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In this work we show that non-deterministic time NTIME(n) is not contained in deterministic time \math and poly-logarithmic space, for any \math. This implies that (infinitely often) satisfiability cannot be solved in time \math and poly-logarithmic space. A similar result is presented for uniform circuits; a log-space uniform circuit of poly-logarithmic width computing satisfiability requires infinitely often almost quadratic size.