# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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__LT', ch4s_numpairs_triu_u_LT)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/numpair/tri__LT', aHLu_FALSITY)).
fof(3, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/numpair/tri__LT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X5]:((p(s(t_bool,X5))=>p(s(t_bool,f)))<=>s(t_bool,X5)=s(t_bool,f)),file('i/f/numpair/tri__LT', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(28, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))))),file('i/f/numpair/tri__LT', ah4s_primu_u_recs_LESSu_u_REFL)).
fof(29, axiom,![X16]:![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_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X16)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X16))))),file('i/f/numpair/tri__LT', ah4s_arithmetics_LESSu_u_TRANS)).
fof(30, 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__LT', ah4s_arithmetics_NOTu_u_LESS)).
fof(31, axiom,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))=>p(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))))))),file('i/f/numpair/tri__LT', ah4s_numpairs_triu_u_LTu_u_I)).
fof(34, axiom,![X16]:![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_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X16)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X16))))),file('i/f/numpair/tri__LT', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(38, 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__LT', ah4s_numerals_numeralu_u_lteu_c1)).
fof(39, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/numpair/tri__LT', aHLu_BOOLu_CASES)).
fof(41, axiom,![X1]:![X2]:(~(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,h4s_nums_suc(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,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2)))))),file('i/f/numpair/tri__LT', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(44, axiom,p(s(t_bool,t)),file('i/f/numpair/tri__LT', aHLu_TRUTH)).
fof(48, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/numpair/tri__LT', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
