# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,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,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_bool,t),file('i/f/integer/INT__LE__REDUCE_c0', ch4s_integers_INTu_u_LEu_u_REDUCEu_c0)).
fof(20, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/integer/INT__LE__REDUCE_c0', aHLu_BOOLu_CASES)).
fof(29, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LE__REDUCE_c0', aHLu_FALSITY)).
fof(35, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(42, axiom,![X14]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(46, axiom,![X14]:![X15]:(~(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,X14))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X14))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,X15)))))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(47, axiom,![X7]:![X5]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X7))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X7))))|s(t_h4s_integers_int,X5)=s(t_h4s_integers_int,X7))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_integers_INTu_u_LEu_u_CALCULATE)).
fof(61, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(64, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_numerals_numeralu_u_distribu_c27)).
fof(65, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,X5),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(77, axiom,![X14]:![X15]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X14))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_arithmetics_LESSu_u_EQ)).
fof(78, axiom,![X14]:![X15]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))))),file('i/f/integer/INT__LE__REDUCE_c0', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
