# 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,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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(37, axiom,![X18]:![X2]:![X10]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),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,X18)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X18))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(38, axiom,![X2]:![X10]:(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,X2)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),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,X10)))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(39, axiom,![X2]:![X10]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X10))),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,X10))),s(t_h4s_nums_num,X2))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_LESSu_u_EQ)).
fof(40, axiom,![X2]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,X2))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(42, axiom,![X2]:![X10]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),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,X10))))),file('i/f/numpair/invtri__unique', ah4s_arithmetics_NOTu_u_LEQ)).
fof(44, axiom,![X10]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),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_arithmetics_ADD1)).
fof(48, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/numpair/invtri__unique', ah4s_numerals_numeralu_u_sucu_c0)).
fof(55, axiom,![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,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(56, 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(58, axiom,~(p(s(t_bool,f))),file('i/f/numpair/invtri__unique', aHLu_FALSITY)).
fof(59, axiom,![X9]:((p(s(t_bool,X9))=>p(s(t_bool,f)))<=>s(t_bool,X9)=s(t_bool,f)),file('i/f/numpair/invtri__unique', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(77, axiom,![X2]:![X10]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X10))),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,X10),s(t_h4s_nums_num,X2))),file('i/f/numpair/invtri__unique', ah4s_numpairs_triu_u_LE)).
# SZS output end CNFRefutation
