# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X2))))=>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),h4s_patricias_empty),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_delete(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X1)))))=s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_remove(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),h4s_patricias_empty),s(t_fun(t_h4s_nums_num,t_bool),X2))),s(t_h4s_nums_num,X1)))),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', ch4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_DELETE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', aHLu_BOOLu_CASES)).
fof(9, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X1]:![X3]:![X2]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X3))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X2)))))=>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),h4s_predu_u_sets_delete(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X1)))))=s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_bools_cond(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X1),s(t_h4s_patricias_ptree(t_h4s_ones_one),X3))),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),X2))),s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_remove(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),X2))),s(t_h4s_nums_num,X1)))))),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', ah4s_patricias_PTREEu_u_OFu_u_NUMSETu_u_DELETE0)).
fof(13, axiom,![X11]:~(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X11),s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty))))),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', ah4s_patricias_INu_u_PTREEu_u_EMPTY)).
fof(16, 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/PTREE__OF__NUMSET__DELETE', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(17, axiom,![X6]:p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X6),h4s_patricias_empty)))),file('i/f/patricia/PTREE__OF__NUMSET__DELETE', ah4s_patricias_EMPTYu_u_ISu_u_PTREE)).
# SZS output end CNFRefutation
