# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X1)))=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_c0', ch4s_numpairs_triu_u_equ_u_0u_c0)).
fof(5, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),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,X5))),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_ADDu_u_SYM)).
fof(30, axiom,![X1]:![X5]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X5)<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_ADDu_u_INVu_u_0u_u_EQ)).
fof(33, 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_c0', ah4s_numpairs_triu_u_defu_c0)).
fof(43, axiom,![X1]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_SUCu_u_NOT)).
fof(44, axiom,![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_SUBu_u_EQUALu_u_0)).
fof(52, axiom,![X5]:(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_numu_u_CASES)).
fof(64, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),file('i/f/numpair/tri__eq__0_c0', ah4s_numerals_numeralu_u_addu_c6)).
fof(66, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))))),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(68, 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_c0', ah4s_numpairs_triu_u_defu_c1)).
fof(73, axiom,![X19]:![X20]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,X20),file('i/f/numpair/tri__eq__0_c0', ah4s_arithmetics_ADDu_u_SUB)).
# SZS output end CNFRefutation
