# 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),X1))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1)))=s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,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),X1)))))),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', ch4s_patricias_INu_u_PTREEu_u_OFu_u_NUMSETu_u_EMPTY)).
fof(8, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(34, axiom,![X15]:![X1]:![X2]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X15))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X1)))))=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,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),X15),s(t_fun(t_h4s_nums_num,t_bool),X1))))))<=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X2),s(t_h4s_patricias_ptree(t_h4s_ones_one),X15))))|p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))))))),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_INu_u_PTREEu_u_OFu_u_NUMSET)).
fof(36, axiom,![X2]:~(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X2),s(t_h4s_patricias_ptree(t_h4s_ones_one),h4s_patricias_empty))))),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_INu_u_PTREEu_u_EMPTY)).
fof(41, axiom,~(p(s(t_bool,f))),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', aHLu_FALSITY)).
fof(43, axiom,![X15]:((p(s(t_bool,X15))=>p(s(t_bool,f)))<=>s(t_bool,X15)=s(t_bool,f)),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(58, axiom,![X8]:p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(X8),h4s_patricias_empty)))),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', ah4s_patricias_EMPTYu_u_ISu_u_PTREE)).
fof(81, axiom,![X15]:(s(t_bool,X15)=s(t_bool,t)|s(t_bool,X15)=s(t_bool,f)),file('i/f/patricia/IN__PTREE__OF__NUMSET__EMPTY', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
