# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_arithmetics_u_2b(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)))))))))))))=>s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X1)),file('i/f/numpair/invtri__unique', ch4s_numpairs_invtriu_u_unique)).
fof(2, 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__unique', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, axiom,![X13]:![X2]:![X14]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(15, axiom,![X2]: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,X2))))),s(t_h4s_nums_num,X2)))),file('i/f/numpair/invtri__unique', ah4s_numpairs_invtriu_u_lower)).
fof(16, axiom,![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),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,X2))),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__unique', ah4s_numpairs_invtriu_u_upper)).
fof(17, axiom,![X2]:![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X2))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_LESSu_u_EQ)).
fof(18, axiom,![X2]:![X14]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X14))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_NOTu_u_LESS)).
fof(19, axiom,![X2]:![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2))),file('i/f/numpair/invtri__unique', ah4s_numpairs_triu_u_LE)).
fof(20, axiom,![X2]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X14))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_ADDu_u_SYM)).
fof(21, axiom,![X13]:![X2]:![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(22, axiom,![X2]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X2))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(24, axiom,![X2]:![X14]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X14))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_NOTu_u_LEQ)).
fof(25, axiom,![X2]:![X14]:(~(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X2))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X2))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X14)))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(26, axiom,~(p(s(t_bool,f))),file('i/f/numpair/invtri__unique', aHLu_FALSITY)).
fof(30, axiom,![X6]:((p(s(t_bool,X6))=>p(s(t_bool,f)))<=>s(t_bool,X6)=s(t_bool,f)),file('i/f/numpair/invtri__unique', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
# SZS output end CNFRefutation
