# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numpair/tri__eq__0_c1', ch4s_numpairs_triu_u_equ_u_0u_c1)).
fof(14, axiom,![X1]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numpair/tri__eq__0_c1', ah4s_nums_NOTu_u_SUC)).
fof(15, axiom,![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/numpair/tri__eq__0_c1', ah4s_arithmetics_numu_u_CASES)).
fof(16, axiom,![X1]:![X8]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numpair/tri__eq__0_c1', ah4s_arithmetics_ADDu_u_EQu_u_0)).
fof(17, 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/tri__eq__0_c1', ah4s_numpairs_triu_u_defu_c0)).
fof(18, 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/tri__eq__0_c1', ah4s_numpairs_triu_u_defu_c1)).
# SZS output end CNFRefutation
