# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(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,X1))),s(t_h4s_integers_int,X2))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,X2))))))),file('i/f/integer/LE__NUM__OF__INT', ch4s_integers_LEu_u_NUMu_u_OFu_u_INT)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/integer/LE__NUM__OF__INT', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(37, axiom,![X1]:![X28]: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,X28))),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,X28),s(t_h4s_nums_num,X1))),file('i/f/integer/LE__NUM__OF__INT', ah4s_integers_INTu_u_LE)).
fof(38, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/integer/LE__NUM__OF__INT', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(50, axiom,![X1]:s(t_h4s_nums_num,h4s_integers_num(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,X1),file('i/f/integer/LE__NUM__OF__INT', ah4s_integers_NUMu_u_OFu_u_INT)).
fof(53, axiom,![X2]:(p(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,h4s_nums_0))),s(t_h4s_integers_int,X2))))=>?[X1]:s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))),file('i/f/integer/LE__NUM__OF__INT', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(55, axiom,![X21]:![X18]:![X15]:((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X18))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,X21)))))=>p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X21))))),file('i/f/integer/LE__NUM__OF__INT', ah4s_integers_INTu_u_LEu_u_TRANS)).
fof(77, axiom,~(p(s(t_bool,f))),file('i/f/integer/LE__NUM__OF__INT', aHLu_FALSITY)).
fof(78, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/integer/LE__NUM__OF__INT', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
