# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X1),X2))))=>s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(X1),h4s_patricias_add(s(t_h4s_patricias_ptree(X1),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,X1),h4s_pairs_u_2c(s(t_h4s_nums_num,X3),s(X1,X4)))))))=s(t_h4s_nums_num,h4s_bools_cond(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),X2))))))),s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(X1),X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(X1),X2))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/patricia/SIZE__ADD', ch4s_patricias_SIZEu_u_ADD)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/patricia/SIZE__ADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(19, axiom,![X1]:![X5]:![X6]:s(X1,h4s_bools_cond(s(t_bool,t0),s(X1,X6),s(X1,X5)))=s(X1,X6),file('i/f/patricia/SIZE__ADD', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(20, axiom,![X1]:![X5]:![X6]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X6),s(X1,X5)))=s(X1,X5),file('i/f/patricia/SIZE__ADD', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(21, axiom,![X1]:![X10]:![X7]:![X11]:![X8]:![X15]:![X16]:((s(t_bool,X16)=s(t_bool,X15)&((p(s(t_bool,X15))=>s(X1,X8)=s(X1,X11))&(~(p(s(t_bool,X15)))=>s(X1,X7)=s(X1,X10))))=>s(X1,h4s_bools_cond(s(t_bool,X16),s(X1,X8),s(X1,X7)))=s(X1,h4s_bools_cond(s(t_bool,X15),s(X1,X11),s(X1,X10)))),file('i/f/patricia/SIZE__ADD', ah4s_bools_CONDu_u_CONG)).
fof(22, axiom,![X17]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/patricia/SIZE__ADD', ah4s_arithmetics_ADD1)).
fof(23, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_patricias_size(s(t_h4s_patricias_ptree(X1),X2)))=s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),X2))))),file('i/f/patricia/SIZE__ADD', ah4s_patricias_SIZEu_u_def)).
fof(24, axiom,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X1),X2))))&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),X2)))))))))=>s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),h4s_patricias_add(s(t_h4s_patricias_ptree(X1),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,X1),h4s_pairs_u_2c(s(t_h4s_nums_num,X3),s(X1,X4)))))))=s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),X2)))),file('i/f/patricia/SIZE__ADD', ah4s_patricias_PERMu_u_NOTu_u_ADD)).
fof(25, axiom,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X1),X2))))&~(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),X2))))))))))=>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_add(s(t_h4s_patricias_ptree(X1),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,X1),h4s_pairs_u_2c(s(t_h4s_nums_num,X3),s(X1,X4))))))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,X3),s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(X1),X2))))))))),file('i/f/patricia/SIZE__ADD', ah4s_patricias_PERMu_u_ADD)).
fof(26, axiom,p(s(t_bool,t0)),file('i/f/patricia/SIZE__ADD', aHLu_TRUTH)).
fof(32, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)<=>p(s(t_bool,X2))),file('i/f/patricia/SIZE__ADD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(33, axiom,~(p(s(t_bool,f))),file('i/f/patricia/SIZE__ADD', aHLu_FALSITY)).
fof(40, axiom,![X1]:![X2]:![X20]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X20),s(t_h4s_lists_list(X1),X2)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X2))))),file('i/f/patricia/SIZE__ADD', ah4s_lists_LENGTH0u_c1)).
fof(41, axiom,![X1]:![X21]:![X22]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X22),s(t_h4s_lists_list(X1),X21))))=>s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X22)))=s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X21)))),file('i/f/patricia/SIZE__ADD', ah4s_sortings_PERMu_u_LENGTH)).
# SZS output end CNFRefutation
