# 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_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(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,f),file('i/f/integer/INT__LT__REDUCE_c4', ch4s_integers_INTu_u_LTu_u_REDUCEu_c4)).
fof(28, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LT__REDUCE_c4', aHLu_FALSITY)).
fof(29, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/integer/INT__LT__REDUCE_c4', aHLu_BOOLu_CASES)).
fof(31, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_bools_NOTu_u_CLAUSESu_c2)).
fof(39, axiom,![X1]:![X9]: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,X1))),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,X9)))))))=s(t_bool,f),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c3)).
fof(40, axiom,![X8]:(s(t_bool,f)=s(t_bool,X8)<=>~(p(s(t_bool,X8)))),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(54, axiom,![X1]:![X9]: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,X9))),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,X9),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_integers_INTu_u_LT)).
fof(64, axiom,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_nums_0)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_integers_INTu_u_NEGu_u_0)).
fof(75, axiom,![X9]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(79, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_arithmetics_ALTu_u_ZERO)).
fof(80, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/integer/INT__LT__REDUCE_c4', ah4s_arithmetics_NUMERALu_u_DEF)).
# SZS output end CNFRefutation
