# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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__upper', ch4s_numpairs_invtriu_u_upper)).
fof(10, axiom,![X1]:![X13]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X1))),file('i/f/numpair/invtri__upper', ah4s_arithmetics_LESSu_u_EQ)).
fof(11, axiom,![X1]:![X13]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),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,X13))))),file('i/f/numpair/invtri__upper', ah4s_arithmetics_NOTu_u_LESS)).
fof(12, axiom,![X1]:![X14]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14)))))))))),file('i/f/numpair/invtri__upper', ah4s_numpairs_SNDu_u_invtri0)).
fof(13, 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__upper', ah4s_numpairs_triu_u_defu_c0)).
fof(14, 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__upper', ah4s_numpairs_triu_u_defu_c1)).
fof(15, axiom,![X1]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14))))))),s(t_h4s_nums_num,h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14)))))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X14))))),file('i/f/numpair/invtri__upper', ah4s_numpairs_invtri0u_u_thm)).
fof(16, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X13),file('i/f/numpair/invtri__upper', ah4s_arithmetics_ADDu_u_0)).
fof(17, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X13),file('i/f/numpair/invtri__upper', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(18, axiom,![X1]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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,X13))),file('i/f/numpair/invtri__upper', ah4s_arithmetics_ADDu_u_SYM)).
fof(20, axiom,![X15]:![X1]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X15)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X15))),file('i/f/numpair/invtri__upper', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(21, axiom,![X15]:![X1]:![X13]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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__upper', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(22, axiom,![X13]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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__upper', ah4s_arithmetics_ADD1)).
fof(23, axiom,![X1]: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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1))),file('i/f/numpair/invtri__upper', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(26, axiom,![X1]:s(t_h4s_nums_num,h4s_numpairs_invtri(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_numpairs_invtri0(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/numpair/invtri__upper', ah4s_numpairs_invtriu_u_def)).
# SZS output end CNFRefutation
