# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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,X2)<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/SUB__EQ__EQ__0', ch4s_arithmetics_SUBu_u_EQu_u_EQu_u_0)).
fof(15, axiom,![X1]:![X2]:(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_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__EQ__EQ__0', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(16, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(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__EQ__EQ__0', ah4s_arithmetics_SUBu_c0)).
fof(18, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X2),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_SUBu_u_0u_c1)).
fof(27, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X2)=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_ADDu_u_INVu_u_0)).
fof(28, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_ADDu_u_EQu_u_0)).
fof(43, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X1),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_ADDu_u_SYM)).
fof(59, axiom,![X17]:![X18]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X18))),s(t_h4s_nums_num,X17))),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_SUBu_u_PLUS)).
fof(61, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X1)))=s(t_h4s_nums_num,X2)),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_SUBu_u_ADD)).
fof(68, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__EQ__EQ__0', aHLu_TRUTH)).
fof(69, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__EQ__EQ__0', aHLu_FALSITY)).
fof(72, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(92, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/arithmetic/SUB__EQ__EQ__0', aHLu_BOOLu_CASES)).
fof(99, 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/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_NOTu_u_LESS)).
fof(100, axiom,![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_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/arithmetic/SUB__EQ__EQ__0', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
# SZS output end CNFRefutation
