axiom,![X4]:s(t_h4s_ones_one,X4)=s(t_h4s_ones_one,h4s_ones_one0),file('i/f/patricia/PEEK__INSERT__PTREE', ah4s_ones_one1)).
fof(6, axiom,![X5]:![X1]:![X2]:![X3]:![X6]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X5),X1))))=>?[X4]:((p(s(t_bool,X4))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3))&s(t_h4s_options_option(X5),h4s_patricias_peek(s(t_h4s_patricias_ptree(X5),h4s_patricias_add(s(t_h4s_patricias_ptree(X5),X1),s(t_h4s_pairs_prod(t_h4s_nums_num,X5),h4s_pairs_u_2c(s(t_h4s_nums_num,X2),s(X5,X6))))),s(t_h4s_nums_num,X3)))=s(t_h4s_options_option(X5),h4s_bools_cond(s(t_bool,X4),s(t_h4s_options_option(X5),h4s_options_some(s(X5,X6))),s(t_h4s_options_option(X5),h4s_patricias_peek(s(t_h4s_patricias_ptree(X5),X1),s(t_h4s_nums_num,X3))))))),file('i/f/patricia/PEEK__INSERT__PTREE', ah4s_patricias_PEEKu_u_ADD)).
fof(7, axiom,![X4]:![X1]:![X7]:s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_add(s(t_h4s_patricias_ptree(t_h4s_ones_one),X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_ones_one),h4s_pairs_u_2c(s(t_h4s_nums_num,X7),s(t_h4s_ones_one,X4)))))=s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_insertu_u_ptree(s(t_h4s_nums_num,X7),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))),file('i/f/patricia/PEEK__INSERT__PTREE', ah4s_patricias_ADDu_u_INSERT)).
# SZS output end CNFRefutation
