# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X1)<=>(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ch4s_arithmetics_SUBu_u_RIGHTu_u_EQ)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, axiom,![X1]:![X2]:![X3]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))<=>(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X2)|(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_nums_0))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_u_LEFTu_u_EQ)).
fof(14, axiom,![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(15, axiom,![X3]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X3)))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(16, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(17, axiom,![X2]:![X3]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3)),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_EQUALu_u_ANTISYM)).
fof(18, axiom,![X2]:![X3]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),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,X3))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_NOTu_u_LESS)).
fof(19, axiom,![X2]:![X3]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(20, axiom,![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(21, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),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,X3),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ)).
fof(22, axiom,![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X3)),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_u_ADD)).
fof(24, axiom,![X2]:![X3]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X3),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,X3)))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(27, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X3),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_EQu_u_MONOu_u_ADDu_u_EQ)).
fof(34, axiom,![X2]:![X3]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_u_LESSu_u_EQ)).
fof(36, axiom,![X2]:![X3]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),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,X3))),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_EQ)).
fof(40, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,X3),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(42, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(47, axiom,![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_c0)).
fof(49, axiom,![X2]:![X3]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X3)<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_ADDu_u_INVu_u_0u_u_EQ)).
fof(50, axiom,![X2]:~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_nums_NOTu_u_SUC)).
fof(52, axiom,![X3]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_numu_u_CASES)).
fof(53, axiom,![X2]:![X3]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X3)<=>(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_SUBu_u_EQu_u_EQu_u_0)).
fof(56, axiom,![X3]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,X3)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_LESSu_u_0u_u_CASES)).
fof(57, axiom,![X2]:![X3]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_ADDu_u_SYM)).
fof(58, axiom,![X15]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,X14),file('i/f/arithmetic/SUB__RIGHT__EQ', ah4s_arithmetics_ADDu_u_SUB)).
# SZS output end CNFRefutation
