# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))),file('i/f/numpair/invtri__le', ch4s_numpairs_invtriu_u_le)).
fof(14, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/numpair/invtri__le', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, axiom,![X15]:![X1]:![X17]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X15)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X15))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(26, axiom,![X15]:![X1]:![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X15)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X15))),file('i/f/numpair/invtri__le', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(27, axiom,![X1]:![X17]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X1)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17)))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(28, axiom,![X1]:![X17]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X1)))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(30, axiom,![X15]:![X1]:![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X17)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X15))),file('i/f/numpair/invtri__le', ah4s_arithmetics_LEu_u_ADDu_u_RCANCEL)).
fof(31, axiom,![X17]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X17)))),file('i/f/numpair/invtri__le', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(32, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,X1))))),s(t_h4s_nums_num,X1)))),file('i/f/numpair/invtri__le', ah4s_numpairs_invtriu_u_lower)).
fof(33, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,X1))),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/numpair/invtri__le', ah4s_numpairs_invtriu_u_upper)).
fof(36, axiom,![X1]:s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,X1),file('i/f/numpair/invtri__le', ah4s_numpairs_invtriu_u_linverse)).
fof(37, axiom,![X1]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))),file('i/f/numpair/invtri__le', ah4s_arithmetics_ADDu_u_SYM)).
fof(40, axiom,s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numpair/invtri__le', ah4s_numpairs_triu_u_defu_c0)).
fof(41, axiom,![X1]:s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1))))),file('i/f/numpair/invtri__le', ah4s_numpairs_triu_u_defu_c1)).
fof(42, axiom,![X1]:![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))),file('i/f/numpair/invtri__le', ah4s_numpairs_triu_u_LE)).
fof(43, axiom,![X1]:![X17]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X17)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))),file('i/f/numpair/invtri__le', ah4s_numpairs_triu_u_LT)).
fof(44, axiom,![X1]:![X17]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_NOTu_u_LESS)).
fof(50, axiom,![X1]:![X17]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(51, axiom,![X1]:![X17]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_LESSu_u_IMPu_u_LESSu_u_ORu_u_EQ)).
fof(54, axiom,![X1]:![X17]:~((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17)))))),file('i/f/numpair/invtri__le', ah4s_arithmetics_LESSu_u_ANTISYM)).
fof(59, 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/numpair/invtri__le', ah4s_arithmetics_ADD1)).
fof(61, axiom,![X11]:![X7]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X11)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),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/numpair/invtri__le', ah4s_arithmetics_LEu_u_LT1)).
# SZS output end CNFRefutation
