# 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),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_inu_u_ptree(s(t_h4s_nums_num,X3),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))))))<=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X2))))|p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X1))))))),file('i/f/patricia/IN__PTREE__UNION__PTREE', ch4s_patricias_INu_u_PTREEu_u_UNIONu_u_PTREE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/patricia/IN__PTREE__UNION__PTREE', aHLu_TRUTH)).
fof(6, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/patricia/IN__PTREE__UNION__PTREE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X4]:![X3]:(p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X4))))=>s(t_bool,h4s_bools_in(s(t_h4s_nums_num,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),X4)))))=s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X4)))),file('i/f/patricia/IN__PTREE__UNION__PTREE', ah4s_patricias_INu_u_NUMSETu_u_OFu_u_PTREE)).
fof(11, axiom,![X4]:![X11]:![X3]:((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(t_h4s_ones_one),X4))))&p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X11)))))=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,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),X4),s(t_fun(t_h4s_nums_num,t_bool),X11))))))<=>(p(s(t_bool,h4s_patricias_inu_u_ptree(s(t_h4s_nums_num,X3),s(t_h4s_patricias_ptree(t_h4s_ones_one),X4))))|p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X3),s(t_fun(t_h4s_nums_num,t_bool),X11))))))),file('i/f/patricia/IN__PTREE__UNION__PTREE', ah4s_patricias_INu_u_PTREEu_u_OFu_u_NUMSET)).
fof(12, 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/IN__PTREE__UNION__PTREE', ah4s_patricias_UNIONu_u_PTREEu_u_def)).
fof(13, axiom,![X4]:p(s(t_bool,h4s_predu_u_sets_finite(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),X4)))))),file('i/f/patricia/IN__PTREE__UNION__PTREE', ah4s_patricias_FINITEu_u_NUMSETu_u_OFu_u_PTREE)).
fof(14, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/patricia/IN__PTREE__UNION__PTREE', aHLu_BOOLu_CASES)).
fof(16, axiom,~(p(s(t_bool,f))),file('i/f/patricia/IN__PTREE__UNION__PTREE', aHLu_FALSITY)).
# SZS output end CNFRefutation
