# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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),X1)))))=>p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_unionu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))))),file('i/f/patricia/UNION__PTREE__IS__PTREE', ch4s_patricias_UNIONu_u_PTREEu_u_ISu_u_PTREE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/patricia/UNION__PTREE__IS__PTREE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/patricia/UNION__PTREE__IS__PTREE', aHLu_FALSITY)).
fof(5, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/patricia/UNION__PTREE__IS__PTREE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(47, axiom,![X3]:![X17]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X3))))=>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),X3),s(t_fun(t_h4s_nums_num,t_bool),X17))))))),file('i/f/patricia/UNION__PTREE__IS__PTREE', ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_ISu_u_PTREE)).
fof(59, axiom,![X1]:![X2]:s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_unionu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X2),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1)))=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),X2),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/UNION__PTREE__IS__PTREE', ah4s_patricias_UNIONu_u_PTREEu_u_def)).
fof(62, axiom,![X3]: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),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),X3))))),file('i/f/patricia/UNION__PTREE__IS__PTREE', ah4s_patricias_NUMSETu_u_OFu_u_PTREEu_u_def)).
fof(63, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/patricia/UNION__PTREE__IS__PTREE', aHLu_BOOLu_CASES)).
fof(66, axiom,~(s(t_bool,t)=s(t_bool,f)),file('i/f/patricia/UNION__PTREE__IS__PTREE', ah4s_bools_BOOLu_u_EQu_u_DISTINCTu_c0)).
# SZS output end CNFRefutation
