# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/numpair/tri__LT', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/numpair/tri__LT', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/numpair/tri__LT', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X8))))))),file('i/f/numpair/tri__LT', ah4s_numpairs_triu_u_LTu_u_I)).
fof(18, axiom,![X13]:![X14]:((p(s(t_bool,X14))=>p(s(t_bool,X13)))=>((p(s(t_bool,X13))=>p(s(t_bool,X14)))=>s(t_bool,X14)=s(t_bool,X13))),file('i/f/numpair/tri__LT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/numpair/tri__LT', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(22, axiom,![X1]:(s(t_bool,t)=s(t_bool,X1)<=>p(s(t_bool,X1))),file('i/f/numpair/tri__LT', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(59, axiom,![X7]:![X8]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X7))),file('i/f/numpair/tri__LT', ah4s_arithmetics_LESSu_u_EQ)).
fof(63, axiom,![X7]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numpair/tri__LT', ah4s_numerals_numeralu_u_lteu_c2)).
fof(64, axiom,![X7]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X7))))),file('i/f/numpair/tri__LT', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(75, axiom,![X7]:![X8]:(~(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X7))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X8)))))),file('i/f/numpair/tri__LT', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(87, axiom,![X7]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))))))<=>(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))),file('i/f/numpair/tri__LT', ah4s_primu_u_recs_LESSu_u_THM)).
fof(110, axiom,![X7]:![X8]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))))),file('i/f/numpair/tri__LT', ah4s_arithmetics_NOTu_u_LESSu_u_EQUAL)).
fof(113, axiom,![X7]:![X8]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))),file('i/f/numpair/tri__LT', ah4s_arithmetics_LESSu_u_EQu_u_MONO)).
fof(133, conjecture,![X7]:![X8]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_numpairs_tri(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))),file('i/f/numpair/tri__LT', ch4s_numpairs_triu_u_LT)).
# SZS output end CNFRefutation
