# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))=>![X3]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X3)))=s(t_bool,h4s_arithmetics_u_3cu_3d(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,X3)))))),file('i/f/arithmetic/SUB__LESS__EQ__ADD', ch4s_arithmetics_SUBu_u_LESSu_u_EQu_u_ADD)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__LESS__EQ__ADD', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__LESS__EQ__ADD', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/arithmetic/SUB__LESS__EQ__ADD', aHLu_BOOLu_CASES)).
fof(6, axiom,![X3]:![X2]:(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_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X3))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X3))),file('i/f/arithmetic/SUB__LESS__EQ__ADD', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(7, axiom,![X3]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X3),s(t_h4s_nums_num,X2))),file('i/f/arithmetic/SUB__LESS__EQ__ADD', ah4s_arithmetics_ADDu_u_SYM)).
fof(8, axiom,![X1]:![X3]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X3)))=s(t_h4s_nums_num,X1)<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3))))),file('i/f/arithmetic/SUB__LESS__EQ__ADD', ah4s_arithmetics_ADDu_u_EQu_u_SUB)).
fof(9, axiom,![X8]:![X9]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9))))=>![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,X10)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/SUB__LESS__EQ__ADD', ah4s_arithmetics_LESSu_u_EQu_u_SUBu_u_LESS)).
# SZS output end CNFRefutation
