# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X2))),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,X2),s(t_h4s_nums_num,X1))),file('i/f/numpair/tri__LE', ch4s_numpairs_triu_u_LE)).
fof(4, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numpair/tri__LE', ah4s_numerals_numeralu_u_lteu_c1)).
fof(5, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),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,X2))))),file('i/f/numpair/tri__LE', ah4s_arithmetics_NOTu_u_LESS)).
fof(9, axiom,![X1]:![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),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,X2))),s(t_h4s_nums_num,X1))),file('i/f/numpair/tri__LE', ah4s_arithmetics_LESSu_u_EQ)).
fof(16, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),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,X2))))),file('i/f/numpair/tri__LE', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(18, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/numpair/tri__LE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(46, axiom,![X1]:![X2]: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,X2)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/numpair/tri__LE', ah4s_numpairs_triu_u_LT)).
fof(57, axiom,~(p(s(t_bool,f))),file('i/f/numpair/tri__LE', aHLu_FALSITY)).
fof(58, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/numpair/tri__LE', aHLu_BOOLu_CASES)).
fof(59, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/numpair/tri__LE', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(61, axiom,![X9]:(s(t_bool,f)=s(t_bool,X9)<=>~(p(s(t_bool,X9)))),file('i/f/numpair/tri__LE', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
