# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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,X1))))),s(t_h4s_nums_num,X1)))),file('i/f/numpair/invtri__lower', ch4s_numpairs_invtriu_u_lower)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/numpair/invtri__lower', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/numpair/invtri__lower', aHLu_FALSITY)).
fof(10, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/numpair/invtri__lower', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/numpair/invtri__lower', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(17, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/numpair/invtri__lower', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(18, axiom,![X1]:![X14]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,X1)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),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,X14)))))),file('i/f/numpair/invtri__lower', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(20, axiom,![X1]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),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,X14))),file('i/f/numpair/invtri__lower', ah4s_arithmetics_ADDu_u_SYM)).
fof(22, axiom,![X13]:![X1]:![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))=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__lower', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(23, axiom,![X1]:![X14]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X14))))),file('i/f/numpair/invtri__lower', ah4s_arithmetics_NOTu_u_LEQ)).
fof(24, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/numpair/invtri__lower', ah4s_numerals_numeralu_u_distribu_c27)).
fof(26, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X14),file('i/f/numpair/invtri__lower', ah4s_arithmetics_ADDu_u_0)).
fof(28, 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__lower', ah4s_numpairs_triu_u_defu_c0)).
fof(29, axiom,![X1]:![X15]: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,X15))))))),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,X15)))))))=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,X15))))),file('i/f/numpair/invtri__lower', ah4s_numpairs_invtri0u_u_thm)).
fof(30, 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__lower', ah4s_numpairs_invtriu_u_def)).
fof(31, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/numpair/invtri__lower', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
