# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))))))))),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__LT__REDUCE_c5', ch4s_integers_INTu_u_LTu_u_REDUCEu_c5)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integer/INT__LT__REDUCE_c5', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LT__REDUCE_c5', aHLu_FALSITY)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/integer/INT__LT__REDUCE_c5', aHLu_BOOLu_CASES)).
fof(17, axiom,![X2]:(s(t_bool,t)=s(t_bool,X2)<=>p(s(t_bool,X2))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(19, axiom,![X2]:(s(t_bool,f)=s(t_bool,X2)<=>~(p(s(t_bool,X2)))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(25, 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/INT__LT__REDUCE_c5', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(26, axiom,![X1]:![X12]:(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,X1)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),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,X12)))))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(28, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_numerals_numeralu_u_distribu_c27)).
fof(32, axiom,![X1]:![X12]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12))))))<=>(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c2)).
fof(34, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_BIT10)).
fof(36, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_ONE)).
fof(37, axiom,![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(39, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X4),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(40, axiom,![X1]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X12))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_ADDu_u_SYM)).
fof(41, axiom,![X11]:![X1]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X11))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(45, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(48, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_TIMES2)).
fof(50, axiom,![X1]:![X12]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X1)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_LESSu_u_EQ)).
fof(51, axiom,![X1]:![X12]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),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,X12))))),file('i/f/integer/INT__LT__REDUCE_c5', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
