# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', aHLu_FALSITY)).
fof(5, axiom,![X7]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X7]:![X10]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7))))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(15, axiom,![X7]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7))))|s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,X7))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(16, axiom,![X7]:![X10]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X10))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_ADDu_u_SYM)).
fof(22, axiom,![X7]:![X10]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X10))))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_NOTu_u_LESS)).
fof(28, axiom,![X19]:![X15]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X15))))=>![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X14)))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X14)))))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_LESSu_u_EQu_u_SUBu_u_LESS)).
fof(31, axiom,![X14]:![X19]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X19))))=>![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X14)))))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_LESSu_u_EQu_u_ADDu_u_SUB)).
fof(37, axiom,![X14]:![X19]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X19))))=>![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X14)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X19)))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_SUBu_u_SUB)).
fof(59, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(66, axiom,![X7]:![X10]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X10)<=>(s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_nums_0)|s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_SUBu_u_EQu_u_EQu_u_0)).
fof(78, axiom,![X7]:![X10]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X10)<=>s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_ADDu_u_INVu_u_0u_u_EQ)).
fof(118, axiom,![X7]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7))))<=>?[X16]:s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X16)))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ah4s_arithmetics_LESSu_u_EQu_u_EXISTS)).
fof(133, conjecture,![X16]:![X7]:![X10]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X16))))))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X7))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,h4s_nums_0)))))),file('i/f/arithmetic/SUB__LEFT__LESS__EQ', ch4s_arithmetics_SUBu_u_LEFTu_u_LESSu_u_EQ)).
# SZS output end CNFRefutation
