# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT', ch4s_integers_INTu_u_LT)).
fof(3, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/integer/INT__LT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(15, 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/integer/INT__LT', ah4s_arithmetics_NOTu_u_LESS)).
fof(17, axiom,![X4]:![X5]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4))))=>~(s(t_h4s_integers_int,X5)=s(t_h4s_integers_int,X4))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LTu_u_IMPu_u_NE)).
fof(19, axiom,![X4]:![X5]:(s(t_h4s_integers_int,X5)=s(t_h4s_integers_int,X4)|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4))))|p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X5)))))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(20, axiom,![X5]:~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X5))))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LTu_u_REFL)).
fof(33, axiom,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LE)).
fof(35, axiom,![X4]:![X5]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X5)))))),file('i/f/integer/INT__LT', ah4s_integers_intu_u_le0)).
fof(37, axiom,![X5]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X5)))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(38, axiom,![X4]:![X5]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4))))|s(t_h4s_integers_int,X5)=s(t_h4s_integers_int,X4))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LEu_u_LT)).
fof(39, axiom,![X4]:![X5]:~((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X5)))))),file('i/f/integer/INT__LT', ah4s_integers_INTu_u_LETu_u_ANTISYM)).
# SZS output end CNFRefutation
