0.05/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.16 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.7ChiNIqLf6 0.16/0.37 % Computer : n005.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.16/0.37 % CPULimit : 960 0.16/0.37 % DateTime : Thu Jul 2 06:47:06 EDT 2020 0.16/0.37 % CPUTime : 0.16/0.37 % Running portfolio for 120 s 0.16/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.16/0.37 % Number of cores: 8 0.16/0.38 % Python version: Python 3.6.8 0.16/0.38 % Running in FO mode 5.30/5.51 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 5.30/5.51 % Solved by: fo/fo7.sh 5.30/5.51 To remain in the chosen logic fragment, unification with booleans has been disabled. 5.30/5.51 % done 35311 iterations in 4.975s 5.30/5.51 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 5.30/5.51 % SZS output start Refutation 5.30/5.51 tff(ax10, axiom, 5.30/5.51 (((e10 = op1(e10,op1(e10,e11))) | (op1(e13,op1(e13,e11)) = e13) | 5.30/5.51 (e12 = op1(e12,op1(e12,e11))) | (op1(e11,op1(e11,e11)) = e11)) & 5.30/5.51 ((op1(e11,op1(e11,e13)) = e11) | (op1(e13,op1(e13,e13)) = e13) | 5.30/5.51 (e12 = op1(e12,op1(e12,e13))) | (e10 = op1(e10,op1(e10,e13)))) & 5.30/5.51 (((op1(e10,e10) = e10) & (e10 = op1(e10,e10)) & (op1(e11,e11) != e10) & 5.30/5.51 (op1(e12,e12) != e10) & (e10 != op1(e13,e13)) & (e10 != op1(e10,e10))) | 5.30/5.51 ((e10 = op1(e10,e12)) & (op1(e13,e13) != e12) & (e12 != op1(e12,e12)) & 5.30/5.51 (e12 != op1(e11,e11)) & (op1(e10,e10) != e12) & (op1(e12,e10) = e10)) | 5.30/5.51 ((op1(e10,e13) = e10) & (e10 = op1(e13,e10)) & (e13 != op1(e11,e11)) & 5.30/5.51 (e13 != op1(e13,e13)) & (e13 != op1(e12,e12)) & (op1(e10,e10) != e13)) | 5.30/5.51 ((op1(e11,e11) != e12) & (e12 != op1(e13,e13)) & (op1(e12,e12) != e12) & 5.30/5.51 (e12 != op1(e10,e10)) & (e11 = op1(e12,e11)) & (e11 = op1(e11,e12))) | 5.30/5.51 ((e13 != op1(e11,e11)) & (op1(e12,e12) != e13) & (e13 != op1(e13,e13)) & 5.30/5.51 (e13 != op1(e10,e10)) & (e11 = op1(e13,e11)) & (op1(e11,e13) = e11)) | 5.30/5.51 ((op1(e12,e12) != e12) & (e12 != op1(e13,e13)) & (e12 != op1(e11,e11)) & 5.30/5.51 (e12 != op1(e10,e10)) & (op1(e12,e12) = e12) & (e12 = op1(e12,e12))) | 5.30/5.51 ((e12 != op1(e11,e11)) & (op1(e13,e13) != e12) & (e12 != op1(e12,e12)) & 5.30/5.51 (op1(e10,e10) != e12) & (e13 = op1(e12,e13)) & (e13 = op1(e13,e12))) | 5.30/5.51 ((op1(e10,e10) != e13) & (op1(e11,e11) != e13) & (op1(e13,e13) != e13) & 5.30/5.51 (op1(e12,e12) != e13) & (op1(e13,e13) = e13) & (op1(e13,e13) = e13)) | 5.30/5.51 ((op1(e13,e11) = e13) & (e13 = op1(e11,e13)) & (op1(e10,e10) != e11) & 5.30/5.51 (op1(e11,e11) != e11) & (e11 != op1(e13,e13)) & (e11 != op1(e12,e12))) | 5.30/5.51 ((op1(e13,e10) = e13) & (op1(e10,e13) = e13) & (op1(e11,e11) != e10) & 5.30/5.51 (e10 != op1(e12,e12)) & (e10 != op1(e13,e13)) & (e10 != op1(e10,e10))) | 5.30/5.51 ((e13 != op1(e10,e10)) & (op1(e12,e12) != e13) & (op1(e13,e13) != e13) & 5.30/5.51 (e13 != op1(e11,e11)) & (op1(e13,e12) = e12) & (e12 = op1(e12,e13))) | 5.30/5.51 ((op1(e10,e10) != e11) & (e11 != op1(e11,e11)) & (e11 != op1(e12,e12)) & 5.30/5.51 (op1(e13,e13) != e11) & (op1(e11,e12) = e12) & (op1(e12,e11) = e12)) | 5.30/5.51 ((op1(e12,e10) = e12) & (e10 != op1(e12,e12)) & (op1(e13,e13) != e10) & 5.30/5.51 (e10 != op1(e11,e11)) & (op1(e10,e10) != e10) & (op1(e10,e12) = e12)) | 5.30/5.51 ((e11 != op1(e11,e11)) & (op1(e13,e13) != e11) & (op1(e12,e12) != e11) & 5.30/5.51 (e11 != op1(e10,e10)) & (e11 = op1(e11,e11)) & (e11 = op1(e11,e11))) | 5.30/5.51 ((e11 = op1(e11,e10)) & (e11 = op1(e10,e11)) & (op1(e11,e11) != e10) & 5.30/5.51 (op1(e13,e13) != e10) & (op1(e12,e12) != e10) & (e10 != op1(e10,e10))) | 5.30/5.51 ((e10 = op1(e10,e11)) & (op1(e11,e10) = e10) & (op1(e13,e13) != e11) & 5.30/5.51 (e11 != op1(e12,e12)) & (op1(e11,e11) != e11) & (op1(e10,e10) != e11))) & 5.30/5.51 ((op1(e10,op1(e10,e12)) = e10) | (e11 = op1(e11,op1(e11,e12))) | 5.30/5.51 (e13 = op1(e13,op1(e13,e12))) | (op1(e12,op1(e12,e12)) = e12)) & 5.30/5.51 ((e10 = op1(e10,op1(e10,e10))) | (e11 = op1(e11,op1(e11,e10))) | 5.30/5.51 (op1(e12,op1(e12,e10)) = e12) | (op1(e13,op1(e13,e10)) = e13)))). 5.30/5.51 tff(zf_stmt_0, axiom, 5.30/5.51 (zip_tseitin_3 => 5.30/5.51 ((e11 = op1(e11,e12)) & (e11 = op1(e12,e11)) & (e12 != op1(e10,e10)) & 5.30/5.51 (op1(e12,e12) != e12) & (e12 != op1(e13,e13)) & (op1(e11,e11) != e12)))). 5.30/5.51 tff('0', plain, (e11 = op1(e12, e11) | ~ zip_tseitin_3), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_0])). 5.30/5.51 tff('1', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['0'])). 5.30/5.51 tff(zf_stmt_1, axiom, 5.30/5.51 (zip_tseitin_14 => 5.30/5.51 ((e10 != op1(e10,e10)) & (op1(e12,e12) != e10) & (op1(e13,e13) != e10) & 5.30/5.51 (op1(e11,e11) != e10) & (e11 = op1(e10,e11)) & (e11 = op1(e11,e10))))). 5.30/5.51 tff('2', plain, (e11 = op1(e10, e11) | ~ zip_tseitin_14), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_1])). 5.30/5.51 tff('3', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.51 inference('split', [status(esa)], ['2'])). 5.30/5.51 tff(ax5, axiom, 5.30/5.51 ((op1(e11,e10) != op1(e12,e10)) & (op1(e12,e11) != op1(e10,e11)) & 5.30/5.51 (op1(e11,e11) != op1(e13,e11)) & (op1(e11,e12) != op1(e10,e12)) & 5.30/5.51 (op1(e10,e12) != op1(e13,e12)) & (op1(e12,e12) != op1(e11,e12)) & 5.30/5.51 (op1(e11,e12) != op1(e13,e12)) & (op1(e10,e13) != op1(e11,e13)) & 5.30/5.51 (op1(e10,e13) != op1(e12,e13)) & (op1(e12,e13) != op1(e11,e13)) & 5.30/5.51 (op1(e11,e13) != op1(e13,e13)) & (op1(e10,e11) != op1(e10,e12)) & 5.30/5.51 (op1(e11,e10) != op1(e11,e12)) & (op1(e11,e10) != op1(e11,e13)) & 5.30/5.51 (op1(e11,e11) != op1(e11,e13)) & (op1(e11,e13) != op1(e11,e12)) & 5.30/5.51 (op1(e12,e10) != op1(e12,e12)) & (op1(e12,e13) != op1(e12,e11)) & 5.30/5.51 (op1(e12,e12) != op1(e12,e13)) & (op1(e13,e12) != op1(e13,e11)) & 5.30/5.51 (op1(e13,e12) != op1(e13,e13)) & (op1(e13,e13) != op1(e13,e11)) & 5.30/5.51 (op1(e13,e10) != op1(e13,e13)) & (op1(e13,e10) != op1(e13,e12)) & 5.30/5.51 (op1(e13,e11) != op1(e13,e10)) & (op1(e12,e11) != op1(e12,e12)) & 5.30/5.51 (op1(e12,e10) != op1(e12,e13)) & (op1(e12,e11) != op1(e12,e10)) & 5.30/5.51 (op1(e11,e12) != op1(e11,e11)) & (op1(e11,e10) != op1(e11,e11)) & 5.30/5.51 (op1(e10,e13) != op1(e10,e12)) & (op1(e10,e11) != op1(e10,e13)) & 5.30/5.51 (op1(e10,e10) != op1(e10,e13)) & (op1(e10,e12) != op1(e10,e10)) & 5.30/5.51 (op1(e10,e11) != op1(e10,e10)) & (op1(e13,e13) != op1(e12,e13)) & 5.30/5.51 (op1(e10,e13) != op1(e13,e13)) & (op1(e12,e12) != op1(e13,e12)) & 5.30/5.51 (op1(e12,e12) != op1(e10,e12)) & (op1(e13,e11) != op1(e12,e11)) & 5.30/5.51 (op1(e12,e11) != op1(e11,e11)) & (op1(e13,e11) != op1(e10,e11)) & 5.30/5.51 (op1(e10,e11) != op1(e11,e11)) & (op1(e12,e10) != op1(e13,e10)) & 5.30/5.51 (op1(e13,e10) != op1(e11,e10)) & (op1(e13,e10) != op1(e10,e10)) & 5.30/5.51 (op1(e10,e10) != op1(e12,e10)) & (op1(e10,e10) != op1(e11,e10)))). 5.30/5.51 tff('4', plain, op1(e12, e11) != op1(e10, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('5', plain, (op1(e12, e11) != e11) <= ((e11 = op1(e10, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['3', '4'])). 5.30/5.51 tff('6', plain, 5.30/5.51 (e11 != e11) <= ((e11 = op1(e12, e11)) & (e11 = op1(e10, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['1', '5'])). 5.30/5.51 tff('7', plain, ~ (e11 = op1(e10, e11)) | ~ (e11 = op1(e12, e11)), 5.30/5.51 inference('simplify', [status(thm)], ['6'])). 5.30/5.51 tff(ax1, axiom, 5.30/5.51 (((op1(e10,e10) = e11) | (e12 = op1(e10,e10)) | (e13 = op1(e10,e10)) | 5.30/5.51 (e10 = op1(e10,e10))) & 5.30/5.51 ((op1(e10,e13) = e10) | (op1(e10,e13) = e13) | (op1(e10,e13) = e12) | 5.30/5.51 (op1(e10,e13) = e11)) & 5.30/5.51 ((e10 = op1(e11,e10)) | (op1(e11,e10) = e13) | (e12 = op1(e11,e10)) | 5.30/5.51 (e11 = op1(e11,e10))) & 5.30/5.51 ((op1(e12,e11) = e10) | (e13 = op1(e12,e11)) | (e12 = op1(e12,e11)) | 5.30/5.51 (e11 = op1(e12,e11))) & 5.30/5.51 ((op1(e12,e12) = e10) | (e13 = op1(e12,e12)) | (op1(e12,e12) = e12) | 5.30/5.51 (op1(e12,e12) = e11)) & 5.30/5.51 ((op1(e13,e10) = e11) | (op1(e13,e10) = e12) | (op1(e13,e10) = e13) | 5.30/5.51 (e10 = op1(e13,e10))) & 5.30/5.51 ((op1(e13,e11) = e11) | (e13 = op1(e13,e11)) | (op1(e13,e11) = e12) | 5.30/5.51 (e10 = op1(e13,e11))) & 5.30/5.51 ((op1(e13,e12) = e12) | (e13 = op1(e13,e12)) | (e11 = op1(e13,e12)) | 5.30/5.51 (op1(e13,e12) = e10)) & 5.30/5.51 ((op1(e13,e13) = e10) | (op1(e13,e13) = e11) | (op1(e13,e13) = e13) | 5.30/5.51 (e12 = op1(e13,e13))) & 5.30/5.51 ((op1(e12,e13) = e10) | (e13 = op1(e12,e13)) | (e12 = op1(e12,e13)) | 5.30/5.51 (op1(e12,e13) = e11)) & 5.30/5.51 ((op1(e12,e10) = e11) | (op1(e12,e10) = e13) | (op1(e12,e10) = e12) | 5.30/5.51 (e10 = op1(e12,e10))) & 5.30/5.51 ((op1(e11,e13) = e10) | (op1(e11,e13) = e13) | (op1(e11,e13) = e12) | 5.30/5.51 (op1(e11,e13) = e11)) & 5.30/5.51 ((e13 = op1(e11,e12)) | (e12 = op1(e11,e12)) | (op1(e11,e12) = e11) | 5.30/5.51 (e10 = op1(e11,e12))) & 5.30/5.51 ((e10 = op1(e11,e11)) | (e11 = op1(e11,e11)) | (op1(e11,e11) = e13) | 5.30/5.51 (e12 = op1(e11,e11))) & 5.30/5.51 ((e13 = op1(e10,e12)) | (op1(e10,e12) = e12) | (e11 = op1(e10,e12)) | 5.30/5.51 (op1(e10,e12) = e10)) & 5.30/5.51 ((e11 = op1(e10,e11)) | (op1(e10,e11) = e12) | (e13 = op1(e10,e11)) | 5.30/5.51 (op1(e10,e11) = e10)))). 5.30/5.51 tff('8', plain, 5.30/5.51 (e11 = op1(e10, e11) 5.30/5.51 | op1(e10, e11) = e12 5.30/5.51 | e13 = op1(e10, e11) 5.30/5.51 | op1(e10, e11) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('9', plain, 5.30/5.51 (op1(e10, e11) = e10) | (e11 = op1(e10, e11)) | (op1(e10, e11) = e12) | 5.30/5.51 (e13 = op1(e10, e11)), inference('split', [status(esa)], ['8'])). 5.30/5.51 tff('10', plain, 5.30/5.51 (op1(e13, e11) = e11 5.30/5.51 | e13 = op1(e13, e11) 5.30/5.51 | op1(e13, e11) = e12 5.30/5.51 | e10 = op1(e13, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('11', plain, op1(e13, e13) != op1(e13, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff(ax12, axiom, 5.30/5.51 ((op1(op1(e13,op1(e13,e13)),e13) = e10) & (op1(e13,e13) = e11) & 5.30/5.51 (e12 = op1(e13,op1(e13,e13))))). 5.30/5.51 tff('12', plain, op1(e13, e13) = e11, inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('13', plain, e11 != op1(e13, e11), 5.30/5.51 inference('demod', [status(thm)], ['11', '12'])). 5.30/5.51 tff('14', plain, 5.30/5.51 (e13 = op1(e13, e11) | op1(e13, e11) = e12 | e10 = op1(e13, e11)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['10', '13'])). 5.30/5.51 tff('15', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.51 inference('split', [status(esa)], ['14'])). 5.30/5.51 tff(zf_stmt_2, type, zip_tseitin_15 : $o). 5.30/5.51 tff(zf_stmt_3, axiom, 5.30/5.51 (zip_tseitin_15 => 5.30/5.51 ((op1(e10,e10) != e11) & (op1(e11,e11) != e11) & (e11 != op1(e12,e12)) & 5.30/5.51 (op1(e13,e13) != e11) & (op1(e11,e10) = e10) & (e10 = op1(e10,e11))))). 5.30/5.51 tff(zf_stmt_4, type, zip_tseitin_14 : $o). 5.30/5.51 tff(zf_stmt_5, type, zip_tseitin_13 : $o). 5.30/5.51 tff(zf_stmt_6, axiom, 5.30/5.51 (zip_tseitin_13 => 5.30/5.51 ((e11 = op1(e11,e11)) & (e11 = op1(e11,e11)) & (e11 != op1(e10,e10)) & 5.30/5.51 (op1(e12,e12) != e11) & (op1(e13,e13) != e11) & (e11 != op1(e11,e11))))). 5.30/5.51 tff(zf_stmt_7, type, zip_tseitin_12 : $o). 5.30/5.51 tff(zf_stmt_8, axiom, 5.30/5.51 (zip_tseitin_12 => 5.30/5.51 ((op1(e10,e12) = e12) & (op1(e10,e10) != e10) & (e10 != op1(e11,e11)) & 5.30/5.51 (op1(e13,e13) != e10) & (e10 != op1(e12,e12)) & (op1(e12,e10) = e12)))). 5.30/5.51 tff(zf_stmt_9, type, zip_tseitin_11 : $o). 5.30/5.51 tff(zf_stmt_10, axiom, 5.30/5.51 (zip_tseitin_11 => 5.30/5.51 ((op1(e12,e11) = e12) & (op1(e11,e12) = e12) & (op1(e13,e13) != e11) & 5.30/5.51 (e11 != op1(e12,e12)) & (e11 != op1(e11,e11)) & (op1(e10,e10) != e11)))). 5.30/5.51 tff(zf_stmt_11, type, zip_tseitin_10 : $o). 5.30/5.51 tff(zf_stmt_12, axiom, 5.30/5.51 (zip_tseitin_10 => 5.30/5.51 ((e12 = op1(e12,e13)) & (op1(e13,e12) = e12) & (e13 != op1(e11,e11)) & 5.30/5.51 (op1(e13,e13) != e13) & (op1(e12,e12) != e13) & (e13 != op1(e10,e10))))). 5.30/5.51 tff(zf_stmt_13, type, zip_tseitin_9 : $o). 5.30/5.51 tff(zf_stmt_14, axiom, 5.30/5.51 (zip_tseitin_9 => 5.30/5.51 ((e10 != op1(e10,e10)) & (e10 != op1(e13,e13)) & (e10 != op1(e12,e12)) & 5.30/5.51 (op1(e11,e11) != e10) & (op1(e10,e13) = e13) & (op1(e13,e10) = e13)))). 5.30/5.51 tff(zf_stmt_15, type, zip_tseitin_8 : $o). 5.30/5.51 tff(zf_stmt_16, axiom, 5.30/5.51 (zip_tseitin_8 => 5.30/5.51 ((e11 != op1(e12,e12)) & (e11 != op1(e13,e13)) & (op1(e11,e11) != e11) & 5.30/5.51 (op1(e10,e10) != e11) & (e13 = op1(e11,e13)) & (op1(e13,e11) = e13)))). 5.30/5.51 tff(zf_stmt_17, type, zip_tseitin_7 : $o). 5.30/5.51 tff(zf_stmt_18, axiom, 5.30/5.51 (zip_tseitin_7 => 5.30/5.51 ((op1(e13,e13) = e13) & (op1(e13,e13) = e13) & (op1(e12,e12) != e13) & 5.30/5.51 (op1(e13,e13) != e13) & (op1(e11,e11) != e13) & (op1(e10,e10) != e13)))). 5.30/5.51 tff(zf_stmt_19, type, zip_tseitin_6 : $o). 5.30/5.51 tff(zf_stmt_20, axiom, 5.30/5.51 (zip_tseitin_6 => 5.30/5.51 ((e13 = op1(e13,e12)) & (e13 = op1(e12,e13)) & (op1(e10,e10) != e12) & 5.30/5.51 (e12 != op1(e12,e12)) & (op1(e13,e13) != e12) & (e12 != op1(e11,e11))))). 5.30/5.51 tff(zf_stmt_21, type, zip_tseitin_5 : $o). 5.30/5.51 tff(zf_stmt_22, axiom, 5.30/5.51 (zip_tseitin_5 => 5.30/5.51 ((e12 = op1(e12,e12)) & (op1(e12,e12) = e12) & (e12 != op1(e10,e10)) & 5.30/5.51 (e12 != op1(e11,e11)) & (e12 != op1(e13,e13)) & (op1(e12,e12) != e12)))). 5.30/5.51 tff(zf_stmt_23, type, zip_tseitin_4 : $o). 5.30/5.51 tff(zf_stmt_24, axiom, 5.30/5.51 (zip_tseitin_4 => 5.30/5.51 ((op1(e11,e13) = e11) & (e11 = op1(e13,e11)) & (e13 != op1(e10,e10)) & 5.30/5.51 (e13 != op1(e13,e13)) & (op1(e12,e12) != e13) & (e13 != op1(e11,e11))))). 5.30/5.51 tff(zf_stmt_25, type, zip_tseitin_3 : $o). 5.30/5.51 tff(zf_stmt_26, type, zip_tseitin_2 : $o). 5.30/5.51 tff(zf_stmt_27, axiom, 5.30/5.51 (zip_tseitin_2 => 5.30/5.51 ((op1(e10,e10) != e13) & (e13 != op1(e12,e12)) & (e13 != op1(e13,e13)) & 5.30/5.51 (e13 != op1(e11,e11)) & (e10 = op1(e13,e10)) & (op1(e10,e13) = e10)))). 5.30/5.51 tff(zf_stmt_28, type, zip_tseitin_1 : $o). 5.30/5.51 tff(zf_stmt_29, axiom, 5.30/5.51 (zip_tseitin_1 => 5.30/5.51 ((op1(e12,e10) = e10) & (op1(e10,e10) != e12) & (e12 != op1(e11,e11)) & 5.30/5.51 (e12 != op1(e12,e12)) & (op1(e13,e13) != e12) & (e10 = op1(e10,e12))))). 5.30/5.51 tff(zf_stmt_30, type, zip_tseitin_0 : $o). 5.30/5.51 tff(zf_stmt_31, axiom, 5.30/5.51 (zip_tseitin_0 => 5.30/5.51 ((e10 != op1(e10,e10)) & (e10 != op1(e13,e13)) & (op1(e12,e12) != e10) & 5.30/5.51 (op1(e11,e11) != e10) & (e10 = op1(e10,e10)) & (op1(e10,e10) = e10)))). 5.30/5.51 tff(zf_stmt_32, axiom, 5.30/5.51 (((op1(e13,op1(e13,e10)) = e13) | (op1(e12,op1(e12,e10)) = e12) | 5.30/5.51 (e11 = op1(e11,op1(e11,e10))) | (e10 = op1(e10,op1(e10,e10)))) & 5.30/5.51 ((op1(e12,op1(e12,e12)) = e12) | (e13 = op1(e13,op1(e13,e12))) | 5.30/5.51 (e11 = op1(e11,op1(e11,e12))) | (op1(e10,op1(e10,e12)) = e10)) & 5.30/5.51 (zip_tseitin_15 | zip_tseitin_14 | zip_tseitin_13 | zip_tseitin_12 | 5.30/5.51 zip_tseitin_11 | zip_tseitin_10 | zip_tseitin_9 | zip_tseitin_8 | 5.30/5.51 zip_tseitin_7 | zip_tseitin_6 | zip_tseitin_5 | zip_tseitin_4 | 5.30/5.51 zip_tseitin_3 | zip_tseitin_2 | zip_tseitin_1 | zip_tseitin_0) & 5.30/5.51 ((e10 = op1(e10,op1(e10,e13))) | (e12 = op1(e12,op1(e12,e13))) | 5.30/5.51 (op1(e13,op1(e13,e13)) = e13) | (op1(e11,op1(e11,e13)) = e11)) & 5.30/5.51 ((op1(e11,op1(e11,e11)) = e11) | (e12 = op1(e12,op1(e12,e11))) | 5.30/5.51 (op1(e13,op1(e13,e11)) = e13) | (e10 = op1(e10,op1(e10,e11)))))). 5.30/5.51 tff('16', plain, 5.30/5.51 (op1(e11, op1(e11, e11)) = e11 5.30/5.51 | e12 = op1(e12, op1(e12, e11)) 5.30/5.51 | op1(e13, op1(e13, e11)) = e13 5.30/5.51 | e10 = op1(e10, op1(e10, e11))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('17', plain, 5.30/5.51 (op1(e13, op1(e13, e11)) = e13) <= ((op1(e13, op1(e13, e11)) = e13)), 5.30/5.51 inference('split', [status(esa)], ['16'])). 5.30/5.51 tff('18', plain, 5.30/5.51 (op1(e13, e12) = e13) 5.30/5.51 <= ((op1(e13, e11) = e12) & (op1(e13, op1(e13, e11)) = e13)), 5.30/5.51 inference('sup+', [status(thm)], ['15', '17'])). 5.30/5.51 tff('19', plain, 5.30/5.51 (op1(e13, e10) = e11 5.30/5.51 | op1(e13, e10) = e12 5.30/5.51 | op1(e13, e10) = e13 5.30/5.51 | e10 = op1(e13, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('20', plain, op1(e13, e10) != op1(e13, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('21', plain, op1(e13, e13) = e11, inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('22', plain, op1(e13, e10) != e11, 5.30/5.51 inference('demod', [status(thm)], ['20', '21'])). 5.30/5.51 tff('23', plain, 5.30/5.51 (op1(e13, e10) = e12 | op1(e13, e10) = e13 | e10 = op1(e13, e10)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['19', '22'])). 5.30/5.51 tff('24', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.51 inference('split', [status(esa)], ['23'])). 5.30/5.51 tff('25', plain, op1(e13, e10) != op1(e13, e12), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('26', plain, (e13 != op1(e13, e12)) <= ((op1(e13, e10) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['24', '25'])). 5.30/5.51 tff('27', plain, 5.30/5.51 (e13 != e13) 5.30/5.51 <= ((op1(e13, e10) = e13) & 5.30/5.51 (op1(e13, e11) = e12) & 5.30/5.51 (op1(e13, op1(e13, e11)) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['18', '26'])). 5.30/5.51 tff('28', plain, 5.30/5.51 ~ (op1(e13, op1(e13, e11)) = e13) | ~ (op1(e13, e10) = e13) | 5.30/5.51 ~ (op1(e13, e11) = e12), inference('simplify', [status(thm)], ['27'])). 5.30/5.51 tff('29', plain, (op1(e11, e11) != e10 | ~ zip_tseitin_9), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_14])). 5.30/5.51 tff('30', plain, ~ (e10 = op1(e11, e11)) | ~ ( zip_tseitin_9), 5.30/5.51 inference('split', [status(esa)], ['29'])). 5.30/5.51 tff(ax2, axiom, 5.30/5.51 (((e10 = op1(e10,e10)) | (op1(e11,e10) = e10) | (op1(e12,e10) = e10) | 5.30/5.51 (e10 = op1(e13,e10))) & 5.30/5.51 ((op1(e10,e10) = e11) | (e11 = op1(e10,e11)) | (e11 = op1(e10,e12)) | 5.30/5.51 (op1(e10,e13) = e11)) & 5.30/5.51 ((e11 = op1(e10,e10)) | (e11 = op1(e11,e10)) | (e11 = op1(e12,e10)) | 5.30/5.51 (e11 = op1(e13,e10))) & 5.30/5.51 ((op1(e11,e11) = e10) | (op1(e11,e12) = e10) | (op1(e11,e13) = e10) | 5.30/5.51 (op1(e11,e10) = e10)) & 5.30/5.51 ((op1(e11,e11) = e12) | (op1(e12,e11) = e12) | (op1(e13,e11) = e12) | 5.30/5.51 (op1(e10,e11) = e12)) & 5.30/5.51 ((e13 = op1(e10,e11)) | (op1(e11,e11) = e13) | (e13 = op1(e13,e11)) | 5.30/5.51 (op1(e12,e11) = e13)) & 5.30/5.51 ((op1(e12,e11) = e10) | (op1(e12,e13) = e10) | (op1(e12,e12) = e10) | 5.30/5.51 (op1(e12,e10) = e10)) & 5.30/5.51 ((op1(e12,e12) = e10) | (op1(e13,e12) = e10) | (e10 = op1(e11,e12)) | 5.30/5.51 (e10 = op1(e10,e12))) & 5.30/5.51 ((op1(e12,e12) = e11) | (e11 = op1(e12,e13)) | (e11 = op1(e12,e11)) | 5.30/5.51 (op1(e12,e10) = e11)) & 5.30/5.51 ((e11 = op1(e10,e12)) | (op1(e11,e12) = e11) | (e11 = op1(e12,e12)) | 5.30/5.51 (op1(e13,e12) = e11)) & 5.30/5.51 ((e12 = op1(e12,e10)) | (op1(e12,e11) = e12) | (e12 = op1(e12,e12)) | 5.30/5.51 (e12 = op1(e12,e13))) & 5.30/5.51 ((e13 = op1(e12,e12)) | (e13 = op1(e13,e12)) | (e13 = op1(e11,e12)) | 5.30/5.51 (op1(e10,e12) = e13)) & 5.30/5.51 ((op1(e13,e10) = e10) | (op1(e13,e13) = e10) | (e10 = op1(e13,e12)) | 5.30/5.51 (e10 = op1(e13,e11))) & 5.30/5.51 ((e11 = op1(e12,e13)) | (e11 = op1(e13,e13)) | (op1(e11,e13) = e11) | 5.30/5.51 (op1(e10,e13) = e11)) & 5.30/5.51 ((op1(e10,e13) = e12) | (e12 = op1(e13,e13)) | (e12 = op1(e12,e13)) | 5.30/5.51 (op1(e11,e13) = e12)) & 5.30/5.51 ((op1(e10,e13) = e13) | (op1(e11,e13) = e13) | (op1(e12,e13) = e13) | 5.30/5.51 (op1(e13,e13) = e13)) & 5.30/5.51 ((op1(e13,e11) = e13) | (e13 = op1(e13,e13)) | (op1(e13,e12) = e13) | 5.30/5.51 (op1(e13,e10) = e13)) & 5.30/5.51 ((e12 = op1(e13,e10)) | (e12 = op1(e13,e13)) | (op1(e13,e12) = e12) | 5.30/5.51 (e12 = op1(e13,e11))) & 5.30/5.51 ((op1(e13,e11) = e11) | (e11 = op1(e13,e12)) | (op1(e13,e13) = e11) | 5.30/5.51 (e11 = op1(e13,e10))) & 5.30/5.51 ((op1(e13,e13) = e10) | (e10 = op1(e12,e13)) | (e10 = op1(e11,e13)) | 5.30/5.51 (e10 = op1(e10,e13))) & 5.30/5.51 ((e13 = op1(e12,e10)) | (e13 = op1(e12,e11)) | (op1(e12,e12) = e13) | 5.30/5.51 (e13 = op1(e12,e13))) & 5.30/5.51 ((op1(e11,e12) = e12) | (e12 = op1(e12,e12)) | (op1(e13,e12) = e12) | 5.30/5.51 (e12 = op1(e10,e12))) & 5.30/5.51 ((e13 = op1(e11,e12)) | (e13 = op1(e11,e13)) | (op1(e11,e11) = e13) | 5.30/5.51 (e13 = op1(e11,e10))) & 5.30/5.51 ((e12 = op1(e11,e11)) | (e12 = op1(e11,e12)) | (op1(e11,e13) = e12) | 5.30/5.51 (op1(e11,e10) = e12)) & 5.30/5.51 ((op1(e11,e11) = e11) | (e11 = op1(e12,e11)) | (op1(e13,e11) = e11) | 5.30/5.51 (e11 = op1(e10,e11))) & 5.30/5.51 ((op1(e11,e10) = e11) | (e11 = op1(e11,e13)) | (e11 = op1(e11,e12)) | 5.30/5.51 (e11 = op1(e11,e11))) & 5.30/5.51 ((e10 = op1(e10,e11)) | (op1(e13,e11) = e10) | (e10 = op1(e12,e11)) | 5.30/5.51 (op1(e11,e11) = e10)) & 5.30/5.51 ((e13 = op1(e10,e10)) | (op1(e13,e10) = e13) | (e13 = op1(e12,e10)) | 5.30/5.51 (e13 = op1(e11,e10))) & 5.30/5.51 ((e13 = op1(e10,e12)) | (op1(e10,e13) = e13) | (op1(e10,e11) = e13) | 5.30/5.51 (e13 = op1(e10,e10))) & 5.30/5.51 ((e12 = op1(e11,e10)) | (op1(e13,e10) = e12) | (e12 = op1(e12,e10)) | 5.30/5.51 (e12 = op1(e10,e10))) & 5.30/5.51 ((op1(e10,e10) = e12) | (e12 = op1(e10,e11)) | (op1(e10,e13) = e12) | 5.30/5.51 (e12 = op1(e10,e12))) & 5.30/5.51 ((op1(e10,e10) = e10) | (e10 = op1(e10,e13)) | (op1(e10,e12) = e10) | 5.30/5.51 (e10 = op1(e10,e11))))). 5.30/5.51 tff('31', plain, 5.30/5.51 (e11 = op1(e10, e12) 5.30/5.51 | op1(e11, e12) = e11 5.30/5.51 | e11 = op1(e12, e12) 5.30/5.51 | op1(e13, e12) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('32', plain, op1(e13, e12) != op1(e13, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('33', plain, op1(e13, e13) = e11, inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('34', plain, op1(e13, e12) != e11, 5.30/5.51 inference('demod', [status(thm)], ['32', '33'])). 5.30/5.51 tff('35', plain, 5.30/5.51 (e11 = op1(e10, e12) | op1(e11, e12) = e11 | e11 = op1(e12, e12)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['31', '34'])). 5.30/5.51 tff('36', plain, 5.30/5.51 (op1(e11, e12) = e11) | (op1(e12, e12) = e11) | (e11 = op1(e10, e12)), 5.30/5.51 inference('split', [status(esa)], ['35'])). 5.30/5.51 tff('37', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.51 inference('split', [status(esa)], ['2'])). 5.30/5.51 tff('38', plain, (op1(e10, e11) = e10) <= ((op1(e10, e11) = e10)), 5.30/5.51 inference('split', [status(esa)], ['8'])). 5.30/5.51 tff('39', plain, 5.30/5.51 (e11 = e10) <= ((op1(e10, e11) = e10) & (e11 = op1(e10, e11))), 5.30/5.51 inference('sup+', [status(thm)], ['37', '38'])). 5.30/5.51 tff(ax7, axiom, 5.30/5.51 ((e10 != e11) & (e11 != e12) & (e12 != e13) & (e11 != e13) & 5.30/5.51 (e13 != e10) & (e10 != e12))). 5.30/5.51 tff('40', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('41', plain, ~ (e11 = op1(e10, e11)) | ~ (op1(e10, e11) = e10), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['39', '40'])). 5.30/5.51 tff('42', plain, (op1(e11, e11) != e10 | ~ zip_tseitin_14), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_1])). 5.30/5.51 tff('43', plain, ~ (e10 = op1(e11, e11)) | ~ ( zip_tseitin_14), 5.30/5.51 inference('split', [status(esa)], ['42'])). 5.30/5.51 tff('44', plain, 5.30/5.51 (op1(e12, e12) = e10 5.30/5.51 | e13 = op1(e12, e12) 5.30/5.51 | op1(e12, e12) = e12 5.30/5.51 | op1(e12, e12) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('45', plain, 5.30/5.51 (e13 = op1(e12, e12)) | (op1(e12, e12) = e11) | (op1(e12, e12) = e12) | 5.30/5.51 (op1(e12, e12) = e10), inference('split', [status(esa)], ['44'])). 5.30/5.51 tff('46', plain, (op1(e12, e12) = e10) <= ((op1(e12, e12) = e10)), 5.30/5.51 inference('split', [status(esa)], ['44'])). 5.30/5.51 tff('47', plain, 5.30/5.51 (op1(e12, e13) = e10 5.30/5.51 | e13 = op1(e12, e13) 5.30/5.51 | e12 = op1(e12, e13) 5.30/5.51 | op1(e12, e13) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('48', plain, op1(e13, e13) != op1(e12, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('49', plain, op1(e13, e13) = e11, inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('50', plain, e11 != op1(e12, e13), 5.30/5.51 inference('demod', [status(thm)], ['48', '49'])). 5.30/5.51 tff('51', plain, 5.30/5.51 (op1(e12, e13) = e10 | e13 = op1(e12, e13) | e12 = op1(e12, e13)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['47', '50'])). 5.30/5.51 tff('52', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['51'])). 5.30/5.51 tff('53', plain, op1(e12, e12) != op1(e12, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('54', plain, (op1(e12, e12) != e10) <= ((op1(e12, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['52', '53'])). 5.30/5.51 tff('55', plain, 5.30/5.51 (e10 != e10) <= ((op1(e12, e12) = e10) & (op1(e12, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['46', '54'])). 5.30/5.51 tff('56', plain, ~ (op1(e12, e12) = e10) | ~ (op1(e12, e13) = e10), 5.30/5.51 inference('simplify', [status(thm)], ['55'])). 5.30/5.51 tff('57', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.51 inference('split', [status(esa)], ['44'])). 5.30/5.51 tff('58', plain, 5.30/5.51 (e13 = op1(e11, e12) 5.30/5.51 | e12 = op1(e11, e12) 5.30/5.51 | op1(e11, e12) = e11 5.30/5.51 | e10 = op1(e11, e12)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('59', plain, (op1(e11, e12) = e11) <= ((op1(e11, e12) = e11)), 5.30/5.51 inference('split', [status(esa)], ['58'])). 5.30/5.51 tff('60', plain, op1(e12, e12) != op1(e11, e12), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('61', plain, (op1(e12, e12) != e11) <= ((op1(e11, e12) = e11)), 5.30/5.51 inference('sup-', [status(thm)], ['59', '60'])). 5.30/5.51 tff('62', plain, 5.30/5.51 (e11 != e11) <= ((op1(e12, e12) = e11) & (op1(e11, e12) = e11)), 5.30/5.51 inference('sup-', [status(thm)], ['57', '61'])). 5.30/5.51 tff('63', plain, ~ (op1(e12, e12) = e11) | ~ (op1(e11, e12) = e11), 5.30/5.51 inference('simplify', [status(thm)], ['62'])). 5.30/5.51 tff('64', plain, 5.30/5.51 (e10 = op1(e11, e11) 5.30/5.51 | e11 = op1(e11, e11) 5.30/5.51 | op1(e11, e11) = e13 5.30/5.51 | e12 = op1(e11, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('65', plain, (e12 = op1(e11, e11)) <= ((e12 = op1(e11, e11))), 5.30/5.51 inference('split', [status(esa)], ['64'])). 5.30/5.51 tff('66', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.51 inference('split', [status(esa)], ['14'])). 5.30/5.51 tff('67', plain, op1(e11, e11) != op1(e13, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('68', plain, (op1(e11, e11) != e12) <= ((op1(e13, e11) = e12)), 5.30/5.51 inference('sup-', [status(thm)], ['66', '67'])). 5.30/5.51 tff('69', plain, 5.30/5.51 (e12 != e12) <= ((op1(e13, e11) = e12) & (e12 = op1(e11, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['65', '68'])). 5.30/5.51 tff('70', plain, ~ (e12 = op1(e11, e11)) | ~ (op1(e13, e11) = e12), 5.30/5.51 inference('simplify', [status(thm)], ['69'])). 5.30/5.51 tff('71', plain, 5.30/5.51 (e13 = op1(e10, e12) 5.30/5.51 | op1(e10, e12) = e12 5.30/5.51 | e11 = op1(e10, e12) 5.30/5.51 | op1(e10, e12) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('72', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.51 inference('split', [status(esa)], ['71'])). 5.30/5.51 tff('73', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.51 inference('split', [status(esa)], ['71'])). 5.30/5.51 tff('74', plain, 5.30/5.51 (op1(e12, op1(e12, e12)) = e12 5.30/5.51 | e13 = op1(e13, op1(e13, e12)) 5.30/5.51 | e11 = op1(e11, op1(e11, e12)) 5.30/5.51 | op1(e10, op1(e10, e12)) = e10), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('75', plain, 5.30/5.51 (op1(e10, op1(e10, e12)) = e10) <= ((op1(e10, op1(e10, e12)) = e10)), 5.30/5.51 inference('split', [status(esa)], ['74'])). 5.30/5.51 tff('76', plain, 5.30/5.51 (op1(e10, e12) = e10) 5.30/5.51 <= ((op1(e10, e12) = e12) & (op1(e10, op1(e10, e12)) = e10)), 5.30/5.51 inference('sup+', [status(thm)], ['73', '75'])). 5.30/5.51 tff('77', plain, 5.30/5.51 (e12 = e10) <= ((op1(e10, e12) = e12) & (op1(e10, op1(e10, e12)) = e10)), 5.30/5.51 inference('sup+', [status(thm)], ['72', '76'])). 5.30/5.51 tff('78', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('79', plain, ~ (op1(e10, op1(e10, e12)) = e10) | ~ (op1(e10, e12) = e12), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['77', '78'])). 5.30/5.51 tff('80', plain, 5.30/5.51 (op1(e11, e13) = e10 5.30/5.51 | op1(e11, e13) = e13 5.30/5.51 | op1(e11, e13) = e12 5.30/5.51 | op1(e11, e13) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('81', plain, (op1(e11, e13) = e12) <= ((op1(e11, e13) = e12)), 5.30/5.51 inference('split', [status(esa)], ['80'])). 5.30/5.51 tff('82', plain, (op1(e11, e13) = e10) <= ((op1(e11, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['80'])). 5.30/5.51 tff('83', plain, 5.30/5.51 (e12 = e10) <= ((op1(e11, e13) = e12) & (op1(e11, e13) = e10)), 5.30/5.51 inference('sup+', [status(thm)], ['81', '82'])). 5.30/5.51 tff('84', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('85', plain, ~ (op1(e11, e13) = e10) | ~ (op1(e11, e13) = e12), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['83', '84'])). 5.30/5.51 tff('86', plain, 5.30/5.51 (op1(e13, e11) = e13 5.30/5.51 | e13 = op1(e13, e13) 5.30/5.51 | op1(e13, e12) = e13 5.30/5.51 | op1(e13, e10) = e13), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('87', plain, 5.30/5.51 (op1(e13, e10) = e13) | (e13 = op1(e13, e12)) | (e13 = op1(e13, e11)) | 5.30/5.51 (op1(e13, e13) = e13), inference('split', [status(esa)], ['86'])). 5.30/5.51 tff('88', plain, 5.30/5.51 (op1(e13, e10) = e11 5.30/5.51 | op1(e13, e10) = e12 5.30/5.51 | op1(e13, e10) = e13 5.30/5.51 | e10 = op1(e13, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('89', plain, 5.30/5.51 (e10 = op1(e13, e10)) | (op1(e13, e10) = e13) | (op1(e13, e10) = e11) | 5.30/5.51 (op1(e13, e10) = e12), inference('split', [status(esa)], ['88'])). 5.30/5.51 tff(ax11, axiom, 5.30/5.51 (((e20 = op2(e20,op2(e20,e20))) | (op2(e21,op2(e21,e20)) = e21) | 5.30/5.51 (op2(e22,op2(e22,e20)) = e22) | (e23 = op2(e23,op2(e23,e20)))) & 5.30/5.51 ((e21 = op2(e21,op2(e21,e21))) | (e23 = op2(e23,op2(e23,e21))) | 5.30/5.51 (e22 = op2(e22,op2(e22,e21))) | (op2(e20,op2(e20,e21)) = e20)) & 5.30/5.51 ((e21 = op2(e21,op2(e21,e22))) | (e23 = op2(e23,op2(e23,e22))) | 5.30/5.51 (op2(e22,op2(e22,e22)) = e22) | (op2(e20,op2(e20,e22)) = e20)) & 5.30/5.51 (((op2(e20,e20) != e20) & (op2(e23,e23) != e20) & (e20 != op2(e22,e22)) & 5.30/5.51 (e20 != op2(e21,e21)) & (e20 = op2(e20,e20)) & (op2(e20,e20) = e20)) | 5.30/5.51 ((op2(e20,e23) = e20) & (op2(e23,e20) = e20) & (op2(e23,e23) != e23) & 5.30/5.51 (e23 != op2(e22,e22)) & (op2(e21,e21) != e23) & (op2(e20,e20) != e23)) | 5.30/5.51 ((e21 != op2(e21,e21)) & (op2(e23,e23) != e21) & (e21 != op2(e22,e22)) & 5.30/5.51 (e21 != op2(e20,e20)) & (e21 = op2(e21,e21)) & (op2(e21,e21) = e21)) | 5.30/5.51 ((op2(e22,e21) = e21) & (e22 != op2(e23,e23)) & (e22 != op2(e22,e22)) & 5.30/5.51 (op2(e21,e21) != e22) & (op2(e20,e20) != e22) & (op2(e21,e22) = e21)) | 5.30/5.51 ((op2(e20,e22) = e22) & (op2(e22,e22) != e20) & (op2(e23,e23) != e20) & 5.30/5.51 (e20 != op2(e21,e21)) & (e20 != op2(e20,e20)) & (e22 = op2(e22,e20))) | 5.30/5.51 ((e21 != op2(e21,e21)) & (op2(e22,e22) != e21) & (op2(e23,e23) != e21) & 5.30/5.51 (op2(e20,e20) != e21) & (op2(e21,e22) = e22) & (e22 = op2(e22,e21))) | 5.30/5.51 ((e22 != op2(e20,e20)) & (e22 != op2(e21,e21)) & (e22 != op2(e22,e22)) & 5.30/5.51 (op2(e23,e23) != e22) & (op2(e22,e22) = e22) & (op2(e22,e22) = e22)) | 5.30/5.51 ((op2(e23,e23) != e21) & (e21 != op2(e22,e22)) & (e21 != op2(e21,e21)) & 5.30/5.51 (e21 != op2(e20,e20)) & (e23 = op2(e21,e23)) & (op2(e23,e21) = e23)) | 5.30/5.51 ((op2(e23,e23) = e23) & (op2(e20,e20) != e23) & (op2(e23,e23) != e23) & 5.30/5.51 (e23 != op2(e22,e22)) & (op2(e21,e21) != e23) & (e23 = op2(e23,e23))) | 5.30/5.51 ((op2(e23,e22) = e23) & (op2(e20,e20) != e22) & (op2(e22,e22) != e22) & 5.30/5.51 (op2(e23,e23) != e22) & (op2(e21,e21) != e22) & (e23 = op2(e22,e23))) | 5.30/5.51 ((op2(e23,e20) = e23) & (e23 = op2(e20,e23)) & (op2(e23,e23) != e20) & 5.30/5.51 (op2(e22,e22) != e20) & (op2(e21,e21) != e20) & (op2(e20,e20) != e20)) | 5.30/5.51 ((op2(e22,e23) = e22) & (op2(e23,e22) = e22) & (e23 != op2(e20,e20)) & 5.30/5.51 (op2(e23,e23) != e23) & (e23 != op2(e22,e22)) & (op2(e21,e21) != e23)) | 5.30/5.51 ((e21 = op2(e21,e23)) & (op2(e23,e23) != e23) & (op2(e22,e22) != e23) & 5.30/5.51 (e23 != op2(e21,e21)) & (e23 != op2(e20,e20)) & (e21 = op2(e23,e21))) | 5.30/5.51 ((e21 = op2(e20,e21)) & (e20 != op2(e20,e20)) & (op2(e23,e23) != e20) & 5.30/5.51 (op2(e22,e22) != e20) & (e20 != op2(e21,e21)) & (op2(e21,e20) = e21)) | 5.30/5.51 ((op2(e20,e20) != e22) & (op2(e21,e21) != e22) & (op2(e22,e22) != e22) & 5.30/5.51 (e22 != op2(e23,e23)) & (op2(e22,e20) = e20) & (e20 = op2(e20,e22))) | 5.30/5.51 ((e20 = op2(e20,e21)) & (e20 = op2(e21,e20)) & (e21 != op2(e20,e20)) & 5.30/5.51 (e21 != op2(e21,e21)) & (op2(e23,e23) != e21) & (e21 != op2(e22,e22)))) & 5.30/5.51 ((op2(e20,op2(e20,e23)) = e20) | (e21 = op2(e21,op2(e21,e23))) | 5.30/5.51 (op2(e22,op2(e22,e23)) = e22) | (e23 = op2(e23,op2(e23,e23)))))). 5.30/5.51 tff(zf_stmt_33, type, zip_tseitin_31 : $o). 5.30/5.51 tff(zf_stmt_34, axiom, 5.30/5.51 (zip_tseitin_31 => 5.30/5.51 ((e21 != op2(e22,e22)) & (op2(e23,e23) != e21) & (e21 != op2(e21,e21)) & 5.30/5.51 (e21 != op2(e20,e20)) & (e20 = op2(e21,e20)) & (e20 = op2(e20,e21))))). 5.30/5.51 tff(zf_stmt_35, type, zip_tseitin_30 : $o). 5.30/5.51 tff(zf_stmt_36, axiom, 5.30/5.51 (zip_tseitin_30 => 5.30/5.51 ((e20 = op2(e20,e22)) & (op2(e22,e20) = e20) & (e22 != op2(e23,e23)) & 5.30/5.51 (op2(e22,e22) != e22) & (op2(e21,e21) != e22) & (op2(e20,e20) != e22)))). 5.30/5.51 tff(zf_stmt_37, type, zip_tseitin_29 : $o). 5.30/5.51 tff(zf_stmt_38, axiom, 5.30/5.51 (zip_tseitin_29 => 5.30/5.51 ((op2(e21,e20) = e21) & (e20 != op2(e21,e21)) & (op2(e22,e22) != e20) & 5.30/5.51 (op2(e23,e23) != e20) & (e20 != op2(e20,e20)) & (e21 = op2(e20,e21))))). 5.30/5.51 tff(zf_stmt_39, type, zip_tseitin_28 : $o). 5.30/5.51 tff(zf_stmt_40, axiom, 5.30/5.51 (zip_tseitin_28 => 5.30/5.51 ((e21 = op2(e23,e21)) & (e23 != op2(e20,e20)) & (e23 != op2(e21,e21)) & 5.30/5.51 (op2(e22,e22) != e23) & (op2(e23,e23) != e23) & (e21 = op2(e21,e23))))). 5.30/5.51 tff(zf_stmt_41, type, zip_tseitin_27 : $o). 5.30/5.51 tff(zf_stmt_42, axiom, 5.30/5.51 (zip_tseitin_27 => 5.30/5.51 ((op2(e21,e21) != e23) & (e23 != op2(e22,e22)) & (op2(e23,e23) != e23) & 5.30/5.51 (e23 != op2(e20,e20)) & (op2(e23,e22) = e22) & (op2(e22,e23) = e22)))). 5.30/5.51 tff(zf_stmt_43, type, zip_tseitin_26 : $o). 5.30/5.51 tff(zf_stmt_44, axiom, 5.30/5.51 (zip_tseitin_26 => 5.30/5.51 ((op2(e20,e20) != e20) & (op2(e21,e21) != e20) & (op2(e22,e22) != e20) & 5.30/5.51 (op2(e23,e23) != e20) & (e23 = op2(e20,e23)) & (op2(e23,e20) = e23)))). 5.30/5.51 tff(zf_stmt_45, type, zip_tseitin_25 : $o). 5.30/5.51 tff(zf_stmt_46, axiom, 5.30/5.51 (zip_tseitin_25 => 5.30/5.51 ((e23 = op2(e22,e23)) & (op2(e21,e21) != e22) & (op2(e23,e23) != e22) & 5.30/5.51 (op2(e22,e22) != e22) & (op2(e20,e20) != e22) & (op2(e23,e22) = e23)))). 5.30/5.51 tff(zf_stmt_47, type, zip_tseitin_24 : $o). 5.30/5.51 tff(zf_stmt_48, axiom, 5.30/5.51 (zip_tseitin_24 => 5.30/5.51 ((e23 = op2(e23,e23)) & (op2(e21,e21) != e23) & (e23 != op2(e22,e22)) & 5.30/5.51 (op2(e23,e23) != e23) & (op2(e20,e20) != e23) & (op2(e23,e23) = e23)))). 5.30/5.51 tff(zf_stmt_49, type, zip_tseitin_23 : $o). 5.30/5.51 tff(zf_stmt_50, axiom, 5.30/5.51 (zip_tseitin_23 => 5.30/5.51 ((op2(e23,e21) = e23) & (e23 = op2(e21,e23)) & (e21 != op2(e20,e20)) & 5.30/5.51 (e21 != op2(e21,e21)) & (e21 != op2(e22,e22)) & (op2(e23,e23) != e21)))). 5.30/5.51 tff(zf_stmt_51, type, zip_tseitin_22 : $o). 5.30/5.51 tff(zf_stmt_52, axiom, 5.30/5.51 (zip_tseitin_22 => 5.30/5.51 ((op2(e22,e22) = e22) & (op2(e22,e22) = e22) & (op2(e23,e23) != e22) & 5.30/5.51 (e22 != op2(e22,e22)) & (e22 != op2(e21,e21)) & (e22 != op2(e20,e20))))). 5.30/5.51 tff(zf_stmt_53, type, zip_tseitin_21 : $o). 5.30/5.51 tff(zf_stmt_54, axiom, 5.30/5.51 (zip_tseitin_21 => 5.30/5.51 ((e22 = op2(e22,e21)) & (op2(e21,e22) = e22) & (op2(e20,e20) != e21) & 5.30/5.51 (op2(e23,e23) != e21) & (op2(e22,e22) != e21) & (e21 != op2(e21,e21))))). 5.30/5.51 tff(zf_stmt_55, type, zip_tseitin_20 : $o). 5.30/5.51 tff(zf_stmt_56, axiom, 5.30/5.51 (zip_tseitin_20 => 5.30/5.51 ((e22 = op2(e22,e20)) & (e20 != op2(e20,e20)) & (e20 != op2(e21,e21)) & 5.30/5.51 (op2(e23,e23) != e20) & (op2(e22,e22) != e20) & (op2(e20,e22) = e22)))). 5.30/5.51 tff(zf_stmt_57, type, zip_tseitin_19 : $o). 5.30/5.51 tff(zf_stmt_58, axiom, 5.30/5.51 (zip_tseitin_19 => 5.30/5.51 ((op2(e21,e22) = e21) & (op2(e20,e20) != e22) & (op2(e21,e21) != e22) & 5.30/5.51 (e22 != op2(e22,e22)) & (e22 != op2(e23,e23)) & (op2(e22,e21) = e21)))). 5.30/5.51 tff(zf_stmt_59, type, zip_tseitin_18 : $o). 5.30/5.51 tff(zf_stmt_60, axiom, 5.30/5.51 (zip_tseitin_18 => 5.30/5.51 ((op2(e21,e21) = e21) & (e21 = op2(e21,e21)) & (e21 != op2(e20,e20)) & 5.30/5.51 (e21 != op2(e22,e22)) & (op2(e23,e23) != e21) & (e21 != op2(e21,e21))))). 5.30/5.51 tff(zf_stmt_61, type, zip_tseitin_17 : $o). 5.30/5.51 tff(zf_stmt_62, axiom, 5.30/5.51 (zip_tseitin_17 => 5.30/5.51 ((op2(e20,e20) != e23) & (op2(e21,e21) != e23) & (e23 != op2(e22,e22)) & 5.30/5.51 (op2(e23,e23) != e23) & (op2(e23,e20) = e20) & (op2(e20,e23) = e20)))). 5.30/5.51 tff(zf_stmt_63, type, zip_tseitin_16 : $o). 5.30/5.51 tff(zf_stmt_64, axiom, 5.30/5.51 (zip_tseitin_16 => 5.30/5.51 ((op2(e20,e20) = e20) & (e20 = op2(e20,e20)) & (e20 != op2(e21,e21)) & 5.30/5.51 (e20 != op2(e22,e22)) & (op2(e23,e23) != e20) & (op2(e20,e20) != e20)))). 5.30/5.51 tff(zf_stmt_65, axiom, 5.30/5.51 (((e23 = op2(e23,op2(e23,e23))) | (op2(e22,op2(e22,e23)) = e22) | 5.30/5.51 (e21 = op2(e21,op2(e21,e23))) | (op2(e20,op2(e20,e23)) = e20)) & 5.30/5.51 (zip_tseitin_31 | zip_tseitin_30 | zip_tseitin_29 | zip_tseitin_28 | 5.30/5.51 zip_tseitin_27 | zip_tseitin_26 | zip_tseitin_25 | zip_tseitin_24 | 5.30/5.51 zip_tseitin_23 | zip_tseitin_22 | zip_tseitin_21 | zip_tseitin_20 | 5.30/5.51 zip_tseitin_19 | zip_tseitin_18 | zip_tseitin_17 | zip_tseitin_16) & 5.30/5.51 ((op2(e20,op2(e20,e22)) = e20) | (op2(e22,op2(e22,e22)) = e22) | 5.30/5.51 (e23 = op2(e23,op2(e23,e22))) | (e21 = op2(e21,op2(e21,e22)))) & 5.30/5.51 ((op2(e20,op2(e20,e21)) = e20) | (e22 = op2(e22,op2(e22,e21))) | 5.30/5.51 (e23 = op2(e23,op2(e23,e21))) | (e21 = op2(e21,op2(e21,e21)))) & 5.30/5.51 ((e23 = op2(e23,op2(e23,e20))) | (op2(e22,op2(e22,e20)) = e22) | 5.30/5.51 (op2(e21,op2(e21,e20)) = e21) | (e20 = op2(e20,op2(e20,e20)))))). 5.30/5.51 tff('90', plain, 5.30/5.51 (e23 = op2(e23, op2(e23, e23)) 5.30/5.51 | op2(e22, op2(e22, e23)) = e22 5.30/5.51 | e21 = op2(e21, op2(e21, e23)) 5.30/5.51 | op2(e20, op2(e20, e23)) = e20), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.51 tff('91', plain, 5.30/5.51 (op2(e22, op2(e22, e23)) = e22) | (e21 = op2(e21, op2(e21, e23))) | 5.30/5.51 (op2(e20, op2(e20, e23)) = e20) | (e23 = op2(e23, op2(e23, e23))), 5.30/5.51 inference('split', [status(esa)], ['90'])). 5.30/5.51 tff(ax13, axiom, 5.30/5.51 ((e21 = op2(e23,e23)) & (e22 = op2(e23,op2(e23,e23))) & 5.30/5.51 (op2(op2(e23,op2(e23,e23)),e23) = e20))). 5.30/5.51 tff('92', plain, e22 = op2(e23, op2(e23, e23)), 5.30/5.51 inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('93', plain, e21 = op2(e23, e23), inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('94', plain, e22 = op2(e23, e21), 5.30/5.51 inference('demod', [status(thm)], ['92', '93'])). 5.30/5.51 tff('95', plain, 5.30/5.51 (e23 = op2(e23, op2(e23, e23))) <= ((e23 = op2(e23, op2(e23, e23)))), 5.30/5.51 inference('split', [status(esa)], ['90'])). 5.30/5.51 tff('96', plain, e21 = op2(e23, e23), inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('97', plain, (e23 = op2(e23, e21)) <= ((e23 = op2(e23, op2(e23, e23)))), 5.30/5.51 inference('demod', [status(thm)], ['95', '96'])). 5.30/5.51 tff('98', plain, (e23 = e22) <= ((e23 = op2(e23, op2(e23, e23)))), 5.30/5.51 inference('sup+', [status(thm)], ['94', '97'])). 5.30/5.51 tff(ax8, axiom, 5.30/5.51 ((e21 != e20) & (e22 != e20) & (e21 != e22) & (e22 != e23) & 5.30/5.51 (e21 != e23) & (e23 != e20))). 5.30/5.51 tff('99', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.51 tff('100', plain, ~ (e23 = op2(e23, op2(e23, e23))), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['98', '99'])). 5.30/5.51 tff(ax4, axiom, 5.30/5.51 (((op2(e22,e20) = e20) | (op2(e23,e20) = e20) | (op2(e21,e20) = e20) | 5.30/5.51 (e20 = op2(e20,e20))) & 5.30/5.51 ((e22 = op2(e20,e20)) | (op2(e21,e20) = e22) | (e22 = op2(e23,e20)) | 5.30/5.51 (e22 = op2(e22,e20))) & 5.30/5.51 ((op2(e20,e22) = e23) | (e23 = op2(e20,e23)) | (op2(e20,e21) = e23) | 5.30/5.51 (e23 = op2(e20,e20))) & 5.30/5.51 ((e23 = op2(e20,e20)) | (e23 = op2(e21,e20)) | (op2(e23,e20) = e23) | 5.30/5.51 (op2(e22,e20) = e23)) & 5.30/5.51 ((op2(e21,e20) = e21) | (op2(e21,e21) = e21) | (op2(e21,e23) = e21) | 5.30/5.51 (e21 = op2(e21,e22))) & 5.30/5.51 ((e22 = op2(e21,e20)) | (op2(e21,e22) = e22) | (op2(e21,e23) = e22) | 5.30/5.51 (e22 = op2(e21,e21))) & 5.30/5.51 ((e22 = op2(e20,e21)) | (e22 = op2(e21,e21)) | (op2(e22,e21) = e22) | 5.30/5.51 (op2(e23,e21) = e22)) & 5.30/5.51 ((op2(e21,e21) = e23) | (e23 = op2(e23,e21)) | (e23 = op2(e22,e21)) | 5.30/5.51 (op2(e20,e21) = e23)) & 5.30/5.51 ((e20 = op2(e20,e22)) | (op2(e23,e22) = e20) | (op2(e22,e22) = e20) | 5.30/5.51 (e20 = op2(e21,e22))) & 5.30/5.51 ((op2(e22,e23) = e21) | (op2(e22,e22) = e21) | (op2(e22,e21) = e21) | 5.30/5.51 (e21 = op2(e22,e20))) & 5.30/5.51 ((e22 = op2(e21,e22)) | (op2(e23,e22) = e22) | (e22 = op2(e22,e22)) | 5.30/5.51 (op2(e20,e22) = e22)) & 5.30/5.51 ((e20 = op2(e20,e23)) | (e20 = op2(e23,e23)) | (op2(e22,e23) = e20) | 5.30/5.51 (e20 = op2(e21,e23))) & 5.30/5.51 ((e21 = op2(e23,e21)) | (op2(e23,e22) = e21) | (e21 = op2(e23,e23)) | 5.30/5.51 (op2(e23,e20) = e21)) & 5.30/5.51 ((e21 = op2(e20,e23)) | (e21 = op2(e22,e23)) | (e21 = op2(e23,e23)) | 5.30/5.51 (e21 = op2(e21,e23))) & 5.30/5.51 ((op2(e23,e20) = e22) | (op2(e23,e21) = e22) | (e22 = op2(e23,e22)) | 5.30/5.51 (e22 = op2(e23,e23))) & 5.30/5.51 ((e23 = op2(e22,e23)) | (op2(e23,e23) = e23) | (e23 = op2(e21,e23)) | 5.30/5.51 (e23 = op2(e20,e23))) & 5.30/5.51 ((e23 = op2(e23,e20)) | (op2(e23,e22) = e23) | (op2(e23,e23) = e23) | 5.30/5.51 (op2(e23,e21) = e23)) & 5.30/5.51 ((e22 = op2(e22,e23)) | (e22 = op2(e23,e23)) | (op2(e21,e23) = e22) | 5.30/5.51 (op2(e20,e23) = e22)) & 5.30/5.51 ((e20 = op2(e23,e21)) | (op2(e23,e23) = e20) | (e20 = op2(e23,e22)) | 5.30/5.51 (op2(e23,e20) = e20)) & 5.30/5.51 ((e23 = op2(e22,e22)) | (op2(e23,e22) = e23) | (op2(e21,e22) = e23) | 5.30/5.51 (op2(e20,e22) = e23)) & 5.30/5.51 ((e23 = op2(e22,e20)) | (op2(e22,e23) = e23) | (e23 = op2(e22,e22)) | 5.30/5.51 (op2(e22,e21) = e23)) & 5.30/5.51 ((e22 = op2(e22,e21)) | (e22 = op2(e22,e23)) | (op2(e22,e22) = e22) | 5.30/5.51 (op2(e22,e20) = e22)) & 5.30/5.51 ((op2(e20,e22) = e21) | (e21 = op2(e22,e22)) | (op2(e23,e22) = e21) | 5.30/5.51 (e21 = op2(e21,e22))) & 5.30/5.51 ((e20 = op2(e22,e20)) | (e20 = op2(e22,e21)) | (e20 = op2(e22,e23)) | 5.30/5.51 (e20 = op2(e22,e22))) & 5.30/5.51 ((e23 = op2(e21,e20)) | (op2(e21,e21) = e23) | (e23 = op2(e21,e23)) | 5.30/5.51 (e23 = op2(e21,e22))) & 5.30/5.51 ((e21 = op2(e20,e21)) | (op2(e22,e21) = e21) | (e21 = op2(e23,e21)) | 5.30/5.51 (op2(e21,e21) = e21)) & 5.30/5.51 ((e20 = op2(e23,e21)) | (e20 = op2(e22,e21)) | (op2(e21,e21) = e20) | 5.30/5.51 (e20 = op2(e20,e21))) & 5.30/5.51 ((op2(e21,e20) = e20) | (op2(e21,e21) = e20) | (op2(e21,e22) = e20) | 5.30/5.51 (e20 = op2(e21,e23))) & 5.30/5.51 ((op2(e20,e20) = e22) | (e22 = op2(e20,e21)) | (op2(e20,e23) = e22) | 5.30/5.51 (e22 = op2(e20,e22))) & 5.30/5.51 ((op2(e20,e20) = e21) | (e21 = op2(e21,e20)) | (e21 = op2(e23,e20)) | 5.30/5.51 (e21 = op2(e22,e20))) & 5.30/5.51 ((op2(e20,e20) = e21) | (e21 = op2(e20,e23)) | (op2(e20,e22) = e21) | 5.30/5.51 (e21 = op2(e20,e21))) & 5.30/5.51 ((e20 = op2(e20,e21)) | (op2(e20,e22) = e20) | (e20 = op2(e20,e23)) | 5.30/5.51 (op2(e20,e20) = e20)))). 5.30/5.51 tff('101', plain, 5.30/5.51 (e23 = op2(e22, e22) 5.30/5.51 | op2(e23, e22) = e23 5.30/5.51 | op2(e21, e22) = e23 5.30/5.51 | op2(e20, e22) = e23), 5.30/5.51 inference('cnf', [status(esa)], [ax4])). 5.30/5.51 tff(ax16, axiom, 5.30/5.51 ((op2(op2(e22,op2(e22,e22)),e22) = h3(e10)) & (h3(e11) = op2(e22,e22)) & 5.30/5.51 (h3(e12) = op2(e22,op2(e22,e22))) & (h3(e13) = e22))). 5.30/5.51 tff('102', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('103', plain, 5.30/5.51 (e23 = h3(e11) 5.30/5.51 | op2(e23, e22) = e23 5.30/5.51 | op2(e21, e22) = e23 5.30/5.51 | op2(e20, e22) = e23), 5.30/5.51 inference('demod', [status(thm)], ['101', '102'])). 5.30/5.51 tff('104', plain, 5.30/5.51 (op2(e21, e22) = e23) | (e23 = op2(e23, e22)) | (e23 = h3(e11)) | 5.30/5.51 (op2(e20, e22) = e23), inference('split', [status(esa)], ['103'])). 5.30/5.51 tff(ax3, axiom, 5.30/5.51 (((op2(e20,e20) = e23) | (op2(e20,e20) = e22) | (op2(e20,e20) = e21) | 5.30/5.51 (op2(e20,e20) = e20)) & 5.30/5.51 ((op2(e20,e21) = e20) | (e23 = op2(e20,e21)) | (e22 = op2(e20,e21)) | 5.30/5.51 (e21 = op2(e20,e21))) & 5.30/5.51 ((op2(e21,e22) = e22) | (op2(e21,e22) = e23) | (e21 = op2(e21,e22)) | 5.30/5.51 (op2(e21,e22) = e20)) & 5.30/5.51 ((e21 = op2(e22,e20)) | (e23 = op2(e22,e20)) | (e22 = op2(e22,e20)) | 5.30/5.51 (op2(e22,e20) = e20)) & 5.30/5.51 ((e21 = op2(e22,e21)) | (op2(e22,e21) = e23) | (op2(e22,e21) = e22) | 5.30/5.51 (e20 = op2(e22,e21))) & 5.30/5.51 ((op2(e23,e21) = e20) | (op2(e23,e21) = e22) | (e23 = op2(e23,e21)) | 5.30/5.51 (e21 = op2(e23,e21))) & 5.30/5.51 ((op2(e23,e23) = e20) | (op2(e23,e23) = e22) | (e23 = op2(e23,e23)) | 5.30/5.51 (e21 = op2(e23,e23))) & 5.30/5.51 ((e20 = op2(e23,e22)) | (e21 = op2(e23,e22)) | (e23 = op2(e23,e22)) | 5.30/5.51 (op2(e23,e22) = e22)) & 5.30/5.51 ((op2(e23,e20) = e20) | (op2(e23,e20) = e23) | (op2(e23,e20) = e22) | 5.30/5.51 (e21 = op2(e23,e20))) & 5.30/5.51 ((e20 = op2(e22,e23)) | (op2(e22,e23) = e21) | (e22 = op2(e22,e23)) | 5.30/5.51 (op2(e22,e23) = e23)) & 5.30/5.51 ((op2(e22,e22) = e20) | (op2(e22,e22) = e21) | (op2(e22,e22) = e23) | 5.30/5.51 (e22 = op2(e22,e22))) & 5.30/5.51 ((e20 = op2(e21,e23)) | (e22 = op2(e21,e23)) | (op2(e21,e23) = e23) | 5.30/5.51 (e21 = op2(e21,e23))) & 5.30/5.51 ((e20 = op2(e21,e21)) | (op2(e21,e21) = e21) | (op2(e21,e21) = e23) | 5.30/5.51 (e22 = op2(e21,e21))) & 5.30/5.51 ((e20 = op2(e21,e20)) | (op2(e21,e20) = e22) | (e23 = op2(e21,e20)) | 5.30/5.51 (e21 = op2(e21,e20))) & 5.30/5.51 ((op2(e20,e23) = e21) | (e23 = op2(e20,e23)) | (op2(e20,e23) = e22) | 5.30/5.51 (e20 = op2(e20,e23))) & 5.30/5.51 ((op2(e20,e22) = e20) | (op2(e20,e22) = e23) | (op2(e20,e22) = e22) | 5.30/5.51 (e21 = op2(e20,e22))))). 5.30/5.51 tff('105', plain, 5.30/5.51 (op2(e22, e22) = e20 5.30/5.51 | op2(e22, e22) = e21 5.30/5.51 | op2(e22, e22) = e23 5.30/5.51 | e22 = op2(e22, e22)), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('106', plain, (e22 = op2(e22, e22)) <= ((e22 = op2(e22, e22))), 5.30/5.51 inference('split', [status(esa)], ['105'])). 5.30/5.51 tff('107', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('108', plain, (h3(e11) = e22) <= ((e22 = op2(e22, e22))), 5.30/5.51 inference('sup+', [status(thm)], ['106', '107'])). 5.30/5.51 tff('109', plain, 5.30/5.51 (op2(e22, op2(e22, e23)) = e22) <= ((op2(e22, op2(e22, e23)) = e22)), 5.30/5.51 inference('split', [status(esa)], ['90'])). 5.30/5.51 tff('110', plain, op2(op2(e23, op2(e23, e23)), e23) = e20, 5.30/5.51 inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('111', plain, e21 = op2(e23, e23), 5.30/5.51 inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('112', plain, e22 = op2(e23, e21), 5.30/5.51 inference('demod', [status(thm)], ['92', '93'])). 5.30/5.51 tff('113', plain, op2(e22, e23) = e20, 5.30/5.51 inference('demod', [status(thm)], ['110', '111', '112'])). 5.30/5.51 tff('114', plain, (op2(e22, e20) = e22) <= ((op2(e22, op2(e22, e23)) = e22)), 5.30/5.51 inference('demod', [status(thm)], ['109', '113'])). 5.30/5.51 tff(ax6, axiom, 5.30/5.51 ((op2(e20,e20) != op2(e22,e20)) & (op2(e20,e21) != op2(e22,e21)) & 5.30/5.51 (op2(e20,e21) != op2(e23,e21)) & (op2(e22,e21) != op2(e21,e21)) & 5.30/5.51 (op2(e21,e21) != op2(e23,e21)) & (op2(e22,e22) != op2(e20,e22)) & 5.30/5.51 (op2(e21,e22) != op2(e22,e22)) & (op2(e23,e22) != op2(e21,e22)) & 5.30/5.51 (op2(e23,e22) != op2(e22,e22)) & (op2(e21,e23) != op2(e20,e23)) & 5.30/5.51 (op2(e20,e23) != op2(e22,e23)) & (op2(e22,e23) != op2(e23,e23)) & 5.30/5.51 (op2(e20,e20) != op2(e20,e22)) & (op2(e20,e23) != op2(e20,e20)) & 5.30/5.51 (op2(e20,e21) != op2(e20,e22)) & (op2(e21,e21) != op2(e21,e20)) & 5.30/5.51 (op2(e21,e20) != op2(e21,e23)) & (op2(e21,e22) != op2(e21,e23)) & 5.30/5.51 (op2(e22,e20) != op2(e22,e21)) & (op2(e22,e21) != op2(e22,e22)) & 5.30/5.51 (op2(e22,e21) != op2(e22,e23)) & (op2(e23,e22) != op2(e23,e20)) & 5.30/5.51 (op2(e23,e22) != op2(e23,e23)) & (op2(e23,e23) != op2(e23,e21)) & 5.30/5.51 (op2(e23,e22) != op2(e23,e21)) & (op2(e23,e20) != op2(e23,e23)) & 5.30/5.51 (op2(e23,e20) != op2(e23,e21)) & (op2(e22,e23) != op2(e22,e22)) & 5.30/5.51 (op2(e22,e23) != op2(e22,e20)) & (op2(e22,e22) != op2(e22,e20)) & 5.30/5.51 (op2(e21,e23) != op2(e21,e21)) & (op2(e21,e22) != op2(e21,e21)) & 5.30/5.51 (op2(e21,e20) != op2(e21,e22)) & (op2(e20,e23) != op2(e20,e22)) & 5.30/5.51 (op2(e20,e23) != op2(e20,e21)) & (op2(e20,e20) != op2(e20,e21)) & 5.30/5.51 (op2(e23,e23) != op2(e21,e23)) & (op2(e21,e23) != op2(e22,e23)) & 5.30/5.51 (op2(e23,e23) != op2(e20,e23)) & (op2(e20,e22) != op2(e23,e22)) & 5.30/5.51 (op2(e21,e22) != op2(e20,e22)) & (op2(e22,e21) != op2(e23,e21)) & 5.30/5.51 (op2(e20,e21) != op2(e21,e21)) & (op2(e22,e20) != op2(e23,e20)) & 5.30/5.51 (op2(e21,e20) != op2(e23,e20)) & (op2(e22,e20) != op2(e21,e20)) & 5.30/5.51 (op2(e20,e20) != op2(e23,e20)) & (op2(e21,e20) != op2(e20,e20)))). 5.30/5.51 tff('115', plain, op2(e22, e22) != op2(e22, e20), 5.30/5.51 inference('cnf', [status(esa)], [ax6])). 5.30/5.51 tff('116', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('117', plain, h3(e11) != op2(e22, e20), 5.30/5.51 inference('demod', [status(thm)], ['115', '116'])). 5.30/5.51 tff('118', plain, (h3(e11) != e22) <= ((op2(e22, op2(e22, e23)) = e22)), 5.30/5.51 inference('sup-', [status(thm)], ['114', '117'])). 5.30/5.51 tff('119', plain, 5.30/5.51 (e22 != e22) <= ((e22 = op2(e22, e22)) & (op2(e22, op2(e22, e23)) = e22)), 5.30/5.51 inference('sup-', [status(thm)], ['108', '118'])). 5.30/5.51 tff('120', plain, 5.30/5.51 ~ (e22 = op2(e22, e22)) | ~ (op2(e22, op2(e22, e23)) = e22), 5.30/5.51 inference('simplify', [status(thm)], ['119'])). 5.30/5.51 tff('121', plain, 5.30/5.51 (e23 = op2(e22, e23) 5.30/5.51 | op2(e23, e23) = e23 5.30/5.51 | e23 = op2(e21, e23) 5.30/5.51 | e23 = op2(e20, e23)), 5.30/5.51 inference('cnf', [status(esa)], [ax4])). 5.30/5.51 tff('122', plain, (e23 = op2(e20, e23)) <= ((e23 = op2(e20, e23))), 5.30/5.51 inference('split', [status(esa)], ['121'])). 5.30/5.51 tff('123', plain, 5.30/5.51 (e23 = op2(e23, op2(e23, e23)) 5.30/5.51 | op2(e22, op2(e22, e23)) = e22 5.30/5.51 | e21 = op2(e21, op2(e21, e23)) 5.30/5.51 | op2(e20, op2(e20, e23)) = e20), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.51 tff('124', plain, e21 = op2(e23, e23), 5.30/5.51 inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('125', plain, 5.30/5.51 (e23 = op2(e23, e21) 5.30/5.51 | op2(e22, op2(e22, e23)) = e22 5.30/5.51 | e21 = op2(e21, op2(e21, e23)) 5.30/5.51 | op2(e20, op2(e20, e23)) = e20), 5.30/5.51 inference('demod', [status(thm)], ['123', '124'])). 5.30/5.51 tff(ax17, axiom, 5.30/5.51 ((h4(e10) = op2(op2(e23,op2(e23,e23)),e23)) & 5.30/5.51 (h4(e12) = op2(e23,op2(e23,e23))) & (h4(e11) = op2(e23,e23)) & 5.30/5.51 (h4(e13) = e23))). 5.30/5.51 tff('126', plain, h4(e12) = op2(e23, op2(e23, e23)), 5.30/5.51 inference('cnf', [status(esa)], [ax17])). 5.30/5.51 tff('127', plain, e21 = op2(e23, e23), 5.30/5.51 inference('cnf', [status(esa)], [ax13])). 5.30/5.51 tff('128', plain, h4(e12) = op2(e23, e21), 5.30/5.51 inference('demod', [status(thm)], ['126', '127'])). 5.30/5.51 tff('129', plain, 5.30/5.51 (e23 = h4(e12) 5.30/5.51 | op2(e22, op2(e22, e23)) = e22 5.30/5.51 | e21 = op2(e21, op2(e21, e23)) 5.30/5.51 | op2(e20, op2(e20, e23)) = e20), 5.30/5.51 inference('demod', [status(thm)], ['125', '128'])). 5.30/5.51 tff('130', plain, 5.30/5.51 (op2(e20, op2(e20, e23)) = e20) <= ((op2(e20, op2(e20, e23)) = e20)), 5.30/5.51 inference('split', [status(esa)], ['129'])). 5.30/5.51 tff('131', plain, 5.30/5.51 (op2(e20, e23) = e20) 5.30/5.51 <= ((e23 = op2(e20, e23)) & (op2(e20, op2(e20, e23)) = e20)), 5.30/5.51 inference('sup+', [status(thm)], ['122', '130'])). 5.30/5.51 tff('132', plain, op2(e20, e23) != op2(e22, e23), 5.30/5.51 inference('cnf', [status(esa)], [ax6])). 5.30/5.51 tff('133', plain, op2(e22, e23) = e20, 5.30/5.51 inference('demod', [status(thm)], ['110', '111', '112'])). 5.30/5.51 tff('134', plain, op2(e20, e23) != e20, 5.30/5.51 inference('demod', [status(thm)], ['132', '133'])). 5.30/5.51 tff('135', plain, 5.30/5.51 ~ (op2(e20, op2(e20, e23)) = e20) | ~ (e23 = op2(e20, e23)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['131', '134'])). 5.30/5.51 tff('136', plain, (e23 = op2(e20, e23)) <= ((e23 = op2(e20, e23))), 5.30/5.51 inference('split', [status(esa)], ['121'])). 5.30/5.51 tff('137', plain, 5.30/5.51 (e22 = op2(e22, e23) 5.30/5.51 | e22 = op2(e23, e23) 5.30/5.51 | op2(e21, e23) = e22 5.30/5.51 | op2(e20, e23) = e22), 5.30/5.51 inference('cnf', [status(esa)], [ax4])). 5.30/5.51 tff('138', plain, (op2(e20, e23) = e22) <= ((op2(e20, e23) = e22)), 5.30/5.51 inference('split', [status(esa)], ['137'])). 5.30/5.51 tff('139', plain, 5.30/5.51 (e23 = e22) <= ((op2(e20, e23) = e22) & (e23 = op2(e20, e23))), 5.30/5.51 inference('sup+', [status(thm)], ['136', '138'])). 5.30/5.51 tff('140', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.51 tff('141', plain, ~ (op2(e20, e23) = e22) | ~ (e23 = op2(e20, e23)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['139', '140'])). 5.30/5.51 tff('142', plain, 5.30/5.51 (e20 = op2(e23, e22) 5.30/5.51 | e21 = op2(e23, e22) 5.30/5.51 | e23 = op2(e23, e22) 5.30/5.51 | op2(e23, e22) = e22), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('143', plain, (e23 = op2(e23, e22)) <= ((e23 = op2(e23, e22))), 5.30/5.51 inference('split', [status(esa)], ['142'])). 5.30/5.51 tff('144', plain, 5.30/5.51 (op2(e23, e20) = e20 5.30/5.51 | op2(e23, e20) = e23 5.30/5.51 | op2(e23, e20) = e22 5.30/5.51 | e21 = op2(e23, e20)), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('145', plain, (op2(e23, e20) = e23) <= ((op2(e23, e20) = e23)), 5.30/5.51 inference('split', [status(esa)], ['144'])). 5.30/5.51 tff('146', plain, op2(e23, e22) != op2(e23, e20), 5.30/5.51 inference('cnf', [status(esa)], [ax6])). 5.30/5.51 tff('147', plain, (op2(e23, e22) != e23) <= ((op2(e23, e20) = e23)), 5.30/5.51 inference('sup-', [status(thm)], ['145', '146'])). 5.30/5.51 tff('148', plain, 5.30/5.51 (e23 != e23) <= ((e23 = op2(e23, e22)) & (op2(e23, e20) = e23)), 5.30/5.51 inference('sup-', [status(thm)], ['143', '147'])). 5.30/5.51 tff('149', plain, ~ (e23 = op2(e23, e22)) | ~ (op2(e23, e20) = e23), 5.30/5.51 inference('simplify', [status(thm)], ['148'])). 5.30/5.51 tff('150', plain, 5.30/5.51 (op2(e22, e22) = e21) | (e22 = op2(e22, e22)) | (op2(e22, e22) = e20) | 5.30/5.51 (op2(e22, e22) = e23), inference('split', [status(esa)], ['105'])). 5.30/5.51 tff('151', plain, (op2(e22, e22) = e20) <= ((op2(e22, e22) = e20)), 5.30/5.51 inference('split', [status(esa)], ['105'])). 5.30/5.51 tff('152', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('153', plain, (h3(e11) = e20) <= ((op2(e22, e22) = e20)), 5.30/5.51 inference('sup+', [status(thm)], ['151', '152'])). 5.30/5.51 tff('154', plain, 5.30/5.51 (e20 = op2(e22, e23) 5.30/5.51 | op2(e22, e23) = e21 5.30/5.51 | e22 = op2(e22, e23) 5.30/5.51 | op2(e22, e23) = e23), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('155', plain, (e20 = op2(e22, e23)) <= ((e20 = op2(e22, e23))), 5.30/5.51 inference('split', [status(esa)], ['154'])). 5.30/5.51 tff('156', plain, op2(e22, e23) != op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax6])). 5.30/5.51 tff('157', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('158', plain, op2(e22, e23) != h3(e11), 5.30/5.51 inference('demod', [status(thm)], ['156', '157'])). 5.30/5.51 tff('159', plain, (e20 != h3(e11)) <= ((e20 = op2(e22, e23))), 5.30/5.51 inference('sup-', [status(thm)], ['155', '158'])). 5.30/5.51 tff('160', plain, 5.30/5.51 (e20 != e20) <= ((e20 = op2(e22, e23)) & (op2(e22, e22) = e20)), 5.30/5.51 inference('sup-', [status(thm)], ['153', '159'])). 5.30/5.51 tff('161', plain, ~ (op2(e22, e22) = e20) | ~ (e20 = op2(e22, e23)), 5.30/5.51 inference('simplify', [status(thm)], ['160'])). 5.30/5.51 tff('162', plain, (op2(e22, e22) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.51 inference('split', [status(esa)], ['105'])). 5.30/5.51 tff('163', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('164', plain, (h3(e11) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.51 inference('sup+', [status(thm)], ['162', '163'])). 5.30/5.51 tff('165', plain, 5.30/5.51 (op2(e20, e22) = e21 5.30/5.51 | e21 = op2(e22, e22) 5.30/5.51 | op2(e23, e22) = e21 5.30/5.51 | e21 = op2(e21, e22)), 5.30/5.51 inference('cnf', [status(esa)], [ax4])). 5.30/5.51 tff('166', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('167', plain, 5.30/5.51 (op2(e20, e22) = e21 5.30/5.51 | e21 = h3(e11) 5.30/5.51 | op2(e23, e22) = e21 5.30/5.51 | e21 = op2(e21, e22)), 5.30/5.51 inference('demod', [status(thm)], ['165', '166'])). 5.30/5.51 tff('168', plain, (op2(e20, e22) = e21) <= ((e21 = op2(e20, e22))), 5.30/5.51 inference('split', [status(esa)], ['167'])). 5.30/5.51 tff('169', plain, op2(e22, e22) != op2(e20, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax6])). 5.30/5.51 tff('170', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('171', plain, h3(e11) != op2(e20, e22), 5.30/5.51 inference('demod', [status(thm)], ['169', '170'])). 5.30/5.51 tff('172', plain, (h3(e11) != e21) <= ((e21 = op2(e20, e22))), 5.30/5.51 inference('sup-', [status(thm)], ['168', '171'])). 5.30/5.51 tff('173', plain, 5.30/5.51 (e21 != e21) <= ((op2(e22, e22) = e21) & (e21 = op2(e20, e22))), 5.30/5.51 inference('sup-', [status(thm)], ['164', '172'])). 5.30/5.51 tff('174', plain, ~ (e21 = op2(e20, e22)) | ~ (op2(e22, e22) = e21), 5.30/5.51 inference('simplify', [status(thm)], ['173'])). 5.30/5.51 tff('175', plain, 5.30/5.51 (op2(e20, e22) = e20 5.30/5.51 | op2(e20, e22) = e23 5.30/5.51 | op2(e20, e22) = e22 5.30/5.51 | e21 = op2(e20, e22)), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('176', plain, 5.30/5.51 (op2(e20, e22) = e22) | (e21 = op2(e20, e22)) | (op2(e20, e22) = e23) | 5.30/5.51 (op2(e20, e22) = e20), inference('split', [status(esa)], ['175'])). 5.30/5.51 tff('177', plain, (e23 = op2(e20, e23) | ~ zip_tseitin_26), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_44])). 5.30/5.51 tff('178', plain, (e23 = op2(e20, e23)) | ~ ( zip_tseitin_26), 5.30/5.51 inference('split', [status(esa)], ['177'])). 5.30/5.51 tff('179', plain, 5.30/5.51 (op2(e20, e22) = e23 5.30/5.51 | e23 = op2(e20, e23) 5.30/5.51 | op2(e20, e21) = e23 5.30/5.51 | e23 = op2(e20, e20)), 5.30/5.51 inference('cnf', [status(esa)], [ax4])). 5.30/5.51 tff('180', plain, (op2(e20, e22) = e23) <= ((op2(e20, e22) = e23)), 5.30/5.51 inference('split', [status(esa)], ['179'])). 5.30/5.51 tff('181', plain, (e23 = op2(e20, e23)) <= ((e23 = op2(e20, e23))), 5.30/5.51 inference('split', [status(esa)], ['121'])). 5.30/5.51 tff('182', plain, op2(e20, e23) != op2(e20, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax6])). 5.30/5.51 tff('183', plain, (e23 != op2(e20, e22)) <= ((e23 = op2(e20, e23))), 5.30/5.51 inference('sup-', [status(thm)], ['181', '182'])). 5.30/5.51 tff('184', plain, 5.30/5.51 (e23 != e23) <= ((e23 = op2(e20, e23)) & (op2(e20, e22) = e23)), 5.30/5.51 inference('sup-', [status(thm)], ['180', '183'])). 5.30/5.51 tff('185', plain, ~ (op2(e20, e22) = e23) | ~ (e23 = op2(e20, e23)), 5.30/5.51 inference('simplify', [status(thm)], ['184'])). 5.30/5.51 tff('186', plain, (op2(e20, e22) = e22 | ~ zip_tseitin_20), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_56])). 5.30/5.51 tff('187', plain, ~ ( zip_tseitin_20) | (op2(e20, e22) = e22), 5.30/5.51 inference('split', [status(esa)], ['186'])). 5.30/5.51 tff('188', plain, 5.30/5.51 (op2(e21, e22) = e22 5.30/5.51 | op2(e21, e22) = e23 5.30/5.51 | e21 = op2(e21, e22) 5.30/5.51 | op2(e21, e22) = e20), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('189', plain, (op2(e21, e22) = e23) <= ((op2(e21, e22) = e23)), 5.30/5.51 inference('split', [status(esa)], ['188'])). 5.30/5.51 tff('190', plain, 5.30/5.51 (e20 = op2(e21, e23) 5.30/5.51 | e22 = op2(e21, e23) 5.30/5.51 | op2(e21, e23) = e23 5.30/5.51 | e21 = op2(e21, e23)), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('191', plain, (e22 = op2(e21, e23)) <= ((e22 = op2(e21, e23))), 5.30/5.51 inference('split', [status(esa)], ['190'])). 5.30/5.51 tff('192', plain, 5.30/5.51 (e21 = op2(e21, op2(e21, e23))) <= ((e21 = op2(e21, op2(e21, e23)))), 5.30/5.51 inference('split', [status(esa)], ['90'])). 5.30/5.51 tff('193', plain, 5.30/5.51 (e21 = op2(e21, e22)) 5.30/5.51 <= ((e22 = op2(e21, e23)) & (e21 = op2(e21, op2(e21, e23)))), 5.30/5.51 inference('sup+', [status(thm)], ['191', '192'])). 5.30/5.51 tff('194', plain, 5.30/5.51 (e21 = e23) 5.30/5.51 <= ((op2(e21, e22) = e23) & 5.30/5.51 (e22 = op2(e21, e23)) & 5.30/5.51 (e21 = op2(e21, op2(e21, e23)))), 5.30/5.51 inference('sup+', [status(thm)], ['189', '193'])). 5.30/5.51 tff('195', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.51 tff('196', plain, 5.30/5.51 ~ (e21 = op2(e21, op2(e21, e23))) | ~ (op2(e21, e22) = e23) | 5.30/5.51 ~ (e22 = op2(e21, e23)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['194', '195'])). 5.30/5.51 tff('197', plain, 5.30/5.51 (op1(e13, e10) = e10 5.30/5.51 | op1(e13, e13) = e10 5.30/5.51 | e10 = op1(e13, e12) 5.30/5.51 | e10 = op1(e13, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('198', plain, 5.30/5.51 (e10 = op1(e13, e10)) | (op1(e13, e12) = e10) | (e10 = op1(e13, e11)) | 5.30/5.51 (op1(e13, e13) = e10), inference('split', [status(esa)], ['197'])). 5.30/5.51 tff(co1, conjecture, 5.30/5.51 (((h1(op1(e10,e10)) = op2(h1(e10),h1(e10))) & 5.30/5.51 (h1(op1(e10,e11)) = op2(h1(e10),h1(e11))) & 5.30/5.51 (h1(op1(e10,e12)) = op2(h1(e10),h1(e12))) & 5.30/5.51 (h1(op1(e10,e13)) = op2(h1(e10),h1(e13))) & 5.30/5.51 (h1(op1(e12,e10)) = op2(h1(e12),h1(e10))) & 5.30/5.51 (op2(h1(e12),h1(e11)) = h1(op1(e12,e11))) & 5.30/5.51 (h1(op1(e12,e13)) = op2(h1(e12),h1(e13))) & 5.30/5.51 (op2(h1(e13),h1(e10)) = h1(op1(e13,e10))) & 5.30/5.51 (h1(op1(e13,e11)) = op2(h1(e13),h1(e11))) & 5.30/5.51 (h1(op1(e13,e12)) = op2(h1(e13),h1(e12))) & 5.30/5.51 (op2(h1(e13),h1(e13)) = h1(op1(e13,e13))) & 5.30/5.51 ((e20 = h1(e10)) | (h1(e13) = e20) | (h1(e12) = e20) | (h1(e11) = e20)) & 5.30/5.51 ((h1(e13) = e23) | (h1(e12) = e23) | (e23 = h1(e11)) | (e23 = h1(e10))) & 5.30/5.51 ((e22 = h1(e13)) | (e22 = h1(e12)) | (e22 = h1(e11)) | (e22 = h1(e10))) & 5.30/5.51 ((e21 = h1(e10)) | (h1(e11) = e21) | (e21 = h1(e12)) | (e21 = h1(e13))) & 5.30/5.51 (h1(op1(e12,e12)) = op2(h1(e12),h1(e12))) & 5.30/5.51 (op2(h1(e11),h1(e13)) = h1(op1(e11,e13))) & 5.30/5.51 (op2(h1(e11),h1(e12)) = h1(op1(e11,e12))) & 5.30/5.51 (op2(h1(e11),h1(e11)) = h1(op1(e11,e11))) & 5.30/5.51 (op2(h1(e11),h1(e10)) = h1(op1(e11,e10)))) | 5.30/5.51 ((h3(op1(e10,e10)) = op2(h3(e10),h3(e10))) & 5.30/5.51 (op2(h3(e10),h3(e11)) = h3(op1(e10,e11))) & 5.30/5.51 (op2(h3(e10),h3(e12)) = h3(op1(e10,e12))) & 5.30/5.51 (h3(op1(e10,e13)) = op2(h3(e10),h3(e13))) & 5.30/5.51 (h3(op1(e11,e10)) = op2(h3(e11),h3(e10))) & 5.30/5.51 (op2(h3(e11),h3(e11)) = h3(op1(e11,e11))) & 5.30/5.51 (op2(h3(e11),h3(e12)) = h3(op1(e11,e12))) & 5.30/5.51 (h3(op1(e12,e10)) = op2(h3(e12),h3(e10))) & 5.30/5.51 (op2(h3(e12),h3(e11)) = h3(op1(e12,e11))) & 5.30/5.51 (op2(h3(e13),h3(e10)) = h3(op1(e13,e10))) & 5.30/5.51 (h3(op1(e13,e12)) = op2(h3(e13),h3(e12))) & 5.30/5.51 (op2(h3(e13),h3(e13)) = h3(op1(e13,e13))) & 5.30/5.51 ((h3(e10) = e20) | (e20 = h3(e12)) | (h3(e13) = e20) | (h3(e11) = e20)) & 5.30/5.51 ((e21 = h3(e10)) | (h3(e13) = e21) | (h3(e12) = e21) | (h3(e11) = e21)) & 5.30/5.51 ((h3(e11) = e22) | (e22 = h3(e13)) | (h3(e12) = e22) | (h3(e10) = e22)) & 5.30/5.51 ((e23 = h3(e11)) | (e23 = h3(e13)) | (h3(e12) = e23) | (h3(e10) = e23)) & 5.30/5.51 (op2(h3(e13),h3(e11)) = h3(op1(e13,e11))) & 5.30/5.51 (h3(op1(e12,e13)) = op2(h3(e12),h3(e13))) & 5.30/5.51 (op2(h3(e12),h3(e12)) = h3(op1(e12,e12))) & 5.30/5.51 (h3(op1(e11,e13)) = op2(h3(e11),h3(e13)))) | 5.30/5.51 ((op2(h4(e10),h4(e10)) = h4(op1(e10,e10))) & 5.30/5.51 (op2(h4(e10),h4(e11)) = h4(op1(e10,e11))) & 5.30/5.51 (op2(h4(e11),h4(e10)) = h4(op1(e11,e10))) & 5.30/5.51 (h4(op1(e11,e11)) = op2(h4(e11),h4(e11))) & 5.30/5.51 (h4(op1(e11,e12)) = op2(h4(e11),h4(e12))) & 5.30/5.51 (op2(h4(e12),h4(e10)) = h4(op1(e12,e10))) & 5.30/5.51 (h4(op1(e13,e10)) = op2(h4(e13),h4(e10))) & 5.30/5.51 (op2(h4(e13),h4(e12)) = h4(op1(e13,e12))) & 5.30/5.51 ((e20 = h4(e10)) | (e20 = h4(e13)) | (e20 = h4(e12)) | (h4(e11) = e20)) & 5.30/5.51 ((e21 = h4(e10)) | (e21 = h4(e11)) | (h4(e12) = e21) | (h4(e13) = e21)) & 5.30/5.51 ((h4(e12) = e22) | (h4(e13) = e22) | (e22 = h4(e11)) | (h4(e10) = e22)) & 5.30/5.51 ((h4(e12) = e23) | (h4(e13) = e23) | (h4(e11) = e23) | (e23 = h4(e10))) & 5.30/5.51 (op2(h4(e13),h4(e13)) = h4(op1(e13,e13))) & 5.30/5.51 (h4(op1(e13,e11)) = op2(h4(e13),h4(e11))) & 5.30/5.51 (h4(op1(e12,e13)) = op2(h4(e12),h4(e13))) & 5.30/5.51 (op2(h4(e12),h4(e12)) = h4(op1(e12,e12))) & 5.30/5.51 (h4(op1(e12,e11)) = op2(h4(e12),h4(e11))) & 5.30/5.51 (h4(op1(e11,e13)) = op2(h4(e11),h4(e13))) & 5.30/5.51 (h4(op1(e10,e13)) = op2(h4(e10),h4(e13))) & 5.30/5.51 (h4(op1(e10,e12)) = op2(h4(e10),h4(e12)))) | 5.30/5.51 ((h2(op1(e10,e11)) = op2(h2(e10),h2(e11))) & 5.30/5.51 (op2(h2(e10),h2(e12)) = h2(op1(e10,e12))) & 5.30/5.51 (h2(op1(e11,e10)) = op2(h2(e11),h2(e10))) & 5.30/5.51 (h2(op1(e11,e11)) = op2(h2(e11),h2(e11))) & 5.30/5.51 (h2(op1(e11,e13)) = op2(h2(e11),h2(e13))) & 5.30/5.51 (h2(op1(e12,e10)) = op2(h2(e12),h2(e10))) & 5.30/5.51 (op2(h2(e12),h2(e11)) = h2(op1(e12,e11))) & 5.30/5.51 (op2(h2(e12),h2(e12)) = h2(op1(e12,e12))) & 5.30/5.51 (op2(h2(e13),h2(e12)) = h2(op1(e13,e12))) & 5.30/5.51 ((h2(e10) = e20) | (e20 = h2(e11)) | (h2(e12) = e20) | (h2(e13) = e20)) & 5.30/5.51 ((h2(e10) = e22) | (h2(e12) = e22) | (e22 = h2(e13)) | (e22 = h2(e11))) & 5.30/5.51 ((e23 = h2(e13)) | (h2(e12) = e23) | (e23 = h2(e11)) | (h2(e10) = e23)) & 5.30/5.51 ((e21 = h2(e12)) | (e21 = h2(e13)) | (h2(e11) = e21) | (e21 = h2(e10))) & 5.30/5.51 (op2(h2(e13),h2(e13)) = h2(op1(e13,e13))) & 5.30/5.51 (op2(h2(e13),h2(e11)) = h2(op1(e13,e11))) & 5.30/5.51 (op2(h2(e13),h2(e10)) = h2(op1(e13,e10))) & 5.30/5.51 (h2(op1(e12,e13)) = op2(h2(e12),h2(e13))) & 5.30/5.51 (op2(h2(e11),h2(e12)) = h2(op1(e11,e12))) & 5.30/5.51 (op2(h2(e10),h2(e13)) = h2(op1(e10,e13))) & 5.30/5.51 (op2(h2(e10),h2(e10)) = h2(op1(e10,e10)))))). 5.30/5.51 tff(zf_stmt_66, negated_conjecture, 5.30/5.51 (~ 5.30/5.51 (((h1(op1(e10,e10)) = op2(h1(e10),h1(e10))) & 5.30/5.51 (h1(op1(e10,e11)) = op2(h1(e10),h1(e11))) & 5.30/5.51 (h1(op1(e10,e12)) = op2(h1(e10),h1(e12))) & 5.30/5.51 (h1(op1(e10,e13)) = op2(h1(e10),h1(e13))) & 5.30/5.51 (h1(op1(e12,e10)) = op2(h1(e12),h1(e10))) & 5.30/5.51 (op2(h1(e12),h1(e11)) = h1(op1(e12,e11))) & 5.30/5.51 (h1(op1(e12,e13)) = op2(h1(e12),h1(e13))) & 5.30/5.51 (op2(h1(e13),h1(e10)) = h1(op1(e13,e10))) & 5.30/5.51 (h1(op1(e13,e11)) = op2(h1(e13),h1(e11))) & 5.30/5.51 (h1(op1(e13,e12)) = op2(h1(e13),h1(e12))) & 5.30/5.51 (op2(h1(e13),h1(e13)) = h1(op1(e13,e13))) & 5.30/5.51 ((e20 = h1(e10)) | (h1(e13) = e20) | (h1(e12) = e20) | (h1(e11) = e20)) & 5.30/5.51 ((h1(e13) = e23) | (h1(e12) = e23) | (e23 = h1(e11)) | (e23 = h1(e10))) & 5.30/5.51 ((e22 = h1(e13)) | (e22 = h1(e12)) | (e22 = h1(e11)) | (e22 = h1(e10))) & 5.30/5.51 ((e21 = h1(e10)) | (h1(e11) = e21) | (e21 = h1(e12)) | (e21 = h1(e13))) & 5.30/5.51 (h1(op1(e12,e12)) = op2(h1(e12),h1(e12))) & 5.30/5.51 (op2(h1(e11),h1(e13)) = h1(op1(e11,e13))) & 5.30/5.51 (op2(h1(e11),h1(e12)) = h1(op1(e11,e12))) & 5.30/5.51 (op2(h1(e11),h1(e11)) = h1(op1(e11,e11))) & 5.30/5.51 (op2(h1(e11),h1(e10)) = h1(op1(e11,e10)))) | 5.30/5.51 ((h3(op1(e10,e10)) = op2(h3(e10),h3(e10))) & 5.30/5.51 (op2(h3(e10),h3(e11)) = h3(op1(e10,e11))) & 5.30/5.51 (op2(h3(e10),h3(e12)) = h3(op1(e10,e12))) & 5.30/5.51 (h3(op1(e10,e13)) = op2(h3(e10),h3(e13))) & 5.30/5.51 (h3(op1(e11,e10)) = op2(h3(e11),h3(e10))) & 5.30/5.51 (op2(h3(e11),h3(e11)) = h3(op1(e11,e11))) & 5.30/5.51 (op2(h3(e11),h3(e12)) = h3(op1(e11,e12))) & 5.30/5.51 (h3(op1(e12,e10)) = op2(h3(e12),h3(e10))) & 5.30/5.51 (op2(h3(e12),h3(e11)) = h3(op1(e12,e11))) & 5.30/5.51 (op2(h3(e13),h3(e10)) = h3(op1(e13,e10))) & 5.30/5.51 (h3(op1(e13,e12)) = op2(h3(e13),h3(e12))) & 5.30/5.51 (op2(h3(e13),h3(e13)) = h3(op1(e13,e13))) & 5.30/5.51 ((h3(e10) = e20) | (e20 = h3(e12)) | (h3(e13) = e20) | (h3(e11) = e20)) & 5.30/5.51 ((e21 = h3(e10)) | (h3(e13) = e21) | (h3(e12) = e21) | (h3(e11) = e21)) & 5.30/5.51 ((h3(e11) = e22) | (e22 = h3(e13)) | (h3(e12) = e22) | (h3(e10) = e22)) & 5.30/5.51 ((e23 = h3(e11)) | (e23 = h3(e13)) | (h3(e12) = e23) | (h3(e10) = e23)) & 5.30/5.51 (op2(h3(e13),h3(e11)) = h3(op1(e13,e11))) & 5.30/5.51 (h3(op1(e12,e13)) = op2(h3(e12),h3(e13))) & 5.30/5.51 (op2(h3(e12),h3(e12)) = h3(op1(e12,e12))) & 5.30/5.51 (h3(op1(e11,e13)) = op2(h3(e11),h3(e13)))) | 5.30/5.51 ((op2(h4(e10),h4(e10)) = h4(op1(e10,e10))) & 5.30/5.51 (op2(h4(e10),h4(e11)) = h4(op1(e10,e11))) & 5.30/5.51 (op2(h4(e11),h4(e10)) = h4(op1(e11,e10))) & 5.30/5.51 (h4(op1(e11,e11)) = op2(h4(e11),h4(e11))) & 5.30/5.51 (h4(op1(e11,e12)) = op2(h4(e11),h4(e12))) & 5.30/5.51 (op2(h4(e12),h4(e10)) = h4(op1(e12,e10))) & 5.30/5.51 (h4(op1(e13,e10)) = op2(h4(e13),h4(e10))) & 5.30/5.51 (op2(h4(e13),h4(e12)) = h4(op1(e13,e12))) & 5.30/5.51 ((e20 = h4(e10)) | (e20 = h4(e13)) | (e20 = h4(e12)) | (h4(e11) = e20)) & 5.30/5.51 ((e21 = h4(e10)) | (e21 = h4(e11)) | (h4(e12) = e21) | (h4(e13) = e21)) & 5.30/5.51 ((h4(e12) = e22) | (h4(e13) = e22) | (e22 = h4(e11)) | (h4(e10) = e22)) & 5.30/5.51 ((h4(e12) = e23) | (h4(e13) = e23) | (h4(e11) = e23) | (e23 = h4(e10))) & 5.30/5.51 (op2(h4(e13),h4(e13)) = h4(op1(e13,e13))) & 5.30/5.51 (h4(op1(e13,e11)) = op2(h4(e13),h4(e11))) & 5.30/5.51 (h4(op1(e12,e13)) = op2(h4(e12),h4(e13))) & 5.30/5.51 (op2(h4(e12),h4(e12)) = h4(op1(e12,e12))) & 5.30/5.51 (h4(op1(e12,e11)) = op2(h4(e12),h4(e11))) & 5.30/5.51 (h4(op1(e11,e13)) = op2(h4(e11),h4(e13))) & 5.30/5.51 (h4(op1(e10,e13)) = op2(h4(e10),h4(e13))) & 5.30/5.51 (h4(op1(e10,e12)) = op2(h4(e10),h4(e12)))) | 5.30/5.51 ((h2(op1(e10,e11)) = op2(h2(e10),h2(e11))) & 5.30/5.51 (op2(h2(e10),h2(e12)) = h2(op1(e10,e12))) & 5.30/5.51 (h2(op1(e11,e10)) = op2(h2(e11),h2(e10))) & 5.30/5.51 (h2(op1(e11,e11)) = op2(h2(e11),h2(e11))) & 5.30/5.51 (h2(op1(e11,e13)) = op2(h2(e11),h2(e13))) & 5.30/5.51 (h2(op1(e12,e10)) = op2(h2(e12),h2(e10))) & 5.30/5.51 (op2(h2(e12),h2(e11)) = h2(op1(e12,e11))) & 5.30/5.51 (op2(h2(e12),h2(e12)) = h2(op1(e12,e12))) & 5.30/5.51 (op2(h2(e13),h2(e12)) = h2(op1(e13,e12))) & 5.30/5.51 ((h2(e10) = e20) | (e20 = h2(e11)) | (h2(e12) = e20) | (h2(e13) = e20)) & 5.30/5.51 ((h2(e10) = e22) | (h2(e12) = e22) | (e22 = h2(e13)) | (e22 = h2(e11))) & 5.30/5.51 ((e23 = h2(e13)) | (h2(e12) = e23) | (e23 = h2(e11)) | (h2(e10) = e23)) & 5.30/5.51 ((e21 = h2(e12)) | (e21 = h2(e13)) | (h2(e11) = e21) | (e21 = h2(e10))) & 5.30/5.51 (op2(h2(e13),h2(e13)) = h2(op1(e13,e13))) & 5.30/5.51 (op2(h2(e13),h2(e11)) = h2(op1(e13,e11))) & 5.30/5.51 (op2(h2(e13),h2(e10)) = h2(op1(e13,e10))) & 5.30/5.51 (h2(op1(e12,e13)) = op2(h2(e12),h2(e13))) & 5.30/5.51 (op2(h2(e11),h2(e12)) = h2(op1(e11,e12))) & 5.30/5.51 (op2(h2(e10),h2(e13)) = h2(op1(e10,e13))) & 5.30/5.51 (op2(h2(e10),h2(e10)) = h2(op1(e10,e10))))))). 5.30/5.51 tff('199', plain, 5.30/5.51 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.51 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(e11) != e21 5.30/5.51 | e22 != h3(e13) 5.30/5.51 | h3(e12) != e23 5.30/5.51 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.51 tff('200', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('201', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('202', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('203', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('204', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('205', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('206', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('207', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('208', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('209', plain, h3(e12) = op2(e22, op2(e22, e22)), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('210', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('211', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.51 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.51 tff('212', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('213', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('214', plain, 5.30/5.51 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.51 | h3(e11) != h3(e11) 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(e11) != e21 5.30/5.51 | e22 != e22 5.30/5.51 | h3(e12) != e23 5.30/5.51 | h3(e12) != h3(op1(e13, e11)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.51 inference('demod', [status(thm)], 5.30/5.51 ['199', '200', '201', '202', '203', '204', '205', '206', 5.30/5.51 '207', '208', '211', '212', '213'])). 5.30/5.51 tff('215', plain, 5.30/5.51 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.51 | h3(e12) != h3(op1(e13, e11)) 5.30/5.51 | h3(e12) != e23 5.30/5.51 | h3(e11) != e21 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.51 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.51 inference('simplify', [status(thm)], ['214'])). 5.30/5.51 tff('216', plain, 5.30/5.51 ~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) | 5.30/5.51 ~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) | ~ (h3(e11) = e21) | 5.30/5.51 ~ (h3(op1(e12, e10)) = op2(h3(e12), h3(e10))) | ~ (h3(e10) = e20) | 5.30/5.51 ~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) | 5.30/5.51 ~ (op2(e22, h3(e10)) = h3(op1(e13, e10))) | 5.30/5.51 ~ (h3(e12) = h3(op1(e13, e11))) | 5.30/5.51 ~ (op2(h3(e12), h3(e12)) = h3(op1(e12, e12))) | 5.30/5.51 ~ (op2(h3(e10), h3(e11)) = h3(op1(e10, e11))) | 5.30/5.51 ~ (h3(op1(e10, e13)) = op2(h3(e10), e22)) | 5.30/5.51 ~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) | 5.30/5.51 ~ (op2(h3(e10), h3(e12)) = h3(op1(e10, e12))) | 5.30/5.51 ~ (h3(op1(e13, e12)) = op2(e22, h3(e12))) | 5.30/5.51 ~ (h3(op1(e12, e13)) = op2(h3(e12), e22)) | ~ (h3(e12) = e23) | 5.30/5.51 ~ (op2(h3(e12), h3(e11)) = h3(op1(e12, e11))) | 5.30/5.51 ~ (h3(op1(e11, e13)) = op2(h3(e11), e22)), 5.30/5.51 inference('split', [status(esa)], ['215'])). 5.30/5.51 tff('217', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.51 inference('split', [status(esa)], ['14'])). 5.30/5.51 tff('218', plain, 5.30/5.51 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.51 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(e12) != e21 5.30/5.51 | h3(e11) != e22 5.30/5.51 | e23 != h3(e11) 5.30/5.51 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.51 tff('219', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('220', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('221', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('222', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('223', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('224', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('225', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('226', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('227', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.51 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.51 tff('228', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('229', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('230', plain, 5.30/5.51 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.51 | h3(e11) != h3(e11) 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(e12) != e21 5.30/5.51 | h3(e11) != e22 5.30/5.51 | e23 != h3(e11) 5.30/5.51 | h3(e12) != h3(op1(e13, e11)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.51 inference('demod', [status(thm)], 5.30/5.51 ['218', '219', '220', '221', '222', '223', '224', '225', 5.30/5.51 '226', '227', '228', '229'])). 5.30/5.51 tff('231', plain, 5.30/5.51 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.51 | h3(e12) != h3(op1(e13, e11)) 5.30/5.51 | e23 != h3(e11) 5.30/5.51 | h3(e11) != e22 5.30/5.51 | h3(e12) != e21 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.51 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.51 inference('simplify', [status(thm)], ['230'])). 5.30/5.51 tff('232', plain, 5.30/5.51 (h3(e12) != h3(op1(e13, e11))) <= (~ (h3(e12) = h3(op1(e13, e11)))), 5.30/5.51 inference('split', [status(esa)], ['231'])). 5.30/5.51 tff('233', plain, 5.30/5.51 (h3(e12) != h3(e12)) 5.30/5.51 <= (~ (h3(e12) = h3(op1(e13, e11))) & (op1(e13, e11) = e12)), 5.30/5.51 inference('sup-', [status(thm)], ['217', '232'])). 5.30/5.51 tff('234', plain, (h3(e12) = h3(op1(e13, e11))) | ~ (op1(e13, e11) = e12), 5.30/5.51 inference('simplify', [status(thm)], ['233'])). 5.30/5.51 tff('235', plain, op2(op2(e22, op2(e22, e22)), e22) = h3(e10), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('236', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('237', plain, op2(op2(e22, h3(e11)), e22) = h3(e10), 5.30/5.51 inference('demod', [status(thm)], ['235', '236'])). 5.30/5.51 tff('238', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.51 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.51 tff('239', plain, op2(h3(e12), e22) = h3(e10), 5.30/5.51 inference('demod', [status(thm)], ['237', '238'])). 5.30/5.51 tff('240', plain, op1(op1(e13, op1(e13, e13)), e13) = e10, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('241', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('242', plain, e12 = op1(e13, op1(e13, e13)), 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('243', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('244', plain, e12 = op1(e13, e11), 5.30/5.51 inference('demod', [status(thm)], ['242', '243'])). 5.30/5.51 tff('245', plain, op1(e12, e13) = e10, 5.30/5.51 inference('demod', [status(thm)], ['240', '241', '244'])). 5.30/5.51 tff('246', plain, 5.30/5.51 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.51 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(e11) != e21 5.30/5.51 | e22 != h3(e13) 5.30/5.51 | h3(e10) != e23 5.30/5.51 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.51 tff('247', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('248', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('249', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('250', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('251', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('252', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('253', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('254', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('255', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('256', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.51 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.51 tff('257', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('258', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('259', plain, 5.30/5.51 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.51 | h3(e11) != h3(e11) 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(e11) != e21 5.30/5.51 | e22 != e22 5.30/5.51 | h3(e10) != e23 5.30/5.51 | h3(e12) != h3(op1(e13, e11)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.51 inference('demod', [status(thm)], 5.30/5.51 ['246', '247', '248', '249', '250', '251', '252', '253', 5.30/5.51 '254', '255', '256', '257', '258'])). 5.30/5.51 tff('260', plain, 5.30/5.51 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.51 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.51 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.51 | h3(e12) != h3(op1(e13, e11)) 5.30/5.51 | h3(e10) != e23 5.30/5.51 | h3(e11) != e21 5.30/5.51 | h3(e10) != e20 5.30/5.51 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.51 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.51 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.51 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.51 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.51 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.51 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.51 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.51 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.51 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.51 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.51 inference('simplify', [status(thm)], ['259'])). 5.30/5.51 tff('261', plain, 5.30/5.51 (h3(op1(e12, e13)) != op2(h3(e12), e22)) 5.30/5.51 <= (~ (h3(op1(e12, e13)) = op2(h3(e12), e22))), 5.30/5.51 inference('split', [status(esa)], ['260'])). 5.30/5.51 tff('262', plain, 5.30/5.51 (h3(e10) != op2(h3(e12), e22)) 5.30/5.51 <= (~ (h3(op1(e12, e13)) = op2(h3(e12), e22))), 5.30/5.51 inference('sup-', [status(thm)], ['245', '261'])). 5.30/5.51 tff('263', plain, 5.30/5.51 (h3(e10) != h3(e10)) <= (~ (h3(op1(e12, e13)) = op2(h3(e12), e22))), 5.30/5.51 inference('sup-', [status(thm)], ['239', '262'])). 5.30/5.51 tff('264', plain, (h3(op1(e12, e13)) = op2(h3(e12), e22)), 5.30/5.51 inference('simplify', [status(thm)], ['263'])). 5.30/5.51 tff('265', plain, 5.30/5.51 (op2(e22, e22) = e20 5.30/5.51 | op2(e22, e22) = e21 5.30/5.51 | op2(e22, e22) = e23 5.30/5.51 | e22 = op2(e22, e22)), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('266', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('267', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('268', plain, h3(e11) = op2(e22, e22), 5.30/5.51 inference('cnf', [status(esa)], [ax16])). 5.30/5.51 tff('269', plain, 5.30/5.51 (h3(e11) = e20 | h3(e11) = e21 | op2(e22, e22) = e23 | e22 = h3(e11)), 5.30/5.51 inference('demod', [status(thm)], ['265', '266', '267', '268'])). 5.30/5.51 tff('270', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.51 inference('split', [status(esa)], ['269'])). 5.30/5.51 tff('271', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.51 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.51 tff('272', plain, (h3(e12) = op2(e22, e21)) <= ((h3(e11) = e21)), 5.30/5.51 inference('sup+', [status(thm)], ['270', '271'])). 5.30/5.51 tff('273', plain, 5.30/5.51 (e21 = op2(e22, e21) 5.30/5.51 | op2(e22, e21) = e23 5.30/5.51 | op2(e22, e21) = e22 5.30/5.51 | e20 = op2(e22, e21)), 5.30/5.51 inference('cnf', [status(esa)], [ax3])). 5.30/5.51 tff('274', plain, (op2(e22, e21) = e23) <= ((op2(e22, e21) = e23)), 5.30/5.51 inference('split', [status(esa)], ['273'])). 5.30/5.51 tff('275', plain, 5.30/5.51 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.51 inference('sup+', [status(thm)], ['272', '274'])). 5.30/5.51 tff('276', plain, (op2(e21, e22) = e23) <= ((op2(e21, e22) = e23)), 5.30/5.51 inference('split', [status(esa)], ['188'])). 5.30/5.51 tff('277', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.51 inference('split', [status(esa)], ['269'])). 5.30/5.51 tff('278', plain, (op1(e11, e13) = e12) <= ((op1(e11, e13) = e12)), 5.30/5.51 inference('split', [status(esa)], ['80'])). 5.30/5.51 tff('279', plain, 5.30/5.51 (op1(e13, e11) = e11 5.30/5.51 | e13 = op1(e13, e11) 5.30/5.51 | op1(e13, e11) = e12 5.30/5.51 | e10 = op1(e13, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('280', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.51 inference('split', [status(esa)], ['279'])). 5.30/5.51 tff('281', plain, e12 = op1(e13, e11), 5.30/5.51 inference('demod', [status(thm)], ['242', '243'])). 5.30/5.51 tff('282', plain, (e12 = e13) <= ((e13 = op1(e13, e11))), 5.30/5.51 inference('sup+', [status(thm)], ['280', '281'])). 5.30/5.51 tff('283', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('284', plain, ~ (e13 = op1(e13, e11)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['282', '283'])). 5.30/5.51 tff('285', plain, (e10 = op1(e13, e11)) <= ((e10 = op1(e13, e11))), 5.30/5.51 inference('split', [status(esa)], ['279'])). 5.30/5.51 tff('286', plain, e12 = op1(e13, e11), 5.30/5.51 inference('demod', [status(thm)], ['242', '243'])). 5.30/5.51 tff('287', plain, (e12 = e10) <= ((e10 = op1(e13, e11))), 5.30/5.51 inference('sup+', [status(thm)], ['285', '286'])). 5.30/5.51 tff('288', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('289', plain, ~ (e10 = op1(e13, e11)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['287', '288'])). 5.30/5.51 tff('290', plain, 5.30/5.51 (op1(e13, e11) = e12) | (e10 = op1(e13, e11)) | (e13 = op1(e13, e11)), 5.30/5.51 inference('split', [status(esa)], ['14'])). 5.30/5.51 tff('291', plain, 5.30/5.51 (op1(e12, e12) = e10 5.30/5.51 | op1(e13, e12) = e10 5.30/5.51 | e10 = op1(e11, e12) 5.30/5.51 | e10 = op1(e10, e12)), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('292', plain, 5.30/5.51 (op1(e13, e12) = e10) | (e10 = op1(e11, e12)) | (op1(e12, e12) = e10) | 5.30/5.51 (op1(e10, e12) = e10), inference('split', [status(esa)], ['291'])). 5.30/5.51 tff('293', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.51 inference('split', [status(esa)], ['44'])). 5.30/5.51 tff('294', plain, 5.30/5.51 (op1(e12, op1(e12, e12)) = e12 5.30/5.51 | e13 = op1(e13, op1(e13, e12)) 5.30/5.51 | e11 = op1(e11, op1(e11, e12)) 5.30/5.51 | op1(e10, op1(e10, e12)) = e10), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('295', plain, 5.30/5.51 (op1(e12, op1(e12, e12)) = e12) <= ((op1(e12, op1(e12, e12)) = e12)), 5.30/5.51 inference('split', [status(esa)], ['294'])). 5.30/5.51 tff('296', plain, 5.30/5.51 (op1(e12, e11) = e12) 5.30/5.51 <= ((op1(e12, e12) = e11) & (op1(e12, op1(e12, e12)) = e12)), 5.30/5.51 inference('sup+', [status(thm)], ['293', '295'])). 5.30/5.51 tff('297', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.51 inference('split', [status(esa)], ['14'])). 5.30/5.51 tff('298', plain, op1(e13, e11) != op1(e12, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('299', plain, (e12 != op1(e12, e11)) <= ((op1(e13, e11) = e12)), 5.30/5.51 inference('sup-', [status(thm)], ['297', '298'])). 5.30/5.51 tff('300', plain, 5.30/5.51 (e12 != e12) 5.30/5.51 <= ((op1(e12, e12) = e11) & 5.30/5.51 (op1(e13, e11) = e12) & 5.30/5.51 (op1(e12, op1(e12, e12)) = e12)), 5.30/5.51 inference('sup-', [status(thm)], ['296', '299'])). 5.30/5.51 tff('301', plain, 5.30/5.51 ~ (op1(e12, op1(e12, e12)) = e12) | ~ (op1(e12, e12) = e11) | 5.30/5.51 ~ (op1(e13, e11) = e12), inference('simplify', [status(thm)], ['300'])). 5.30/5.51 tff('302', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('303', plain, (e13 = op1(e13, e12) | ~ zip_tseitin_6), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_20])). 5.30/5.51 tff('304', plain, (e13 = op1(e13, e12)) <= ((e13 = op1(e13, e12))), 5.30/5.51 inference('split', [status(esa)], ['303'])). 5.30/5.51 tff('305', plain, 5.30/5.51 (e13 = op1(e13, op1(e13, e12))) <= ((e13 = op1(e13, op1(e13, e12)))), 5.30/5.51 inference('split', [status(esa)], ['294'])). 5.30/5.51 tff('306', plain, 5.30/5.51 (e13 = op1(e13, e13)) 5.30/5.51 <= ((e13 = op1(e13, e12)) & (e13 = op1(e13, op1(e13, e12)))), 5.30/5.51 inference('sup+', [status(thm)], ['304', '305'])). 5.30/5.51 tff('307', plain, 5.30/5.51 (e13 = e11) <= ((e13 = op1(e13, e12)) & (e13 = op1(e13, op1(e13, e12)))), 5.30/5.51 inference('sup+', [status(thm)], ['302', '306'])). 5.30/5.51 tff('308', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('309', plain, 5.30/5.51 ~ (e13 = op1(e13, e12)) | ~ (e13 = op1(e13, op1(e13, e12))), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['307', '308'])). 5.30/5.51 tff('310', plain, (e13 = op1(e13, e12)) <= ((e13 = op1(e13, e12))), 5.30/5.51 inference('split', [status(esa)], ['303'])). 5.30/5.51 tff('311', plain, 5.30/5.51 (op1(e13, e12) = e12 5.30/5.51 | e13 = op1(e13, e12) 5.30/5.51 | e11 = op1(e13, e12) 5.30/5.51 | op1(e13, e12) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('312', plain, (op1(e13, e12) = e10) <= ((op1(e13, e12) = e10)), 5.30/5.51 inference('split', [status(esa)], ['311'])). 5.30/5.51 tff('313', plain, 5.30/5.51 (e13 = e10) <= ((op1(e13, e12) = e10) & (e13 = op1(e13, e12))), 5.30/5.51 inference('sup+', [status(thm)], ['310', '312'])). 5.30/5.51 tff('314', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('315', plain, ~ (e13 = op1(e13, e12)) | ~ (op1(e13, e12) = e10), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['313', '314'])). 5.30/5.51 tff('316', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['0'])). 5.30/5.51 tff('317', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.51 inference('split', [status(esa)], ['64'])). 5.30/5.51 tff('318', plain, op1(e12, e11) != op1(e11, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('319', plain, (op1(e12, e11) != e11) <= ((e11 = op1(e11, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['317', '318'])). 5.30/5.51 tff('320', plain, 5.30/5.51 (e11 != e11) <= ((e11 = op1(e12, e11)) & (e11 = op1(e11, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['316', '319'])). 5.30/5.51 tff('321', plain, ~ (e11 = op1(e12, e11)) | ~ (e11 = op1(e11, e11)), 5.30/5.51 inference('simplify', [status(thm)], ['320'])). 5.30/5.51 tff('322', plain, 5.30/5.51 (op1(e10, e13) = e10 5.30/5.51 | op1(e10, e13) = e13 5.30/5.51 | op1(e10, e13) = e12 5.30/5.51 | op1(e10, e13) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('323', plain, op1(e10, e13) != op1(e13, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('324', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('325', plain, op1(e10, e13) != e11, 5.30/5.51 inference('demod', [status(thm)], ['323', '324'])). 5.30/5.51 tff('326', plain, 5.30/5.51 (op1(e10, e13) = e10 | op1(e10, e13) = e13 | op1(e10, e13) = e12), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['322', '325'])). 5.30/5.51 tff('327', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.51 inference('split', [status(esa)], ['326'])). 5.30/5.51 tff('328', plain, (op1(e10, e13) = e10 | ~ zip_tseitin_2), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_27])). 5.30/5.51 tff('329', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['328'])). 5.30/5.51 tff('330', plain, 5.30/5.51 (e13 = e10) <= ((op1(e10, e13) = e13) & (op1(e10, e13) = e10)), 5.30/5.51 inference('sup+', [status(thm)], ['327', '329'])). 5.30/5.51 tff('331', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('332', plain, ~ (op1(e10, e13) = e10) | ~ (op1(e10, e13) = e13), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['330', '331'])). 5.30/5.51 tff('333', plain, 5.30/5.51 (e10 = op1(e11, e10) 5.30/5.51 | op1(e11, e10) = e13 5.30/5.51 | e12 = op1(e11, e10) 5.30/5.51 | e11 = op1(e11, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('334', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.51 inference('split', [status(esa)], ['333'])). 5.30/5.51 tff('335', plain, (op1(e11, e13) = e10) <= ((op1(e11, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['80'])). 5.30/5.51 tff('336', plain, 5.30/5.51 (e10 = op1(e10, op1(e10, e13)) 5.30/5.51 | e12 = op1(e12, op1(e12, e13)) 5.30/5.51 | op1(e13, op1(e13, e13)) = e13 5.30/5.51 | op1(e11, op1(e11, e13)) = e11), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('337', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('338', plain, 5.30/5.51 (e10 = op1(e10, op1(e10, e13)) 5.30/5.51 | e12 = op1(e12, op1(e12, e13)) 5.30/5.51 | op1(e13, e11) = e13 5.30/5.51 | op1(e11, op1(e11, e13)) = e11), 5.30/5.51 inference('demod', [status(thm)], ['336', '337'])). 5.30/5.51 tff('339', plain, 5.30/5.51 (op1(e11, op1(e11, e13)) = e11) <= ((op1(e11, op1(e11, e13)) = e11)), 5.30/5.51 inference('split', [status(esa)], ['338'])). 5.30/5.51 tff('340', plain, 5.30/5.51 (op1(e11, e10) = e11) 5.30/5.51 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.51 inference('sup+', [status(thm)], ['335', '339'])). 5.30/5.51 tff('341', plain, 5.30/5.51 (e12 = e11) 5.30/5.51 <= ((e12 = op1(e11, e10)) & 5.30/5.51 (op1(e11, e13) = e10) & 5.30/5.51 (op1(e11, op1(e11, e13)) = e11)), 5.30/5.51 inference('sup+', [status(thm)], ['334', '340'])). 5.30/5.51 tff('342', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('343', plain, 5.30/5.51 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (e12 = op1(e11, e10)) | 5.30/5.51 ~ (op1(e11, e13) = e10), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['341', '342'])). 5.30/5.51 tff('344', plain, (e10 = op1(e11, e11)) <= ((e10 = op1(e11, e11))), 5.30/5.51 inference('split', [status(esa)], ['64'])). 5.30/5.51 tff('345', plain, (op1(e11, e13) = e10) <= ((op1(e11, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['80'])). 5.30/5.51 tff('346', plain, op1(e11, e11) != op1(e11, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('347', plain, (op1(e11, e11) != e10) <= ((op1(e11, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['345', '346'])). 5.30/5.51 tff('348', plain, 5.30/5.51 (e10 != e10) <= ((op1(e11, e13) = e10) & (e10 = op1(e11, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['344', '347'])). 5.30/5.51 tff('349', plain, ~ (e10 = op1(e11, e11)) | ~ (op1(e11, e13) = e10), 5.30/5.51 inference('simplify', [status(thm)], ['348'])). 5.30/5.51 tff('350', plain, 5.30/5.51 (e13 = op1(e10, e12) 5.30/5.51 | op1(e10, e12) = e12 5.30/5.51 | e11 = op1(e10, e12) 5.30/5.51 | op1(e10, e12) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('351', plain, (e13 = op1(e10, e12)) <= ((e13 = op1(e10, e12))), 5.30/5.51 inference('split', [status(esa)], ['350'])). 5.30/5.51 tff('352', plain, 5.30/5.51 (e11 = op1(e10, e11) 5.30/5.51 | op1(e10, e11) = e12 5.30/5.51 | e13 = op1(e10, e11) 5.30/5.51 | op1(e10, e11) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('353', plain, (op1(e10, e11) = e12) <= ((op1(e10, e11) = e12)), 5.30/5.51 inference('split', [status(esa)], ['352'])). 5.30/5.51 tff('354', plain, 5.30/5.51 (op1(e11, op1(e11, e11)) = e11 5.30/5.51 | e12 = op1(e12, op1(e12, e11)) 5.30/5.51 | op1(e13, op1(e13, e11)) = e13 5.30/5.51 | e10 = op1(e10, op1(e10, e11))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('355', plain, 5.30/5.51 (e10 = op1(e10, op1(e10, e11))) <= ((e10 = op1(e10, op1(e10, e11)))), 5.30/5.51 inference('split', [status(esa)], ['354'])). 5.30/5.51 tff('356', plain, 5.30/5.51 (e10 = op1(e10, e12)) 5.30/5.51 <= ((op1(e10, e11) = e12) & (e10 = op1(e10, op1(e10, e11)))), 5.30/5.51 inference('sup+', [status(thm)], ['353', '355'])). 5.30/5.51 tff('357', plain, 5.30/5.51 (e10 = e13) 5.30/5.51 <= ((e13 = op1(e10, e12)) & 5.30/5.51 (op1(e10, e11) = e12) & 5.30/5.51 (e10 = op1(e10, op1(e10, e11)))), 5.30/5.51 inference('sup+', [status(thm)], ['351', '356'])). 5.30/5.51 tff('358', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('359', plain, 5.30/5.51 ~ (e10 = op1(e10, op1(e10, e11))) | ~ (e13 = op1(e10, e12)) | 5.30/5.51 ~ (op1(e10, e11) = e12), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['357', '358'])). 5.30/5.51 tff('360', plain, (e13 = op1(e13, e12)) <= ((e13 = op1(e13, e12))), 5.30/5.51 inference('split', [status(esa)], ['303'])). 5.30/5.51 tff('361', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.51 inference('split', [status(esa)], ['279'])). 5.30/5.51 tff('362', plain, op1(e13, e12) != op1(e13, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('363', plain, (op1(e13, e12) != e13) <= ((e13 = op1(e13, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['361', '362'])). 5.30/5.51 tff('364', plain, 5.30/5.51 (e13 != e13) <= ((e13 = op1(e13, e11)) & (e13 = op1(e13, e12))), 5.30/5.51 inference('sup-', [status(thm)], ['360', '363'])). 5.30/5.51 tff('365', plain, ~ (e13 = op1(e13, e11)) | ~ (e13 = op1(e13, e12)), 5.30/5.51 inference('simplify', [status(thm)], ['364'])). 5.30/5.51 tff('366', plain, 5.30/5.51 (op1(e11, e11) = e10 5.30/5.51 | op1(e11, e12) = e10 5.30/5.51 | op1(e11, e13) = e10 5.30/5.51 | op1(e11, e10) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('367', plain, 5.30/5.51 (e10 = op1(e11, e10)) | (e10 = op1(e11, e12)) | (op1(e11, e13) = e10) | 5.30/5.51 (e10 = op1(e11, e11)), inference('split', [status(esa)], ['366'])). 5.30/5.51 tff('368', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.51 inference('split', [status(esa)], ['279'])). 5.30/5.51 tff('369', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.51 inference('split', [status(esa)], ['23'])). 5.30/5.51 tff('370', plain, op1(e13, e11) != op1(e13, e10), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('371', plain, (op1(e13, e11) != e13) <= ((op1(e13, e10) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['369', '370'])). 5.30/5.51 tff('372', plain, 5.30/5.51 (e13 != e13) <= ((op1(e13, e10) = e13) & (e13 = op1(e13, e11))), 5.30/5.51 inference('sup-', [status(thm)], ['368', '371'])). 5.30/5.51 tff('373', plain, ~ (e13 = op1(e13, e11)) | ~ (op1(e13, e10) = e13), 5.30/5.51 inference('simplify', [status(thm)], ['372'])). 5.30/5.51 tff('374', plain, (e13 = op1(e12, e12)) <= ((e13 = op1(e12, e12))), 5.30/5.51 inference('split', [status(esa)], ['44'])). 5.30/5.51 tff('375', plain, 5.30/5.51 (op1(e12, e10) = e11 5.30/5.51 | op1(e12, e10) = e13 5.30/5.51 | op1(e12, e10) = e12 5.30/5.51 | e10 = op1(e12, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('376', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.51 inference('split', [status(esa)], ['375'])). 5.30/5.51 tff('377', plain, op1(e12, e10) != op1(e12, e12), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('378', plain, (e13 != op1(e12, e12)) <= ((op1(e12, e10) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['376', '377'])). 5.30/5.51 tff('379', plain, 5.30/5.51 (e13 != e13) <= ((e13 = op1(e12, e12)) & (op1(e12, e10) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['374', '378'])). 5.30/5.51 tff('380', plain, ~ (e13 = op1(e12, e12)) | ~ (op1(e12, e10) = e13), 5.30/5.51 inference('simplify', [status(thm)], ['379'])). 5.30/5.51 tff('381', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['0'])). 5.30/5.51 tff('382', plain, (op1(e12, e11) = e12 | ~ zip_tseitin_11), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_10])). 5.30/5.51 tff('383', plain, (op1(e12, e11) = e12) <= ((e12 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['382'])). 5.30/5.51 tff('384', plain, 5.30/5.51 (e11 = e12) <= ((e12 = op1(e12, e11)) & (e11 = op1(e12, e11))), 5.30/5.51 inference('sup+', [status(thm)], ['381', '383'])). 5.30/5.51 tff('385', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('386', plain, ~ (e11 = op1(e12, e11)) | ~ (e12 = op1(e12, e11)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['384', '385'])). 5.30/5.51 tff('387', plain, (e12 = op1(e12, e13) | ~ zip_tseitin_10), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_12])). 5.30/5.51 tff('388', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.51 inference('split', [status(esa)], ['387'])). 5.30/5.51 tff('389', plain, 5.30/5.51 (op1(e10, e13) = e10 5.30/5.51 | op1(e10, e13) = e13 5.30/5.51 | op1(e10, e13) = e12 5.30/5.51 | op1(e10, e13) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('390', plain, (op1(e10, e13) = e12) <= ((op1(e10, e13) = e12)), 5.30/5.51 inference('split', [status(esa)], ['389'])). 5.30/5.51 tff('391', plain, op1(e10, e13) != op1(e12, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('392', plain, (e12 != op1(e12, e13)) <= ((op1(e10, e13) = e12)), 5.30/5.51 inference('sup-', [status(thm)], ['390', '391'])). 5.30/5.51 tff('393', plain, 5.30/5.51 (e12 != e12) <= ((op1(e10, e13) = e12) & (e12 = op1(e12, e13))), 5.30/5.51 inference('sup-', [status(thm)], ['388', '392'])). 5.30/5.51 tff('394', plain, ~ (e12 = op1(e12, e13)) | ~ (op1(e10, e13) = e12), 5.30/5.51 inference('simplify', [status(thm)], ['393'])). 5.30/5.51 tff('395', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['51'])). 5.30/5.51 tff('396', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.51 inference('split', [status(esa)], ['387'])). 5.30/5.51 tff('397', plain, 5.30/5.51 (e12 = e10) <= ((op1(e12, e13) = e10) & (e12 = op1(e12, e13))), 5.30/5.51 inference('sup+', [status(thm)], ['395', '396'])). 5.30/5.51 tff('398', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('399', plain, ~ (e12 = op1(e12, e13)) | ~ (op1(e12, e13) = e10), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['397', '398'])). 5.30/5.51 tff('400', plain, 5.30/5.51 (op1(e13, e12) = e12 5.30/5.51 | e13 = op1(e13, e12) 5.30/5.51 | e11 = op1(e13, e12) 5.30/5.51 | op1(e13, e12) = e10), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('401', plain, op1(e13, e12) != e11, 5.30/5.51 inference('demod', [status(thm)], ['32', '33'])). 5.30/5.51 tff('402', plain, 5.30/5.51 (op1(e13, e12) = e12 | e13 = op1(e13, e12) | op1(e13, e12) = e10), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['400', '401'])). 5.30/5.51 tff('403', plain, (op1(e13, e12) = e12) <= ((op1(e13, e12) = e12)), 5.30/5.51 inference('split', [status(esa)], ['402'])). 5.30/5.51 tff('404', plain, (e13 = op1(e13, e12)) <= ((e13 = op1(e13, e12))), 5.30/5.51 inference('split', [status(esa)], ['303'])). 5.30/5.51 tff('405', plain, 5.30/5.51 (e13 = e12) <= ((op1(e13, e12) = e12) & (e13 = op1(e13, e12))), 5.30/5.51 inference('sup+', [status(thm)], ['403', '404'])). 5.30/5.51 tff('406', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('407', plain, ~ (op1(e13, e12) = e12) | ~ (e13 = op1(e13, e12)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['405', '406'])). 5.30/5.51 tff('408', plain, (op1(e12, e11) = e12) <= ((e12 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['382'])). 5.30/5.51 tff('409', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.51 inference('split', [status(esa)], ['387'])). 5.30/5.51 tff('410', plain, op1(e12, e13) != op1(e12, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('411', plain, (e12 != op1(e12, e11)) <= ((e12 = op1(e12, e13))), 5.30/5.51 inference('sup-', [status(thm)], ['409', '410'])). 5.30/5.51 tff('412', plain, 5.30/5.51 (e12 != e12) <= ((e12 = op1(e12, e11)) & (e12 = op1(e12, e13))), 5.30/5.51 inference('sup-', [status(thm)], ['408', '411'])). 5.30/5.51 tff('413', plain, ~ (e12 = op1(e12, e13)) | ~ (e12 = op1(e12, e11)), 5.30/5.51 inference('simplify', [status(thm)], ['412'])). 5.30/5.51 tff('414', plain, 5.30/5.51 (op1(e11, e11) = e12 5.30/5.51 | op1(e12, e11) = e12 5.30/5.51 | op1(e13, e11) = e12 5.30/5.51 | op1(e10, e11) = e12), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('415', plain, 5.30/5.51 (op1(e13, e11) = e12) | (e12 = op1(e11, e11)) | (e12 = op1(e12, e11)) | 5.30/5.51 (op1(e10, e11) = e12), inference('split', [status(esa)], ['414'])). 5.30/5.51 tff('416', plain, 5.30/5.51 (op1(e11, op1(e11, e11)) = e11) | (e10 = op1(e10, op1(e10, e11))) | 5.30/5.51 (e12 = op1(e12, op1(e12, e11))) | (op1(e13, op1(e13, e11)) = e13), 5.30/5.51 inference('split', [status(esa)], ['354'])). 5.30/5.51 tff('417', plain, 5.30/5.51 (op1(e10, e10) = e11 5.30/5.51 | e12 = op1(e10, e10) 5.30/5.51 | e13 = op1(e10, e10) 5.30/5.51 | e10 = op1(e10, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('418', plain, (op1(e10, e10) = e11) <= ((op1(e10, e10) = e11)), 5.30/5.51 inference('split', [status(esa)], ['417'])). 5.30/5.51 tff('419', plain, 5.30/5.51 (op1(e10, e10) = e11 5.30/5.51 | e12 = op1(e10, e10) 5.30/5.51 | e13 = op1(e10, e10) 5.30/5.51 | e10 = op1(e10, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('420', plain, (e13 = op1(e10, e10)) <= ((e13 = op1(e10, e10))), 5.30/5.51 inference('split', [status(esa)], ['419'])). 5.30/5.51 tff('421', plain, 5.30/5.51 (e13 = e11) <= ((op1(e10, e10) = e11) & (e13 = op1(e10, e10))), 5.30/5.51 inference('sup+', [status(thm)], ['418', '420'])). 5.30/5.51 tff('422', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('423', plain, ~ (e13 = op1(e10, e10)) | ~ (op1(e10, e10) = e11), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['421', '422'])). 5.30/5.51 tff('424', plain, (e13 != op1(e10, e10) | ~ zip_tseitin_10), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_12])). 5.30/5.51 tff('425', plain, ~ ( zip_tseitin_10) | ~ (e13 = op1(e10, e10)), 5.30/5.51 inference('split', [status(esa)], ['424'])). 5.30/5.51 tff('426', plain, (op1(e10, e10) = e11) <= ((op1(e10, e10) = e11)), 5.30/5.51 inference('split', [status(esa)], ['417'])). 5.30/5.51 tff('427', plain, 5.30/5.51 (op1(e13, op1(e13, e10)) = e13 5.30/5.51 | op1(e12, op1(e12, e10)) = e12 5.30/5.51 | e11 = op1(e11, op1(e11, e10)) 5.30/5.51 | e10 = op1(e10, op1(e10, e10))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('428', plain, 5.30/5.51 (e10 = op1(e10, op1(e10, e10))) <= ((e10 = op1(e10, op1(e10, e10)))), 5.30/5.51 inference('split', [status(esa)], ['427'])). 5.30/5.51 tff('429', plain, 5.30/5.51 (e10 = op1(e10, e11)) 5.30/5.51 <= ((op1(e10, e10) = e11) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.51 inference('sup+', [status(thm)], ['426', '428'])). 5.30/5.51 tff('430', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['328'])). 5.30/5.51 tff('431', plain, op1(e10, e11) != op1(e10, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('432', plain, (op1(e10, e11) != e10) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['430', '431'])). 5.30/5.51 tff('433', plain, 5.30/5.51 (e10 != e10) 5.30/5.51 <= ((op1(e10, e10) = e11) & 5.30/5.51 (op1(e10, e13) = e10) & 5.30/5.51 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.51 inference('sup-', [status(thm)], ['429', '432'])). 5.30/5.51 tff('434', plain, 5.30/5.51 ~ (op1(e10, e13) = e10) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.51 ~ (op1(e10, e10) = e11), inference('simplify', [status(thm)], ['433'])). 5.30/5.51 tff('435', plain, 5.30/5.51 (op1(e12, e10) = e11 5.30/5.51 | op1(e12, e10) = e13 5.30/5.51 | op1(e12, e10) = e12 5.30/5.51 | e10 = op1(e12, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('436', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.51 inference('split', [status(esa)], ['435'])). 5.30/5.51 tff('437', plain, 5.30/5.51 (op1(e11, e10) = e11) 5.30/5.51 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.51 inference('sup+', [status(thm)], ['335', '339'])). 5.30/5.51 tff('438', plain, op1(e11, e10) != op1(e12, e10), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('439', plain, 5.30/5.51 (e11 != op1(e12, e10)) 5.30/5.51 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.51 inference('sup-', [status(thm)], ['437', '438'])). 5.30/5.51 tff('440', plain, 5.30/5.51 (e11 != e11) 5.30/5.51 <= ((op1(e12, e10) = e11) & 5.30/5.51 (op1(e11, e13) = e10) & 5.30/5.51 (op1(e11, op1(e11, e13)) = e11)), 5.30/5.51 inference('sup-', [status(thm)], ['436', '439'])). 5.30/5.51 tff('441', plain, 5.30/5.51 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (op1(e12, e10) = e11) | 5.30/5.51 ~ (op1(e11, e13) = e10), inference('simplify', [status(thm)], ['440'])). 5.30/5.51 tff('442', plain, (e10 = op1(e10, e10) | ~ zip_tseitin_0), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_31])). 5.30/5.51 tff('443', plain, (e10 = op1(e10, e10)) <= ((e10 = op1(e10, e10))), 5.30/5.51 inference('split', [status(esa)], ['442'])). 5.30/5.51 tff('444', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['328'])). 5.30/5.51 tff('445', plain, op1(e10, e10) != op1(e10, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('446', plain, (op1(e10, e10) != e10) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['444', '445'])). 5.30/5.51 tff('447', plain, 5.30/5.51 (e10 != e10) <= ((e10 = op1(e10, e10)) & (op1(e10, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['443', '446'])). 5.30/5.51 tff('448', plain, ~ (e10 = op1(e10, e10)) | ~ (op1(e10, e13) = e10), 5.30/5.51 inference('simplify', [status(thm)], ['447'])). 5.30/5.51 tff('449', plain, 5.30/5.51 (op1(e13, e13) = e10 5.30/5.51 | e10 = op1(e12, e13) 5.30/5.51 | e10 = op1(e11, e13) 5.30/5.51 | e10 = op1(e10, e13)), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('450', plain, 5.30/5.51 (op1(e12, e13) = e10) | (op1(e11, e13) = e10) | (op1(e13, e13) = e10) | 5.30/5.51 (op1(e10, e13) = e10), inference('split', [status(esa)], ['449'])). 5.30/5.51 tff('451', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('452', plain, 5.30/5.51 (op1(e13, e13) = e10 5.30/5.51 | op1(e13, e13) = e11 5.30/5.51 | op1(e13, e13) = e13 5.30/5.51 | e12 = op1(e13, e13)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('453', plain, (op1(e13, e13) = e10) <= ((op1(e13, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['452'])). 5.30/5.51 tff('454', plain, (e11 = e10) <= ((op1(e13, e13) = e10)), 5.30/5.51 inference('sup+', [status(thm)], ['451', '453'])). 5.30/5.51 tff('455', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('456', plain, ~ (op1(e13, e13) = e10), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['454', '455'])). 5.30/5.51 tff('457', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.51 inference('split', [status(esa)], ['333'])). 5.30/5.51 tff('458', plain, (op1(e11, e13) = e10) <= ((op1(e11, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['80'])). 5.30/5.51 tff('459', plain, op1(e11, e10) != op1(e11, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('460', plain, (op1(e11, e10) != e10) <= ((op1(e11, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['458', '459'])). 5.30/5.51 tff('461', plain, 5.30/5.51 (e10 != e10) <= ((e10 = op1(e11, e10)) & (op1(e11, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['457', '460'])). 5.30/5.51 tff('462', plain, ~ (op1(e11, e13) = e10) | ~ (e10 = op1(e11, e10)), 5.30/5.51 inference('simplify', [status(thm)], ['461'])). 5.30/5.51 tff('463', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.51 inference('split', [status(esa)], ['333'])). 5.30/5.51 tff('464', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.51 inference('split', [status(esa)], ['333'])). 5.30/5.51 tff('465', plain, 5.30/5.51 (e10 = e12) <= ((e12 = op1(e11, e10)) & (e10 = op1(e11, e10))), 5.30/5.51 inference('sup+', [status(thm)], ['463', '464'])). 5.30/5.51 tff('466', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('467', plain, ~ (e12 = op1(e11, e10)) | ~ (e10 = op1(e11, e10)), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['465', '466'])). 5.30/5.51 tff('468', plain, (e12 = op1(e10, e10)) <= ((e12 = op1(e10, e10))), 5.30/5.51 inference('split', [status(esa)], ['419'])). 5.30/5.51 tff('469', plain, 5.30/5.51 (e10 = op1(e10, op1(e10, e10))) <= ((e10 = op1(e10, op1(e10, e10)))), 5.30/5.51 inference('split', [status(esa)], ['427'])). 5.30/5.51 tff('470', plain, 5.30/5.51 (e10 = op1(e10, e12)) 5.30/5.51 <= ((e12 = op1(e10, e10)) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.51 inference('sup+', [status(thm)], ['468', '469'])). 5.30/5.51 tff('471', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('split', [status(esa)], ['328'])). 5.30/5.51 tff('472', plain, op1(e10, e13) != op1(e10, e12), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('473', plain, (e10 != op1(e10, e12)) <= ((op1(e10, e13) = e10)), 5.30/5.51 inference('sup-', [status(thm)], ['471', '472'])). 5.30/5.51 tff('474', plain, 5.30/5.51 (e10 != e10) 5.30/5.51 <= ((e12 = op1(e10, e10)) & 5.30/5.51 (op1(e10, e13) = e10) & 5.30/5.51 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.51 inference('sup-', [status(thm)], ['470', '473'])). 5.30/5.51 tff('475', plain, 5.30/5.51 ~ (op1(e10, e13) = e10) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.51 ~ (e12 = op1(e10, e10)), inference('simplify', [status(thm)], ['474'])). 5.30/5.51 tff('476', plain, (e13 = op1(e12, e13) | ~ zip_tseitin_6), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_20])). 5.30/5.51 tff('477', plain, ~ ( zip_tseitin_6) | (e13 = op1(e12, e13)), 5.30/5.51 inference('split', [status(esa)], ['476'])). 5.30/5.51 tff('478', plain, (op1(e12, e10) = e12 | ~ zip_tseitin_12), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_8])). 5.30/5.51 tff('479', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.51 inference('split', [status(esa)], ['478'])). 5.30/5.51 tff('480', plain, 5.30/5.51 (op1(e12, e11) = e10 5.30/5.51 | e13 = op1(e12, e11) 5.30/5.51 | e12 = op1(e12, e11) 5.30/5.51 | e11 = op1(e12, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('481', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['480'])). 5.30/5.51 tff('482', plain, 5.30/5.51 (e12 = op1(e12, op1(e12, e11))) <= ((e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('split', [status(esa)], ['354'])). 5.30/5.51 tff('483', plain, 5.30/5.51 (e12 = op1(e12, e13)) 5.30/5.51 <= ((e13 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('sup+', [status(thm)], ['481', '482'])). 5.30/5.51 tff('484', plain, op1(e12, e10) != op1(e12, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('485', plain, 5.30/5.51 (op1(e12, e10) != e12) 5.30/5.51 <= ((e13 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('sup-', [status(thm)], ['483', '484'])). 5.30/5.51 tff('486', plain, 5.30/5.51 (e12 != e12) 5.30/5.51 <= ((e13 = op1(e12, e11)) & 5.30/5.51 (op1(e12, e10) = e12) & 5.30/5.51 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('sup-', [status(thm)], ['479', '485'])). 5.30/5.51 tff('487', plain, 5.30/5.51 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (e13 = op1(e12, e11)) | 5.30/5.51 ~ (op1(e12, e10) = e12), inference('simplify', [status(thm)], ['486'])). 5.30/5.51 tff('488', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.51 inference('split', [status(esa)], ['333'])). 5.30/5.51 tff('489', plain, (e10 = op1(e13, e10) | ~ zip_tseitin_2), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_27])). 5.30/5.51 tff('490', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.51 inference('split', [status(esa)], ['489'])). 5.30/5.51 tff('491', plain, op1(e13, e10) != op1(e11, e10), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('492', plain, (e10 != op1(e11, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.51 inference('sup-', [status(thm)], ['490', '491'])). 5.30/5.51 tff('493', plain, 5.30/5.51 (e10 != e10) <= ((e10 = op1(e11, e10)) & (e10 = op1(e13, e10))), 5.30/5.51 inference('sup-', [status(thm)], ['488', '492'])). 5.30/5.51 tff('494', plain, ~ (e10 = op1(e13, e10)) | ~ (e10 = op1(e11, e10)), 5.30/5.51 inference('simplify', [status(thm)], ['493'])). 5.30/5.51 tff('495', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.51 inference('split', [status(esa)], ['435'])). 5.30/5.51 tff('496', plain, 5.30/5.51 (op1(e13, op1(e13, e10)) = e13 5.30/5.51 | op1(e12, op1(e12, e10)) = e12 5.30/5.51 | e11 = op1(e11, op1(e11, e10)) 5.30/5.51 | e10 = op1(e10, op1(e10, e10))), 5.30/5.51 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.51 tff('497', plain, 5.30/5.51 (op1(e12, op1(e12, e10)) = e12) <= ((op1(e12, op1(e12, e10)) = e12)), 5.30/5.51 inference('split', [status(esa)], ['496'])). 5.30/5.51 tff('498', plain, 5.30/5.51 (op1(e12, e11) = e12) 5.30/5.51 <= ((op1(e12, e10) = e11) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.51 inference('sup+', [status(thm)], ['495', '497'])). 5.30/5.51 tff('499', plain, 5.30/5.51 (e12 = op1(e12, op1(e12, e11))) <= ((e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('split', [status(esa)], ['354'])). 5.30/5.51 tff('500', plain, 5.30/5.51 (e12 = op1(e12, e12)) 5.30/5.51 <= ((op1(e12, e10) = e11) & 5.30/5.51 (op1(e12, op1(e12, e10)) = e12) & 5.30/5.51 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('sup+', [status(thm)], ['498', '499'])). 5.30/5.51 tff('501', plain, 5.30/5.51 (op1(e12, e11) = e12) 5.30/5.51 <= ((op1(e12, e10) = e11) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.51 inference('sup+', [status(thm)], ['495', '497'])). 5.30/5.51 tff('502', plain, op1(e12, e11) != op1(e12, e12), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('503', plain, 5.30/5.51 (e12 != op1(e12, e12)) 5.30/5.51 <= ((op1(e12, e10) = e11) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.51 inference('sup-', [status(thm)], ['501', '502'])). 5.30/5.51 tff('504', plain, 5.30/5.51 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e10) = e11) | 5.30/5.51 ~ (op1(e12, op1(e12, e10)) = e12), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['500', '503'])). 5.30/5.51 tff('505', plain, 5.30/5.51 (op1(e11, e13) = e10 5.30/5.51 | op1(e11, e13) = e13 5.30/5.51 | op1(e11, e13) = e12 5.30/5.51 | op1(e11, e13) = e11), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('506', plain, op1(e11, e13) != op1(e13, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('507', plain, op1(e13, e13) = e11, 5.30/5.51 inference('cnf', [status(esa)], [ax12])). 5.30/5.51 tff('508', plain, op1(e11, e13) != e11, 5.30/5.51 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.51 tff('509', plain, 5.30/5.51 (op1(e11, e13) = e10 | op1(e11, e13) = e13 | op1(e11, e13) = e12), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['505', '508'])). 5.30/5.51 tff('510', plain, (op1(e11, e13) = e13) <= ((op1(e11, e13) = e13)), 5.30/5.51 inference('split', [status(esa)], ['509'])). 5.30/5.51 tff('511', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.51 inference('split', [status(esa)], ['326'])). 5.30/5.51 tff('512', plain, op1(e10, e13) != op1(e11, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('513', plain, (e13 != op1(e11, e13)) <= ((op1(e10, e13) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['511', '512'])). 5.30/5.51 tff('514', plain, 5.30/5.51 (e13 != e13) <= ((op1(e10, e13) = e13) & (op1(e11, e13) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['510', '513'])). 5.30/5.51 tff('515', plain, ~ (op1(e11, e13) = e13) | ~ (op1(e10, e13) = e13), 5.30/5.51 inference('simplify', [status(thm)], ['514'])). 5.30/5.51 tff('516', plain, 5.30/5.51 (e13 = op1(e11, e12) 5.30/5.51 | e13 = op1(e11, e13) 5.30/5.51 | op1(e11, e11) = e13 5.30/5.51 | e13 = op1(e11, e10)), 5.30/5.51 inference('cnf', [status(esa)], [ax2])). 5.30/5.51 tff('517', plain, 5.30/5.51 (e13 = op1(e11, e12)) | (op1(e11, e11) = e13) | (op1(e11, e10) = e13) | 5.30/5.51 (op1(e11, e13) = e13), inference('split', [status(esa)], ['516'])). 5.30/5.51 tff('518', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.51 inference('split', [status(esa)], ['480'])). 5.30/5.51 tff('519', plain, 5.30/5.51 (e10 = op1(e11, e11) 5.30/5.51 | e11 = op1(e11, e11) 5.30/5.51 | op1(e11, e11) = e13 5.30/5.51 | e12 = op1(e11, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('520', plain, (op1(e11, e11) = e13) <= ((op1(e11, e11) = e13)), 5.30/5.51 inference('split', [status(esa)], ['519'])). 5.30/5.51 tff('521', plain, op1(e12, e11) != op1(e11, e11), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('522', plain, (op1(e12, e11) != e13) <= ((op1(e11, e11) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['520', '521'])). 5.30/5.51 tff('523', plain, 5.30/5.51 (e13 != e13) <= ((e13 = op1(e12, e11)) & (op1(e11, e11) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['518', '522'])). 5.30/5.51 tff('524', plain, ~ (op1(e11, e11) = e13) | ~ (e13 = op1(e12, e11)), 5.30/5.51 inference('simplify', [status(thm)], ['523'])). 5.30/5.51 tff('525', plain, 5.30/5.51 (op1(e12, e11) = e10 5.30/5.51 | e13 = op1(e12, e11) 5.30/5.51 | e12 = op1(e12, e11) 5.30/5.51 | e11 = op1(e12, e11)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('526', plain, (op1(e12, e11) = e10) <= ((op1(e12, e11) = e10)), 5.30/5.51 inference('split', [status(esa)], ['525'])). 5.30/5.51 tff('527', plain, 5.30/5.51 (e12 = op1(e12, op1(e12, e11))) <= ((e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('split', [status(esa)], ['354'])). 5.30/5.51 tff('528', plain, 5.30/5.51 (e12 = op1(e12, e10)) 5.30/5.51 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.51 tff('529', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.51 inference('split', [status(esa)], ['333'])). 5.30/5.51 tff('530', plain, op1(e11, e10) != op1(e12, e10), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('531', plain, (e12 != op1(e12, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.51 inference('sup-', [status(thm)], ['529', '530'])). 5.30/5.51 tff('532', plain, 5.30/5.51 (e12 != e12) 5.30/5.51 <= ((e12 = op1(e11, e10)) & 5.30/5.51 (op1(e12, e11) = e10) & 5.30/5.51 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.51 inference('sup-', [status(thm)], ['528', '531'])). 5.30/5.51 tff('533', plain, 5.30/5.51 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e11) = e10) | 5.30/5.51 ~ (e12 = op1(e11, e10)), inference('simplify', [status(thm)], ['532'])). 5.30/5.51 tff('534', plain, 5.30/5.51 (op1(e10, e13) = e13) | (op1(e10, e13) = e10) | (op1(e10, e13) = e12), 5.30/5.51 inference('split', [status(esa)], ['326'])). 5.30/5.51 tff('535', plain, (e13 = op1(e10, e10)) <= ((e13 = op1(e10, e10))), 5.30/5.51 inference('split', [status(esa)], ['419'])). 5.30/5.51 tff('536', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.51 inference('split', [status(esa)], ['326'])). 5.30/5.51 tff('537', plain, op1(e10, e10) != op1(e10, e13), 5.30/5.51 inference('cnf', [status(esa)], [ax5])). 5.30/5.51 tff('538', plain, (op1(e10, e10) != e13) <= ((op1(e10, e13) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['536', '537'])). 5.30/5.51 tff('539', plain, 5.30/5.51 (e13 != e13) <= ((e13 = op1(e10, e10)) & (op1(e10, e13) = e13)), 5.30/5.51 inference('sup-', [status(thm)], ['535', '538'])). 5.30/5.51 tff('540', plain, ~ (e13 = op1(e10, e10)) | ~ (op1(e10, e13) = e13), 5.30/5.51 inference('simplify', [status(thm)], ['539'])). 5.30/5.51 tff('541', plain, (op1(e13, e12) = e12) <= ((op1(e13, e12) = e12)), 5.30/5.51 inference('split', [status(esa)], ['402'])). 5.30/5.51 tff('542', plain, (op1(e13, e12) = e12) <= ((op1(e13, e12) = e12)), 5.30/5.51 inference('split', [status(esa)], ['402'])). 5.30/5.51 tff('543', plain, 5.30/5.51 (e13 = op1(e13, op1(e13, e12))) <= ((e13 = op1(e13, op1(e13, e12)))), 5.30/5.51 inference('split', [status(esa)], ['294'])). 5.30/5.51 tff('544', plain, 5.30/5.51 (e13 = op1(e13, e12)) 5.30/5.51 <= ((op1(e13, e12) = e12) & (e13 = op1(e13, op1(e13, e12)))), 5.30/5.51 inference('sup+', [status(thm)], ['542', '543'])). 5.30/5.51 tff('545', plain, 5.30/5.51 (e13 = e12) <= ((op1(e13, e12) = e12) & (e13 = op1(e13, op1(e13, e12)))), 5.30/5.51 inference('sup+', [status(thm)], ['541', '544'])). 5.30/5.51 tff('546', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.51 tff('547', plain, 5.30/5.51 ~ (op1(e13, e12) = e12) | ~ (e13 = op1(e13, op1(e13, e12))), 5.30/5.51 inference('simplify_reflect-', [status(thm)], ['545', '546'])). 5.30/5.51 tff('548', plain, 5.30/5.51 (e13 = op1(e11, e12) 5.30/5.51 | e12 = op1(e11, e12) 5.30/5.51 | op1(e11, e12) = e11 5.30/5.51 | e10 = op1(e11, e12)), 5.30/5.51 inference('cnf', [status(esa)], [ax1])). 5.30/5.51 tff('549', plain, (e13 = op1(e11, e12)) <= ((e13 = op1(e11, e12))), 5.30/5.51 inference('split', [status(esa)], ['548'])). 5.30/5.51 tff('550', plain, 5.30/5.51 (e11 = op1(e11, op1(e11, e12))) <= ((e11 = op1(e11, op1(e11, e12)))), 5.30/5.51 inference('split', [status(esa)], ['294'])). 5.30/5.51 tff('551', plain, 5.30/5.51 (e11 = op1(e11, e13)) 5.30/5.52 <= ((e13 = op1(e11, e12)) & (e11 = op1(e11, op1(e11, e12)))), 5.30/5.52 inference('sup+', [status(thm)], ['549', '550'])). 5.30/5.52 tff('552', plain, op1(e11, e13) != e11, 5.30/5.52 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.52 tff('553', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e12))) | ~ (e13 = op1(e11, e12)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['551', '552'])). 5.30/5.52 tff('554', plain, 5.30/5.52 (e13 = op1(e12, e12) 5.30/5.52 | e13 = op1(e13, e12) 5.30/5.52 | e13 = op1(e11, e12) 5.30/5.52 | op1(e10, e12) = e13), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('555', plain, 5.30/5.52 (e13 = op1(e11, e12)) | (e13 = op1(e12, e12)) | (e13 = op1(e10, e12)) | 5.30/5.52 (e13 = op1(e13, e12)), inference('split', [status(esa)], ['554'])). 5.30/5.52 tff('556', plain, (e12 = op1(e10, e10)) <= ((e12 = op1(e10, e10))), 5.30/5.52 inference('split', [status(esa)], ['419'])). 5.30/5.52 tff('557', plain, 5.30/5.52 (e10 = op1(e10, e12)) 5.30/5.52 <= ((e12 = op1(e10, e10)) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['468', '469'])). 5.30/5.52 tff('558', plain, 5.30/5.52 (op1(e10, op1(e10, e12)) = e10) <= ((op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('split', [status(esa)], ['74'])). 5.30/5.52 tff('559', plain, 5.30/5.52 (op1(e10, e10) = e10) 5.30/5.52 <= ((e12 = op1(e10, e10)) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10))) & 5.30/5.52 (op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('sup+', [status(thm)], ['557', '558'])). 5.30/5.52 tff('560', plain, 5.30/5.52 (e12 = e10) 5.30/5.52 <= ((e12 = op1(e10, e10)) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10))) & 5.30/5.52 (op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('sup+', [status(thm)], ['556', '559'])). 5.30/5.52 tff('561', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('562', plain, 5.30/5.52 ~ (op1(e10, op1(e10, e12)) = e10) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 ~ (e12 = op1(e10, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['560', '561'])). 5.30/5.52 tff('563', plain, 5.30/5.52 (e10 = op1(e10, e12)) 5.30/5.52 <= ((e12 = op1(e10, e10)) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['468', '469'])). 5.30/5.52 tff('564', plain, (op1(e13, e12) = e10) <= ((op1(e13, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['311'])). 5.30/5.52 tff('565', plain, op1(e10, e12) != op1(e13, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('566', plain, (op1(e10, e12) != e10) <= ((op1(e13, e12) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['564', '565'])). 5.30/5.52 tff('567', plain, 5.30/5.52 (e10 != e10) 5.30/5.52 <= ((e12 = op1(e10, e10)) & 5.30/5.52 (op1(e13, e12) = e10) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['563', '566'])). 5.30/5.52 tff('568', plain, 5.30/5.52 ~ (e12 = op1(e10, e10)) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 ~ (op1(e13, e12) = e10), inference('simplify', [status(thm)], ['567'])). 5.30/5.52 tff('569', plain, (e13 = op1(e10, e12)) <= ((e13 = op1(e10, e12))), 5.30/5.52 inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('570', plain, 5.30/5.52 (e10 = op1(e10, e12)) 5.30/5.52 <= ((e12 = op1(e10, e10)) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['468', '469'])). 5.30/5.52 tff('571', plain, 5.30/5.52 (e10 = e13) 5.30/5.52 <= ((e12 = op1(e10, e10)) & 5.30/5.52 (e13 = op1(e10, e12)) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['569', '570'])). 5.30/5.52 tff('572', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('573', plain, 5.30/5.52 ~ (e13 = op1(e10, e12)) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 ~ (e12 = op1(e10, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['571', '572'])). 5.30/5.52 tff('574', plain, 5.30/5.52 (op1(e10, e10) = e11) | (e10 = op1(e10, e10)) | (e12 = op1(e10, e10)) | 5.30/5.52 (e13 = op1(e10, e10)), inference('split', [status(esa)], ['419'])). 5.30/5.52 tff('575', plain, (e13 = op1(e10, e10)) <= ((e13 = op1(e10, e10))), 5.30/5.52 inference('split', [status(esa)], ['419'])). 5.30/5.52 tff('576', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('577', plain, op1(e13, e10) != op1(e10, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('578', plain, (e13 != op1(e10, e10)) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['576', '577'])). 5.30/5.52 tff('579', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e10, e10)) & (op1(e13, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['575', '578'])). 5.30/5.52 tff('580', plain, ~ (e13 = op1(e10, e10)) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['579'])). 5.30/5.52 tff('581', plain, 5.30/5.52 (e13 = op1(e13, op1(e13, e12))) | (op1(e12, op1(e12, e12)) = e12) | 5.30/5.52 (op1(e10, op1(e10, e12)) = e10) | (e11 = op1(e11, op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['294'])). 5.30/5.52 tff('582', plain, (op1(e12, e10) = e10 | ~ zip_tseitin_1), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_29])). 5.30/5.52 tff('583', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('584', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('585', plain, 5.30/5.52 (op1(e12, op1(e12, e10)) = e12) <= ((op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('split', [status(esa)], ['496'])). 5.30/5.52 tff('586', plain, 5.30/5.52 (op1(e12, e10) = e12) 5.30/5.52 <= ((e10 = op1(e12, e10)) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['584', '585'])). 5.30/5.52 tff('587', plain, 5.30/5.52 (e10 = e12) <= ((e10 = op1(e12, e10)) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['583', '586'])). 5.30/5.52 tff('588', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('589', plain, 5.30/5.52 ~ (op1(e12, op1(e12, e10)) = e12) | ~ (e10 = op1(e12, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['587', '588'])). 5.30/5.52 tff('590', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('591', plain, (e10 = op1(e10, e10)) <= ((e10 = op1(e10, e10))), 5.30/5.52 inference('split', [status(esa)], ['442'])). 5.30/5.52 tff('592', plain, op1(e10, e10) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('593', plain, (e10 != op1(e12, e10)) <= ((e10 = op1(e10, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['591', '592'])). 5.30/5.52 tff('594', plain, 5.30/5.52 (e10 != e10) <= ((e10 = op1(e10, e10)) & (e10 = op1(e12, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['590', '593'])). 5.30/5.52 tff('595', plain, ~ (e10 = op1(e10, e10)) | ~ (e10 = op1(e12, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['594'])). 5.30/5.52 tff('596', plain, 5.30/5.52 (op1(e12, e11) = e10 5.30/5.52 | op1(e12, e13) = e10 5.30/5.52 | op1(e12, e12) = e10 5.30/5.52 | op1(e12, e10) = e10), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('597', plain, 5.30/5.52 (op1(e12, e13) = e10) | (e10 = op1(e12, e10)) | (op1(e12, e11) = e10) | 5.30/5.52 (op1(e12, e12) = e10), inference('split', [status(esa)], ['596'])). 5.30/5.52 tff('598', plain, 5.30/5.52 (e12 = op1(e12, e13)) 5.30/5.52 <= ((e13 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['481', '482'])). 5.30/5.52 tff('599', plain, (e12 != op1(e12, e13)) <= ((op1(e10, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['390', '391'])). 5.30/5.52 tff('600', plain, 5.30/5.52 (e12 != e12) 5.30/5.52 <= ((op1(e10, e13) = e12) & 5.30/5.52 (e13 = op1(e12, e11)) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup-', [status(thm)], ['598', '599'])). 5.30/5.52 tff('601', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (e13 = op1(e12, e11)) | 5.30/5.52 ~ (op1(e10, e13) = e12), inference('simplify', [status(thm)], ['600'])). 5.30/5.52 tff('602', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.52 inference('split', [status(esa)], ['51'])). 5.30/5.52 tff('603', plain, 5.30/5.52 (e12 = op1(e12, e13)) 5.30/5.52 <= ((e13 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['481', '482'])). 5.30/5.52 tff('604', plain, 5.30/5.52 (e12 = e10) 5.30/5.52 <= ((e13 = op1(e12, e11)) & 5.30/5.52 (op1(e12, e13) = e10) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['602', '603'])). 5.30/5.52 tff('605', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('606', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e13) = e10) | 5.30/5.52 ~ (e13 = op1(e12, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['604', '605'])). 5.30/5.52 tff('607', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['480'])). 5.30/5.52 tff('608', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('609', plain, op1(e12, e11) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('610', plain, (op1(e12, e11) != e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['608', '609'])). 5.30/5.52 tff('611', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e12, e11)) & (op1(e12, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['607', '610'])). 5.30/5.52 tff('612', plain, ~ (op1(e12, e10) = e13) | ~ (e13 = op1(e12, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['611'])). 5.30/5.52 tff('613', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.52 inference('split', [status(esa)], ['328'])). 5.30/5.52 tff('614', plain, 5.30/5.52 (e10 = op1(e10, op1(e10, e13)) 5.30/5.52 | e12 = op1(e12, op1(e12, e13)) 5.30/5.52 | op1(e13, op1(e13, e13)) = e13 5.30/5.52 | op1(e11, op1(e11, e13)) = e11), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.52 tff('615', plain, 5.30/5.52 (e10 = op1(e10, op1(e10, e13))) <= ((e10 = op1(e10, op1(e10, e13)))), 5.30/5.52 inference('split', [status(esa)], ['614'])). 5.30/5.52 tff('616', plain, 5.30/5.52 (e10 = op1(e10, e10)) 5.30/5.52 <= ((op1(e10, e13) = e10) & (e10 = op1(e10, op1(e10, e13)))), 5.30/5.52 inference('sup+', [status(thm)], ['613', '615'])). 5.30/5.52 tff('617', plain, (op1(e10, e10) != e10) <= ((op1(e10, e13) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['444', '445'])). 5.30/5.52 tff('618', plain, 5.30/5.52 ~ (op1(e10, e13) = e10) | ~ (e10 = op1(e10, op1(e10, e13))), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['616', '617'])). 5.30/5.52 tff('619', plain, (op1(e11, e13) = e12) <= ((op1(e11, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['80'])). 5.30/5.52 tff('620', plain, 5.30/5.52 (op1(e11, op1(e11, e13)) = e11) <= ((op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('split', [status(esa)], ['338'])). 5.30/5.52 tff('621', plain, 5.30/5.52 (op1(e11, e12) = e11) 5.30/5.52 <= ((op1(e11, e13) = e12) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['619', '620'])). 5.30/5.52 tff('622', plain, (e11 = op1(e11, e10) | ~ zip_tseitin_14), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_1])). 5.30/5.52 tff('623', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('624', plain, op1(e11, e10) != op1(e11, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('625', plain, (e11 != op1(e11, e12)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['623', '624'])). 5.30/5.52 tff('626', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((e11 = op1(e11, e10)) & 5.30/5.52 (op1(e11, e13) = e12) & 5.30/5.52 (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['621', '625'])). 5.30/5.52 tff('627', plain, 5.30/5.52 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (e11 = op1(e11, e10)) | 5.30/5.52 ~ (op1(e11, e13) = e12), inference('simplify', [status(thm)], ['626'])). 5.30/5.52 tff('628', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['71'])). 5.30/5.52 tff('629', plain, (op1(e13, e12) = e12) <= ((op1(e13, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['402'])). 5.30/5.52 tff('630', plain, op1(e10, e12) != op1(e13, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('631', plain, (op1(e10, e12) != e12) <= ((op1(e13, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['629', '630'])). 5.30/5.52 tff('632', plain, 5.30/5.52 (e12 != e12) <= ((op1(e13, e12) = e12) & (op1(e10, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['628', '631'])). 5.30/5.52 tff('633', plain, ~ (op1(e13, e12) = e12) | ~ (op1(e10, e12) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['632'])). 5.30/5.52 tff('634', plain, 5.30/5.52 (op1(e10, e13) = e13) | (op1(e10, e13) = e10) | (op1(e10, e13) = e11) | 5.30/5.52 (op1(e10, e13) = e12), inference('split', [status(esa)], ['389'])). 5.30/5.52 tff('635', plain, (e13 = op1(e12, e13) | ~ zip_tseitin_6), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_20])). 5.30/5.52 tff('636', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['635'])). 5.30/5.52 tff('637', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['635'])). 5.30/5.52 tff('638', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e13))) <= ((e12 = op1(e12, op1(e12, e13)))), 5.30/5.52 inference('split', [status(esa)], ['614'])). 5.30/5.52 tff('639', plain, 5.30/5.52 (e12 = op1(e12, e13)) 5.30/5.52 <= ((e13 = op1(e12, e13)) & (e12 = op1(e12, op1(e12, e13)))), 5.30/5.52 inference('sup+', [status(thm)], ['637', '638'])). 5.30/5.52 tff('640', plain, 5.30/5.52 (e12 = e13) <= ((e13 = op1(e12, e13)) & (e12 = op1(e12, op1(e12, e13)))), 5.30/5.52 inference('sup+', [status(thm)], ['636', '639'])). 5.30/5.52 tff('641', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('642', plain, 5.30/5.52 ~ (e13 = op1(e12, e13)) | ~ (e12 = op1(e12, op1(e12, e13))), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['640', '641'])). 5.30/5.52 tff('643', plain, (e12 = op1(e12, e13) | ~ zip_tseitin_10), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_12])). 5.30/5.52 tff('644', plain, ~ ( zip_tseitin_10) | (e12 = op1(e12, e13)), 5.30/5.52 inference('split', [status(esa)], ['643'])). 5.30/5.52 tff('645', plain, 5.30/5.52 (e13 = op1(e12, e10) 5.30/5.52 | e13 = op1(e12, e11) 5.30/5.52 | op1(e12, e12) = e13 5.30/5.52 | e13 = op1(e12, e13)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('646', plain, 5.30/5.52 (e13 = op1(e12, e11)) | (e13 = op1(e12, e12)) | (op1(e12, e10) = e13) | 5.30/5.52 (e13 = op1(e12, e13)), inference('split', [status(esa)], ['645'])). 5.30/5.52 tff('647', plain, 5.30/5.52 (e12 = op1(e12, e10)) 5.30/5.52 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.52 tff('648', plain, 5.30/5.52 (op1(e12, op1(e12, e10)) = e12) <= ((op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('split', [status(esa)], ['496'])). 5.30/5.52 tff('649', plain, 5.30/5.52 (op1(e12, e12) = e12) 5.30/5.52 <= ((op1(e12, e11) = e10) & 5.30/5.52 (op1(e12, op1(e12, e10)) = e12) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['647', '648'])). 5.30/5.52 tff('650', plain, (e12 != op1(e12, e12) | ~ zip_tseitin_1), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_29])). 5.30/5.52 tff('651', plain, (e12 != op1(e12, e12)) <= (~ (op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['650'])). 5.30/5.52 tff('652', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('653', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('654', plain, 5.30/5.52 (e11 = op1(e11, op1(e11, e10))) <= ((e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('655', plain, 5.30/5.52 (e11 = op1(e11, e10)) 5.30/5.52 <= ((e10 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['653', '654'])). 5.30/5.52 tff('656', plain, 5.30/5.52 (e11 = e10) <= ((e10 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['652', '655'])). 5.30/5.52 tff('657', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('658', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (e10 = op1(e11, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['656', '657'])). 5.30/5.52 tff('659', plain, 5.30/5.52 (e10 = op1(e10, e10) 5.30/5.52 | op1(e11, e10) = e10 5.30/5.52 | op1(e12, e10) = e10 5.30/5.52 | e10 = op1(e13, e10)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('660', plain, 5.30/5.52 (e10 = op1(e13, e10)) | (e10 = op1(e11, e10)) | (e10 = op1(e12, e10)) | 5.30/5.52 (e10 = op1(e10, e10)), inference('split', [status(esa)], ['659'])). 5.30/5.52 tff('661', plain, 5.30/5.52 (op1(e10, e10) = e12 5.30/5.52 | e12 = op1(e10, e11) 5.30/5.52 | op1(e10, e13) = e12 5.30/5.52 | e12 = op1(e10, e12)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('662', plain, 5.30/5.52 (e12 = op1(e10, e10)) | (op1(e10, e11) = e12) | (op1(e10, e13) = e12) | 5.30/5.52 (op1(e10, e12) = e12), inference('split', [status(esa)], ['661'])). 5.30/5.52 tff('663', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('664', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.52 inference('split', [status(esa)], ['51'])). 5.30/5.52 tff('665', plain, op1(e12, e10) != op1(e12, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('666', plain, (op1(e12, e10) != e10) <= ((op1(e12, e13) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['664', '665'])). 5.30/5.52 tff('667', plain, 5.30/5.52 (e10 != e10) <= ((op1(e12, e13) = e10) & (e10 = op1(e12, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['663', '666'])). 5.30/5.52 tff('668', plain, ~ (e10 = op1(e12, e10)) | ~ (op1(e12, e13) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['667'])). 5.30/5.52 tff('669', plain, (op1(e10, e11) = e12) <= ((op1(e10, e11) = e12)), 5.30/5.52 inference('split', [status(esa)], ['352'])). 5.30/5.52 tff('670', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('split', [status(esa)], ['14'])). 5.30/5.52 tff('671', plain, op1(e13, e11) != op1(e10, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('672', plain, (e12 != op1(e10, e11)) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['670', '671'])). 5.30/5.52 tff('673', plain, 5.30/5.52 (e12 != e12) <= ((op1(e13, e11) = e12) & (op1(e10, e11) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['669', '672'])). 5.30/5.52 tff('674', plain, ~ (op1(e10, e11) = e12) | ~ (op1(e13, e11) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['673'])). 5.30/5.52 tff('675', plain, (e10 = op1(e10, e12) | ~ zip_tseitin_1), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_29])). 5.30/5.52 tff('676', plain, (e10 = op1(e10, e12)) <= ((op1(e10, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['675'])). 5.30/5.52 tff('677', plain, (op1(e10, e12) != e10) <= ((op1(e13, e12) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['564', '565'])). 5.30/5.52 tff('678', plain, 5.30/5.52 (e10 != e10) <= ((op1(e13, e12) = e10) & (op1(e10, e12) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['676', '677'])). 5.30/5.52 tff('679', plain, ~ (op1(e10, e12) = e10) | ~ (op1(e13, e12) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['678'])). 5.30/5.52 tff('680', plain, 5.30/5.52 (e12 = op1(e13, e10) 5.30/5.52 | e12 = op1(e13, e13) 5.30/5.52 | op1(e13, e12) = e12 5.30/5.52 | e12 = op1(e13, e11)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('681', plain, 5.30/5.52 (op1(e13, e12) = e12) | (op1(e13, e11) = e12) | (op1(e13, e10) = e12) | 5.30/5.52 (e12 = op1(e13, e13)), inference('split', [status(esa)], ['680'])). 5.30/5.52 tff('682', plain, 5.30/5.52 (op1(e13, e12) = e12) | (e13 = op1(e13, e12)) | (op1(e13, e12) = e10), 5.30/5.52 inference('split', [status(esa)], ['402'])). 5.30/5.52 tff('683', plain, (e13 = op1(e10, e12)) <= ((e13 = op1(e10, e12))), 5.30/5.52 inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('684', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['326'])). 5.30/5.52 tff('685', plain, op1(e10, e13) != op1(e10, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('686', plain, (e13 != op1(e10, e12)) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['684', '685'])). 5.30/5.52 tff('687', plain, 5.30/5.52 (e13 != e13) <= ((op1(e10, e13) = e13) & (e13 = op1(e10, e12))), 5.30/5.52 inference('sup-', [status(thm)], ['683', '686'])). 5.30/5.52 tff('688', plain, ~ (op1(e10, e13) = e13) | ~ (e13 = op1(e10, e12)), 5.30/5.52 inference('simplify', [status(thm)], ['687'])). 5.30/5.52 tff('689', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['326'])). 5.30/5.52 tff('690', plain, (op1(e10, e13) = e12) <= ((op1(e10, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['389'])). 5.30/5.52 tff('691', plain, 5.30/5.52 (e13 = e12) <= ((op1(e10, e13) = e13) & (op1(e10, e13) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['689', '690'])). 5.30/5.52 tff('692', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('693', plain, ~ (op1(e10, e13) = e12) | ~ (op1(e10, e13) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['691', '692'])). 5.30/5.52 tff('694', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['635'])). 5.30/5.52 tff('695', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['326'])). 5.30/5.52 tff('696', plain, op1(e10, e13) != op1(e12, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('697', plain, (e13 != op1(e12, e13)) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['695', '696'])). 5.30/5.52 tff('698', plain, 5.30/5.52 (e13 != e13) <= ((op1(e10, e13) = e13) & (e13 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['694', '697'])). 5.30/5.52 tff('699', plain, ~ (e13 = op1(e12, e13)) | ~ (op1(e10, e13) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['698'])). 5.30/5.52 tff('700', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('701', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('702', plain, 5.30/5.52 (op1(e13, op1(e13, e10)) = e13) <= ((op1(e13, op1(e13, e10)) = e13)), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('703', plain, 5.30/5.52 (op1(e13, e13) = e13) 5.30/5.52 <= ((op1(e13, e10) = e13) & (op1(e13, op1(e13, e10)) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['701', '702'])). 5.30/5.52 tff('704', plain, 5.30/5.52 (e11 = e13) <= ((op1(e13, e10) = e13) & (op1(e13, op1(e13, e10)) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['700', '703'])). 5.30/5.52 tff('705', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('706', plain, 5.30/5.52 ~ (op1(e13, op1(e13, e10)) = e13) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['704', '705'])). 5.30/5.52 tff('707', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('708', plain, (op1(e13, e10) = e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['88'])). 5.30/5.52 tff('709', plain, 5.30/5.52 (e13 = e12) <= ((op1(e13, e10) = e13) & (op1(e13, e10) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['707', '708'])). 5.30/5.52 tff('710', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('711', plain, ~ (op1(e13, e10) = e12) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['709', '710'])). 5.30/5.52 tff('712', plain, (e13 = op1(e13, e12)) <= ((e13 = op1(e13, e12))), 5.30/5.52 inference('split', [status(esa)], ['303'])). 5.30/5.52 tff('713', plain, (e13 != op1(e13, e12)) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['24', '25'])). 5.30/5.52 tff('714', plain, 5.30/5.52 (e13 != e13) <= ((op1(e13, e10) = e13) & (e13 = op1(e13, e12))), 5.30/5.52 inference('sup-', [status(thm)], ['712', '713'])). 5.30/5.52 tff('715', plain, ~ (e13 = op1(e13, e12)) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['714'])). 5.30/5.52 tff('716', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('717', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('718', plain, op1(e12, e10) != op1(e13, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('719', plain, (op1(e12, e10) != e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['717', '718'])). 5.30/5.52 tff('720', plain, 5.30/5.52 (e13 != e13) <= ((op1(e13, e10) = e13) & (op1(e12, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['716', '719'])). 5.30/5.52 tff('721', plain, ~ (op1(e13, e10) = e13) | ~ (op1(e12, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['720'])). 5.30/5.52 tff('722', plain, (e10 != op1(e10, e10) | ~ zip_tseitin_9), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_14])). 5.30/5.52 tff('723', plain, ~ (e10 = op1(e10, e10)) | ~ ( zip_tseitin_9), 5.30/5.52 inference('split', [status(esa)], ['722'])). 5.30/5.52 tff('724', plain, (op1(e10, e13) = e13 | ~ zip_tseitin_9), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_14])). 5.30/5.52 tff('725', plain, ~ ( zip_tseitin_9) | (op1(e10, e13) = e13), 5.30/5.52 inference('split', [status(esa)], ['724'])). 5.30/5.52 tff('726', plain, (op1(e13, e10) = e13 | ~ zip_tseitin_9), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_14])). 5.30/5.52 tff('727', plain, ~ ( zip_tseitin_9) | (op1(e13, e10) = e13), 5.30/5.52 inference('split', [status(esa)], ['726'])). 5.30/5.52 tff('728', plain, 5.30/5.52 ( zip_tseitin_15 5.30/5.52 | zip_tseitin_14 5.30/5.52 | zip_tseitin_13 5.30/5.52 | zip_tseitin_12 5.30/5.52 | zip_tseitin_11 5.30/5.52 | zip_tseitin_10 5.30/5.52 | zip_tseitin_9 5.30/5.52 | zip_tseitin_8 5.30/5.52 | zip_tseitin_7 5.30/5.52 | zip_tseitin_6 5.30/5.52 | zip_tseitin_5 5.30/5.52 | zip_tseitin_4 5.30/5.52 | zip_tseitin_3 5.30/5.52 | zip_tseitin_2 5.30/5.52 | zip_tseitin_1 5.30/5.52 | zip_tseitin_0), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_32])). 5.30/5.52 tff('729', plain, 5.30/5.52 ( zip_tseitin_14) | ( zip_tseitin_2) | ( zip_tseitin_8) | 5.30/5.52 ( zip_tseitin_15) | ( zip_tseitin_5) | ( zip_tseitin_11) | 5.30/5.52 ( zip_tseitin_0) | ( zip_tseitin_7) | ( zip_tseitin_4) | 5.30/5.52 ( zip_tseitin_9) | ( zip_tseitin_1) | ( zip_tseitin_3) | 5.30/5.52 ( zip_tseitin_12) | ( zip_tseitin_13) | ( zip_tseitin_10) | 5.30/5.52 ( zip_tseitin_6), inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('730', plain, ( zip_tseitin_8) <= (( zip_tseitin_8)), 5.30/5.52 inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('731', plain, (e11 != op1(e13, e13) | ~ zip_tseitin_8), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_16])). 5.30/5.52 tff('732', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('733', plain, (e11 != e11 | ~ zip_tseitin_8), 5.30/5.52 inference('demod', [status(thm)], ['731', '732'])). 5.30/5.52 tff('734', plain, ~ zip_tseitin_8, 5.30/5.52 inference('simplify', [status(thm)], ['733'])). 5.30/5.52 tff('735', plain, ~ ( zip_tseitin_8), 5.30/5.52 inference('sup-', [status(thm)], ['730', '734'])). 5.30/5.52 tff('736', plain, ( zip_tseitin_15) <= (( zip_tseitin_15)), 5.30/5.52 inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('737', plain, (op1(e13, e13) != e11 | ~ zip_tseitin_15), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_3])). 5.30/5.52 tff('738', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('739', plain, (e11 != e11 | ~ zip_tseitin_15), 5.30/5.52 inference('demod', [status(thm)], ['737', '738'])). 5.30/5.52 tff('740', plain, ~ zip_tseitin_15, 5.30/5.52 inference('simplify', [status(thm)], ['739'])). 5.30/5.52 tff('741', plain, ~ ( zip_tseitin_15), 5.30/5.52 inference('sup-', [status(thm)], ['736', '740'])). 5.30/5.52 tff('742', plain, (op1(e12, e12) != e12 | ~ zip_tseitin_5), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_22])). 5.30/5.52 tff('743', plain, ~ ( zip_tseitin_5) | ~ (op1(e12, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['742'])). 5.30/5.52 tff('744', plain, (e12 = op1(e12, e12) | ~ zip_tseitin_5), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_22])). 5.30/5.52 tff('745', plain, ~ ( zip_tseitin_5) | (op1(e12, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['744'])). 5.30/5.52 tff('746', plain, ( zip_tseitin_11) <= (( zip_tseitin_11)), 5.30/5.52 inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('747', plain, (op1(e13, e13) != e11 | ~ zip_tseitin_11), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_10])). 5.30/5.52 tff('748', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('749', plain, (e11 != e11 | ~ zip_tseitin_11), 5.30/5.52 inference('demod', [status(thm)], ['747', '748'])). 5.30/5.52 tff('750', plain, ~ zip_tseitin_11, 5.30/5.52 inference('simplify', [status(thm)], ['749'])). 5.30/5.52 tff('751', plain, ~ ( zip_tseitin_11), 5.30/5.52 inference('sup-', [status(thm)], ['746', '750'])). 5.30/5.52 tff('752', plain, (e10 = op1(e10, e10) | ~ zip_tseitin_0), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_31])). 5.30/5.52 tff('753', plain, ~ ( zip_tseitin_0) | (e10 = op1(e10, e10)), 5.30/5.52 inference('split', [status(esa)], ['752'])). 5.30/5.52 tff('754', plain, (e10 != op1(e10, e10) | ~ zip_tseitin_0), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_31])). 5.30/5.52 tff('755', plain, ~ (e10 = op1(e10, e10)) | ~ ( zip_tseitin_0), 5.30/5.52 inference('split', [status(esa)], ['754'])). 5.30/5.52 tff('756', plain, ( zip_tseitin_7) <= (( zip_tseitin_7)), 5.30/5.52 inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('757', plain, (op1(e13, e13) = e13 | ~ zip_tseitin_7), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_18])). 5.30/5.52 tff('758', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('759', plain, (e11 = e13 | ~ zip_tseitin_7), 5.30/5.52 inference('demod', [status(thm)], ['757', '758'])). 5.30/5.52 tff('760', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('761', plain, ~ zip_tseitin_7, 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['759', '760'])). 5.30/5.52 tff('762', plain, ~ ( zip_tseitin_7), 5.30/5.52 inference('sup-', [status(thm)], ['756', '761'])). 5.30/5.52 tff('763', plain, ( zip_tseitin_4) <= (( zip_tseitin_4)), 5.30/5.52 inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('764', plain, (op1(e11, e13) = e11 | ~ zip_tseitin_4), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_24])). 5.30/5.52 tff('765', plain, op1(e11, e13) != e11, 5.30/5.52 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.52 tff('766', plain, ~ zip_tseitin_4, 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['764', '765'])). 5.30/5.52 tff('767', plain, ~ ( zip_tseitin_4), 5.30/5.52 inference('sup-', [status(thm)], ['763', '766'])). 5.30/5.52 tff('768', plain, (e11 != op1(e11, e11) | ~ zip_tseitin_13), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_6])). 5.30/5.52 tff('769', plain, ~ ( zip_tseitin_13) | ~ (e11 = op1(e11, e11)), 5.30/5.52 inference('split', [status(esa)], ['768'])). 5.30/5.52 tff('770', plain, (e11 = op1(e11, e11) | ~ zip_tseitin_13), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_6])). 5.30/5.52 tff('771', plain, ~ ( zip_tseitin_13) | (e11 = op1(e11, e11)), 5.30/5.52 inference('split', [status(esa)], ['770'])). 5.30/5.52 tff('772', plain, (e11 = op1(e10, e12)) <= ((e11 = op1(e10, e12))), 5.30/5.52 inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('773', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('split', [status(esa)], ['2'])). 5.30/5.52 tff('774', plain, op1(e10, e11) != op1(e10, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('775', plain, (e11 != op1(e10, e12)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['773', '774'])). 5.30/5.52 tff('776', plain, 5.30/5.52 (e11 != e11) <= ((e11 = op1(e10, e12)) & (e11 = op1(e10, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['772', '775'])). 5.30/5.52 tff('777', plain, ~ (e11 = op1(e10, e12)) | ~ (e11 = op1(e10, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['776'])). 5.30/5.52 tff('778', plain, (op1(e11, e12) = e11) <= ((op1(e11, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['58'])). 5.30/5.52 tff('779', plain, (e11 != op1(e11, e12)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['623', '624'])). 5.30/5.52 tff('780', plain, 5.30/5.52 (e11 != e11) <= ((e11 = op1(e11, e10)) & (op1(e11, e12) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['778', '779'])). 5.30/5.52 tff('781', plain, ~ (op1(e11, e12) = e11) | ~ (e11 = op1(e11, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['780'])). 5.30/5.52 tff('782', plain, (e11 = op1(e10, e11) | ~ zip_tseitin_14), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_1])). 5.30/5.52 tff('783', plain, (e11 = op1(e10, e11)) | ~ ( zip_tseitin_14), 5.30/5.52 inference('split', [status(esa)], ['782'])). 5.30/5.52 tff('784', plain, (e11 = op1(e11, e10) | ~ zip_tseitin_14), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_1])). 5.30/5.52 tff('785', plain, (e11 = op1(e11, e10)) | ~ ( zip_tseitin_14), 5.30/5.52 inference('split', [status(esa)], ['784'])). 5.30/5.52 tff('786', plain, 5.30/5.52 (e11 = op1(e10, e12) 5.30/5.52 | op1(e11, e12) = e11 5.30/5.52 | e11 = op1(e12, e12) 5.30/5.52 | op1(e13, e12) = e11), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('787', plain, 5.30/5.52 (op1(e12, e12) = e11) | (e11 = op1(e10, e12)) | (e11 = op1(e13, e12)) | 5.30/5.52 (op1(e11, e12) = e11), inference('split', [status(esa)], ['786'])). 5.30/5.52 tff('788', plain, (op1(e10, e12) = e12 | ~ zip_tseitin_12), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_8])). 5.30/5.52 tff('789', plain, ~ ( zip_tseitin_12) | (op1(e10, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['788'])). 5.30/5.52 tff('790', plain, (op1(e13, e12) = e12 | ~ zip_tseitin_10), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_12])). 5.30/5.52 tff('791', plain, (op1(e13, e12) = e12) | ~ ( zip_tseitin_10), 5.30/5.52 inference('split', [status(esa)], ['790'])). 5.30/5.52 tff('792', plain, (e11 = op1(e10, e12)) <= ((e11 = op1(e10, e12))), 5.30/5.52 inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('793', plain, 5.30/5.52 (e10 = op1(e10, e12)) 5.30/5.52 <= ((e12 = op1(e10, e10)) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['468', '469'])). 5.30/5.52 tff('794', plain, 5.30/5.52 (e10 = e11) 5.30/5.52 <= ((e12 = op1(e10, e10)) & 5.30/5.52 (e11 = op1(e10, e12)) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['792', '793'])). 5.30/5.52 tff('795', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('796', plain, 5.30/5.52 ~ (e10 = op1(e10, op1(e10, e10))) | ~ (e11 = op1(e10, e12)) | 5.30/5.52 ~ (e12 = op1(e10, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['794', '795'])). 5.30/5.52 tff('797', plain, 5.30/5.52 (op1(e12, e12) = e10 5.30/5.52 | e13 = op1(e12, e12) 5.30/5.52 | op1(e12, e12) = e12 5.30/5.52 | op1(e12, e12) = e11), 5.30/5.52 inference('cnf', [status(esa)], [ax1])). 5.30/5.52 tff('798', plain, (op1(e12, e12) = e12) <= ((op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['797'])). 5.30/5.52 tff('799', plain, 5.30/5.52 (e12 != op1(e12, e12)) 5.30/5.52 <= ((op1(e12, e10) = e11) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['501', '502'])). 5.30/5.52 tff('800', plain, 5.30/5.52 (e12 != e12) 5.30/5.52 <= ((op1(e12, e12) = e12) & 5.30/5.52 (op1(e12, e10) = e11) & 5.30/5.52 (op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['798', '799'])). 5.30/5.52 tff('801', plain, 5.30/5.52 ~ (op1(e12, e10) = e11) | ~ (op1(e12, op1(e12, e10)) = e12) | 5.30/5.52 ~ (op1(e12, e12) = e12), inference('simplify', [status(thm)], ['800'])). 5.30/5.52 tff('802', plain, 5.30/5.52 (e10 = op1(e11, e10) 5.30/5.52 | op1(e11, e10) = e13 5.30/5.52 | e12 = op1(e11, e10) 5.30/5.52 | e11 = op1(e11, e10)), 5.30/5.52 inference('cnf', [status(esa)], [ax1])). 5.30/5.52 tff('803', plain, (op1(e11, e10) = e13) <= ((op1(e11, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['802'])). 5.30/5.52 tff('804', plain, 5.30/5.52 (e11 = op1(e11, op1(e11, e10))) <= ((e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('805', plain, 5.30/5.52 (e11 = op1(e11, e13)) 5.30/5.52 <= ((op1(e11, e10) = e13) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['803', '804'])). 5.30/5.52 tff('806', plain, op1(e11, e13) != e11, 5.30/5.52 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.52 tff('807', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (op1(e11, e10) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['805', '806'])). 5.30/5.52 tff('808', plain, 5.30/5.52 (e13 = op1(e10, e12)) | (op1(e10, e12) = e12) | (op1(e10, e12) = e10) | 5.30/5.52 (e11 = op1(e10, e12)), inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('809', plain, 5.30/5.52 (e12 = op1(e11, e10) 5.30/5.52 | op1(e13, e10) = e12 5.30/5.52 | e12 = op1(e12, e10) 5.30/5.52 | e12 = op1(e10, e10)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('810', plain, 5.30/5.52 (e12 = op1(e10, e10)) | (e12 = op1(e11, e10)) | (op1(e12, e10) = e12) | 5.30/5.52 (op1(e13, e10) = e12), inference('split', [status(esa)], ['809'])). 5.30/5.52 tff('811', plain, 5.30/5.52 (op1(e12, e10) = e13) | (op1(e12, e10) = e12) | (e10 = op1(e12, e10)) | 5.30/5.52 (op1(e12, e10) = e11), inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('812', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('813', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('split', [status(esa)], ['489'])). 5.30/5.52 tff('814', plain, 5.30/5.52 (e10 = e13) <= ((op1(e13, e10) = e13) & (e10 = op1(e13, e10))), 5.30/5.52 inference('sup+', [status(thm)], ['812', '813'])). 5.30/5.52 tff('815', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('816', plain, ~ (op1(e13, e10) = e13) | ~ (e10 = op1(e13, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['814', '815'])). 5.30/5.52 tff('817', plain, (op1(e10, e10) != e13 | ~ zip_tseitin_2), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_27])). 5.30/5.52 tff('818', plain, ~ (e13 = op1(e10, e10)) | ~ ( zip_tseitin_2), 5.30/5.52 inference('split', [status(esa)], ['817'])). 5.30/5.52 tff('819', plain, 5.30/5.52 (e13 = op1(e10, e10) 5.30/5.52 | op1(e13, e10) = e13 5.30/5.52 | e13 = op1(e12, e10) 5.30/5.52 | e13 = op1(e11, e10)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('820', plain, 5.30/5.52 (op1(e12, e10) = e13) | (op1(e11, e10) = e13) | (e13 = op1(e10, e10)) | 5.30/5.52 (op1(e13, e10) = e13), inference('split', [status(esa)], ['819'])). 5.30/5.52 tff('821', plain, (e13 = op1(e10, e12)) <= ((e13 = op1(e10, e12))), 5.30/5.52 inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('822', plain, (e13 = op1(e13, e12)) <= ((e13 = op1(e13, e12))), 5.30/5.52 inference('split', [status(esa)], ['303'])). 5.30/5.52 tff('823', plain, op1(e10, e12) != op1(e13, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('824', plain, (op1(e10, e12) != e13) <= ((e13 = op1(e13, e12))), 5.30/5.52 inference('sup-', [status(thm)], ['822', '823'])). 5.30/5.52 tff('825', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e13, e12)) & (e13 = op1(e10, e12))), 5.30/5.52 inference('sup-', [status(thm)], ['821', '824'])). 5.30/5.52 tff('826', plain, ~ (e13 = op1(e13, e12)) | ~ (e13 = op1(e10, e12)), 5.30/5.52 inference('simplify', [status(thm)], ['825'])). 5.30/5.52 tff('827', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('828', plain, (op1(e11, e13) = e12) <= ((op1(e11, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['80'])). 5.30/5.52 tff('829', plain, op1(e11, e10) != op1(e11, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('830', plain, (op1(e11, e10) != e12) <= ((op1(e11, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['828', '829'])). 5.30/5.52 tff('831', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e11, e10)) & (op1(e11, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['827', '830'])). 5.30/5.52 tff('832', plain, ~ (e12 = op1(e11, e10)) | ~ (op1(e11, e13) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['831'])). 5.30/5.52 tff('833', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('834', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['635'])). 5.30/5.52 tff('835', plain, op1(e12, e10) != op1(e12, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('836', plain, (op1(e12, e10) != e13) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['834', '835'])). 5.30/5.52 tff('837', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e12, e13)) & (op1(e12, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['833', '836'])). 5.30/5.52 tff('838', plain, ~ (e13 = op1(e12, e13)) | ~ (op1(e12, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['837'])). 5.30/5.52 tff('839', plain, 5.30/5.52 (op1(e13, e12) = e12) | (e13 = op1(e13, e12)) | (op1(e13, e12) = e10) | 5.30/5.52 (e11 = op1(e13, e12)), inference('split', [status(esa)], ['311'])). 5.30/5.52 tff('840', plain, (e11 = op1(e13, e12)) <= ((e11 = op1(e13, e12))), 5.30/5.52 inference('split', [status(esa)], ['311'])). 5.30/5.52 tff('841', plain, op1(e13, e12) != e11, 5.30/5.52 inference('demod', [status(thm)], ['32', '33'])). 5.30/5.52 tff('842', plain, ~ (e11 = op1(e13, e12)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['840', '841'])). 5.30/5.52 tff('843', plain, 5.30/5.52 (op1(e10, e13) = e12 5.30/5.52 | e12 = op1(e13, e13) 5.30/5.52 | e12 = op1(e12, e13) 5.30/5.52 | op1(e11, e13) = e12), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('844', plain, 5.30/5.52 (e12 = op1(e12, e13)) | (op1(e11, e13) = e12) | (e12 = op1(e13, e13)) | 5.30/5.52 (op1(e10, e13) = e12), inference('split', [status(esa)], ['843'])). 5.30/5.52 tff('845', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('846', plain, (e12 = op1(e13, e13)) <= ((e12 = op1(e13, e13))), 5.30/5.52 inference('split', [status(esa)], ['452'])). 5.30/5.52 tff('847', plain, (e12 = e11) <= ((e12 = op1(e13, e13))), 5.30/5.52 inference('sup+', [status(thm)], ['845', '846'])). 5.30/5.52 tff('848', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('849', plain, ~ (e12 = op1(e13, e13)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['847', '848'])). 5.30/5.52 tff('850', plain, 5.30/5.52 (e12 = op1(e12, e13)) | (e13 = op1(e12, e13)) | (op1(e12, e13) = e10), 5.30/5.52 inference('split', [status(esa)], ['51'])). 5.30/5.52 tff('851', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('split', [status(esa)], ['489'])). 5.30/5.52 tff('852', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('split', [status(esa)], ['489'])). 5.30/5.52 tff('853', plain, 5.30/5.52 (op1(e13, op1(e13, e10)) = e13) <= ((op1(e13, op1(e13, e10)) = e13)), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('854', plain, 5.30/5.52 (op1(e13, e10) = e13) 5.30/5.52 <= ((e10 = op1(e13, e10)) & (op1(e13, op1(e13, e10)) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['852', '853'])). 5.30/5.52 tff('855', plain, 5.30/5.52 (e10 = e13) <= ((e10 = op1(e13, e10)) & (op1(e13, op1(e13, e10)) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['851', '854'])). 5.30/5.52 tff('856', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('857', plain, 5.30/5.52 ~ (op1(e13, op1(e13, e10)) = e13) | ~ (e10 = op1(e13, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['855', '856'])). 5.30/5.52 tff('858', plain, (op1(e13, e12) = e10) <= ((op1(e13, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['311'])). 5.30/5.52 tff('859', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('split', [status(esa)], ['489'])). 5.30/5.52 tff('860', plain, op1(e13, e10) != op1(e13, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('861', plain, (e10 != op1(e13, e12)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['859', '860'])). 5.30/5.52 tff('862', plain, 5.30/5.52 (e10 != e10) <= ((e10 = op1(e13, e10)) & (op1(e13, e12) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['858', '861'])). 5.30/5.52 tff('863', plain, ~ (op1(e13, e12) = e10) | ~ (e10 = op1(e13, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['862'])). 5.30/5.52 tff('864', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('split', [status(esa)], ['489'])). 5.30/5.52 tff('865', plain, (op1(e13, e10) = e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['88'])). 5.30/5.52 tff('866', plain, 5.30/5.52 (e10 = e12) <= ((op1(e13, e10) = e12) & (e10 = op1(e13, e10))), 5.30/5.52 inference('sup+', [status(thm)], ['864', '865'])). 5.30/5.52 tff('867', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('868', plain, ~ (op1(e13, e10) = e12) | ~ (e10 = op1(e13, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['866', '867'])). 5.30/5.52 tff('869', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('870', plain, (e10 = op1(e13, e10)) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('split', [status(esa)], ['489'])). 5.30/5.52 tff('871', plain, op1(e12, e10) != op1(e13, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('872', plain, (op1(e12, e10) != e10) <= ((e10 = op1(e13, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['870', '871'])). 5.30/5.52 tff('873', plain, 5.30/5.52 (e10 != e10) <= ((e10 = op1(e13, e10)) & (e10 = op1(e12, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['869', '872'])). 5.30/5.52 tff('874', plain, ~ (e10 = op1(e12, e10)) | ~ (e10 = op1(e13, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['873'])). 5.30/5.52 tff('875', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.52 inference('split', [status(esa)], ['328'])). 5.30/5.52 tff('876', plain, (op1(e10, e13) = e12) <= ((op1(e10, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['389'])). 5.30/5.52 tff('877', plain, 5.30/5.52 (e10 = e12) <= ((op1(e10, e13) = e12) & (op1(e10, e13) = e10)), 5.30/5.52 inference('sup+', [status(thm)], ['875', '876'])). 5.30/5.52 tff('878', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('879', plain, ~ (op1(e10, e13) = e12) | ~ (op1(e10, e13) = e10), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['877', '878'])). 5.30/5.52 tff('880', plain, (e10 = op1(e10, e12)) <= ((op1(e10, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['675'])). 5.30/5.52 tff('881', plain, (e10 != op1(e10, e12)) <= ((op1(e10, e13) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['471', '472'])). 5.30/5.52 tff('882', plain, 5.30/5.52 (e10 != e10) <= ((op1(e10, e13) = e10) & (op1(e10, e12) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['880', '881'])). 5.30/5.52 tff('883', plain, ~ (op1(e10, e12) = e10) | ~ (op1(e10, e13) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['882'])). 5.30/5.52 tff('884', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.52 inference('split', [status(esa)], ['51'])). 5.30/5.52 tff('885', plain, (op1(e10, e13) = e10) <= ((op1(e10, e13) = e10)), 5.30/5.52 inference('split', [status(esa)], ['328'])). 5.30/5.52 tff('886', plain, op1(e10, e13) != op1(e12, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('887', plain, (e10 != op1(e12, e13)) <= ((op1(e10, e13) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['885', '886'])). 5.30/5.52 tff('888', plain, 5.30/5.52 (e10 != e10) <= ((op1(e10, e13) = e10) & (op1(e12, e13) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['884', '887'])). 5.30/5.52 tff('889', plain, ~ (op1(e12, e13) = e10) | ~ (op1(e10, e13) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['888'])). 5.30/5.52 tff('890', plain, (e10 = op1(e13, e10) | ~ zip_tseitin_2), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_27])). 5.30/5.52 tff('891', plain, (e10 = op1(e13, e10)) | ~ ( zip_tseitin_2), 5.30/5.52 inference('split', [status(esa)], ['890'])). 5.30/5.52 tff('892', plain, (op1(e10, e13) = e10 | ~ zip_tseitin_2), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_27])). 5.30/5.52 tff('893', plain, (op1(e10, e13) = e10) | ~ ( zip_tseitin_2), 5.30/5.52 inference('split', [status(esa)], ['892'])). 5.30/5.52 tff('894', plain, (op1(e12, e12) = e12) <= ((op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['797'])). 5.30/5.52 tff('895', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['44'])). 5.30/5.52 tff('896', plain, 5.30/5.52 (e12 = e11) <= ((op1(e12, e12) = e12) & (op1(e12, e12) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['894', '895'])). 5.30/5.52 tff('897', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('898', plain, ~ (op1(e12, e12) = e12) | ~ (op1(e12, e12) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['896', '897'])). 5.30/5.52 tff('899', plain, (op1(e12, e12) = e12) <= ((op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['797'])). 5.30/5.52 tff('900', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['478'])). 5.30/5.52 tff('901', plain, op1(e12, e10) != op1(e12, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('902', plain, (e12 != op1(e12, e12)) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['900', '901'])). 5.30/5.52 tff('903', plain, 5.30/5.52 (e12 != e12) <= ((op1(e12, e12) = e12) & (op1(e12, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['899', '902'])). 5.30/5.52 tff('904', plain, ~ (op1(e12, e10) = e12) | ~ (op1(e12, e12) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['903'])). 5.30/5.52 tff('905', plain, (op1(e12, e12) = e12) <= ((op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['797'])). 5.30/5.52 tff('906', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['387'])). 5.30/5.52 tff('907', plain, op1(e12, e12) != op1(e12, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('908', plain, (op1(e12, e12) != e12) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['906', '907'])). 5.30/5.52 tff('909', plain, 5.30/5.52 (e12 != e12) <= ((op1(e12, e12) = e12) & (e12 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['905', '908'])). 5.30/5.52 tff('910', plain, ~ (op1(e12, e12) = e12) | ~ (e12 = op1(e12, e13)), 5.30/5.52 inference('simplify', [status(thm)], ['909'])). 5.30/5.52 tff('911', plain, (op1(e12, e12) = e12) <= ((op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['797'])). 5.30/5.52 tff('912', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['71'])). 5.30/5.52 tff('913', plain, op1(e12, e12) != op1(e10, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('914', plain, (op1(e12, e12) != e12) <= ((op1(e10, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['912', '913'])). 5.30/5.52 tff('915', plain, 5.30/5.52 (e12 != e12) <= ((op1(e12, e12) = e12) & (op1(e10, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['911', '914'])). 5.30/5.52 tff('916', plain, ~ (op1(e10, e12) = e12) | ~ (op1(e12, e12) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['915'])). 5.30/5.52 tff('917', plain, (op1(e12, e12) = e12) <= ((op1(e12, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['797'])). 5.30/5.52 tff('918', plain, (op1(e13, e12) = e12) <= ((op1(e13, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['402'])). 5.30/5.52 tff('919', plain, op1(e12, e12) != op1(e13, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('920', plain, (op1(e12, e12) != e12) <= ((op1(e13, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['918', '919'])). 5.30/5.52 tff('921', plain, 5.30/5.52 (e12 != e12) <= ((op1(e12, e12) = e12) & (op1(e13, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['917', '920'])). 5.30/5.52 tff('922', plain, ~ (op1(e12, e12) = e12) | ~ (op1(e13, e12) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['921'])). 5.30/5.52 tff('923', plain, (e12 != op1(e12, e12) | ~ zip_tseitin_1), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_29])). 5.30/5.52 tff('924', plain, ~ ( zip_tseitin_1) | ~ (op1(e12, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['923'])). 5.30/5.52 tff('925', plain, (op1(e12, e12) != e12 | ~ zip_tseitin_3), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_0])). 5.30/5.52 tff('926', plain, ~ ( zip_tseitin_3) | ~ (op1(e12, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['925'])). 5.30/5.52 tff('927', plain, (e12 != op1(e12, e12) | ~ zip_tseitin_6), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_20])). 5.30/5.52 tff('928', plain, ~ ( zip_tseitin_6) | ~ (op1(e12, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['927'])). 5.30/5.52 tff('929', plain, 5.30/5.52 (op1(e12, op1(e12, e10)) = e12) | (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 (op1(e13, op1(e13, e10)) = e13) | (e11 = op1(e11, op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('930', plain, ~ (op1(e12, e12) = e12), 5.30/5.52 inference('sat_resolution*', [status(thm)], 5.30/5.52 ['658', '660', '662', '668', '674', '679', '681', '682', 5.30/5.52 '688', '693', '699', '706', '711', '715', '721', '723', 5.30/5.52 '725', '727', '729', '735', '741', '743', '745', '751', 5.30/5.52 '753', '755', '762', '767', '769', '771', '777', '781', 5.30/5.52 '783', '785', '787', '789', '791', '796', '801', '807', 5.30/5.52 '808', '810', '811', '816', '818', '820', '826', '832', 5.30/5.52 '838', '839', '842', '844', '849', '850', '857', '863', 5.30/5.52 '868', '874', '879', '883', '889', '891', '893', '898', 5.30/5.52 '904', '910', '916', '922', '924', '926', '928', '929'])). 5.30/5.52 tff('931', plain, e12 != op1(e12, e12), 5.30/5.52 inference('simpl_trail', [status(thm)], ['651', '930'])). 5.30/5.52 tff('932', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e11) = e10) | 5.30/5.52 ~ (op1(e12, op1(e12, e10)) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['649', '931'])). 5.30/5.52 tff('933', plain, 5.30/5.52 (e12 = op1(e12, e10)) 5.30/5.52 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.52 tff('934', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['387'])). 5.30/5.52 tff('935', plain, op1(e12, e10) != op1(e12, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('936', plain, (op1(e12, e10) != e12) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['934', '935'])). 5.30/5.52 tff('937', plain, 5.30/5.52 (e12 != e12) 5.30/5.52 <= ((op1(e12, e11) = e10) & 5.30/5.52 (e12 = op1(e12, e13)) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup-', [status(thm)], ['933', '936'])). 5.30/5.52 tff('938', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e11) = e10) | 5.30/5.52 ~ (e12 = op1(e12, e13)), inference('simplify', [status(thm)], ['937'])). 5.30/5.52 tff('939', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('940', plain, 5.30/5.52 (e12 = op1(e12, e10)) 5.30/5.52 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.52 tff('941', plain, 5.30/5.52 (e12 = e13) 5.30/5.52 <= ((op1(e12, e11) = e10) & 5.30/5.52 (op1(e12, e10) = e13) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['939', '940'])). 5.30/5.52 tff('942', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('943', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e10) = e13) | 5.30/5.52 ~ (op1(e12, e11) = e10), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['941', '942'])). 5.30/5.52 tff('944', plain, 5.30/5.52 (e12 = op1(e12, e10)) 5.30/5.52 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.52 tff('945', plain, (e12 = op1(e10, e10)) <= ((e12 = op1(e10, e10))), 5.30/5.52 inference('split', [status(esa)], ['419'])). 5.30/5.52 tff('946', plain, op1(e10, e10) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('947', plain, (e12 != op1(e12, e10)) <= ((e12 = op1(e10, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['945', '946'])). 5.30/5.52 tff('948', plain, 5.30/5.52 (e12 != e12) 5.30/5.52 <= ((e12 = op1(e10, e10)) & 5.30/5.52 (op1(e12, e11) = e10) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup-', [status(thm)], ['944', '947'])). 5.30/5.52 tff('949', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (e12 = op1(e10, e10)) | 5.30/5.52 ~ (op1(e12, e11) = e10), inference('simplify', [status(thm)], ['948'])). 5.30/5.52 tff('950', plain, (op1(e12, e11) = e10) <= ((op1(e12, e11) = e10)), 5.30/5.52 inference('split', [status(esa)], ['525'])). 5.30/5.52 tff('951', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['480'])). 5.30/5.52 tff('952', plain, 5.30/5.52 (e13 = e10) <= ((op1(e12, e11) = e10) & (e13 = op1(e12, e11))), 5.30/5.52 inference('sup+', [status(thm)], ['950', '951'])). 5.30/5.52 tff('953', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('954', plain, ~ (op1(e12, e11) = e10) | ~ (e13 = op1(e12, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['952', '953'])). 5.30/5.52 tff('955', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('split', [status(esa)], ['14'])). 5.30/5.52 tff('956', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.52 inference('split', [status(esa)], ['279'])). 5.30/5.52 tff('957', plain, 5.30/5.52 (e13 = e12) <= ((op1(e13, e11) = e12) & (e13 = op1(e13, e11))), 5.30/5.52 inference('sup+', [status(thm)], ['955', '956'])). 5.30/5.52 tff('958', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('959', plain, ~ (e13 = op1(e13, e11)) | ~ (op1(e13, e11) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['957', '958'])). 5.30/5.52 tff('960', plain, 5.30/5.52 (op1(e12, e11) = e12) 5.30/5.52 <= ((op1(e12, e12) = e11) & (op1(e12, op1(e12, e12)) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['293', '295'])). 5.30/5.52 tff('961', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e11))) <= ((e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('split', [status(esa)], ['354'])). 5.30/5.52 tff('962', plain, 5.30/5.52 (e12 = op1(e12, e12)) 5.30/5.52 <= ((op1(e12, e12) = e11) & 5.30/5.52 (op1(e12, op1(e12, e12)) = e12) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['960', '961'])). 5.30/5.52 tff('963', plain, e12 != op1(e12, e12), 5.30/5.52 inference('simpl_trail', [status(thm)], ['651', '930'])). 5.30/5.52 tff('964', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, op1(e12, e12)) = e12) | 5.30/5.52 ~ (op1(e12, e12) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['962', '963'])). 5.30/5.52 tff('965', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['44'])). 5.30/5.52 tff('966', plain, (e13 = op1(e12, e12)) <= ((e13 = op1(e12, e12))), 5.30/5.52 inference('split', [status(esa)], ['44'])). 5.30/5.52 tff('967', plain, 5.30/5.52 (e13 = e11) <= ((op1(e12, e12) = e11) & (e13 = op1(e12, e12))), 5.30/5.52 inference('sup+', [status(thm)], ['965', '966'])). 5.30/5.52 tff('968', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('969', plain, ~ (e13 = op1(e12, e12)) | ~ (op1(e12, e12) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['967', '968'])). 5.30/5.52 tff('970', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['44'])). 5.30/5.52 tff('971', plain, (op1(e12, e12) = e10) <= ((op1(e12, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['44'])). 5.30/5.52 tff('972', plain, 5.30/5.52 (e11 = e10) <= ((op1(e12, e12) = e11) & (op1(e12, e12) = e10)), 5.30/5.52 inference('sup+', [status(thm)], ['970', '971'])). 5.30/5.52 tff('973', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('974', plain, ~ (op1(e12, e12) = e10) | ~ (op1(e12, e12) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['972', '973'])). 5.30/5.52 tff('975', plain, 5.30/5.52 (op1(e12, e12) = e11 5.30/5.52 | e11 = op1(e12, e13) 5.30/5.52 | e11 = op1(e12, e11) 5.30/5.52 | op1(e12, e10) = e11), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('976', plain, 5.30/5.52 (op1(e12, e12) = e11) | (e11 = op1(e12, e11)) | (op1(e12, e13) = e11) | 5.30/5.52 (op1(e12, e10) = e11), inference('split', [status(esa)], ['975'])). 5.30/5.52 tff('977', plain, 5.30/5.52 (op1(e12, e13) = e10 5.30/5.52 | e13 = op1(e12, e13) 5.30/5.52 | e12 = op1(e12, e13) 5.30/5.52 | op1(e12, e13) = e11), 5.30/5.52 inference('cnf', [status(esa)], [ax1])). 5.30/5.52 tff('978', plain, (op1(e12, e13) = e11) <= ((op1(e12, e13) = e11)), 5.30/5.52 inference('split', [status(esa)], ['977'])). 5.30/5.52 tff('979', plain, e11 != op1(e12, e13), 5.30/5.52 inference('demod', [status(thm)], ['48', '49'])). 5.30/5.52 tff('980', plain, ~ (op1(e12, e13) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['978', '979'])). 5.30/5.52 tff('981', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.52 inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('982', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('983', plain, op1(e11, e10) != op1(e11, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('984', plain, (e11 != op1(e11, e11)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['982', '983'])). 5.30/5.52 tff('985', plain, 5.30/5.52 (e11 != e11) <= ((e11 = op1(e11, e10)) & (e11 = op1(e11, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['981', '984'])). 5.30/5.52 tff('986', plain, ~ (e11 = op1(e11, e10)) | ~ (e11 = op1(e11, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['985'])). 5.30/5.52 tff('987', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('988', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('989', plain, op1(e11, e10) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('990', plain, (e11 != op1(e12, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['988', '989'])). 5.30/5.52 tff('991', plain, 5.30/5.52 (e11 != e11) <= ((e11 = op1(e11, e10)) & (op1(e12, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['987', '990'])). 5.30/5.52 tff('992', plain, ~ (op1(e12, e10) = e11) | ~ (e11 = op1(e11, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['991'])). 5.30/5.52 tff('993', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('994', plain, (op1(e10, e10) = e11) <= ((op1(e10, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['417'])). 5.30/5.52 tff('995', plain, op1(e10, e10) != op1(e11, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('996', plain, (e11 != op1(e11, e10)) <= ((op1(e10, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['994', '995'])). 5.30/5.52 tff('997', plain, 5.30/5.52 (e11 != e11) <= ((op1(e10, e10) = e11) & (e11 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['993', '996'])). 5.30/5.52 tff('998', plain, ~ (e11 = op1(e11, e10)) | ~ (op1(e10, e10) = e11), 5.30/5.52 inference('simplify', [status(thm)], ['997'])). 5.30/5.52 tff('999', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.52 inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('1000', plain, 5.30/5.52 (op1(e11, e10) = e11) 5.30/5.52 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['335', '339'])). 5.30/5.52 tff('1001', plain, op1(e11, e10) != op1(e11, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1002', plain, 5.30/5.52 (e11 != op1(e11, e11)) 5.30/5.52 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1000', '1001'])). 5.30/5.52 tff('1003', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((op1(e11, e13) = e10) & 5.30/5.52 (e11 = op1(e11, e11)) & 5.30/5.52 (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['999', '1002'])). 5.30/5.52 tff('1004', plain, 5.30/5.52 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (op1(e11, e13) = e10) | 5.30/5.52 ~ (e11 = op1(e11, e11)), inference('simplify', [status(thm)], ['1003'])). 5.30/5.52 tff('1005', plain, 5.30/5.52 (e12 = op1(e12, e13)) 5.30/5.52 <= ((e13 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['481', '482'])). 5.30/5.52 tff('1006', plain, (op1(e11, e13) = e12) <= ((op1(e11, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['80'])). 5.30/5.52 tff('1007', plain, op1(e12, e13) != op1(e11, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1008', plain, (op1(e12, e13) != e12) <= ((op1(e11, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1006', '1007'])). 5.30/5.52 tff('1009', plain, 5.30/5.52 (e12 != e12) 5.30/5.52 <= ((e13 = op1(e12, e11)) & 5.30/5.52 (op1(e11, e13) = e12) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup-', [status(thm)], ['1005', '1008'])). 5.30/5.52 tff('1010', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e11, e13) = e12) | 5.30/5.52 ~ (e13 = op1(e12, e11)), inference('simplify', [status(thm)], ['1009'])). 5.30/5.52 tff('1011', plain, 5.30/5.52 (e12 = op1(e12, e13)) 5.30/5.52 <= ((e13 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['481', '482'])). 5.30/5.52 tff('1012', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e13))) <= ((e12 = op1(e12, op1(e12, e13)))), 5.30/5.52 inference('split', [status(esa)], ['614'])). 5.30/5.52 tff('1013', plain, 5.30/5.52 (e12 = op1(e12, e12)) 5.30/5.52 <= ((e13 = op1(e12, e11)) & 5.30/5.52 (e12 = op1(e12, op1(e12, e13))) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1011', '1012'])). 5.30/5.52 tff('1014', plain, e12 != op1(e12, e12), 5.30/5.52 inference('simpl_trail', [status(thm)], ['651', '930'])). 5.30/5.52 tff('1015', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (e12 = op1(e12, op1(e12, e13))) | 5.30/5.52 ~ (e13 = op1(e12, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1013', '1014'])). 5.30/5.52 tff('1016', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['480'])). 5.30/5.52 tff('1017', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['635'])). 5.30/5.52 tff('1018', plain, op1(e12, e13) != op1(e12, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1019', plain, (e13 != op1(e12, e11)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['1017', '1018'])). 5.30/5.52 tff('1020', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e12, e11)) & (e13 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['1016', '1019'])). 5.30/5.52 tff('1021', plain, ~ (e13 = op1(e12, e13)) | ~ (e13 = op1(e12, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['1020'])). 5.30/5.52 tff('1022', plain, (op1(e12, e11) = e10) <= ((op1(e12, e11) = e10)), 5.30/5.52 inference('split', [status(esa)], ['525'])). 5.30/5.52 tff('1023', plain, 5.30/5.52 (e10 = op1(e10, e11)) 5.30/5.52 <= ((op1(e10, e10) = e11) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['426', '428'])). 5.30/5.52 tff('1024', plain, op1(e12, e11) != op1(e10, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1025', plain, 5.30/5.52 (op1(e12, e11) != e10) 5.30/5.52 <= ((op1(e10, e10) = e11) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['1023', '1024'])). 5.30/5.52 tff('1026', plain, 5.30/5.52 (e10 != e10) 5.30/5.52 <= ((op1(e10, e10) = e11) & 5.30/5.52 (op1(e12, e11) = e10) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['1022', '1025'])). 5.30/5.52 tff('1027', plain, 5.30/5.52 ~ (op1(e12, e11) = e10) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 ~ (op1(e10, e10) = e11), inference('simplify', [status(thm)], ['1026'])). 5.30/5.52 tff('1028', plain, 5.30/5.52 (e12 = op1(e12, e10)) 5.30/5.52 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.52 tff('1029', plain, (op1(e13, e10) = e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['88'])). 5.30/5.52 tff('1030', plain, op1(e12, e10) != op1(e13, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1031', plain, (op1(e12, e10) != e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1029', '1030'])). 5.30/5.52 tff('1032', plain, 5.30/5.52 (e12 != e12) 5.30/5.52 <= ((op1(e12, e11) = e10) & 5.30/5.52 (op1(e13, e10) = e12) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup-', [status(thm)], ['1028', '1031'])). 5.30/5.52 tff('1033', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e13, e10) = e12) | 5.30/5.52 ~ (op1(e12, e11) = e10), inference('simplify', [status(thm)], ['1032'])). 5.30/5.52 tff('1034', plain, (op1(e12, e11) = e10) <= ((op1(e12, e11) = e10)), 5.30/5.52 inference('split', [status(esa)], ['525'])). 5.30/5.52 tff('1035', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('1036', plain, op1(e12, e11) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1037', plain, (op1(e12, e11) != e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['1035', '1036'])). 5.30/5.52 tff('1038', plain, 5.30/5.52 (e10 != e10) <= ((op1(e12, e11) = e10) & (e10 = op1(e12, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['1034', '1037'])). 5.30/5.52 tff('1039', plain, ~ (op1(e12, e11) = e10) | ~ (e10 = op1(e12, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['1038'])). 5.30/5.52 tff('1040', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('1041', plain, (op1(e11, e10) = e13) <= ((op1(e11, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['802'])). 5.30/5.52 tff('1042', plain, op1(e11, e10) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1043', plain, (e13 != op1(e12, e10)) <= ((op1(e11, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1041', '1042'])). 5.30/5.52 tff('1044', plain, 5.30/5.52 (e13 != e13) <= ((op1(e11, e10) = e13) & (op1(e12, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1040', '1043'])). 5.30/5.52 tff('1045', plain, ~ (op1(e12, e10) = e13) | ~ (op1(e11, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['1044'])). 5.30/5.52 tff('1046', plain, 5.30/5.52 (op1(e11, e11) = e11 5.30/5.52 | e11 = op1(e12, e11) 5.30/5.52 | op1(e13, e11) = e11 5.30/5.52 | e11 = op1(e10, e11)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1047', plain, 5.30/5.52 (e11 = op1(e11, e11)) | (e11 = op1(e12, e11)) | (op1(e13, e11) = e11) | 5.30/5.52 (e11 = op1(e10, e11)), inference('split', [status(esa)], ['1046'])). 5.30/5.52 tff('1048', plain, (op1(e13, e11) = e11) <= ((op1(e13, e11) = e11)), 5.30/5.52 inference('split', [status(esa)], ['279'])). 5.30/5.52 tff('1049', plain, e11 != op1(e13, e11), 5.30/5.52 inference('demod', [status(thm)], ['11', '12'])). 5.30/5.52 tff('1050', plain, ~ (op1(e13, e11) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1048', '1049'])). 5.30/5.52 tff('1051', plain, (op1(e11, e12) = e11) <= ((op1(e11, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['58'])). 5.30/5.52 tff('1052', plain, 5.30/5.52 (op1(e11, e10) = e11) 5.30/5.52 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['335', '339'])). 5.30/5.52 tff('1053', plain, op1(e11, e10) != op1(e11, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1054', plain, 5.30/5.52 (e11 != op1(e11, e12)) 5.30/5.52 <= ((op1(e11, e13) = e10) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1052', '1053'])). 5.30/5.52 tff('1055', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((op1(e11, e13) = e10) & 5.30/5.52 (op1(e11, e12) = e11) & 5.30/5.52 (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1051', '1054'])). 5.30/5.52 tff('1056', plain, 5.30/5.52 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (op1(e11, e12) = e11) | 5.30/5.52 ~ (op1(e11, e13) = e10), inference('simplify', [status(thm)], ['1055'])). 5.30/5.52 tff('1057', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['326'])). 5.30/5.52 tff('1058', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['326'])). 5.30/5.52 tff('1059', plain, 5.30/5.52 (e10 = op1(e10, op1(e10, e13))) <= ((e10 = op1(e10, op1(e10, e13)))), 5.30/5.52 inference('split', [status(esa)], ['614'])). 5.30/5.52 tff('1060', plain, 5.30/5.52 (e10 = op1(e10, e13)) 5.30/5.52 <= ((op1(e10, e13) = e13) & (e10 = op1(e10, op1(e10, e13)))), 5.30/5.52 inference('sup+', [status(thm)], ['1058', '1059'])). 5.30/5.52 tff('1061', plain, 5.30/5.52 (e10 = e13) <= ((op1(e10, e13) = e13) & (e10 = op1(e10, op1(e10, e13)))), 5.30/5.52 inference('sup+', [status(thm)], ['1057', '1060'])). 5.30/5.52 tff('1062', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1063', plain, 5.30/5.52 ~ (e10 = op1(e10, op1(e10, e13))) | ~ (op1(e10, e13) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1061', '1062'])). 5.30/5.52 tff('1064', plain, 5.30/5.52 (op1(e11, e13) = e12) | (op1(e11, e13) = e10) | (op1(e11, e13) = e11) | 5.30/5.52 (op1(e11, e13) = e13), inference('split', [status(esa)], ['80'])). 5.30/5.52 tff('1065', plain, 5.30/5.52 (op1(e10, e13) = e13 5.30/5.52 | op1(e11, e13) = e13 5.30/5.52 | op1(e12, e13) = e13 5.30/5.52 | op1(e13, e13) = e13), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1066', plain, 5.30/5.52 (op1(e10, e13) = e13) | (op1(e11, e13) = e13) | (e13 = op1(e12, e13)) | 5.30/5.52 (op1(e13, e13) = e13), inference('split', [status(esa)], ['1065'])). 5.30/5.52 tff('1067', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('1068', plain, (op1(e13, e13) = e13) <= ((op1(e13, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['452'])). 5.30/5.52 tff('1069', plain, (e11 = e13) <= ((op1(e13, e13) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['1067', '1068'])). 5.30/5.52 tff('1070', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1071', plain, ~ (op1(e13, e13) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1069', '1070'])). 5.30/5.52 tff('1072', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['480'])). 5.30/5.52 tff('1073', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.52 inference('split', [status(esa)], ['279'])). 5.30/5.52 tff('1074', plain, op1(e13, e11) != op1(e12, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1075', plain, (e13 != op1(e12, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1073', '1074'])). 5.30/5.52 tff('1076', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e12, e11)) & (e13 = op1(e13, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1072', '1075'])). 5.30/5.52 tff('1077', plain, ~ (e13 = op1(e13, e11)) | ~ (e13 = op1(e12, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['1076'])). 5.30/5.52 tff('1078', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['387'])). 5.30/5.52 tff('1079', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e13))) <= ((e12 = op1(e12, op1(e12, e13)))), 5.30/5.52 inference('split', [status(esa)], ['614'])). 5.30/5.52 tff('1080', plain, 5.30/5.52 (e12 = op1(e12, e12)) 5.30/5.52 <= ((e12 = op1(e12, e13)) & (e12 = op1(e12, op1(e12, e13)))), 5.30/5.52 inference('sup+', [status(thm)], ['1078', '1079'])). 5.30/5.52 tff('1081', plain, (op1(e12, e12) != e12) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('sup-', [status(thm)], ['906', '907'])). 5.30/5.52 tff('1082', plain, 5.30/5.52 ~ (e12 = op1(e12, e13)) | ~ (e12 = op1(e12, op1(e12, e13))), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1080', '1081'])). 5.30/5.52 tff('1083', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['387'])). 5.30/5.52 tff('1084', plain, (op1(e12, e13) != e12) <= ((op1(e11, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1006', '1007'])). 5.30/5.52 tff('1085', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e12, e13)) & (op1(e11, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1083', '1084'])). 5.30/5.52 tff('1086', plain, ~ (e12 = op1(e12, e13)) | ~ (op1(e11, e13) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1085'])). 5.30/5.52 tff('1087', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['635'])). 5.30/5.52 tff('1088', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['387'])). 5.30/5.52 tff('1089', plain, 5.30/5.52 (e12 = e13) <= ((e13 = op1(e12, e13)) & (e12 = op1(e12, e13))), 5.30/5.52 inference('sup+', [status(thm)], ['1087', '1088'])). 5.30/5.52 tff('1090', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1091', plain, ~ (e12 = op1(e12, e13)) | ~ (e13 = op1(e12, e13)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1089', '1090'])). 5.30/5.52 tff('1092', plain, 5.30/5.52 (e13 = op1(e12, e11)) | (e11 = op1(e12, e11)) | (e12 = op1(e12, e11)) | 5.30/5.52 (op1(e12, e11) = e10), inference('split', [status(esa)], ['480'])). 5.30/5.52 tff('1093', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1094', plain, 5.30/5.52 (e12 = op1(e12, e10)) 5.30/5.52 <= ((op1(e12, e11) = e10) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['526', '527'])). 5.30/5.52 tff('1095', plain, 5.30/5.52 (e12 = e11) 5.30/5.52 <= ((op1(e12, e11) = e10) & 5.30/5.52 (op1(e12, e10) = e11) & 5.30/5.52 (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1093', '1094'])). 5.30/5.52 tff('1096', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1097', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (op1(e12, e11) = e10) | 5.30/5.52 ~ (op1(e12, e10) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1095', '1096'])). 5.30/5.52 tff('1098', plain, 5.30/5.52 (op1(e11, e10) = e11 5.30/5.52 | e11 = op1(e11, e13) 5.30/5.52 | e11 = op1(e11, e12) 5.30/5.52 | e11 = op1(e11, e11)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1099', plain, 5.30/5.52 (e11 = op1(e11, e11)) | (op1(e11, e12) = e11) | (op1(e11, e13) = e11) | 5.30/5.52 (e11 = op1(e11, e10)), inference('split', [status(esa)], ['1098'])). 5.30/5.52 tff('1100', plain, (op1(e11, e13) = e11) <= ((op1(e11, e13) = e11)), 5.30/5.52 inference('split', [status(esa)], ['80'])). 5.30/5.52 tff('1101', plain, op1(e11, e13) != e11, 5.30/5.52 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.52 tff('1102', plain, ~ (op1(e11, e13) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1100', '1101'])). 5.30/5.52 tff('1103', plain, 5.30/5.52 (e11 = op1(e10, e10) 5.30/5.52 | e11 = op1(e11, e10) 5.30/5.52 | e11 = op1(e12, e10) 5.30/5.52 | e11 = op1(e13, e10)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1104', plain, 5.30/5.52 (op1(e10, e10) = e11) | (e11 = op1(e11, e10)) | (op1(e13, e10) = e11) | 5.30/5.52 (op1(e12, e10) = e11), inference('split', [status(esa)], ['1103'])). 5.30/5.52 tff('1105', plain, (op1(e13, e10) = e11) <= ((op1(e13, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['88'])). 5.30/5.52 tff('1106', plain, op1(e13, e10) != e11, 5.30/5.52 inference('demod', [status(thm)], ['20', '21'])). 5.30/5.52 tff('1107', plain, ~ (op1(e13, e10) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1105', '1106'])). 5.30/5.52 tff('1108', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.52 inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('1109', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('split', [status(esa)], ['2'])). 5.30/5.52 tff('1110', plain, op1(e10, e11) != op1(e11, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1111', plain, (e11 != op1(e11, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1109', '1110'])). 5.30/5.52 tff('1112', plain, 5.30/5.52 (e11 != e11) <= ((e11 = op1(e11, e11)) & (e11 = op1(e10, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1108', '1111'])). 5.30/5.52 tff('1113', plain, ~ (e11 = op1(e10, e11)) | ~ (e11 = op1(e11, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['1112'])). 5.30/5.52 tff('1114', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('split', [status(esa)], ['2'])). 5.30/5.52 tff('1115', plain, (op1(e10, e10) = e11) <= ((op1(e10, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['417'])). 5.30/5.52 tff('1116', plain, op1(e10, e11) != op1(e10, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1117', plain, (op1(e10, e11) != e11) <= ((op1(e10, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1115', '1116'])). 5.30/5.52 tff('1118', plain, 5.30/5.52 (e11 != e11) <= ((op1(e10, e10) = e11) & (e11 = op1(e10, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1114', '1117'])). 5.30/5.52 tff('1119', plain, ~ (e11 = op1(e10, e11)) | ~ (op1(e10, e10) = e11), 5.30/5.52 inference('simplify', [status(thm)], ['1118'])). 5.30/5.52 tff('1120', plain, (op1(e11, e10) = e13) <= ((op1(e11, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['802'])). 5.30/5.52 tff('1121', plain, (op1(e11, e13) = e13) <= ((op1(e11, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['509'])). 5.30/5.52 tff('1122', plain, op1(e11, e10) != op1(e11, e13), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1123', plain, (op1(e11, e10) != e13) <= ((op1(e11, e13) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1121', '1122'])). 5.30/5.52 tff('1124', plain, 5.30/5.52 (e13 != e13) <= ((op1(e11, e10) = e13) & (op1(e11, e13) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1120', '1123'])). 5.30/5.52 tff('1125', plain, ~ (op1(e11, e13) = e13) | ~ (op1(e11, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['1124'])). 5.30/5.52 tff('1126', plain, (op1(e11, e10) = e13) <= ((op1(e11, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['802'])). 5.30/5.52 tff('1127', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('1128', plain, op1(e13, e10) != op1(e11, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1129', plain, (e13 != op1(e11, e10)) <= ((op1(e13, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1127', '1128'])). 5.30/5.52 tff('1130', plain, 5.30/5.52 (e13 != e13) <= ((op1(e11, e10) = e13) & (op1(e13, e10) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1126', '1129'])). 5.30/5.52 tff('1131', plain, ~ (op1(e11, e10) = e13) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['1130'])). 5.30/5.52 tff('1132', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e13))) | (op1(e11, op1(e11, e13)) = e11) | 5.30/5.52 (e13 = op1(e13, e11)) | (e10 = op1(e10, op1(e10, e13))), 5.30/5.52 inference('split', [status(esa)], ['338'])). 5.30/5.52 tff('1133', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['0'])). 5.30/5.52 tff('1134', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['0'])). 5.30/5.52 tff('1135', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e11))) <= ((e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('split', [status(esa)], ['354'])). 5.30/5.52 tff('1136', plain, 5.30/5.52 (e12 = op1(e12, e11)) 5.30/5.52 <= ((e11 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1134', '1135'])). 5.30/5.52 tff('1137', plain, 5.30/5.52 (e12 = e11) <= ((e11 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1133', '1136'])). 5.30/5.52 tff('1138', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1139', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (e11 = op1(e12, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1137', '1138'])). 5.30/5.52 tff('1140', plain, (op1(e12, e11) = e12) <= ((e12 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['382'])). 5.30/5.52 tff('1141', plain, 5.30/5.52 (e12 = op1(e12, op1(e12, e11))) <= ((e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('split', [status(esa)], ['354'])). 5.30/5.52 tff('1142', plain, 5.30/5.52 (e12 = op1(e12, e12)) 5.30/5.52 <= ((e12 = op1(e12, e11)) & (e12 = op1(e12, op1(e12, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1140', '1141'])). 5.30/5.52 tff('1143', plain, (op1(e12, e11) = e12) <= ((e12 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['382'])). 5.30/5.52 tff('1144', plain, op1(e12, e11) != op1(e12, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1145', plain, (e12 != op1(e12, e12)) <= ((e12 = op1(e12, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1143', '1144'])). 5.30/5.52 tff('1146', plain, 5.30/5.52 ~ (e12 = op1(e12, op1(e12, e11))) | ~ (e12 = op1(e12, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1142', '1145'])). 5.30/5.52 tff('1147', plain, 5.30/5.52 (e11 = op1(e11, e11)) | (op1(e11, e11) = e13) | (e10 = op1(e11, e11)) | 5.30/5.52 (e12 = op1(e11, e11)), inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('1148', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('1149', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.52 inference('split', [status(esa)], ['279'])). 5.30/5.52 tff('1150', plain, 5.30/5.52 (op1(e13, op1(e13, e11)) = e13) <= ((op1(e13, op1(e13, e11)) = e13)), 5.30/5.52 inference('split', [status(esa)], ['16'])). 5.30/5.52 tff('1151', plain, 5.30/5.52 (op1(e13, e13) = e13) 5.30/5.52 <= ((e13 = op1(e13, e11)) & (op1(e13, op1(e13, e11)) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['1149', '1150'])). 5.30/5.52 tff('1152', plain, 5.30/5.52 (e11 = e13) <= ((e13 = op1(e13, e11)) & (op1(e13, op1(e13, e11)) = e13)), 5.30/5.52 inference('sup+', [status(thm)], ['1148', '1151'])). 5.30/5.52 tff('1153', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1154', plain, 5.30/5.52 ~ (op1(e13, op1(e13, e11)) = e13) | ~ (e13 = op1(e13, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1152', '1153'])). 5.30/5.52 tff('1155', plain, (op1(e11, e11) = e13) <= ((op1(e11, e11) = e13)), 5.30/5.52 inference('split', [status(esa)], ['519'])). 5.30/5.52 tff('1156', plain, (e13 = op1(e13, e11)) <= ((e13 = op1(e13, e11))), 5.30/5.52 inference('split', [status(esa)], ['279'])). 5.30/5.52 tff('1157', plain, op1(e11, e11) != op1(e13, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1158', plain, (op1(e11, e11) != e13) <= ((e13 = op1(e13, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1156', '1157'])). 5.30/5.52 tff('1159', plain, 5.30/5.52 (e13 != e13) <= ((e13 = op1(e13, e11)) & (op1(e11, e11) = e13)), 5.30/5.52 inference('sup-', [status(thm)], ['1155', '1158'])). 5.30/5.52 tff('1160', plain, ~ (op1(e11, e11) = e13) | ~ (e13 = op1(e13, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['1159'])). 5.30/5.52 tff('1161', plain, (op1(e11, e12) = e11) <= ((op1(e11, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['58'])). 5.30/5.52 tff('1162', plain, (e10 = op1(e11, e11)) <= ((e10 = op1(e11, e11))), 5.30/5.52 inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('1163', plain, 5.30/5.52 (op1(e11, op1(e11, e11)) = e11) <= ((op1(e11, op1(e11, e11)) = e11)), 5.30/5.52 inference('split', [status(esa)], ['354'])). 5.30/5.52 tff('1164', plain, 5.30/5.52 (op1(e11, e10) = e11) 5.30/5.52 <= ((e10 = op1(e11, e11)) & (op1(e11, op1(e11, e11)) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['1162', '1163'])). 5.30/5.52 tff('1165', plain, op1(e11, e10) != op1(e11, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1166', plain, 5.30/5.52 (e11 != op1(e11, e12)) 5.30/5.52 <= ((e10 = op1(e11, e11)) & (op1(e11, op1(e11, e11)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1164', '1165'])). 5.30/5.52 tff('1167', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((op1(e11, e12) = e11) & 5.30/5.52 (e10 = op1(e11, e11)) & 5.30/5.52 (op1(e11, op1(e11, e11)) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1161', '1166'])). 5.30/5.52 tff('1168', plain, 5.30/5.52 ~ (e10 = op1(e11, e11)) | ~ (op1(e11, e12) = e11) | 5.30/5.52 ~ (op1(e11, op1(e11, e11)) = e11), 5.30/5.52 inference('simplify', [status(thm)], ['1167'])). 5.30/5.52 tff('1169', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('split', [status(esa)], ['2'])). 5.30/5.52 tff('1170', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('split', [status(esa)], ['2'])). 5.30/5.52 tff('1171', plain, 5.30/5.52 (e10 = op1(e10, op1(e10, e11))) <= ((e10 = op1(e10, op1(e10, e11)))), 5.30/5.52 inference('split', [status(esa)], ['354'])). 5.30/5.52 tff('1172', plain, 5.30/5.52 (e10 = op1(e10, e11)) 5.30/5.52 <= ((e11 = op1(e10, e11)) & (e10 = op1(e10, op1(e10, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1170', '1171'])). 5.30/5.52 tff('1173', plain, 5.30/5.52 (e10 = e11) <= ((e11 = op1(e10, e11)) & (e10 = op1(e10, op1(e10, e11)))), 5.30/5.52 inference('sup+', [status(thm)], ['1169', '1172'])). 5.30/5.52 tff('1174', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1175', plain, 5.30/5.52 ~ (e10 = op1(e10, op1(e10, e11))) | ~ (e11 = op1(e10, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1173', '1174'])). 5.30/5.52 tff('1176', plain, (op1(e10, e11) = e12) <= ((op1(e10, e11) = e12)), 5.30/5.52 inference('split', [status(esa)], ['352'])). 5.30/5.52 tff('1177', plain, (e11 = op1(e10, e11)) <= ((e11 = op1(e10, e11))), 5.30/5.52 inference('split', [status(esa)], ['2'])). 5.30/5.52 tff('1178', plain, 5.30/5.52 (e11 = e12) <= ((op1(e10, e11) = e12) & (e11 = op1(e10, e11))), 5.30/5.52 inference('sup+', [status(thm)], ['1176', '1177'])). 5.30/5.52 tff('1179', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1180', plain, ~ (op1(e10, e11) = e12) | ~ (e11 = op1(e10, e11)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1178', '1179'])). 5.30/5.52 tff('1181', plain, (e11 = op1(e12, e11) | ~ zip_tseitin_3), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_0])). 5.30/5.52 tff('1182', plain, ~ ( zip_tseitin_3) | (e11 = op1(e12, e11)), 5.30/5.52 inference('split', [status(esa)], ['1181'])). 5.30/5.52 tff('1183', plain, 5.30/5.52 (op1(e10, e10) = e11 5.30/5.52 | e11 = op1(e10, e11) 5.30/5.52 | e11 = op1(e10, e12) 5.30/5.52 | op1(e10, e13) = e11), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1184', plain, 5.30/5.52 (op1(e10, e10) = e11) | (e11 = op1(e10, e11)) | (op1(e10, e13) = e11) | 5.30/5.52 (e11 = op1(e10, e12)), inference('split', [status(esa)], ['1183'])). 5.30/5.52 tff('1185', plain, (op1(e10, e13) = e11) <= ((op1(e10, e13) = e11)), 5.30/5.52 inference('split', [status(esa)], ['389'])). 5.30/5.52 tff('1186', plain, op1(e10, e13) != e11, 5.30/5.52 inference('demod', [status(thm)], ['323', '324'])). 5.30/5.52 tff('1187', plain, ~ (op1(e10, e13) = e11), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1185', '1186'])). 5.30/5.52 tff('1188', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['0'])). 5.30/5.52 tff('1189', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1190', plain, op1(e12, e11) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1191', plain, (op1(e12, e11) != e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1189', '1190'])). 5.30/5.52 tff('1192', plain, 5.30/5.52 (e11 != e11) <= ((e11 = op1(e12, e11)) & (op1(e12, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1188', '1191'])). 5.30/5.52 tff('1193', plain, ~ (op1(e12, e10) = e11) | ~ (e11 = op1(e12, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['1192'])). 5.30/5.52 tff('1194', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1195', plain, (op1(e10, e10) = e11) <= ((op1(e10, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['417'])). 5.30/5.52 tff('1196', plain, op1(e10, e10) != op1(e12, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1197', plain, (e11 != op1(e12, e10)) <= ((op1(e10, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1195', '1196'])). 5.30/5.52 tff('1198', plain, 5.30/5.52 (e11 != e11) <= ((op1(e10, e10) = e11) & (op1(e12, e10) = e11)), 5.30/5.52 inference('sup-', [status(thm)], ['1194', '1197'])). 5.30/5.52 tff('1199', plain, ~ (op1(e12, e10) = e11) | ~ (op1(e10, e10) = e11), 5.30/5.52 inference('simplify', [status(thm)], ['1198'])). 5.30/5.52 tff('1200', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('1201', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1202', plain, 5.30/5.52 (e10 = e11) <= ((op1(e12, e10) = e11) & (e10 = op1(e12, e10))), 5.30/5.52 inference('sup+', [status(thm)], ['1200', '1201'])). 5.30/5.52 tff('1203', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1204', plain, ~ (op1(e12, e10) = e11) | ~ (e10 = op1(e12, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1202', '1203'])). 5.30/5.52 tff('1205', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('1206', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1207', plain, 5.30/5.52 (e13 = e11) <= ((op1(e12, e10) = e13) & (op1(e12, e10) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['1205', '1206'])). 5.30/5.52 tff('1208', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1209', plain, ~ (op1(e12, e10) = e11) | ~ (op1(e12, e10) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1207', '1208'])). 5.30/5.52 tff('1210', plain, 5.30/5.52 (e13 = op1(e11, e12)) | (op1(e11, e12) = e11) | (e12 = op1(e11, e12)) | 5.30/5.52 (e10 = op1(e11, e12)), inference('split', [status(esa)], ['548'])). 5.30/5.52 tff('1211', plain, (op1(e12, e10) = e12 | ~ zip_tseitin_12), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_8])). 5.30/5.52 tff('1212', plain, (op1(e12, e10) = e12) | ~ ( zip_tseitin_12), 5.30/5.52 inference('split', [status(esa)], ['1211'])). 5.30/5.52 tff('1213', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1214', plain, 5.30/5.52 (e11 = op1(e11, op1(e11, e10))) <= ((e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('1215', plain, 5.30/5.52 (e11 = op1(e11, e12)) 5.30/5.52 <= ((e12 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1213', '1214'])). 5.30/5.52 tff('1216', plain, (e11 = op1(e10, e12)) <= ((e11 = op1(e10, e12))), 5.30/5.52 inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('1217', plain, op1(e11, e12) != op1(e10, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1218', plain, (op1(e11, e12) != e11) <= ((e11 = op1(e10, e12))), 5.30/5.52 inference('sup-', [status(thm)], ['1216', '1217'])). 5.30/5.52 tff('1219', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((e12 = op1(e11, e10)) & 5.30/5.52 (e11 = op1(e10, e12)) & 5.30/5.52 (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['1215', '1218'])). 5.30/5.52 tff('1220', plain, 5.30/5.52 ~ (e11 = op1(e10, e12)) | ~ (e11 = op1(e11, op1(e11, e10))) | 5.30/5.52 ~ (e12 = op1(e11, e10)), inference('simplify', [status(thm)], ['1219'])). 5.30/5.52 tff('1221', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['44'])). 5.30/5.52 tff('1222', plain, 5.30/5.52 (e11 = op1(e11, e12)) 5.30/5.52 <= ((e12 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1213', '1214'])). 5.30/5.52 tff('1223', plain, op1(e12, e12) != op1(e11, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1224', plain, 5.30/5.52 (op1(e12, e12) != e11) 5.30/5.52 <= ((e12 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['1222', '1223'])). 5.30/5.52 tff('1225', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((e12 = op1(e11, e10)) & 5.30/5.52 (op1(e12, e12) = e11) & 5.30/5.52 (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['1221', '1224'])). 5.30/5.52 tff('1226', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (op1(e12, e12) = e11) | 5.30/5.52 ~ (e12 = op1(e11, e10)), inference('simplify', [status(thm)], ['1225'])). 5.30/5.52 tff('1227', plain, (e13 = op1(e11, e12)) <= ((e13 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['548'])). 5.30/5.52 tff('1228', plain, 5.30/5.52 (e11 = op1(e11, e12)) 5.30/5.52 <= ((e12 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1213', '1214'])). 5.30/5.52 tff('1229', plain, 5.30/5.52 (e11 = e13) 5.30/5.52 <= ((e12 = op1(e11, e10)) & 5.30/5.52 (e13 = op1(e11, e12)) & 5.30/5.52 (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1227', '1228'])). 5.30/5.52 tff('1230', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1231', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (e13 = op1(e11, e12)) | 5.30/5.52 ~ (e12 = op1(e11, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1229', '1230'])). 5.30/5.52 tff('1232', plain, 5.30/5.52 (e11 = op1(e11, e12)) 5.30/5.52 <= ((e12 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1213', '1214'])). 5.30/5.52 tff('1233', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.52 inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('1234', plain, op1(e11, e12) != op1(e11, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1235', plain, (op1(e11, e12) != e11) <= ((e11 = op1(e11, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1233', '1234'])). 5.30/5.52 tff('1236', plain, 5.30/5.52 (e11 != e11) 5.30/5.52 <= ((e12 = op1(e11, e10)) & 5.30/5.52 (e11 = op1(e11, e11)) & 5.30/5.52 (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup-', [status(thm)], ['1232', '1235'])). 5.30/5.52 tff('1237', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (e11 = op1(e11, e11)) | 5.30/5.52 ~ (e12 = op1(e11, e10)), inference('simplify', [status(thm)], ['1236'])). 5.30/5.52 tff('1238', plain, (e10 = op1(e11, e12)) <= ((e10 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['548'])). 5.30/5.52 tff('1239', plain, 5.30/5.52 (e11 = op1(e11, e12)) 5.30/5.52 <= ((e12 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1213', '1214'])). 5.30/5.52 tff('1240', plain, 5.30/5.52 (e11 = e10) 5.30/5.52 <= ((e12 = op1(e11, e10)) & 5.30/5.52 (e10 = op1(e11, e12)) & 5.30/5.52 (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1238', '1239'])). 5.30/5.52 tff('1241', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1242', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (e10 = op1(e11, e12)) | 5.30/5.52 ~ (e12 = op1(e11, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1240', '1241'])). 5.30/5.52 tff('1243', plain, (e12 = op1(e11, e11)) <= ((e12 = op1(e11, e11))), 5.30/5.52 inference('split', [status(esa)], ['64'])). 5.30/5.52 tff('1244', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1245', plain, op1(e11, e10) != op1(e11, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1246', plain, (e12 != op1(e11, e11)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['1244', '1245'])). 5.30/5.52 tff('1247', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e11, e10)) & (e12 = op1(e11, e11))), 5.30/5.52 inference('sup-', [status(thm)], ['1243', '1246'])). 5.30/5.52 tff('1248', plain, ~ (e12 = op1(e11, e10)) | ~ (e12 = op1(e11, e11)), 5.30/5.52 inference('simplify', [status(thm)], ['1247'])). 5.30/5.52 tff('1249', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1250', plain, (op1(e13, e10) = e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['88'])). 5.30/5.52 tff('1251', plain, op1(e13, e10) != op1(e11, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1252', plain, (e12 != op1(e11, e10)) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1250', '1251'])). 5.30/5.52 tff('1253', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e11, e10)) & (op1(e13, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1249', '1252'])). 5.30/5.52 tff('1254', plain, ~ (e12 = op1(e11, e10)) | ~ (op1(e13, e10) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1253'])). 5.30/5.52 tff('1255', plain, (op1(e11, e12) = e12 | ~ zip_tseitin_11), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_10])). 5.30/5.52 tff('1256', plain, (op1(e11, e12) = e12) <= ((e12 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['1255'])). 5.30/5.52 tff('1257', plain, (e12 = op1(e11, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1258', plain, op1(e11, e10) != op1(e11, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1259', plain, (e12 != op1(e11, e12)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['1257', '1258'])). 5.30/5.52 tff('1260', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e11, e10)) & (e12 = op1(e11, e12))), 5.30/5.52 inference('sup-', [status(thm)], ['1256', '1259'])). 5.30/5.52 tff('1261', plain, ~ (e12 = op1(e11, e10)) | ~ (e12 = op1(e11, e12)), 5.30/5.52 inference('simplify', [status(thm)], ['1260'])). 5.30/5.52 tff('1262', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['478'])). 5.30/5.52 tff('1263', plain, (e12 != op1(e12, e10)) <= ((e12 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['529', '530'])). 5.30/5.52 tff('1264', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e11, e10)) & (op1(e12, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1262', '1263'])). 5.30/5.52 tff('1265', plain, ~ (e12 = op1(e11, e10)) | ~ (op1(e12, e10) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1264'])). 5.30/5.52 tff('1266', plain, 5.30/5.52 (e10 = op1(e11, e10)) | (e11 = op1(e11, e10)) | (e12 = op1(e11, e10)) | 5.30/5.52 (op1(e11, e10) = e13), inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1267', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('1268', plain, 5.30/5.52 (e11 = op1(e11, op1(e11, e10))) <= ((e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('1269', plain, 5.30/5.52 (e11 = op1(e11, e11)) 5.30/5.52 <= ((e11 = op1(e11, e10)) & (e11 = op1(e11, op1(e11, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1267', '1268'])). 5.30/5.52 tff('1270', plain, (e11 != op1(e11, e11)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('sup-', [status(thm)], ['982', '983'])). 5.30/5.52 tff('1271', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e10))) | ~ (e11 = op1(e11, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1269', '1270'])). 5.30/5.52 tff('1272', plain, (op1(e11, e13) = e13) <= ((op1(e11, e13) = e13)), 5.30/5.52 inference('split', [status(esa)], ['509'])). 5.30/5.52 tff('1273', plain, 5.30/5.52 (op1(e11, op1(e11, e13)) = e11) <= ((op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('split', [status(esa)], ['338'])). 5.30/5.52 tff('1274', plain, 5.30/5.52 (op1(e11, e13) = e11) 5.30/5.52 <= ((op1(e11, e13) = e13) & (op1(e11, op1(e11, e13)) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['1272', '1273'])). 5.30/5.52 tff('1275', plain, op1(e11, e13) != e11, 5.30/5.52 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.52 tff('1276', plain, 5.30/5.52 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (op1(e11, e13) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1274', '1275'])). 5.30/5.52 tff('1277', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('1278', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1279', plain, 5.30/5.52 (e10 = e11) <= ((e11 = op1(e11, e10)) & (e10 = op1(e11, e10))), 5.30/5.52 inference('sup+', [status(thm)], ['1277', '1278'])). 5.30/5.52 tff('1280', plain, e10 != e11, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1281', plain, ~ (e11 = op1(e11, e10)) | ~ (e10 = op1(e11, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1279', '1280'])). 5.30/5.52 tff('1282', plain, (op1(e11, e10) = e13) <= ((op1(e11, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['802'])). 5.30/5.52 tff('1283', plain, (e11 = op1(e11, e10)) <= ((e11 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['622'])). 5.30/5.52 tff('1284', plain, 5.30/5.52 (e11 = e13) <= ((op1(e11, e10) = e13) & (e11 = op1(e11, e10))), 5.30/5.52 inference('sup+', [status(thm)], ['1282', '1283'])). 5.30/5.52 tff('1285', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1286', plain, ~ (e11 = op1(e11, e10)) | ~ (op1(e11, e10) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1284', '1285'])). 5.30/5.52 tff('1287', plain, (e10 != op1(e10, e10) | ~ zip_tseitin_14), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_1])). 5.30/5.52 tff('1288', plain, ~ (e10 = op1(e10, e10)) | ~ ( zip_tseitin_14), 5.30/5.52 inference('split', [status(esa)], ['1287'])). 5.30/5.52 tff('1289', plain, (e13 = op1(e13, e12) | ~ zip_tseitin_6), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_20])). 5.30/5.52 tff('1290', plain, ~ ( zip_tseitin_6) | (e13 = op1(e13, e12)), 5.30/5.52 inference('split', [status(esa)], ['1289'])). 5.30/5.52 tff('1291', plain, (op1(e10, e13) = e12) <= ((op1(e10, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['389'])). 5.30/5.52 tff('1292', plain, (e13 = op1(e10, e10)) <= ((e13 = op1(e10, e10))), 5.30/5.52 inference('split', [status(esa)], ['419'])). 5.30/5.52 tff('1293', plain, 5.30/5.52 (e10 = op1(e10, op1(e10, e10))) <= ((e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('1294', plain, 5.30/5.52 (e10 = op1(e10, e13)) 5.30/5.52 <= ((e13 = op1(e10, e10)) & (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1292', '1293'])). 5.30/5.52 tff('1295', plain, 5.30/5.52 (e10 = e12) 5.30/5.52 <= ((e13 = op1(e10, e10)) & 5.30/5.52 (op1(e10, e13) = e12) & 5.30/5.52 (e10 = op1(e10, op1(e10, e10)))), 5.30/5.52 inference('sup+', [status(thm)], ['1291', '1294'])). 5.30/5.52 tff('1296', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1297', plain, 5.30/5.52 ~ (e13 = op1(e10, e10)) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 ~ (op1(e10, e13) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1295', '1296'])). 5.30/5.52 tff('1298', plain, 5.30/5.52 (op1(e13, e10) = e13) | (e10 = op1(e13, e10)) | (op1(e13, e10) = e12), 5.30/5.52 inference('split', [status(esa)], ['23'])). 5.30/5.52 tff('1299', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['71'])). 5.30/5.52 tff('1300', plain, (op1(e10, e13) = e12) <= ((op1(e10, e13) = e12)), 5.30/5.52 inference('split', [status(esa)], ['389'])). 5.30/5.52 tff('1301', plain, op1(e10, e13) != op1(e10, e12), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1302', plain, (e12 != op1(e10, e12)) <= ((op1(e10, e13) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1300', '1301'])). 5.30/5.52 tff('1303', plain, 5.30/5.52 (e12 != e12) <= ((op1(e10, e13) = e12) & (op1(e10, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1299', '1302'])). 5.30/5.52 tff('1304', plain, ~ (op1(e10, e13) = e12) | ~ (op1(e10, e12) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1303'])). 5.30/5.52 tff('1305', plain, (op1(e12, e10) = e10 | ~ zip_tseitin_1), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_29])). 5.30/5.52 tff('1306', plain, ~ ( zip_tseitin_1) | (e10 = op1(e12, e10)), 5.30/5.52 inference('split', [status(esa)], ['1305'])). 5.30/5.52 tff('1307', plain, (e11 = op1(e11, e12) | ~ zip_tseitin_3), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_0])). 5.30/5.52 tff('1308', plain, ~ ( zip_tseitin_3) | (op1(e11, e12) = e11), 5.30/5.52 inference('split', [status(esa)], ['1307'])). 5.30/5.52 tff('1309', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['478'])). 5.30/5.52 tff('1310', plain, (op1(e12, e10) = e11) <= ((op1(e12, e10) = e11)), 5.30/5.52 inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1311', plain, 5.30/5.52 (e12 = e11) <= ((op1(e12, e10) = e12) & (op1(e12, e10) = e11)), 5.30/5.52 inference('sup+', [status(thm)], ['1309', '1310'])). 5.30/5.52 tff('1312', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1313', plain, ~ (op1(e12, e10) = e11) | ~ (op1(e12, e10) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1311', '1312'])). 5.30/5.52 tff('1314', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['478'])). 5.30/5.52 tff('1315', plain, 5.30/5.52 (op1(e12, op1(e12, e10)) = e12) <= ((op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('split', [status(esa)], ['496'])). 5.30/5.52 tff('1316', plain, 5.30/5.52 (op1(e12, e12) = e12) 5.30/5.52 <= ((op1(e12, e10) = e12) & (op1(e12, op1(e12, e10)) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['1314', '1315'])). 5.30/5.52 tff('1317', plain, (e12 != op1(e12, e12)) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['900', '901'])). 5.30/5.52 tff('1318', plain, 5.30/5.52 ~ (op1(e12, op1(e12, e10)) = e12) | ~ (op1(e12, e10) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1316', '1317'])). 5.30/5.52 tff('1319', plain, (op1(e12, e10) = e10) <= ((e10 = op1(e12, e10))), 5.30/5.52 inference('split', [status(esa)], ['582'])). 5.30/5.52 tff('1320', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['478'])). 5.30/5.52 tff('1321', plain, 5.30/5.52 (e10 = e12) <= ((op1(e12, e10) = e12) & (e10 = op1(e12, e10))), 5.30/5.52 inference('sup+', [status(thm)], ['1319', '1320'])). 5.30/5.52 tff('1322', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1323', plain, ~ (e10 = op1(e12, e10)) | ~ (op1(e12, e10) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1321', '1322'])). 5.30/5.52 tff('1324', plain, (op1(e12, e10) = e13) <= ((op1(e12, e10) = e13)), 5.30/5.52 inference('split', [status(esa)], ['375'])). 5.30/5.52 tff('1325', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['478'])). 5.30/5.52 tff('1326', plain, 5.30/5.52 (e13 = e12) <= ((op1(e12, e10) = e13) & (op1(e12, e10) = e12)), 5.30/5.52 inference('sup+', [status(thm)], ['1324', '1325'])). 5.30/5.52 tff('1327', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1328', plain, ~ (op1(e12, e10) = e13) | ~ (op1(e12, e10) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1326', '1327'])). 5.30/5.52 tff('1329', plain, (op1(e11, e12) = e12) <= ((e12 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['1255'])). 5.30/5.52 tff('1330', plain, (op1(e11, e12) = e12) <= ((e12 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['1255'])). 5.30/5.52 tff('1331', plain, 5.30/5.52 (e11 = op1(e11, op1(e11, e12))) <= ((e11 = op1(e11, op1(e11, e12)))), 5.30/5.52 inference('split', [status(esa)], ['294'])). 5.30/5.52 tff('1332', plain, 5.30/5.52 (e11 = op1(e11, e12)) 5.30/5.52 <= ((e12 = op1(e11, e12)) & (e11 = op1(e11, op1(e11, e12)))), 5.30/5.52 inference('sup+', [status(thm)], ['1330', '1331'])). 5.30/5.52 tff('1333', plain, 5.30/5.52 (e11 = e12) <= ((e12 = op1(e11, e12)) & (e11 = op1(e11, op1(e11, e12)))), 5.30/5.52 inference('sup+', [status(thm)], ['1329', '1332'])). 5.30/5.52 tff('1334', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1335', plain, 5.30/5.52 ~ (e11 = op1(e11, op1(e11, e12))) | ~ (e12 = op1(e11, e12)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1333', '1334'])). 5.30/5.52 tff('1336', plain, (op1(e11, e12) = e12) <= ((e12 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['1255'])). 5.30/5.52 tff('1337', plain, (e10 = op1(e11, e12)) <= ((e10 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['548'])). 5.30/5.52 tff('1338', plain, 5.30/5.52 (e10 = e12) <= ((e12 = op1(e11, e12)) & (e10 = op1(e11, e12))), 5.30/5.52 inference('sup+', [status(thm)], ['1336', '1337'])). 5.30/5.52 tff('1339', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1340', plain, ~ (e10 = op1(e11, e12)) | ~ (e12 = op1(e11, e12)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1338', '1339'])). 5.30/5.52 tff('1341', plain, (op1(e11, e12) = e11) <= ((op1(e11, e12) = e11)), 5.30/5.52 inference('split', [status(esa)], ['58'])). 5.30/5.52 tff('1342', plain, (op1(e11, e12) = e12) <= ((e12 = op1(e11, e12))), 5.30/5.52 inference('split', [status(esa)], ['1255'])). 5.30/5.52 tff('1343', plain, 5.30/5.52 (e11 = e12) <= ((op1(e11, e12) = e11) & (e12 = op1(e11, e12))), 5.30/5.52 inference('sup+', [status(thm)], ['1341', '1342'])). 5.30/5.52 tff('1344', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1345', plain, ~ (op1(e11, e12) = e11) | ~ (e12 = op1(e11, e12)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1343', '1344'])). 5.30/5.52 tff('1346', plain, 5.30/5.52 (e12 = op1(e12, e10) 5.30/5.52 | op1(e12, e11) = e12 5.30/5.52 | e12 = op1(e12, e12) 5.30/5.52 | e12 = op1(e12, e13)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1347', plain, 5.30/5.52 (op1(e12, e10) = e12) | (e12 = op1(e12, e13)) | (op1(e12, e12) = e12) | 5.30/5.52 (e12 = op1(e12, e11)), inference('split', [status(esa)], ['1346'])). 5.30/5.52 tff('1348', plain, 5.30/5.52 (op1(e11, e12) = e12 5.30/5.52 | e12 = op1(e12, e12) 5.30/5.52 | op1(e13, e12) = e12 5.30/5.52 | e12 = op1(e10, e12)), 5.30/5.52 inference('cnf', [status(esa)], [ax2])). 5.30/5.52 tff('1349', plain, 5.30/5.52 (op1(e10, e12) = e12) | (e12 = op1(e11, e12)) | (op1(e12, e12) = e12) | 5.30/5.52 (op1(e13, e12) = e12), inference('split', [status(esa)], ['1348'])). 5.30/5.52 tff('1350', plain, 5.30/5.52 (e10 = op1(e11, e10)) | (e10 = op1(e13, e10)) | (e10 = op1(e12, e10)) | 5.30/5.52 (e10 = op1(e10, e10)), inference('split', [status(esa)], ['659'])). 5.30/5.52 tff('1351', plain, 5.30/5.52 (op1(e10, e12) = e12) | (e12 = op1(e10, e10)) | (op1(e10, e11) = e12) | 5.30/5.52 (op1(e10, e13) = e12), inference('split', [status(esa)], ['661'])). 5.30/5.52 tff('1352', plain, 5.30/5.52 (op1(e13, e11) = e12) | (op1(e13, e10) = e12) | (op1(e13, e12) = e12) | 5.30/5.52 (e12 = op1(e13, e13)), inference('split', [status(esa)], ['680'])). 5.30/5.52 tff('1353', plain, 5.30/5.52 (op1(e13, e12) = e10) | (e13 = op1(e13, e12)) | (op1(e13, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['402'])). 5.30/5.52 tff('1354', plain, ~ (e13 = op1(e10, e12)) | ~ (op1(e10, e13) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['687'])). 5.30/5.52 tff('1355', plain, ~ (op1(e12, e10) = e13) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify', [status(thm)], ['720'])). 5.30/5.52 tff('1356', plain, (op1(e10, e13) = e13) | ~ ( zip_tseitin_9), 5.30/5.52 inference('split', [status(esa)], ['724'])). 5.30/5.52 tff('1357', plain, (op1(e13, e10) = e13) | ~ ( zip_tseitin_9), 5.30/5.52 inference('split', [status(esa)], ['726'])). 5.30/5.52 tff('1358', plain, 5.30/5.52 ( zip_tseitin_9) | ( zip_tseitin_3) | ( zip_tseitin_8) | 5.30/5.52 ( zip_tseitin_15) | ( zip_tseitin_5) | ( zip_tseitin_11) | 5.30/5.52 ( zip_tseitin_0) | ( zip_tseitin_7) | ( zip_tseitin_4) | 5.30/5.52 ( zip_tseitin_10) | ( zip_tseitin_2) | ( zip_tseitin_6) | 5.30/5.52 ( zip_tseitin_14) | ( zip_tseitin_13) | ( zip_tseitin_1) | 5.30/5.52 ( zip_tseitin_12), inference('split', [status(esa)], ['728'])). 5.30/5.52 tff('1359', plain, ~ ( zip_tseitin_0) | ~ (e10 = op1(e10, e10)), 5.30/5.52 inference('split', [status(esa)], ['754'])). 5.30/5.52 tff('1360', plain, ~ ( zip_tseitin_14) | (e11 = op1(e10, e11)), 5.30/5.52 inference('split', [status(esa)], ['782'])). 5.30/5.52 tff('1361', plain, ~ ( zip_tseitin_14) | (e11 = op1(e11, e10)), 5.30/5.52 inference('split', [status(esa)], ['784'])). 5.30/5.52 tff('1362', plain, 5.30/5.52 (op1(e12, e12) = e11) | (op1(e11, e12) = e11) | (e11 = op1(e13, e12)) | 5.30/5.52 (e11 = op1(e10, e12)), inference('split', [status(esa)], ['786'])). 5.30/5.52 tff('1363', plain, (op1(e10, e12) = e12) | ~ ( zip_tseitin_12), 5.30/5.52 inference('split', [status(esa)], ['788'])). 5.30/5.52 tff('1364', plain, ~ ( zip_tseitin_10) | (op1(e13, e12) = e12), 5.30/5.52 inference('split', [status(esa)], ['790'])). 5.30/5.52 tff('1365', plain, 5.30/5.52 ~ (e11 = op1(e10, e12)) | ~ (e10 = op1(e10, op1(e10, e10))) | 5.30/5.52 ~ (e12 = op1(e10, e10)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['794', '795'])). 5.30/5.52 tff('1366', plain, 5.30/5.52 ~ (op1(e12, e12) = e12) | ~ (op1(e12, op1(e12, e10)) = e12) | 5.30/5.52 ~ (op1(e12, e10) = e11), inference('simplify', [status(thm)], ['800'])). 5.30/5.52 tff('1367', plain, 5.30/5.52 (op1(e10, e12) = e12) | (e11 = op1(e10, e12)) | (op1(e10, e12) = e10) | 5.30/5.52 (e13 = op1(e10, e12)), inference('split', [status(esa)], ['350'])). 5.30/5.52 tff('1368', plain, 5.30/5.52 (op1(e12, e10) = e12) | (e12 = op1(e11, e10)) | (op1(e13, e10) = e12) | 5.30/5.52 (e12 = op1(e10, e10)), inference('split', [status(esa)], ['809'])). 5.30/5.52 tff('1369', plain, 5.30/5.52 (op1(e12, e10) = e12) | (e10 = op1(e12, e10)) | (op1(e12, e10) = e13) | 5.30/5.52 (op1(e12, e10) = e11), inference('split', [status(esa)], ['435'])). 5.30/5.52 tff('1370', plain, ~ (e10 = op1(e13, e10)) | ~ (op1(e13, e10) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['814', '815'])). 5.30/5.52 tff('1371', plain, ~ ( zip_tseitin_2) | ~ (e13 = op1(e10, e10)), 5.30/5.52 inference('split', [status(esa)], ['817'])). 5.30/5.52 tff('1372', plain, 5.30/5.52 (op1(e13, e10) = e13) | (op1(e11, e10) = e13) | (op1(e12, e10) = e13) | 5.30/5.52 (e13 = op1(e10, e10)), inference('split', [status(esa)], ['819'])). 5.30/5.52 tff('1373', plain, ~ (e13 = op1(e10, e12)) | ~ (e13 = op1(e13, e12)), 5.30/5.52 inference('simplify', [status(thm)], ['825'])). 5.30/5.52 tff('1374', plain, ~ (op1(e12, e10) = e13) | ~ (e13 = op1(e12, e13)), 5.30/5.52 inference('simplify', [status(thm)], ['837'])). 5.30/5.52 tff('1375', plain, 5.30/5.52 (op1(e13, e12) = e10) | (e13 = op1(e13, e12)) | (op1(e13, e12) = e12) | 5.30/5.52 (e11 = op1(e13, e12)), inference('split', [status(esa)], ['311'])). 5.30/5.52 tff('1376', plain, 5.30/5.52 (op1(e12, e13) = e10) | (e12 = op1(e12, e13)) | (e13 = op1(e12, e13)), 5.30/5.52 inference('split', [status(esa)], ['51'])). 5.30/5.52 tff('1377', plain, 5.30/5.52 ~ (e10 = op1(e13, e10)) | ~ (op1(e13, op1(e13, e10)) = e13), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['855', '856'])). 5.30/5.52 tff('1378', plain, ~ (e10 = op1(e13, e10)) | ~ (op1(e13, e12) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['862'])). 5.30/5.52 tff('1379', plain, ~ (e10 = op1(e13, e10)) | ~ (op1(e13, e10) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['866', '867'])). 5.30/5.52 tff('1380', plain, ~ (e10 = op1(e13, e10)) | ~ (e10 = op1(e12, e10)), 5.30/5.52 inference('simplify', [status(thm)], ['873'])). 5.30/5.52 tff('1381', plain, ~ (op1(e10, e13) = e10) | ~ (op1(e10, e13) = e12), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['877', '878'])). 5.30/5.52 tff('1382', plain, ~ (op1(e10, e13) = e10) | ~ (op1(e10, e12) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['882'])). 5.30/5.52 tff('1383', plain, ~ (op1(e10, e13) = e10) | ~ (op1(e12, e13) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['888'])). 5.30/5.52 tff('1384', plain, ~ ( zip_tseitin_2) | (e10 = op1(e13, e10)), 5.30/5.52 inference('split', [status(esa)], ['890'])). 5.30/5.52 tff('1385', plain, ~ ( zip_tseitin_2) | (op1(e10, e13) = e10), 5.30/5.52 inference('split', [status(esa)], ['892'])). 5.30/5.52 tff('1386', plain, ~ (op1(e12, e12) = e12) | ~ (op1(e12, e10) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['903'])). 5.30/5.52 tff('1387', plain, ~ (op1(e12, e12) = e12) | ~ (op1(e10, e12) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['915'])). 5.30/5.52 tff('1388', plain, ~ (op1(e12, e12) = e12) | ~ ( zip_tseitin_1), 5.30/5.52 inference('split', [status(esa)], ['923'])). 5.30/5.52 tff('1389', plain, ~ (op1(e12, e12) = e12) | ~ ( zip_tseitin_3), 5.30/5.52 inference('split', [status(esa)], ['925'])). 5.30/5.52 tff('1390', plain, ~ (op1(e12, e12) = e12) | ~ ( zip_tseitin_6), 5.30/5.52 inference('split', [status(esa)], ['927'])). 5.30/5.52 tff('1391', plain, 5.30/5.52 (e10 = op1(e10, op1(e10, e10))) | (op1(e13, op1(e13, e10)) = e13) | 5.30/5.52 (e11 = op1(e11, op1(e11, e10))) | (op1(e12, op1(e12, e10)) = e12), 5.30/5.52 inference('split', [status(esa)], ['427'])). 5.30/5.52 tff('1392', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('split', [status(esa)], ['14'])). 5.30/5.52 tff('1393', plain, (op1(e13, e10) = e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('split', [status(esa)], ['88'])). 5.30/5.52 tff('1394', plain, op1(e13, e11) != op1(e13, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1395', plain, (op1(e13, e11) != e12) <= ((op1(e13, e10) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1393', '1394'])). 5.30/5.52 tff('1396', plain, 5.30/5.52 (e12 != e12) <= ((op1(e13, e10) = e12) & (op1(e13, e11) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1392', '1395'])). 5.30/5.52 tff('1397', plain, ~ (op1(e13, e10) = e12) | ~ (op1(e13, e11) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1396'])). 5.30/5.52 tff('1398', plain, (op1(e12, e11) = e12) <= ((e12 = op1(e12, e11))), 5.30/5.52 inference('split', [status(esa)], ['382'])). 5.30/5.52 tff('1399', plain, (e12 != op1(e12, e11)) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['297', '298'])). 5.30/5.52 tff('1400', plain, 5.30/5.52 (e12 != e12) <= ((e12 = op1(e12, e11)) & (op1(e13, e11) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1398', '1399'])). 5.30/5.52 tff('1401', plain, ~ (e12 = op1(e12, e11)) | ~ (op1(e13, e11) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1400'])). 5.30/5.52 tff('1402', plain, (op1(e13, e12) = e12) <= ((op1(e13, e12) = e12)), 5.30/5.52 inference('split', [status(esa)], ['402'])). 5.30/5.52 tff('1403', plain, (op1(e13, e11) = e12) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('split', [status(esa)], ['14'])). 5.30/5.52 tff('1404', plain, op1(e13, e12) != op1(e13, e11), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1405', plain, (op1(e13, e12) != e12) <= ((op1(e13, e11) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1403', '1404'])). 5.30/5.52 tff('1406', plain, 5.30/5.52 (e12 != e12) <= ((op1(e13, e11) = e12) & (op1(e13, e12) = e12)), 5.30/5.52 inference('sup-', [status(thm)], ['1402', '1405'])). 5.30/5.52 tff('1407', plain, ~ (op1(e13, e12) = e12) | ~ (op1(e13, e11) = e12), 5.30/5.52 inference('simplify', [status(thm)], ['1406'])). 5.30/5.52 tff('1408', plain, (e10 = op1(e10, e12)) <= ((op1(e10, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['675'])). 5.30/5.52 tff('1409', plain, 5.30/5.52 (op1(e10, op1(e10, e12)) = e10) <= ((op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('split', [status(esa)], ['74'])). 5.30/5.52 tff('1410', plain, 5.30/5.52 (op1(e10, e10) = e10) 5.30/5.52 <= ((op1(e10, e12) = e10) & (op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('sup+', [status(thm)], ['1408', '1409'])). 5.30/5.52 tff('1411', plain, op1(e10, e12) != op1(e10, e10), 5.30/5.52 inference('cnf', [status(esa)], [ax5])). 5.30/5.52 tff('1412', plain, 5.30/5.52 (op1(e10, e12) != e10) 5.30/5.52 <= ((op1(e10, e12) = e10) & (op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('sup-', [status(thm)], ['1410', '1411'])). 5.30/5.52 tff('1413', plain, (e10 = op1(e10, e12)) <= ((op1(e10, e12) = e10)), 5.30/5.52 inference('split', [status(esa)], ['675'])). 5.30/5.52 tff('1414', plain, 5.30/5.52 (e10 != e10) <= ((op1(e10, e12) = e10) & (op1(e10, op1(e10, e12)) = e10)), 5.30/5.52 inference('demod', [status(thm)], ['1412', '1413'])). 5.30/5.52 tff('1415', plain, 5.30/5.52 ~ (op1(e10, op1(e10, e12)) = e10) | ~ (op1(e10, e12) = e10), 5.30/5.52 inference('simplify', [status(thm)], ['1414'])). 5.30/5.52 tff('1416', plain, (e12 = op1(e12, e13)) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('split', [status(esa)], ['387'])). 5.30/5.52 tff('1417', plain, op1(e12, e13) = e10, 5.30/5.52 inference('demod', [status(thm)], ['240', '241', '244'])). 5.30/5.52 tff('1418', plain, (e12 = e10) <= ((e12 = op1(e12, e13))), 5.30/5.52 inference('sup+', [status(thm)], ['1416', '1417'])). 5.30/5.52 tff('1419', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.52 tff('1420', plain, ~ (e12 = op1(e12, e13)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1418', '1419'])). 5.30/5.52 tff('1421', plain, 5.30/5.52 (op1(e11, e13) = e12) | (e12 = op1(e12, e13)) | (e12 = op1(e13, e13)) | 5.30/5.52 (op1(e10, e13) = e12), inference('split', [status(esa)], ['843'])). 5.30/5.52 tff('1422', plain, (op1(e11, e13) = e12), 5.30/5.52 inference('sat_resolution*', [status(thm)], 5.30/5.52 ['284', '289', '290', '292', '301', '309', '315', '321', 5.30/5.52 '332', '343', '349', '359', '365', '367', '373', '380', 5.30/5.52 '386', '394', '399', '407', '413', '415', '416', '423', 5.30/5.52 '425', '434', '441', '448', '450', '456', '462', '467', 5.30/5.52 '475', '477', '487', '494', '504', '515', '517', '524', 5.30/5.52 '533', '534', '540', '547', '553', '555', '562', '568', 5.30/5.52 '573', '574', '580', '581', '589', '595', '597', '601', 5.30/5.52 '606', '612', '618', '627', '633', '634', '642', '644', 5.30/5.52 '646', '932', '938', '943', '949', '954', '959', '964', 5.30/5.52 '969', '974', '976', '980', '986', '992', '998', '1004', 5.30/5.52 '1010', '1015', '1021', '1027', '1033', '1039', '1045', 5.30/5.52 '1047', '1050', '1056', '1063', '1064', '1066', '1071', 5.30/5.52 '1077', '1082', '1086', '1091', '1092', '1097', '1099', 5.30/5.52 '1102', '1104', '1107', '1113', '1119', '1125', '1131', 5.30/5.52 '1132', '1139', '1146', '1147', '1154', '1160', '1168', 5.30/5.52 '1175', '1180', '1182', '1184', '1187', '1193', '1199', 5.30/5.52 '1204', '1209', '1210', '1212', '1220', '1226', '1231', 5.30/5.52 '1237', '1242', '1248', '1254', '1261', '1265', '1266', 5.30/5.52 '1271', '1276', '1281', '1286', '1288', '1290', '1297', 5.30/5.52 '1298', '1304', '1306', '1308', '1313', '1318', '1323', 5.30/5.52 '1328', '1335', '1340', '1345', '1347', '1349', '658', 5.30/5.52 '1350', '1351', '668', '674', '679', '1352', '1353', '1354', 5.30/5.52 '693', '699', '706', '711', '715', '1355', '723', '1356', 5.30/5.52 '1357', '1358', '735', '741', '743', '745', '751', '753', 5.30/5.52 '1359', '762', '767', '769', '771', '777', '781', '1360', 5.30/5.52 '1361', '1362', '1363', '1364', '1365', '1366', '807', 5.30/5.52 '1367', '1368', '1369', '1370', '1371', '1372', '1373', 5.30/5.52 '832', '1374', '1375', '842', '1376', '1377', '1378', '1379', 5.30/5.52 '1380', '1381', '1382', '1383', '1384', '1385', '898', 5.30/5.52 '1386', '910', '1387', '922', '1388', '1389', '1390', '1391', 5.30/5.52 '1397', '1401', '1407', '1415', '849', '1420', '1421'])). 5.30/5.52 tff('1423', plain, op1(e11, e13) = e12, 5.30/5.52 inference('simpl_trail', [status(thm)], ['278', '1422'])). 5.30/5.52 tff('1424', plain, 5.30/5.52 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.52 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.52 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.52 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.52 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.52 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.52 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.52 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.52 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.52 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.52 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.52 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.52 | h3(e10) != e20 5.30/5.52 | h3(e11) != e21 5.30/5.52 | h3(e11) != e22 5.30/5.52 | h3(e12) != e23 5.30/5.52 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.52 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.52 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.52 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.52 tff('1425', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1426', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1427', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1428', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1429', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1430', plain, h3(e11) = op2(e22, e22), 5.30/5.52 inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1431', plain, op1(e13, e13) = e11, 5.30/5.52 inference('cnf', [status(esa)], [ax12])). 5.30/5.52 tff('1432', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1433', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.52 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.52 tff('1434', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1435', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1436', plain, 5.30/5.52 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.52 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.52 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.52 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.52 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.52 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.52 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.52 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.52 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.52 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.52 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.52 | h3(e11) != h3(e11) 5.30/5.52 | h3(e10) != e20 5.30/5.52 | h3(e11) != e21 5.30/5.52 | h3(e11) != e22 5.30/5.52 | h3(e12) != e23 5.30/5.52 | h3(e12) != h3(op1(e13, e11)) 5.30/5.52 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.52 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.52 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.52 inference('demod', [status(thm)], 5.30/5.52 ['1424', '1425', '1426', '1427', '1428', '1429', '1430', 5.30/5.52 '1431', '1432', '1433', '1434', '1435'])). 5.30/5.52 tff('1437', plain, 5.30/5.52 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.52 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.52 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.52 | h3(e12) != h3(op1(e13, e11)) 5.30/5.52 | h3(e12) != e23 5.30/5.52 | h3(e11) != e22 5.30/5.52 | h3(e11) != e21 5.30/5.52 | h3(e10) != e20 5.30/5.52 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.52 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.52 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.52 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.52 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.52 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.52 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.52 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.52 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.52 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.52 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.52 inference('simplify', [status(thm)], ['1436'])). 5.30/5.52 tff('1438', plain, 5.30/5.52 (h3(op1(e11, e13)) != op2(h3(e11), e22)) 5.30/5.52 <= (~ (h3(op1(e11, e13)) = op2(h3(e11), e22))), 5.30/5.52 inference('split', [status(esa)], ['1437'])). 5.30/5.52 tff('1439', plain, 5.30/5.52 (h3(e12) != op2(h3(e11), e22)) 5.30/5.52 <= (~ (h3(op1(e11, e13)) = op2(h3(e11), e22))), 5.30/5.52 inference('sup-', [status(thm)], ['1423', '1438'])). 5.30/5.52 tff('1440', plain, 5.30/5.52 (h3(e12) != op2(e21, e22)) 5.30/5.52 <= (~ (h3(op1(e11, e13)) = op2(h3(e11), e22)) & (h3(e11) = e21)), 5.30/5.52 inference('sup-', [status(thm)], ['277', '1439'])). 5.30/5.52 tff('1441', plain, 5.30/5.52 (h3(e12) != e23) 5.30/5.52 <= (~ (h3(op1(e11, e13)) = op2(h3(e11), e22)) & 5.30/5.52 (op2(e21, e22) = e23) & 5.30/5.52 (h3(e11) = e21)), 5.30/5.52 inference('sup-', [status(thm)], ['276', '1440'])). 5.30/5.52 tff('1442', plain, 5.30/5.52 (e23 != e23) 5.30/5.52 <= (~ (h3(op1(e11, e13)) = op2(h3(e11), e22)) & 5.30/5.52 (op2(e21, e22) = e23) & 5.30/5.52 (op2(e22, e21) = e23) & 5.30/5.52 (h3(e11) = e21)), 5.30/5.52 inference('sup-', [status(thm)], ['275', '1441'])). 5.30/5.52 tff('1443', plain, 5.30/5.52 (h3(op1(e11, e13)) = op2(h3(e11), e22)) | ~ (op2(e21, e22) = e23) | 5.30/5.52 ~ (op2(e22, e21) = e23) | ~ (h3(e11) = e21), 5.30/5.52 inference('simplify', [status(thm)], ['1442'])). 5.30/5.52 tff('1444', plain, 5.30/5.52 (op2(e22, e20) = e20 5.30/5.52 | op2(e23, e20) = e20 5.30/5.52 | op2(e21, e20) = e20 5.30/5.52 | e20 = op2(e20, e20)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1445', plain, (op2(e21, e20) = e20) <= ((e20 = op2(e21, e20))), 5.30/5.52 inference('split', [status(esa)], ['1444'])). 5.30/5.52 tff('1446', plain, (e10 = op1(e11, e10)) <= ((e10 = op1(e11, e10))), 5.30/5.52 inference('split', [status(esa)], ['333'])). 5.30/5.52 tff('1447', plain, (h3(e11) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.52 inference('sup+', [status(thm)], ['162', '163'])). 5.30/5.52 tff('1448', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.52 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.52 tff('1449', plain, (h3(e12) = op2(e22, e21)) <= ((op2(e22, e22) = e21)), 5.30/5.52 inference('sup+', [status(thm)], ['1447', '1448'])). 5.30/5.52 tff('1450', plain, (op2(e22, e21) = e23) <= ((op2(e22, e21) = e23)), 5.30/5.52 inference('split', [status(esa)], ['273'])). 5.30/5.52 tff('1451', plain, 5.30/5.52 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (op2(e22, e22) = e21)), 5.30/5.52 inference('sup+', [status(thm)], ['1449', '1450'])). 5.30/5.52 tff('1452', plain, (op2(e23, e20) = e23 | ~ zip_tseitin_26), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_44])). 5.30/5.52 tff('1453', plain, (op2(e23, e20) = e23) | ~ ( zip_tseitin_26), 5.30/5.52 inference('split', [status(esa)], ['1452'])). 5.30/5.52 tff('1454', plain, (e22 = op2(e22, e20) | ~ zip_tseitin_20), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_56])). 5.30/5.52 tff('1455', plain, (e22 = op2(e22, e20)) | ~ ( zip_tseitin_20), 5.30/5.52 inference('split', [status(esa)], ['1454'])). 5.30/5.52 tff('1456', plain, 5.30/5.52 (e21 = op2(e22, e20) 5.30/5.52 | e23 = op2(e22, e20) 5.30/5.52 | e22 = op2(e22, e20) 5.30/5.52 | op2(e22, e20) = e20), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1457', plain, (e23 = op2(e22, e20)) <= ((e23 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1458', plain, (op2(e23, e20) = e23) <= ((op2(e23, e20) = e23)), 5.30/5.52 inference('split', [status(esa)], ['144'])). 5.30/5.52 tff('1459', plain, op2(e22, e20) != op2(e23, e20), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1460', plain, (op2(e22, e20) != e23) <= ((op2(e23, e20) = e23)), 5.30/5.52 inference('sup-', [status(thm)], ['1458', '1459'])). 5.30/5.52 tff('1461', plain, 5.30/5.52 (e23 != e23) <= ((e23 = op2(e22, e20)) & (op2(e23, e20) = e23)), 5.30/5.52 inference('sup-', [status(thm)], ['1457', '1460'])). 5.30/5.52 tff('1462', plain, ~ (e23 = op2(e22, e20)) | ~ (op2(e23, e20) = e23), 5.30/5.52 inference('simplify', [status(thm)], ['1461'])). 5.30/5.52 tff('1463', plain, 5.30/5.52 (h3(e11) = e21) | (h3(e11) = e22) | (h3(e11) = e20) | 5.30/5.52 (op2(e22, e22) = e23), inference('split', [status(esa)], ['269'])). 5.30/5.52 tff('1464', plain, (h3(e11) = e20) <= ((h3(e11) = e20)), 5.30/5.52 inference('split', [status(esa)], ['269'])). 5.30/5.52 tff('1465', plain, (e20 != h3(e11)) <= ((e20 = op2(e22, e23))), 5.30/5.52 inference('sup-', [status(thm)], ['155', '158'])). 5.30/5.52 tff('1466', plain, (e20 != e20) <= ((e20 = op2(e22, e23)) & (h3(e11) = e20)), 5.30/5.52 inference('sup-', [status(thm)], ['1464', '1465'])). 5.30/5.52 tff('1467', plain, ~ (h3(e11) = e20) | ~ (e20 = op2(e22, e23)), 5.30/5.52 inference('simplify', [status(thm)], ['1466'])). 5.30/5.52 tff('1468', plain, 5.30/5.52 (e23 = op2(e22, e20) 5.30/5.52 | op2(e22, e23) = e23 5.30/5.52 | e23 = op2(e22, e22) 5.30/5.52 | op2(e22, e21) = e23), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1469', plain, h3(e11) = op2(e22, e22), 5.30/5.52 inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1470', plain, 5.30/5.52 (e23 = op2(e22, e20) 5.30/5.52 | op2(e22, e23) = e23 5.30/5.52 | e23 = h3(e11) 5.30/5.52 | op2(e22, e21) = e23), 5.30/5.52 inference('demod', [status(thm)], ['1468', '1469'])). 5.30/5.52 tff('1471', plain, 5.30/5.52 (op2(e22, e21) = e23) | (e23 = op2(e22, e20)) | (op2(e22, e23) = e23) | 5.30/5.52 (e23 = h3(e11)), inference('split', [status(esa)], ['1470'])). 5.30/5.52 tff('1472', plain, (op2(e20, e20) != e20 | ~ zip_tseitin_16), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_64])). 5.30/5.52 tff('1473', plain, ~ ( zip_tseitin_16) | ~ (op2(e20, e20) = e20), 5.30/5.52 inference('split', [status(esa)], ['1472'])). 5.30/5.52 tff('1474', plain, (op2(e20, e20) = e20 | ~ zip_tseitin_16), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_64])). 5.30/5.52 tff('1475', plain, ~ ( zip_tseitin_16) | (op2(e20, e20) = e20), 5.30/5.52 inference('split', [status(esa)], ['1474'])). 5.30/5.52 tff('1476', plain, (e22 != op2(e22, e22) | ~ zip_tseitin_22), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_52])). 5.30/5.52 tff('1477', plain, ~ ( zip_tseitin_22) | ~ (e22 = op2(e22, e22)), 5.30/5.52 inference('split', [status(esa)], ['1476'])). 5.30/5.52 tff('1478', plain, (op2(e22, e22) = e22 | ~ zip_tseitin_22), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_52])). 5.30/5.52 tff('1479', plain, ~ ( zip_tseitin_22) | (e22 = op2(e22, e22)), 5.30/5.52 inference('split', [status(esa)], ['1478'])). 5.30/5.52 tff('1480', plain, (op2(e23, e23) != e21 | ~ zip_tseitin_21), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_54])). 5.30/5.52 tff('1481', plain, ~ ( zip_tseitin_21) | ~ (e21 = op2(e23, e23)), 5.30/5.52 inference('split', [status(esa)], ['1480'])). 5.30/5.52 tff('1482', plain, (op2(e23, e23) != e21 | ~ zip_tseitin_23), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_50])). 5.30/5.52 tff('1483', plain, ~ ( zip_tseitin_23) | ~ (e21 = op2(e23, e23)), 5.30/5.52 inference('split', [status(esa)], ['1482'])). 5.30/5.52 tff('1484', plain, (e21 = op2(e23, e21) | ~ zip_tseitin_28), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_40])). 5.30/5.52 tff('1485', plain, ~ ( zip_tseitin_28) | (e21 = op2(e23, e21)), 5.30/5.52 inference('split', [status(esa)], ['1484'])). 5.30/5.52 tff('1486', plain, (e21 != op2(e21, e21) | ~ zip_tseitin_18), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_60])). 5.30/5.52 tff('1487', plain, ~ ( zip_tseitin_18) | ~ (op2(e21, e21) = e21), 5.30/5.52 inference('split', [status(esa)], ['1486'])). 5.30/5.52 tff('1488', plain, (op2(e21, e21) = e21 | ~ zip_tseitin_18), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_60])). 5.30/5.52 tff('1489', plain, ~ ( zip_tseitin_18) | (op2(e21, e21) = e21), 5.30/5.52 inference('split', [status(esa)], ['1488'])). 5.30/5.52 tff('1490', plain, (op2(e23, e23) != e23 | ~ zip_tseitin_24), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_48])). 5.30/5.52 tff('1491', plain, ~ ( zip_tseitin_24) | ~ (e23 = op2(e23, e23)), 5.30/5.52 inference('split', [status(esa)], ['1490'])). 5.30/5.52 tff('1492', plain, (e23 = op2(e23, e23) | ~ zip_tseitin_24), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_48])). 5.30/5.52 tff('1493', plain, ~ ( zip_tseitin_24) | (e23 = op2(e23, e23)), 5.30/5.52 inference('split', [status(esa)], ['1492'])). 5.30/5.52 tff('1494', plain, (op2(e23, e22) = e22 | ~ zip_tseitin_27), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_42])). 5.30/5.52 tff('1495', plain, ~ ( zip_tseitin_27) | (op2(e23, e22) = e22), 5.30/5.52 inference('split', [status(esa)], ['1494'])). 5.30/5.52 tff('1496', plain, (op2(e20, e23) = e20 | ~ zip_tseitin_17), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_62])). 5.30/5.52 tff('1497', plain, ~ ( zip_tseitin_17) | (e20 = op2(e20, e23)), 5.30/5.52 inference('split', [status(esa)], ['1496'])). 5.30/5.52 tff('1498', plain, 5.30/5.52 (op2(e20, e21) = e20 5.30/5.52 | e23 = op2(e20, e21) 5.30/5.52 | e22 = op2(e20, e21) 5.30/5.52 | e21 = op2(e20, e21)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1499', plain, (op2(e20, e21) = e20) <= ((op2(e20, e21) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1500', plain, (e21 = op2(e20, e21)) <= ((e21 = op2(e20, e21))), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1501', plain, 5.30/5.52 (e21 = e20) <= ((op2(e20, e21) = e20) & (e21 = op2(e20, e21))), 5.30/5.52 inference('sup+', [status(thm)], ['1499', '1500'])). 5.30/5.52 tff('1502', plain, e21 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1503', plain, ~ (e21 = op2(e20, e21)) | ~ (op2(e20, e21) = e20), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1501', '1502'])). 5.30/5.52 tff('1504', plain, (e20 != op2(e21, e21) | ~ zip_tseitin_29), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_38])). 5.30/5.52 tff('1505', plain, ~ ( zip_tseitin_29) | ~ (e20 = op2(e21, e21)), 5.30/5.52 inference('split', [status(esa)], ['1504'])). 5.30/5.52 tff('1506', plain, (e21 = op2(e20, e21) | ~ zip_tseitin_29), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_38])). 5.30/5.52 tff('1507', plain, ~ ( zip_tseitin_29) | (e21 = op2(e20, e21)), 5.30/5.52 inference('split', [status(esa)], ['1506'])). 5.30/5.52 tff('1508', plain, 5.30/5.52 (e20 = op2(e23, e21) 5.30/5.52 | e20 = op2(e22, e21) 5.30/5.52 | op2(e21, e21) = e20 5.30/5.52 | e20 = op2(e20, e21)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1509', plain, 5.30/5.52 (op2(e20, e21) = e20) | (e20 = op2(e21, e21)) | (e20 = op2(e22, e21)) | 5.30/5.52 (op2(e23, e21) = e20), inference('split', [status(esa)], ['1508'])). 5.30/5.52 tff('1510', plain, (e23 = op2(e22, e23) | ~ zip_tseitin_25), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_46])). 5.30/5.52 tff('1511', plain, ~ ( zip_tseitin_25) | (op2(e22, e23) = e23), 5.30/5.52 inference('split', [status(esa)], ['1510'])). 5.30/5.52 tff('1512', plain, 5.30/5.52 (op2(e23, e23) = e20 5.30/5.52 | op2(e23, e23) = e22 5.30/5.52 | e23 = op2(e23, e23) 5.30/5.52 | e21 = op2(e23, e23)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1513', plain, 5.30/5.52 (e21 = op2(e23, e23)) | (e23 = op2(e23, e23)) | (op2(e23, e23) = e22) | 5.30/5.52 (op2(e23, e23) = e20), inference('split', [status(esa)], ['1512'])). 5.30/5.52 tff('1514', plain, (op2(e23, e23) != e21 | ~ zip_tseitin_31), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_34])). 5.30/5.52 tff('1515', plain, ~ ( zip_tseitin_31) | ~ (e21 = op2(e23, e23)), 5.30/5.52 inference('split', [status(esa)], ['1514'])). 5.30/5.52 tff('1516', plain, (e20 != op2(e21, e21) | ~ zip_tseitin_20), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_56])). 5.30/5.52 tff('1517', plain, ~ (e20 = op2(e21, e21)) | ~ ( zip_tseitin_20), 5.30/5.52 inference('split', [status(esa)], ['1516'])). 5.30/5.52 tff('1518', plain, (op2(e21, e21) != e20 | ~ zip_tseitin_26), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_44])). 5.30/5.52 tff('1519', plain, ~ (e20 = op2(e21, e21)) | ~ ( zip_tseitin_26), 5.30/5.52 inference('split', [status(esa)], ['1518'])). 5.30/5.52 tff('1520', plain, (op2(e22, e20) = e20 | ~ zip_tseitin_30), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_36])). 5.30/5.52 tff('1521', plain, ~ ( zip_tseitin_30) | (op2(e22, e20) = e20), 5.30/5.52 inference('split', [status(esa)], ['1520'])). 5.30/5.52 tff('1522', plain, (op2(e22, e22) != e22 | ~ zip_tseitin_30), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_36])). 5.30/5.52 tff('1523', plain, ~ ( zip_tseitin_30) | ~ (e22 = op2(e22, e22)), 5.30/5.52 inference('split', [status(esa)], ['1522'])). 5.30/5.52 tff('1524', plain, (op2(e22, e20) = e20) <= ((op2(e22, e20) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1525', plain, (e22 = op2(e22, e20)) <= ((e22 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1526', plain, 5.30/5.52 (e22 = e20) <= ((op2(e22, e20) = e20) & (e22 = op2(e22, e20))), 5.30/5.52 inference('sup+', [status(thm)], ['1524', '1525'])). 5.30/5.52 tff('1527', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1528', plain, ~ (op2(e22, e20) = e20) | ~ (e22 = op2(e22, e20)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1526', '1527'])). 5.30/5.52 tff(ax15, axiom, 5.30/5.52 ((h2(e13) = e21) & (op2(e21,e21) = h2(e11)) & 5.30/5.52 (op2(e21,op2(e21,e21)) = h2(e12)) & 5.30/5.52 (h2(e10) = op2(op2(e21,op2(e21,e21)),e21)))). 5.30/5.52 tff('1529', plain, op2(e21, e21) = h2(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax15])). 5.30/5.52 tff('1530', plain, 5.30/5.52 (e20 = op2(e21, e21) 5.30/5.52 | op2(e21, e21) = e21 5.30/5.52 | op2(e21, e21) = e23 5.30/5.52 | e22 = op2(e21, e21)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1531', plain, (op2(e21, e21) = e23) <= ((op2(e21, e21) = e23)), 5.30/5.52 inference('split', [status(esa)], ['1530'])). 5.30/5.52 tff('1532', plain, (h2(e11) = e23) <= ((op2(e21, e21) = e23)), 5.30/5.52 inference('sup+', [status(thm)], ['1529', '1531'])). 5.30/5.52 tff('1533', plain, op2(e21, op2(e21, e21)) = h2(e12), 5.30/5.52 inference('cnf', [status(esa)], [ax15])). 5.30/5.52 tff('1534', plain, op2(e21, e21) = h2(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax15])). 5.30/5.52 tff('1535', plain, op2(e21, h2(e11)) = h2(e12), 5.30/5.52 inference('demod', [status(thm)], ['1533', '1534'])). 5.30/5.52 tff('1536', plain, (op2(e21, e23) = h2(e12)) <= ((op2(e21, e21) = e23)), 5.30/5.52 inference('sup+', [status(thm)], ['1532', '1535'])). 5.30/5.52 tff('1537', plain, (e22 = op2(e21, e23)) <= ((e22 = op2(e21, e23))), 5.30/5.52 inference('split', [status(esa)], ['190'])). 5.30/5.52 tff('1538', plain, 5.30/5.52 (e22 = h2(e12)) <= ((e22 = op2(e21, e23)) & (op2(e21, e21) = e23)), 5.30/5.52 inference('sup+', [status(thm)], ['1536', '1537'])). 5.30/5.52 tff('1539', plain, 5.30/5.52 (op2(e20, op2(e20, e21)) = e20 5.30/5.52 | e22 = op2(e22, op2(e22, e21)) 5.30/5.52 | e23 = op2(e23, op2(e23, e21)) 5.30/5.52 | e21 = op2(e21, op2(e21, e21))), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.52 tff('1540', plain, h4(e12) = op2(e23, e21), 5.30/5.52 inference('demod', [status(thm)], ['126', '127'])). 5.30/5.52 tff('1541', plain, op2(e21, e21) = h2(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax15])). 5.30/5.52 tff('1542', plain, op2(e21, h2(e11)) = h2(e12), 5.30/5.52 inference('demod', [status(thm)], ['1533', '1534'])). 5.30/5.52 tff('1543', plain, 5.30/5.52 (op2(e20, op2(e20, e21)) = e20 5.30/5.52 | e22 = op2(e22, op2(e22, e21)) 5.30/5.52 | e23 = op2(e23, h4(e12)) 5.30/5.52 | e21 = h2(e12)), 5.30/5.52 inference('demod', [status(thm)], ['1539', '1540', '1541', '1542'])). 5.30/5.52 tff('1544', plain, (e21 = h2(e12)) <= ((e21 = h2(e12))), 5.30/5.52 inference('split', [status(esa)], ['1543'])). 5.30/5.52 tff('1545', plain, 5.30/5.52 (e21 = e22) 5.30/5.52 <= ((e22 = op2(e21, e23)) & (op2(e21, e21) = e23) & (e21 = h2(e12))), 5.30/5.52 inference('sup+', [status(thm)], ['1538', '1544'])). 5.30/5.52 tff('1546', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1547', plain, 5.30/5.52 ~ (op2(e21, e21) = e23) | ~ (e22 = op2(e21, e23)) | ~ (e21 = h2(e12)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1545', '1546'])). 5.30/5.52 tff('1548', plain, 5.30/5.52 (e22 = op2(e21, e20) 5.30/5.52 | op2(e21, e22) = e22 5.30/5.52 | op2(e21, e23) = e22 5.30/5.52 | e22 = op2(e21, e21)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1549', plain, 5.30/5.52 (e22 = op2(e21, e23)) | (op2(e21, e20) = e22) | (e22 = op2(e21, e21)) | 5.30/5.52 (op2(e21, e22) = e22), inference('split', [status(esa)], ['1548'])). 5.30/5.52 tff('1550', plain, h4(e12) = op2(e23, e21), 5.30/5.52 inference('demod', [status(thm)], ['126', '127'])). 5.30/5.52 tff('1551', plain, 5.30/5.52 (op2(e23, e21) = e20 5.30/5.52 | op2(e23, e21) = e22 5.30/5.52 | e23 = op2(e23, e21) 5.30/5.52 | e21 = op2(e23, e21)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1552', plain, (op2(e23, e21) = e22) <= ((op2(e23, e21) = e22)), 5.30/5.52 inference('split', [status(esa)], ['1551'])). 5.30/5.52 tff('1553', plain, (h4(e12) = e22) <= ((op2(e23, e21) = e22)), 5.30/5.52 inference('sup+', [status(thm)], ['1550', '1552'])). 5.30/5.52 tff('1554', plain, op2(e21, e21) = h2(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax15])). 5.30/5.52 tff('1555', plain, (e22 = op2(e21, e21)) <= ((e22 = op2(e21, e21))), 5.30/5.52 inference('split', [status(esa)], ['1530'])). 5.30/5.52 tff('1556', plain, (e22 = h2(e11)) <= ((e22 = op2(e21, e21))), 5.30/5.52 inference('sup+', [status(thm)], ['1554', '1555'])). 5.30/5.52 tff('1557', plain, op2(e21, e21) != op2(e23, e21), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1558', plain, op2(e21, e21) = h2(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax15])). 5.30/5.52 tff('1559', plain, h4(e12) = op2(e23, e21), 5.30/5.52 inference('demod', [status(thm)], ['126', '127'])). 5.30/5.52 tff('1560', plain, h2(e11) != h4(e12), 5.30/5.52 inference('demod', [status(thm)], ['1557', '1558', '1559'])). 5.30/5.52 tff('1561', plain, (e22 != h4(e12)) <= ((e22 = op2(e21, e21))), 5.30/5.52 inference('sup-', [status(thm)], ['1556', '1560'])). 5.30/5.52 tff('1562', plain, 5.30/5.52 (e22 != e22) <= ((op2(e23, e21) = e22) & (e22 = op2(e21, e21))), 5.30/5.52 inference('sup-', [status(thm)], ['1553', '1561'])). 5.30/5.52 tff('1563', plain, ~ (e22 = op2(e21, e21)) | ~ (op2(e23, e21) = e22), 5.30/5.52 inference('simplify', [status(thm)], ['1562'])). 5.30/5.52 tff(ax14, axiom, 5.30/5.52 ((op2(e20,e20) = h1(e11)) & (h1(e12) = op2(e20,op2(e20,e20))) & 5.30/5.52 (op2(op2(e20,op2(e20,e20)),e20) = h1(e10)) & (e20 = h1(e13)))). 5.30/5.52 tff('1564', plain, op2(e20, e20) = h1(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax14])). 5.30/5.52 tff('1565', plain, (op2(e20, e21) = e20) <= ((op2(e20, e21) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1566', plain, 5.30/5.52 (op2(e20, op2(e20, e21)) = e20) <= ((op2(e20, op2(e20, e21)) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1543'])). 5.30/5.52 tff('1567', plain, 5.30/5.52 (op2(e20, e20) = e20) 5.30/5.52 <= ((op2(e20, e21) = e20) & (op2(e20, op2(e20, e21)) = e20)), 5.30/5.52 inference('sup+', [status(thm)], ['1565', '1566'])). 5.30/5.52 tff('1568', plain, 5.30/5.52 (h1(e11) = e20) 5.30/5.52 <= ((op2(e20, e21) = e20) & (op2(e20, op2(e20, e21)) = e20)), 5.30/5.52 inference('sup+', [status(thm)], ['1564', '1567'])). 5.30/5.52 tff('1569', plain, (op2(e20, e21) = e20) <= ((op2(e20, e21) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1570', plain, op2(e20, e20) != op2(e20, e21), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1571', plain, op2(e20, e20) = h1(e11), 5.30/5.52 inference('cnf', [status(esa)], [ax14])). 5.30/5.52 tff('1572', plain, h1(e11) != op2(e20, e21), 5.30/5.52 inference('demod', [status(thm)], ['1570', '1571'])). 5.30/5.52 tff('1573', plain, (h1(e11) != e20) <= ((op2(e20, e21) = e20)), 5.30/5.52 inference('sup-', [status(thm)], ['1569', '1572'])). 5.30/5.52 tff('1574', plain, 5.30/5.52 ~ (op2(e20, op2(e20, e21)) = e20) | ~ (op2(e20, e21) = e20), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1568', '1573'])). 5.30/5.52 tff('1575', plain, (op2(e20, e21) = e20) <= ((op2(e20, e21) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1576', plain, (e23 = op2(e20, e21)) <= ((e23 = op2(e20, e21))), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1577', plain, 5.30/5.52 (e23 = e20) <= ((op2(e20, e21) = e20) & (e23 = op2(e20, e21))), 5.30/5.52 inference('sup+', [status(thm)], ['1575', '1576'])). 5.30/5.52 tff('1578', plain, e23 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1579', plain, ~ (e23 = op2(e20, e21)) | ~ (op2(e20, e21) = e20), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1577', '1578'])). 5.30/5.52 tff('1580', plain, 5.30/5.52 (op2(e20, e20) = e21 5.30/5.52 | e21 = op2(e20, e23) 5.30/5.52 | op2(e20, e22) = e21 5.30/5.52 | e21 = op2(e20, e21)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1581', plain, 5.30/5.52 (op2(e20, e20) = e21) | (e21 = op2(e20, e22)) | (e21 = op2(e20, e21)) | 5.30/5.52 (op2(e20, e23) = e21), inference('split', [status(esa)], ['1580'])). 5.30/5.52 tff('1582', plain, 5.30/5.52 (op2(e20, e23) = e21 5.30/5.52 | e23 = op2(e20, e23) 5.30/5.52 | op2(e20, e23) = e22 5.30/5.52 | e20 = op2(e20, e23)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1583', plain, (op2(e20, e23) = e21) <= ((op2(e20, e23) = e21)), 5.30/5.52 inference('split', [status(esa)], ['1582'])). 5.30/5.52 tff('1584', plain, op2(e23, e23) != op2(e20, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1585', plain, e21 = op2(e23, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax13])). 5.30/5.52 tff('1586', plain, e21 != op2(e20, e23), 5.30/5.52 inference('demod', [status(thm)], ['1584', '1585'])). 5.30/5.52 tff('1587', plain, (e21 != e21) <= ((op2(e20, e23) = e21)), 5.30/5.52 inference('sup-', [status(thm)], ['1583', '1586'])). 5.30/5.52 tff('1588', plain, ~ (op2(e20, e23) = e21), 5.30/5.52 inference('simplify', [status(thm)], ['1587'])). 5.30/5.52 tff('1589', plain, 5.30/5.52 (e20 = op2(e20, e21) 5.30/5.52 | op2(e20, e22) = e20 5.30/5.52 | e20 = op2(e20, e23) 5.30/5.52 | op2(e20, e20) = e20), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1590', plain, 5.30/5.52 (op2(e20, e21) = e20) | (op2(e20, e20) = e20) | (e20 = op2(e20, e23)) | 5.30/5.52 (op2(e20, e22) = e20), inference('split', [status(esa)], ['1589'])). 5.30/5.52 tff('1591', plain, 5.30/5.52 (e20 = op2(e22, e23)) | (e22 = op2(e22, e23)) | (op2(e22, e23) = e21) | 5.30/5.52 (op2(e22, e23) = e23), inference('split', [status(esa)], ['154'])). 5.30/5.52 tff('1592', plain, (e20 = op2(e22, e23)) <= ((e20 = op2(e22, e23))), 5.30/5.52 inference('split', [status(esa)], ['154'])). 5.30/5.52 tff('1593', plain, 5.30/5.52 (e20 = op2(e20, e23) 5.30/5.52 | e20 = op2(e23, e23) 5.30/5.52 | op2(e22, e23) = e20 5.30/5.52 | e20 = op2(e21, e23)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1594', plain, (e20 = op2(e20, e23)) <= ((e20 = op2(e20, e23))), 5.30/5.52 inference('split', [status(esa)], ['1593'])). 5.30/5.52 tff('1595', plain, op2(e20, e23) != op2(e22, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1596', plain, (e20 != op2(e22, e23)) <= ((e20 = op2(e20, e23))), 5.30/5.52 inference('sup-', [status(thm)], ['1594', '1595'])). 5.30/5.52 tff('1597', plain, 5.30/5.52 (e20 != e20) <= ((e20 = op2(e22, e23)) & (e20 = op2(e20, e23))), 5.30/5.52 inference('sup-', [status(thm)], ['1592', '1596'])). 5.30/5.52 tff('1598', plain, ~ (e20 = op2(e20, e23)) | ~ (e20 = op2(e22, e23)), 5.30/5.52 inference('simplify', [status(thm)], ['1597'])). 5.30/5.52 tff('1599', plain, 5.30/5.52 (e22 = op2(e21, e22) 5.30/5.52 | op2(e23, e22) = e22 5.30/5.52 | e22 = op2(e22, e22) 5.30/5.52 | op2(e20, e22) = e22), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1600', plain, h3(e11) = op2(e22, e22), 5.30/5.52 inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1601', plain, 5.30/5.52 (e22 = op2(e21, e22) 5.30/5.52 | op2(e23, e22) = e22 5.30/5.52 | e22 = h3(e11) 5.30/5.52 | op2(e20, e22) = e22), 5.30/5.52 inference('demod', [status(thm)], ['1599', '1600'])). 5.30/5.52 tff('1602', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.52 inference('split', [status(esa)], ['1601'])). 5.30/5.52 tff('1603', plain, (op2(e20, e22) = e21) <= ((e21 = op2(e20, e22))), 5.30/5.52 inference('split', [status(esa)], ['167'])). 5.30/5.52 tff('1604', plain, 5.30/5.52 (e22 = e21) <= ((op2(e20, e22) = e22) & (e21 = op2(e20, e22))), 5.30/5.52 inference('sup+', [status(thm)], ['1602', '1603'])). 5.30/5.52 tff('1605', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1606', plain, ~ (e21 = op2(e20, e22)) | ~ (op2(e20, e22) = e22), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1604', '1605'])). 5.30/5.52 tff('1607', plain, 5.30/5.52 (op2(e20, e22) = e20 5.30/5.52 | op2(e20, e22) = e23 5.30/5.52 | op2(e20, e22) = e22 5.30/5.52 | e21 = op2(e20, e22)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1608', plain, (op2(e20, e22) = e20) <= ((op2(e20, e22) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1607'])). 5.30/5.52 tff('1609', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.52 inference('split', [status(esa)], ['1601'])). 5.30/5.52 tff('1610', plain, 5.30/5.52 (e20 = e22) <= ((op2(e20, e22) = e20) & (op2(e20, e22) = e22)), 5.30/5.52 inference('sup+', [status(thm)], ['1608', '1609'])). 5.30/5.52 tff('1611', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1612', plain, ~ (op2(e20, e22) = e20) | ~ (op2(e20, e22) = e22), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1610', '1611'])). 5.30/5.52 tff('1613', plain, 5.30/5.52 (op2(e20, e22) = e22) | (op2(e21, e22) = e22) | (op2(e23, e22) = e22) | 5.30/5.52 (h3(e11) = e22), inference('split', [status(esa)], ['1601'])). 5.30/5.52 tff('1614', plain, (op2(e21, e22) = e22) <= ((op2(e21, e22) = e22)), 5.30/5.52 inference('split', [status(esa)], ['188'])). 5.30/5.52 tff('1615', plain, (e21 = op2(e21, e22)) <= ((e21 = op2(e21, e22))), 5.30/5.52 inference('split', [status(esa)], ['188'])). 5.30/5.52 tff('1616', plain, 5.30/5.52 (e21 = e22) <= ((op2(e21, e22) = e22) & (e21 = op2(e21, e22))), 5.30/5.52 inference('sup+', [status(thm)], ['1614', '1615'])). 5.30/5.52 tff('1617', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1618', plain, ~ (op2(e21, e22) = e22) | ~ (e21 = op2(e21, e22)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1616', '1617'])). 5.30/5.52 tff('1619', plain, (e21 = op2(e22, e21)) <= ((e21 = op2(e22, e21))), 5.30/5.52 inference('split', [status(esa)], ['273'])). 5.30/5.52 tff('1620', plain, (e21 = op2(e20, e21)) <= ((e21 = op2(e20, e21))), 5.30/5.52 inference('split', [status(esa)], ['1498'])). 5.30/5.52 tff('1621', plain, op2(e20, e21) != op2(e22, e21), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1622', plain, (e21 != op2(e22, e21)) <= ((e21 = op2(e20, e21))), 5.30/5.52 inference('sup-', [status(thm)], ['1620', '1621'])). 5.30/5.52 tff('1623', plain, 5.30/5.52 (e21 != e21) <= ((e21 = op2(e20, e21)) & (e21 = op2(e22, e21))), 5.30/5.52 inference('sup-', [status(thm)], ['1619', '1622'])). 5.30/5.52 tff('1624', plain, ~ (e21 = op2(e20, e21)) | ~ (e21 = op2(e22, e21)), 5.30/5.52 inference('simplify', [status(thm)], ['1623'])). 5.30/5.52 tff('1625', plain, (e22 != op2(e22, e22) | ~ zip_tseitin_19), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_58])). 5.30/5.52 tff('1626', plain, h3(e11) = op2(e22, e22), 5.30/5.52 inference('cnf', [status(esa)], [ax16])). 5.30/5.52 tff('1627', plain, (e22 != h3(e11) | ~ zip_tseitin_19), 5.30/5.52 inference('demod', [status(thm)], ['1625', '1626'])). 5.30/5.52 tff('1628', plain, ~ ( zip_tseitin_19) | ~ (h3(e11) = e22), 5.30/5.52 inference('split', [status(esa)], ['1627'])). 5.30/5.52 tff('1629', plain, 5.30/5.52 (op2(e20, e20) = e23 5.30/5.52 | op2(e20, e20) = e22 5.30/5.52 | op2(e20, e20) = e21 5.30/5.52 | op2(e20, e20) = e20), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1630', plain, (op2(e20, e20) = e21) <= ((op2(e20, e20) = e21)), 5.30/5.52 inference('split', [status(esa)], ['1629'])). 5.30/5.52 tff('1631', plain, (op2(e20, e20) = e20) <= ((op2(e20, e20) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1629'])). 5.30/5.52 tff('1632', plain, 5.30/5.52 (e21 = e20) <= ((op2(e20, e20) = e21) & (op2(e20, e20) = e20)), 5.30/5.52 inference('sup+', [status(thm)], ['1630', '1631'])). 5.30/5.52 tff('1633', plain, e21 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1634', plain, ~ (op2(e20, e20) = e20) | ~ (op2(e20, e20) = e21), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1632', '1633'])). 5.30/5.52 tff('1635', plain, (op2(e21, e22) = e21 | ~ zip_tseitin_19), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_58])). 5.30/5.52 tff('1636', plain, ~ ( zip_tseitin_19) | (e21 = op2(e21, e22)), 5.30/5.52 inference('split', [status(esa)], ['1635'])). 5.30/5.52 tff('1637', plain, (op2(e22, e21) = e21 | ~ zip_tseitin_19), 5.30/5.52 inference('cnf', [status(esa)], [zf_stmt_58])). 5.30/5.52 tff('1638', plain, ~ ( zip_tseitin_19) | (e21 = op2(e22, e21)), 5.30/5.52 inference('split', [status(esa)], ['1637'])). 5.30/5.52 tff('1639', plain, (e22 = op2(e22, e20)) <= ((e22 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1640', plain, 5.30/5.52 (e20 = op2(e21, e20) 5.30/5.52 | op2(e21, e20) = e22 5.30/5.52 | e23 = op2(e21, e20) 5.30/5.52 | e21 = op2(e21, e20)), 5.30/5.52 inference('cnf', [status(esa)], [ax3])). 5.30/5.52 tff('1641', plain, (op2(e21, e20) = e22) <= ((op2(e21, e20) = e22)), 5.30/5.52 inference('split', [status(esa)], ['1640'])). 5.30/5.52 tff('1642', plain, op2(e22, e20) != op2(e21, e20), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1643', plain, (op2(e22, e20) != e22) <= ((op2(e21, e20) = e22)), 5.30/5.52 inference('sup-', [status(thm)], ['1641', '1642'])). 5.30/5.52 tff('1644', plain, 5.30/5.52 (e22 != e22) <= ((e22 = op2(e22, e20)) & (op2(e21, e20) = e22)), 5.30/5.52 inference('sup-', [status(thm)], ['1639', '1643'])). 5.30/5.52 tff('1645', plain, ~ (op2(e21, e20) = e22) | ~ (e22 = op2(e22, e20)), 5.30/5.52 inference('simplify', [status(thm)], ['1644'])). 5.30/5.52 tff('1646', plain, (op2(e22, e22) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.52 inference('split', [status(esa)], ['105'])). 5.30/5.52 tff('1647', plain, (e22 = op2(e22, e22)) <= ((e22 = op2(e22, e22))), 5.30/5.52 inference('split', [status(esa)], ['105'])). 5.30/5.52 tff('1648', plain, 5.30/5.52 (e22 = e21) <= ((op2(e22, e22) = e21) & (e22 = op2(e22, e22))), 5.30/5.52 inference('sup+', [status(thm)], ['1646', '1647'])). 5.30/5.52 tff('1649', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1650', plain, ~ (e22 = op2(e22, e22)) | ~ (op2(e22, e22) = e21), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1648', '1649'])). 5.30/5.52 tff('1651', plain, (op2(e22, e22) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.52 inference('split', [status(esa)], ['105'])). 5.30/5.52 tff('1652', plain, (op2(e22, e22) = e23) <= ((op2(e22, e22) = e23)), 5.30/5.52 inference('split', [status(esa)], ['105'])). 5.30/5.52 tff('1653', plain, 5.30/5.52 (e21 = e23) <= ((op2(e22, e22) = e21) & (op2(e22, e22) = e23)), 5.30/5.52 inference('sup+', [status(thm)], ['1651', '1652'])). 5.30/5.52 tff('1654', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1655', plain, ~ (op2(e22, e22) = e23) | ~ (op2(e22, e22) = e21), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1653', '1654'])). 5.30/5.52 tff('1656', plain, 5.30/5.52 (op2(e22, e23) = e21 5.30/5.52 | op2(e22, e22) = e21 5.30/5.52 | op2(e22, e21) = e21 5.30/5.52 | e21 = op2(e22, e20)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1657', plain, 5.30/5.52 (op2(e22, e22) = e21) | (e21 = op2(e22, e20)) | (e21 = op2(e22, e21)) | 5.30/5.52 (op2(e22, e23) = e21), inference('split', [status(esa)], ['1656'])). 5.30/5.52 tff('1658', plain, (op2(e22, e23) = e21) <= ((op2(e22, e23) = e21)), 5.30/5.52 inference('split', [status(esa)], ['154'])). 5.30/5.52 tff('1659', plain, op2(e22, e23) != op2(e23, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax6])). 5.30/5.52 tff('1660', plain, e21 = op2(e23, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax13])). 5.30/5.52 tff('1661', plain, op2(e22, e23) != e21, 5.30/5.52 inference('demod', [status(thm)], ['1659', '1660'])). 5.30/5.52 tff('1662', plain, (e21 != e21) <= ((op2(e22, e23) = e21)), 5.30/5.52 inference('sup-', [status(thm)], ['1658', '1661'])). 5.30/5.52 tff('1663', plain, ~ (op2(e22, e23) = e21), 5.30/5.52 inference('simplify', [status(thm)], ['1662'])). 5.30/5.52 tff('1664', plain, (e21 = op2(e22, e20)) <= ((e21 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1665', plain, (e22 = op2(e22, e20)) <= ((e22 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1666', plain, 5.30/5.52 (e22 = e21) <= ((e21 = op2(e22, e20)) & (e22 = op2(e22, e20))), 5.30/5.52 inference('sup+', [status(thm)], ['1664', '1665'])). 5.30/5.52 tff('1667', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1668', plain, ~ (e21 = op2(e22, e20)) | ~ (e22 = op2(e22, e20)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1666', '1667'])). 5.30/5.52 tff('1669', plain, (e21 = op2(e22, e20)) <= ((e21 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1670', plain, (e23 = op2(e22, e20)) <= ((e23 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1671', plain, 5.30/5.52 (e23 = e21) <= ((e21 = op2(e22, e20)) & (e23 = op2(e22, e20))), 5.30/5.52 inference('sup+', [status(thm)], ['1669', '1670'])). 5.30/5.52 tff('1672', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1673', plain, ~ (e21 = op2(e22, e20)) | ~ (e23 = op2(e22, e20)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1671', '1672'])). 5.30/5.52 tff('1674', plain, (e21 = op2(e22, e21)) <= ((e21 = op2(e22, e21))), 5.30/5.52 inference('split', [status(esa)], ['273'])). 5.30/5.52 tff('1675', plain, (e20 = op2(e22, e21)) <= ((e20 = op2(e22, e21))), 5.30/5.52 inference('split', [status(esa)], ['273'])). 5.30/5.52 tff('1676', plain, 5.30/5.52 (e20 = e21) <= ((e21 = op2(e22, e21)) & (e20 = op2(e22, e21))), 5.30/5.52 inference('sup+', [status(thm)], ['1674', '1675'])). 5.30/5.52 tff('1677', plain, e21 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1678', plain, ~ (e20 = op2(e22, e21)) | ~ (e21 = op2(e22, e21)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1676', '1677'])). 5.30/5.52 tff('1679', plain, (op2(e22, e21) = e23) <= ((op2(e22, e21) = e23)), 5.30/5.52 inference('split', [status(esa)], ['273'])). 5.30/5.52 tff('1680', plain, (e20 = op2(e22, e21)) <= ((e20 = op2(e22, e21))), 5.30/5.52 inference('split', [status(esa)], ['273'])). 5.30/5.52 tff('1681', plain, 5.30/5.52 (e20 = e23) <= ((op2(e22, e21) = e23) & (e20 = op2(e22, e21))), 5.30/5.52 inference('sup+', [status(thm)], ['1679', '1680'])). 5.30/5.52 tff('1682', plain, e23 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1683', plain, ~ (e20 = op2(e22, e21)) | ~ (op2(e22, e21) = e23), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1681', '1682'])). 5.30/5.52 tff('1684', plain, (e23 = op2(e22, e20)) <= ((e23 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1685', plain, (e22 = op2(e22, e20)) <= ((e22 = op2(e22, e20))), 5.30/5.52 inference('split', [status(esa)], ['1456'])). 5.30/5.52 tff('1686', plain, 5.30/5.52 (e22 = e23) <= ((e23 = op2(e22, e20)) & (e22 = op2(e22, e20))), 5.30/5.52 inference('sup+', [status(thm)], ['1684', '1685'])). 5.30/5.52 tff('1687', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1688', plain, ~ (e23 = op2(e22, e20)) | ~ (e22 = op2(e22, e20)), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1686', '1687'])). 5.30/5.52 tff('1689', plain, 5.30/5.52 (e22 = op2(e22, e21) 5.30/5.52 | e22 = op2(e22, e23) 5.30/5.52 | op2(e22, e22) = e22 5.30/5.52 | op2(e22, e20) = e22), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1690', plain, 5.30/5.52 (e22 = op2(e22, e20)) | (e22 = op2(e22, e22)) | (op2(e22, e21) = e22) | 5.30/5.52 (e22 = op2(e22, e23)), inference('split', [status(esa)], ['1689'])). 5.30/5.52 tff('1691', plain, (op2(e23, e21) = e20) <= ((op2(e23, e21) = e20)), 5.30/5.52 inference('split', [status(esa)], ['1551'])). 5.30/5.52 tff('1692', plain, e22 = op2(e23, e21), 5.30/5.52 inference('demod', [status(thm)], ['92', '93'])). 5.30/5.52 tff('1693', plain, (e22 = e20) <= ((op2(e23, e21) = e20)), 5.30/5.52 inference('sup+', [status(thm)], ['1691', '1692'])). 5.30/5.52 tff('1694', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1695', plain, ~ (op2(e23, e21) = e20), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1693', '1694'])). 5.30/5.52 tff('1696', plain, (op2(e23, e20) = e23) <= ((op2(e23, e20) = e23)), 5.30/5.52 inference('split', [status(esa)], ['144'])). 5.30/5.52 tff('1697', plain, (op2(e23, e20) = e22) <= ((op2(e23, e20) = e22)), 5.30/5.52 inference('split', [status(esa)], ['144'])). 5.30/5.52 tff('1698', plain, 5.30/5.52 (e23 = e22) <= ((op2(e23, e20) = e23) & (op2(e23, e20) = e22)), 5.30/5.52 inference('sup+', [status(thm)], ['1696', '1697'])). 5.30/5.52 tff('1699', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1700', plain, ~ (op2(e23, e20) = e22) | ~ (op2(e23, e20) = e23), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1698', '1699'])). 5.30/5.52 tff('1701', plain, (op2(e23, e20) = e20) <= ((op2(e23, e20) = e20)), 5.30/5.52 inference('split', [status(esa)], ['144'])). 5.30/5.52 tff('1702', plain, (op2(e23, e20) = e22) <= ((op2(e23, e20) = e22)), 5.30/5.52 inference('split', [status(esa)], ['144'])). 5.30/5.52 tff('1703', plain, 5.30/5.52 (e20 = e22) <= ((op2(e23, e20) = e20) & (op2(e23, e20) = e22)), 5.30/5.52 inference('sup+', [status(thm)], ['1701', '1702'])). 5.30/5.52 tff('1704', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1705', plain, ~ (op2(e23, e20) = e22) | ~ (op2(e23, e20) = e20), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1703', '1704'])). 5.30/5.52 tff('1706', plain, 5.30/5.52 (op2(e23, e20) = e22 5.30/5.52 | op2(e23, e21) = e22 5.30/5.52 | e22 = op2(e23, e22) 5.30/5.52 | e22 = op2(e23, e23)), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1707', plain, 5.30/5.52 (op2(e23, e21) = e22) | (op2(e23, e22) = e22) | (op2(e23, e20) = e22) | 5.30/5.52 (op2(e23, e23) = e22), inference('split', [status(esa)], ['1706'])). 5.30/5.52 tff('1708', plain, e21 = op2(e23, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax13])). 5.30/5.52 tff('1709', plain, (op2(e23, e23) = e22) <= ((op2(e23, e23) = e22)), 5.30/5.52 inference('split', [status(esa)], ['1512'])). 5.30/5.52 tff('1710', plain, (e21 = e22) <= ((op2(e23, e23) = e22)), 5.30/5.52 inference('sup+', [status(thm)], ['1708', '1709'])). 5.30/5.52 tff('1711', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.52 tff('1712', plain, ~ (op2(e23, e23) = e22), 5.30/5.52 inference('simplify_reflect-', [status(thm)], ['1710', '1711'])). 5.30/5.52 tff('1713', plain, 5.30/5.52 (e23 = op2(e23, e20) 5.30/5.52 | op2(e23, e22) = e23 5.30/5.52 | op2(e23, e23) = e23 5.30/5.52 | op2(e23, e21) = e23), 5.30/5.52 inference('cnf', [status(esa)], [ax4])). 5.30/5.52 tff('1714', plain, 5.30/5.52 (op2(e23, e20) = e23) | (e23 = op2(e23, e22)) | (e23 = op2(e23, e23)) | 5.30/5.52 (e23 = op2(e23, e21)), inference('split', [status(esa)], ['1713'])). 5.30/5.52 tff('1715', plain, e21 = op2(e23, e23), 5.30/5.52 inference('cnf', [status(esa)], [ax13])). 5.30/5.52 tff('1716', plain, (e23 = op2(e23, e23)) <= ((e23 = op2(e23, e23))), 5.30/5.53 inference('split', [status(esa)], ['1512'])). 5.30/5.53 tff('1717', plain, (e23 = e21) <= ((e23 = op2(e23, e23))), 5.30/5.53 inference('sup+', [status(thm)], ['1715', '1716'])). 5.30/5.53 tff('1718', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1719', plain, ~ (e23 = op2(e23, e23)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1717', '1718'])). 5.30/5.53 tff('1720', plain, 5.30/5.53 (e20 = op2(e23, e21) 5.30/5.53 | op2(e23, e23) = e20 5.30/5.53 | e20 = op2(e23, e22) 5.30/5.53 | op2(e23, e20) = e20), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('1721', plain, 5.30/5.53 (e20 = op2(e23, e22)) | (op2(e23, e20) = e20) | (op2(e23, e23) = e20) | 5.30/5.53 (op2(e23, e21) = e20), inference('split', [status(esa)], ['1720'])). 5.30/5.53 tff('1722', plain, e21 = op2(e23, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax13])). 5.30/5.53 tff('1723', plain, (op2(e23, e23) = e20) <= ((op2(e23, e23) = e20)), 5.30/5.53 inference('split', [status(esa)], ['1512'])). 5.30/5.53 tff('1724', plain, (e21 = e20) <= ((op2(e23, e23) = e20)), 5.30/5.53 inference('sup+', [status(thm)], ['1722', '1723'])). 5.30/5.53 tff('1725', plain, e21 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1726', plain, ~ (op2(e23, e23) = e20), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1724', '1725'])). 5.30/5.53 tff('1727', plain, (op2(e23, e22) = e22) <= ((op2(e23, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1728', plain, (e23 = op2(e23, e22)) <= ((e23 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1729', plain, 5.30/5.53 (e23 = e22) <= ((op2(e23, e22) = e22) & (e23 = op2(e23, e22))), 5.30/5.53 inference('sup+', [status(thm)], ['1727', '1728'])). 5.30/5.53 tff('1730', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1731', plain, ~ (op2(e23, e22) = e22) | ~ (e23 = op2(e23, e22)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1729', '1730'])). 5.30/5.53 tff('1732', plain, (op2(e23, e22) = e22) <= ((op2(e23, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1733', plain, (e20 = op2(e23, e22)) <= ((e20 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1734', plain, 5.30/5.53 (e20 = e22) <= ((op2(e23, e22) = e22) & (e20 = op2(e23, e22))), 5.30/5.53 inference('sup+', [status(thm)], ['1732', '1733'])). 5.30/5.53 tff('1735', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1736', plain, ~ (op2(e23, e22) = e22) | ~ (e20 = op2(e23, e22)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1734', '1735'])). 5.30/5.53 tff('1737', plain, (op2(e23, e20) = e20) <= ((op2(e23, e20) = e20)), 5.30/5.53 inference('split', [status(esa)], ['144'])). 5.30/5.53 tff('1738', plain, (op2(e23, e20) = e23) <= ((op2(e23, e20) = e23)), 5.30/5.53 inference('split', [status(esa)], ['144'])). 5.30/5.53 tff('1739', plain, 5.30/5.53 (e20 = e23) <= ((op2(e23, e20) = e20) & (op2(e23, e20) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1737', '1738'])). 5.30/5.53 tff('1740', plain, e23 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1741', plain, ~ (op2(e23, e20) = e20) | ~ (op2(e23, e20) = e23), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1739', '1740'])). 5.30/5.53 tff('1742', plain, (e21 = op2(e23, e21)) <= ((e21 = op2(e23, e21))), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1743', plain, (e23 = op2(e23, e21)) <= ((e23 = op2(e23, e21))), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1744', plain, 5.30/5.53 (e23 = e21) <= ((e21 = op2(e23, e21)) & (e23 = op2(e23, e21))), 5.30/5.53 inference('sup+', [status(thm)], ['1742', '1743'])). 5.30/5.53 tff('1745', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1746', plain, ~ (e21 = op2(e23, e21)) | ~ (e23 = op2(e23, e21)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1744', '1745'])). 5.30/5.53 tff('1747', plain, (op2(e23, e21) = e22) <= ((op2(e23, e21) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1748', plain, (e21 = op2(e23, e21)) <= ((e21 = op2(e23, e21))), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1749', plain, 5.30/5.53 (e21 = e22) <= ((op2(e23, e21) = e22) & (e21 = op2(e23, e21))), 5.30/5.53 inference('sup+', [status(thm)], ['1747', '1748'])). 5.30/5.53 tff('1750', plain, e21 != e22, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1751', plain, ~ (e21 = op2(e23, e21)) | ~ (op2(e23, e21) = e22), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1749', '1750'])). 5.30/5.53 tff('1752', plain, (op2(e23, e21) = e20) <= ((op2(e23, e21) = e20)), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1753', plain, (e21 = op2(e23, e21)) <= ((e21 = op2(e23, e21))), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1754', plain, 5.30/5.53 (e21 = e20) <= ((op2(e23, e21) = e20) & (e21 = op2(e23, e21))), 5.30/5.53 inference('sup+', [status(thm)], ['1752', '1753'])). 5.30/5.53 tff('1755', plain, e21 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1756', plain, ~ (e21 = op2(e23, e21)) | ~ (op2(e23, e21) = e20), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1754', '1755'])). 5.30/5.53 tff('1757', plain, (e20 = op2(e23, e22)) <= ((e20 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1758', plain, (e23 = op2(e23, e22)) <= ((e23 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1759', plain, 5.30/5.53 (e23 = e20) <= ((e20 = op2(e23, e22)) & (e23 = op2(e23, e22))), 5.30/5.53 inference('sup+', [status(thm)], ['1757', '1758'])). 5.30/5.53 tff('1760', plain, e23 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1761', plain, ~ (e23 = op2(e23, e22)) | ~ (e20 = op2(e23, e22)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1759', '1760'])). 5.30/5.53 tff('1762', plain, 5.30/5.53 (op2(e23, e21) = e22) | (e23 = op2(e23, e21)) | (e21 = op2(e23, e21)) | 5.30/5.53 (op2(e23, e21) = e20), inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1763', plain, (h4(e12) = e22) <= ((op2(e23, e21) = e22)), 5.30/5.53 inference('sup+', [status(thm)], ['1550', '1552'])). 5.30/5.53 tff('1764', plain, (op2(e22, e21) = e22) <= ((op2(e22, e21) = e22)), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1765', plain, op2(e22, e21) != op2(e23, e21), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('1766', plain, h4(e12) = op2(e23, e21), 5.30/5.53 inference('demod', [status(thm)], ['126', '127'])). 5.30/5.53 tff('1767', plain, op2(e22, e21) != h4(e12), 5.30/5.53 inference('demod', [status(thm)], ['1765', '1766'])). 5.30/5.53 tff('1768', plain, (e22 != h4(e12)) <= ((op2(e22, e21) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['1764', '1767'])). 5.30/5.53 tff('1769', plain, 5.30/5.53 (e22 != e22) <= ((op2(e22, e21) = e22) & (op2(e23, e21) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['1763', '1768'])). 5.30/5.53 tff('1770', plain, ~ (op2(e22, e21) = e22) | ~ (op2(e23, e21) = e22), 5.30/5.53 inference('simplify', [status(thm)], ['1769'])). 5.30/5.53 tff('1771', plain, (e22 = op2(e22, e23)) <= ((e22 = op2(e22, e23))), 5.30/5.53 inference('split', [status(esa)], ['154'])). 5.30/5.53 tff('1772', plain, op2(e22, e23) = e20, 5.30/5.53 inference('demod', [status(thm)], ['110', '111', '112'])). 5.30/5.53 tff('1773', plain, (e22 = e20) <= ((e22 = op2(e22, e23))), 5.30/5.53 inference('sup+', [status(thm)], ['1771', '1772'])). 5.30/5.53 tff('1774', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1775', plain, ~ (e22 = op2(e22, e23)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1773', '1774'])). 5.30/5.53 tff('1776', plain, (op2(e22, e22) = e23) <= ((op2(e22, e22) = e23)), 5.30/5.53 inference('split', [status(esa)], ['105'])). 5.30/5.53 tff('1777', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1778', plain, (h3(e11) = e23) <= ((op2(e22, e22) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1776', '1777'])). 5.30/5.53 tff('1779', plain, (e23 = op2(e22, e20)) <= ((e23 = op2(e22, e20))), 5.30/5.53 inference('split', [status(esa)], ['1456'])). 5.30/5.53 tff('1780', plain, h3(e11) != op2(e22, e20), 5.30/5.53 inference('demod', [status(thm)], ['115', '116'])). 5.30/5.53 tff('1781', plain, (h3(e11) != e23) <= ((e23 = op2(e22, e20))), 5.30/5.53 inference('sup-', [status(thm)], ['1779', '1780'])). 5.30/5.53 tff('1782', plain, 5.30/5.53 (e23 != e23) <= ((e23 = op2(e22, e20)) & (op2(e22, e22) = e23)), 5.30/5.53 inference('sup-', [status(thm)], ['1778', '1781'])). 5.30/5.53 tff('1783', plain, ~ (op2(e22, e22) = e23) | ~ (e23 = op2(e22, e20)), 5.30/5.53 inference('simplify', [status(thm)], ['1782'])). 5.30/5.53 tff('1784', plain, (h3(e11) = e23) <= ((op2(e22, e22) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1776', '1777'])). 5.30/5.53 tff('1785', plain, (op2(e22, e21) = e23) <= ((op2(e22, e21) = e23)), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1786', plain, op2(e22, e21) != op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('1787', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1788', plain, op2(e22, e21) != h3(e11), 5.30/5.53 inference('demod', [status(thm)], ['1786', '1787'])). 5.30/5.53 tff('1789', plain, (e23 != h3(e11)) <= ((op2(e22, e21) = e23)), 5.30/5.53 inference('sup-', [status(thm)], ['1785', '1788'])). 5.30/5.53 tff('1790', plain, 5.30/5.53 (e23 != e23) <= ((op2(e22, e21) = e23) & (op2(e22, e22) = e23)), 5.30/5.53 inference('sup-', [status(thm)], ['1784', '1789'])). 5.30/5.53 tff('1791', plain, ~ (op2(e22, e22) = e23) | ~ (op2(e22, e21) = e23), 5.30/5.53 inference('simplify', [status(thm)], ['1790'])). 5.30/5.53 tff('1792', plain, (op2(e22, e22) = e23) <= ((op2(e22, e22) = e23)), 5.30/5.53 inference('split', [status(esa)], ['105'])). 5.30/5.53 tff('1793', plain, (e22 = op2(e22, e22)) <= ((e22 = op2(e22, e22))), 5.30/5.53 inference('split', [status(esa)], ['105'])). 5.30/5.53 tff('1794', plain, 5.30/5.53 (e22 = e23) <= ((op2(e22, e22) = e23) & (e22 = op2(e22, e22))), 5.30/5.53 inference('sup+', [status(thm)], ['1792', '1793'])). 5.30/5.53 tff('1795', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1796', plain, ~ (op2(e22, e22) = e23) | ~ (e22 = op2(e22, e22)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1794', '1795'])). 5.30/5.53 tff('1797', plain, (e21 = h2(e12)) <= ((e21 = h2(e12))), 5.30/5.53 inference('split', [status(esa)], ['1543'])). 5.30/5.53 tff('1798', plain, (op2(e21, e23) = h2(e12)) <= ((op2(e21, e21) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1532', '1535'])). 5.30/5.53 tff('1799', plain, op2(e23, e23) != op2(e21, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('1800', plain, e21 = op2(e23, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax13])). 5.30/5.53 tff('1801', plain, e21 != op2(e21, e23), 5.30/5.53 inference('demod', [status(thm)], ['1799', '1800'])). 5.30/5.53 tff('1802', plain, (e21 != h2(e12)) <= ((op2(e21, e21) = e23)), 5.30/5.53 inference('sup-', [status(thm)], ['1798', '1801'])). 5.30/5.53 tff('1803', plain, (e21 != e21) <= ((op2(e21, e21) = e23) & (e21 = h2(e12))), 5.30/5.53 inference('sup-', [status(thm)], ['1797', '1802'])). 5.30/5.53 tff('1804', plain, ~ (op2(e21, e21) = e23) | ~ (e21 = h2(e12)), 5.30/5.53 inference('simplify', [status(thm)], ['1803'])). 5.30/5.53 tff('1805', plain, (h3(e11) = e23) <= ((op2(e22, e22) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1776', '1777'])). 5.30/5.53 tff('1806', plain, (e23 = op2(e23, h4(e12))) <= ((e23 = op2(e23, h4(e12)))), 5.30/5.53 inference('split', [status(esa)], ['1543'])). 5.30/5.53 tff('1807', plain, e22 = op2(e23, e21), 5.30/5.53 inference('demod', [status(thm)], ['92', '93'])). 5.30/5.53 tff('1808', plain, h4(e12) = op2(e23, e21), 5.30/5.53 inference('demod', [status(thm)], ['126', '127'])). 5.30/5.53 tff('1809', plain, h4(e12) = e22, 5.30/5.53 inference('sup+', [status(thm)], ['1807', '1808'])). 5.30/5.53 tff('1810', plain, (e23 = op2(e23, e22)) <= ((e23 = op2(e23, h4(e12)))), 5.30/5.53 inference('demod', [status(thm)], ['1806', '1809'])). 5.30/5.53 tff('1811', plain, op2(e23, e22) != op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('1812', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1813', plain, op2(e23, e22) != h3(e11), 5.30/5.53 inference('demod', [status(thm)], ['1811', '1812'])). 5.30/5.53 tff('1814', plain, (e23 != h3(e11)) <= ((e23 = op2(e23, h4(e12)))), 5.30/5.53 inference('sup-', [status(thm)], ['1810', '1813'])). 5.30/5.53 tff('1815', plain, 5.30/5.53 (e23 != e23) <= ((op2(e22, e22) = e23) & (e23 = op2(e23, h4(e12)))), 5.30/5.53 inference('sup-', [status(thm)], ['1805', '1814'])). 5.30/5.53 tff('1816', plain, ~ (e23 = op2(e23, h4(e12))) | ~ (op2(e22, e22) = e23), 5.30/5.53 inference('simplify', [status(thm)], ['1815'])). 5.30/5.53 tff('1817', plain, 5.30/5.53 (op2(e21, e21) = e23 5.30/5.53 | e23 = op2(e23, e21) 5.30/5.53 | e23 = op2(e22, e21) 5.30/5.53 | op2(e20, e21) = e23), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('1818', plain, 5.30/5.53 (op2(e22, e21) = e23) | (op2(e21, e21) = e23) | (e23 = op2(e23, e21)) | 5.30/5.53 (e23 = op2(e20, e21)), inference('split', [status(esa)], ['1817'])). 5.30/5.53 tff('1819', plain, (e23 = op2(e23, e21)) <= ((e23 = op2(e23, e21))), 5.30/5.53 inference('split', [status(esa)], ['1551'])). 5.30/5.53 tff('1820', plain, e22 = op2(e23, e21), 5.30/5.53 inference('demod', [status(thm)], ['92', '93'])). 5.30/5.53 tff('1821', plain, (e22 = e23) <= ((e23 = op2(e23, e21))), 5.30/5.53 inference('sup+', [status(thm)], ['1819', '1820'])). 5.30/5.53 tff('1822', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1823', plain, ~ (e23 = op2(e23, e21)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1821', '1822'])). 5.30/5.53 tff('1824', plain, 5.30/5.53 (e23 = op2(e22, e20) 5.30/5.53 | op2(e22, e23) = e23 5.30/5.53 | e23 = op2(e22, e22) 5.30/5.53 | op2(e22, e21) = e23), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('1825', plain, 5.30/5.53 (op2(e22, e21) = e23) | (e23 = op2(e22, e20)) | (op2(e22, e23) = e23) | 5.30/5.53 (op2(e22, e22) = e23), inference('split', [status(esa)], ['1824'])). 5.30/5.53 tff('1826', plain, (op2(e22, e23) = e23) <= ((op2(e22, e23) = e23)), 5.30/5.53 inference('split', [status(esa)], ['154'])). 5.30/5.53 tff('1827', plain, op2(e22, e23) = e20, 5.30/5.53 inference('demod', [status(thm)], ['110', '111', '112'])). 5.30/5.53 tff('1828', plain, (e23 = e20) <= ((op2(e22, e23) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1826', '1827'])). 5.30/5.53 tff('1829', plain, e23 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1830', plain, ~ (op2(e22, e23) = e23), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1828', '1829'])). 5.30/5.53 tff('1831', plain, (e21 = op2(e22, e21)) <= ((e21 = op2(e22, e21))), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1832', plain, 5.30/5.53 (op2(e20, op2(e20, e21)) = e20 5.30/5.53 | e22 = op2(e22, op2(e22, e21)) 5.30/5.53 | e23 = op2(e23, op2(e23, e21)) 5.30/5.53 | e21 = op2(e21, op2(e21, e21))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.53 tff('1833', plain, 5.30/5.53 (e22 = op2(e22, op2(e22, e21))) <= ((e22 = op2(e22, op2(e22, e21)))), 5.30/5.53 inference('split', [status(esa)], ['1832'])). 5.30/5.53 tff('1834', plain, 5.30/5.53 (e22 = op2(e22, e21)) 5.30/5.53 <= ((e21 = op2(e22, e21)) & (e22 = op2(e22, op2(e22, e21)))), 5.30/5.53 inference('sup+', [status(thm)], ['1831', '1833'])). 5.30/5.53 tff('1835', plain, op2(e22, e21) != h4(e12), 5.30/5.53 inference('demod', [status(thm)], ['1765', '1766'])). 5.30/5.53 tff('1836', plain, h4(e12) = e22, 5.30/5.53 inference('sup+', [status(thm)], ['1807', '1808'])). 5.30/5.53 tff('1837', plain, op2(e22, e21) != e22, 5.30/5.53 inference('demod', [status(thm)], ['1835', '1836'])). 5.30/5.53 tff('1838', plain, 5.30/5.53 ~ (e22 = op2(e22, op2(e22, e21))) | ~ (e21 = op2(e22, e21)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1834', '1837'])). 5.30/5.53 tff('1839', plain, 5.30/5.53 (e21 = h2(e12)) | (op2(e20, op2(e20, e21)) = e20) | 5.30/5.53 (e23 = op2(e23, h4(e12))) | (e22 = op2(e22, op2(e22, e21))), 5.30/5.53 inference('split', [status(esa)], ['1543'])). 5.30/5.53 tff('1840', plain, (e23 = h3(e11)) <= ((e23 = h3(e11))), 5.30/5.53 inference('split', [status(esa)], ['103'])). 5.30/5.53 tff('1841', plain, (e23 != op2(e22, e22) | ~ zip_tseitin_17), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_62])). 5.30/5.53 tff('1842', plain, (e23 != op2(e22, e22)) <= (~ (op2(e22, e22) = e23)), 5.30/5.53 inference('split', [status(esa)], ['1841'])). 5.30/5.53 tff('1843', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1844', plain, (e23 != h3(e11)) <= (~ (op2(e22, e22) = e23)), 5.30/5.53 inference('demod', [status(thm)], ['1842', '1843'])). 5.30/5.53 tff('1845', plain, 5.30/5.53 (e23 != e23) <= (~ (op2(e22, e22) = e23) & (e23 = h3(e11))), 5.30/5.53 inference('sup-', [status(thm)], ['1840', '1844'])). 5.30/5.53 tff('1846', plain, ~ (e23 = h3(e11)) | (op2(e22, e22) = e23), 5.30/5.53 inference('simplify', [status(thm)], ['1845'])). 5.30/5.53 tff('1847', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('1848', plain, (e21 = op2(e22, e21)) <= ((e21 = op2(e22, e21))), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1849', plain, op2(e22, e21) != h3(e11), 5.30/5.53 inference('demod', [status(thm)], ['1786', '1787'])). 5.30/5.53 tff('1850', plain, (e21 != h3(e11)) <= ((e21 = op2(e22, e21))), 5.30/5.53 inference('sup-', [status(thm)], ['1848', '1849'])). 5.30/5.53 tff('1851', plain, (e21 != e21) <= ((e21 = op2(e22, e21)) & (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1847', '1850'])). 5.30/5.53 tff('1852', plain, ~ (e21 = op2(e22, e21)) | ~ (h3(e11) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['1851'])). 5.30/5.53 tff('1853', plain, (op2(e22, e21) = e23) <= ((op2(e22, e21) = e23)), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1854', plain, (e21 = op2(e22, e21)) <= ((e21 = op2(e22, e21))), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1855', plain, 5.30/5.53 (e21 = e23) <= ((op2(e22, e21) = e23) & (e21 = op2(e22, e21))), 5.30/5.53 inference('sup+', [status(thm)], ['1853', '1854'])). 5.30/5.53 tff('1856', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('1857', plain, ~ (e21 = op2(e22, e21)) | ~ (op2(e22, e21) = e23), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1855', '1856'])). 5.30/5.53 tff('1858', plain, 5.30/5.53 ( zip_tseitin_31 5.30/5.53 | zip_tseitin_30 5.30/5.53 | zip_tseitin_29 5.30/5.53 | zip_tseitin_28 5.30/5.53 | zip_tseitin_27 5.30/5.53 | zip_tseitin_26 5.30/5.53 | zip_tseitin_25 5.30/5.53 | zip_tseitin_24 5.30/5.53 | zip_tseitin_23 5.30/5.53 | zip_tseitin_22 5.30/5.53 | zip_tseitin_21 5.30/5.53 | zip_tseitin_20 5.30/5.53 | zip_tseitin_19 5.30/5.53 | zip_tseitin_18 5.30/5.53 | zip_tseitin_17 5.30/5.53 | zip_tseitin_16), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.53 tff('1859', plain, 5.30/5.53 ( zip_tseitin_26) | ( zip_tseitin_20) | ( zip_tseitin_16) | 5.30/5.53 ( zip_tseitin_22) | ( zip_tseitin_21) | ( zip_tseitin_23) | 5.30/5.53 ( zip_tseitin_28) | ( zip_tseitin_18) | ( zip_tseitin_24) | 5.30/5.53 ( zip_tseitin_27) | ( zip_tseitin_17) | ( zip_tseitin_29) | 5.30/5.53 ( zip_tseitin_30) | ( zip_tseitin_25) | ( zip_tseitin_19) | 5.30/5.53 ( zip_tseitin_31), inference('split', [status(esa)], ['1858'])). 5.30/5.53 tff('1860', plain, 5.30/5.53 (op2(e22, e21) = e23) | (e21 = op2(e22, e21)) | (e20 = op2(e22, e21)) | 5.30/5.53 (op2(e22, e21) = e22), inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('1861', plain, (op2(e22, e21) = e23), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['1453', '1455', '1462', '1463', '1467', '1471', '1473', 5.30/5.53 '1475', '1477', '1479', '1481', '1483', '1485', '1487', 5.30/5.53 '1489', '1491', '1493', '1495', '1497', '1503', '1505', 5.30/5.53 '1507', '1509', '1511', '1513', '1515', '1517', '1519', 5.30/5.53 '1521', '1523', '1528', '1547', '1549', '1563', '1574', 5.30/5.53 '1579', '1581', '1588', '1590', '1591', '1598', '1606', 5.30/5.53 '1612', '1613', '1618', '1624', '1628', '1634', '1636', 5.30/5.53 '1638', '1645', '1650', '1655', '1657', '1663', '1668', 5.30/5.53 '1673', '1678', '1683', '1688', '1690', '1695', '1700', 5.30/5.53 '1705', '1707', '1712', '1714', '1719', '1721', '1726', 5.30/5.53 '1731', '1736', '1741', '1746', '1751', '1756', '1761', 5.30/5.53 '1762', '1770', '1775', '1783', '1791', '1796', '1804', 5.30/5.53 '1816', '1818', '1823', '1825', '1830', '1838', '1839', 5.30/5.53 '1846', '1852', '1857', '1859', '1860'])). 5.30/5.53 tff('1862', plain, (h3(e12) = e23) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1451', '1861'])). 5.30/5.53 tff('1863', plain, op2(h3(e12), e22) = h3(e10), 5.30/5.53 inference('demod', [status(thm)], ['237', '238'])). 5.30/5.53 tff('1864', plain, (op2(e23, e22) = h3(e10)) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1862', '1863'])). 5.30/5.53 tff('1865', plain, (e20 = op2(e23, e22)) <= ((e20 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('1866', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1867', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('1868', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1869', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1870', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1871', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1872', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1873', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1874', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('1875', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1876', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('1877', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1878', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1879', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['1867', '1868', '1869', '1870', '1871', '1872', '1873', 5.30/5.53 '1874', '1875', '1876', '1877', '1878'])). 5.30/5.53 tff('1880', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['1879'])). 5.30/5.53 tff('1881', plain, 5.30/5.53 (h3(op1(e11, e10)) != op2(h3(e11), h3(e10))) 5.30/5.53 <= (~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10)))), 5.30/5.53 inference('split', [status(esa)], ['1880'])). 5.30/5.53 tff('1882', plain, 5.30/5.53 (h3(op1(e11, e10)) != op2(h3(e11), e20)) 5.30/5.53 <= (~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1866', '1881'])). 5.30/5.53 tff('1883', plain, (h3(e11) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['162', '163'])). 5.30/5.53 tff('1884', plain, 5.30/5.53 (h3(op1(e11, e10)) != op2(e21, e20)) 5.30/5.53 <= (~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['1882', '1883'])). 5.30/5.53 tff('1885', plain, 5.30/5.53 (h3(e10) != op2(e21, e20)) 5.30/5.53 <= (~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e10 = op1(e11, e10))), 5.30/5.53 inference('sup-', [status(thm)], ['1446', '1884'])). 5.30/5.53 tff('1886', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1887', plain, 5.30/5.53 (e20 != op2(e21, e20)) 5.30/5.53 <= (~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e10 = op1(e11, e10))), 5.30/5.53 inference('demod', [status(thm)], ['1885', '1886'])). 5.30/5.53 tff('1888', plain, 5.30/5.53 (e20 != e20) 5.30/5.53 <= (~ (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e20 = op2(e21, e20)) & 5.30/5.53 (e10 = op1(e11, e10))), 5.30/5.53 inference('sup-', [status(thm)], ['1445', '1887'])). 5.30/5.53 tff('1889', plain, 5.30/5.53 (h3(op1(e11, e10)) = op2(h3(e11), h3(e10))) | ~ (e10 = op1(e11, e10)) | 5.30/5.53 ~ (e20 = op2(e21, e20)) | ~ (op2(e22, e22) = e21) | 5.30/5.53 ~ (e20 = op2(e23, e22)), inference('simplify', [status(thm)], ['1888'])). 5.30/5.53 tff('1890', plain, op2(e20, e20) = h1(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax14])). 5.30/5.53 tff('1891', plain, (op2(e20, e20) = e21) <= ((op2(e20, e20) = e21)), 5.30/5.53 inference('split', [status(esa)], ['1629'])). 5.30/5.53 tff('1892', plain, (h1(e11) = e21) <= ((op2(e20, e20) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1890', '1891'])). 5.30/5.53 tff('1893', plain, (op1(e10, e10) = e11) <= ((op1(e10, e10) = e11)), 5.30/5.53 inference('split', [status(esa)], ['417'])). 5.30/5.53 tff('1894', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1895', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e12) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('1896', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1897', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1898', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1899', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1900', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1901', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1902', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('1903', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1904', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('1905', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1906', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1907', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e12) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['1895', '1896', '1897', '1898', '1899', '1900', '1901', 5.30/5.53 '1902', '1903', '1904', '1905', '1906'])). 5.30/5.53 tff('1908', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e12) != e23 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e12) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['1907'])). 5.30/5.53 tff('1909', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10))) 5.30/5.53 <= (~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10)))), 5.30/5.53 inference('split', [status(esa)], ['1908'])). 5.30/5.53 tff('1910', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), e20)) 5.30/5.53 <= (~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1894', '1909'])). 5.30/5.53 tff('1911', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1912', plain, op2(e20, e20) = h1(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax14])). 5.30/5.53 tff('1913', plain, 5.30/5.53 (h3(op1(e10, e10)) != h1(e11)) 5.30/5.53 <= (~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['1910', '1911', '1912'])). 5.30/5.53 tff('1914', plain, 5.30/5.53 (h3(e11) != h1(e11)) 5.30/5.53 <= (~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e10, e10) = e11)), 5.30/5.53 inference('sup-', [status(thm)], ['1893', '1913'])). 5.30/5.53 tff('1915', plain, (h3(e11) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['162', '163'])). 5.30/5.53 tff('1916', plain, 5.30/5.53 (e21 != h1(e11)) 5.30/5.53 <= (~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e10, e10) = e11)), 5.30/5.53 inference('demod', [status(thm)], ['1914', '1915'])). 5.30/5.53 tff('1917', plain, 5.30/5.53 (e21 != e21) 5.30/5.53 <= (~ (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) & 5.30/5.53 (op2(e20, e20) = e21) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e10, e10) = e11)), 5.30/5.53 inference('sup-', [status(thm)], ['1892', '1916'])). 5.30/5.53 tff('1918', plain, 5.30/5.53 (h3(op1(e10, e10)) = op2(h3(e10), h3(e10))) | ~ (op1(e10, e10) = e11) | 5.30/5.53 ~ (e20 = op2(e23, e22)) | ~ (op2(e20, e20) = e21) | 5.30/5.53 ~ (op2(e22, e22) = e21), inference('simplify', [status(thm)], ['1917'])). 5.30/5.53 tff('1919', plain, (op1(e10, e11) = e10) <= ((op1(e10, e11) = e10)), 5.30/5.53 inference('split', [status(esa)], ['8'])). 5.30/5.53 tff('1920', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1921', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e12) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('1922', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1923', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1924', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1925', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1926', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1927', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1928', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('1929', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1930', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('1931', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1932', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1933', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e12) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['1921', '1922', '1923', '1924', '1925', '1926', '1927', 5.30/5.53 '1928', '1929', '1930', '1931', '1932'])). 5.30/5.53 tff('1934', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e12) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['1933'])). 5.30/5.53 tff('1935', plain, 5.30/5.53 (op2(h3(e10), h3(e11)) != h3(op1(e10, e11))) 5.30/5.53 <= (~ (op2(h3(e10), h3(e11)) = h3(op1(e10, e11)))), 5.30/5.53 inference('split', [status(esa)], ['1934'])). 5.30/5.53 tff('1936', plain, 5.30/5.53 (op2(e20, h3(e11)) != h3(op1(e10, e11))) 5.30/5.53 <= (~ (op2(h3(e10), h3(e11)) = h3(op1(e10, e11))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1920', '1935'])). 5.30/5.53 tff('1937', plain, (h3(e11) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['162', '163'])). 5.30/5.53 tff('1938', plain, (op2(e20, e21) = e20) <= ((op2(e20, e21) = e20)), 5.30/5.53 inference('split', [status(esa)], ['1498'])). 5.30/5.53 tff('1939', plain, (op2(e20, e21) = e20), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['1453', '1455', '1462', '1463', '1467', '1471', '1521', 5.30/5.53 '1523', '1528', '1547', '1549', '1563', '1574', '1579', 5.30/5.53 '1581', '1588', '1590', '1606', '1612', '1613', '1618', 5.30/5.53 '1624', '1628', '1634', '1636', '1645', '1860', '1783', 5.30/5.53 '1791', '1804', '1816', '1818', '1838', '1839', '1846', 5.30/5.53 '1852', '1857', '1638', '1473', '1475', '1477', '1479', 5.30/5.53 '1481', '1483', '1485', '1487', '1489', '1491', '1493', 5.30/5.53 '1495', '1591', '1598', '1497', '1650', '1655', '1657', 5.30/5.53 '1663', '1690', '1825', '1668', '1673', '1796', '1695', 5.30/5.53 '1700', '1705', '1707', '1714', '1721', '1731', '1736', 5.30/5.53 '1741', '1746', '1751', '1756', '1761', '1823', '1762', 5.30/5.53 '1770', '1775', '1678', '1683', '1688', '1503', '1505', 5.30/5.53 '1507', '1830', '1511', '1726', '1712', '1719', '1513', 5.30/5.53 '1515', '1517', '1519', '1859', '1509'])). 5.30/5.53 tff('1940', plain, op2(e20, e21) = e20, 5.30/5.53 inference('simpl_trail', [status(thm)], ['1938', '1939'])). 5.30/5.53 tff('1941', plain, 5.30/5.53 (e20 != h3(op1(e10, e11))) 5.30/5.53 <= (~ (op2(h3(e10), h3(e11)) = h3(op1(e10, e11))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['1936', '1937', '1940'])). 5.30/5.53 tff('1942', plain, 5.30/5.53 (e20 != h3(e10)) 5.30/5.53 <= (~ (op2(h3(e10), h3(e11)) = h3(op1(e10, e11))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e10, e11) = e10)), 5.30/5.53 inference('sup-', [status(thm)], ['1919', '1941'])). 5.30/5.53 tff('1943', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1944', plain, 5.30/5.53 (e20 != e20) 5.30/5.53 <= (~ (op2(h3(e10), h3(e11)) = h3(op1(e10, e11))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e10, e11) = e10)), 5.30/5.53 inference('demod', [status(thm)], ['1942', '1943'])). 5.30/5.53 tff('1945', plain, 5.30/5.53 (op2(h3(e10), h3(e11)) = h3(op1(e10, e11))) | ~ (op1(e10, e11) = e10) | 5.30/5.53 ~ (e20 = op2(e23, e22)) | ~ (op2(e22, e22) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['1944'])). 5.30/5.53 tff('1946', plain, (e23 = op2(e20, e23)) <= ((e23 = op2(e20, e23))), 5.30/5.53 inference('split', [status(esa)], ['121'])). 5.30/5.53 tff('1947', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1948', plain, (h3(e12) = e23) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1451', '1861'])). 5.30/5.53 tff('1949', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('1950', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1951', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1952', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1953', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1954', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1955', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1956', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('1957', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1958', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('1959', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1960', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1961', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['1949', '1950', '1951', '1952', '1953', '1954', '1955', 5.30/5.53 '1956', '1957', '1958', '1959', '1960'])). 5.30/5.53 tff('1962', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['1961'])). 5.30/5.53 tff('1963', plain, 5.30/5.53 (op2(h3(e10), h3(e12)) != h3(op1(e10, e12))) 5.30/5.53 <= (~ (op2(h3(e10), h3(e12)) = h3(op1(e10, e12)))), 5.30/5.53 inference('split', [status(esa)], ['1962'])). 5.30/5.53 tff('1964', plain, 5.30/5.53 (op2(h3(e10), e23) != h3(op1(e10, e12))) 5.30/5.53 <= (~ (op2(h3(e10), h3(e12)) = h3(op1(e10, e12))) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1948', '1963'])). 5.30/5.53 tff('1965', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.53 inference('split', [status(esa)], ['71'])). 5.30/5.53 tff('1966', plain, (op1(e12, e10) = e12) <= ((op1(e12, e10) = e12)), 5.30/5.53 inference('split', [status(esa)], ['478'])). 5.30/5.53 tff('1967', plain, (e12 != op1(e12, e10)) <= ((e12 = op1(e10, e10))), 5.30/5.53 inference('sup-', [status(thm)], ['945', '946'])). 5.30/5.53 tff('1968', plain, 5.30/5.53 (e12 != e12) <= ((e12 = op1(e10, e10)) & (op1(e12, e10) = e12)), 5.30/5.53 inference('sup-', [status(thm)], ['1966', '1967'])). 5.30/5.53 tff('1969', plain, ~ (e12 = op1(e10, e10)) | ~ (op1(e12, e10) = e12), 5.30/5.53 inference('simplify', [status(thm)], ['1968'])). 5.30/5.53 tff('1970', plain, (op1(e10, e12) = e12), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['292', '301', '309', '315', '321', '332', '343', '349', 5.30/5.53 '359', '365', '367', '373', '380', '386', '394', '399', 5.30/5.53 '407', '413', '415', '416', '423', '425', '434', '441', 5.30/5.53 '448', '450', '456', '462', '467', '475', '477', '487', 5.30/5.53 '494', '504', '515', '517', '524', '533', '534', '540', 5.30/5.53 '547', '553', '555', '562', '568', '573', '574', '580', 5.30/5.53 '581', '589', '595', '597', '601', '606', '612', '618', 5.30/5.53 '627', '633', '634', '642', '644', '646', '932', '938', 5.30/5.53 '943', '949', '954', '959', '964', '969', '974', '976', 5.30/5.53 '980', '986', '992', '998', '1004', '1010', '1015', '1021', 5.30/5.53 '1027', '1033', '1039', '1045', '1047', '1050', '1056', 5.30/5.53 '1063', '1064', '1066', '1071', '1077', '1082', '1086', 5.30/5.53 '1091', '1092', '1097', '1099', '1102', '1104', '1107', 5.30/5.53 '1113', '1119', '1125', '1131', '1132', '1139', '1146', 5.30/5.53 '1147', '1154', '1160', '1168', '1175', '1180', '1182', 5.30/5.53 '1184', '1187', '1193', '1199', '1204', '1209', '1210', 5.30/5.53 '1212', '1220', '1226', '1231', '1237', '1242', '1248', 5.30/5.53 '1254', '1261', '1265', '1266', '1271', '1276', '1281', 5.30/5.53 '1286', '1288', '1290', '1297', '1298', '1304', '1306', 5.30/5.53 '1308', '1313', '1318', '1323', '1328', '1335', '1340', 5.30/5.53 '1345', '1349', '1397', '1407', '1415', '284', '289', '290', 5.30/5.53 '1401', '658', '1350', '668', '674', '679', '1352', '1353', 5.30/5.53 '1354', '693', '699', '706', '711', '715', '1355', '723', 5.30/5.53 '1356', '1357', '1358', '735', '741', '743', '745', '751', 5.30/5.53 '753', '1359', '762', '767', '769', '771', '777', '781', 5.30/5.53 '1360', '1361', '1362', '1363', '1364', '1365', '1366', 5.30/5.53 '807', '1367', '1368', '1369', '1370', '1371', '1372', 5.30/5.53 '1373', '832', '1374', '1375', '842', '1421', '849', '1376', 5.30/5.53 '1377', '1378', '1379', '1380', '1381', '1382', '1383', 5.30/5.53 '1384', '1385', '898', '1386', '910', '1387', '922', '1388', 5.30/5.53 '1389', '1390', '1391', '1420', '1347', '1969', '1351'])). 5.30/5.53 tff('1971', plain, op1(e10, e12) = e12, 5.30/5.53 inference('simpl_trail', [status(thm)], ['1965', '1970'])). 5.30/5.53 tff('1972', plain, (h3(e12) = e23) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1451', '1861'])). 5.30/5.53 tff('1973', plain, 5.30/5.53 (op2(h3(e10), e23) != e23) 5.30/5.53 <= (~ (op2(h3(e10), h3(e12)) = h3(op1(e10, e12))) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['1964', '1971', '1972'])). 5.30/5.53 tff('1974', plain, 5.30/5.53 (op2(e20, e23) != e23) 5.30/5.53 <= (~ (op2(h3(e10), h3(e12)) = h3(op1(e10, e12))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1947', '1973'])). 5.30/5.53 tff('1975', plain, 5.30/5.53 (e23 != e23) 5.30/5.53 <= (~ (op2(h3(e10), h3(e12)) = h3(op1(e10, e12))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e23 = op2(e20, e23))), 5.30/5.53 inference('sup-', [status(thm)], ['1946', '1974'])). 5.30/5.53 tff('1976', plain, 5.30/5.53 (op2(h3(e10), h3(e12)) = h3(op1(e10, e12))) | ~ (e20 = op2(e23, e22)) | 5.30/5.53 ~ (op2(e22, e22) = e21) | ~ (e23 = op2(e20, e23)), 5.30/5.53 inference('simplify', [status(thm)], ['1975'])). 5.30/5.53 tff('1977', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('1978', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('1979', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.53 inference('split', [status(esa)], ['326'])). 5.30/5.53 tff('1980', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('1981', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1982', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1983', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1984', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1985', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1986', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1987', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('1988', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1989', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('1990', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1991', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1992', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['1980', '1981', '1982', '1983', '1984', '1985', '1986', 5.30/5.53 '1987', '1988', '1989', '1990', '1991'])). 5.30/5.53 tff('1993', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e12) != e23 5.30/5.53 | h3(e10) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['1992'])). 5.30/5.53 tff('1994', plain, 5.30/5.53 (h3(op1(e10, e13)) != op2(h3(e10), e22)) 5.30/5.53 <= (~ (h3(op1(e10, e13)) = op2(h3(e10), e22))), 5.30/5.53 inference('split', [status(esa)], ['1993'])). 5.30/5.53 tff('1995', plain, 5.30/5.53 (h3(e13) != op2(h3(e10), e22)) 5.30/5.53 <= (~ (h3(op1(e10, e13)) = op2(h3(e10), e22)) & (op1(e10, e13) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['1979', '1994'])). 5.30/5.53 tff('1996', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('1997', plain, 5.30/5.53 (e22 != op2(h3(e10), e22)) 5.30/5.53 <= (~ (h3(op1(e10, e13)) = op2(h3(e10), e22)) & (op1(e10, e13) = e13)), 5.30/5.53 inference('demod', [status(thm)], ['1995', '1996'])). 5.30/5.53 tff('1998', plain, (e13 = op1(e12, e13)) <= ((e13 = op1(e12, e13))), 5.30/5.53 inference('split', [status(esa)], ['635'])). 5.30/5.53 tff('1999', plain, op1(e12, e13) = e10, 5.30/5.53 inference('demod', [status(thm)], ['240', '241', '244'])). 5.30/5.53 tff('2000', plain, (e13 = e10) <= ((e13 = op1(e12, e13))), 5.30/5.53 inference('sup+', [status(thm)], ['1998', '1999'])). 5.30/5.53 tff('2001', plain, e13 != e10, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2002', plain, ~ (e13 = op1(e12, e13)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2000', '2001'])). 5.30/5.53 tff('2003', plain, (op1(e11, e13) = e13) <= ((op1(e11, e13) = e13)), 5.30/5.53 inference('split', [status(esa)], ['509'])). 5.30/5.53 tff('2004', plain, (op1(e11, e13) = e12) <= ((op1(e11, e13) = e12)), 5.30/5.53 inference('split', [status(esa)], ['80'])). 5.30/5.53 tff('2005', plain, 5.30/5.53 (e13 = e12) <= ((op1(e11, e13) = e13) & (op1(e11, e13) = e12)), 5.30/5.53 inference('sup+', [status(thm)], ['2003', '2004'])). 5.30/5.53 tff('2006', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2007', plain, ~ (op1(e11, e13) = e13) | ~ (op1(e11, e13) = e12), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2005', '2006'])). 5.30/5.53 tff('2008', plain, (op1(e10, e13) = e13), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['2002', '284', '289', '290', '292', '301', '309', '315', 5.30/5.53 '321', '332', '343', '349', '359', '365', '367', '373', 5.30/5.53 '380', '386', '394', '399', '407', '413', '415', '416', 5.30/5.53 '423', '425', '434', '441', '448', '450', '456', '462', 5.30/5.53 '467', '475', '477', '487', '494', '504', '515', '517', 5.30/5.53 '524', '533', '534', '540', '547', '553', '555', '562', 5.30/5.53 '568', '573', '574', '580', '581', '589', '595', '597', 5.30/5.53 '601', '606', '612', '618', '627', '633', '634', '642', 5.30/5.53 '644', '646', '932', '938', '943', '949', '954', '959', 5.30/5.53 '964', '969', '974', '976', '980', '986', '992', '998', 5.30/5.53 '1004', '1010', '1015', '1021', '1027', '1033', '1039', 5.30/5.53 '1045', '1047', '1050', '1056', '1063', '1064', '1071', 5.30/5.53 '1077', '1082', '1086', '1091', '1092', '1097', '1099', 5.30/5.53 '1102', '1104', '1107', '1113', '1119', '1125', '1131', 5.30/5.53 '1132', '1139', '1146', '1147', '1154', '1160', '1168', 5.30/5.53 '1175', '1180', '1182', '1184', '1187', '1193', '1199', 5.30/5.53 '1204', '1209', '1210', '1212', '1220', '1226', '1231', 5.30/5.53 '1237', '1242', '1248', '1254', '1261', '1265', '1266', 5.30/5.53 '1271', '1276', '1281', '1286', '1288', '1290', '1297', 5.30/5.53 '1298', '1304', '1306', '1308', '1313', '1318', '1323', 5.30/5.53 '1328', '1335', '1340', '1345', '1347', '1349', '658', 5.30/5.53 '1350', '1351', '668', '674', '679', '1352', '1353', '1354', 5.30/5.53 '693', '699', '706', '711', '715', '1355', '723', '1356', 5.30/5.53 '1357', '1358', '735', '741', '743', '745', '751', '753', 5.30/5.53 '1359', '762', '767', '769', '771', '777', '781', '1360', 5.30/5.53 '1361', '1362', '1363', '1364', '1365', '1366', '807', 5.30/5.53 '1367', '1368', '1369', '1370', '1371', '1372', '1373', 5.30/5.53 '832', '1374', '1375', '842', '1376', '1377', '1378', '1379', 5.30/5.53 '1380', '1381', '1382', '1383', '1384', '1385', '898', 5.30/5.53 '1386', '910', '1387', '922', '1388', '1389', '1390', '1391', 5.30/5.53 '1397', '1401', '1407', '1415', '849', '1420', '1421', 5.30/5.53 '2007', '1066'])). 5.30/5.53 tff('2009', plain, 5.30/5.53 (e22 != op2(h3(e10), e22)) <= (~ (h3(op1(e10, e13)) = op2(h3(e10), e22))), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1997', '2008'])). 5.30/5.53 tff('2010', plain, 5.30/5.53 (e22 != op2(e20, e22)) 5.30/5.53 <= (~ (h3(op1(e10, e13)) = op2(h3(e10), e22)) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['1978', '2009'])). 5.30/5.53 tff('2011', plain, 5.30/5.53 (e22 != e22) 5.30/5.53 <= (~ (h3(op1(e10, e13)) = op2(h3(e10), e22)) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['1977', '2010'])). 5.30/5.53 tff('2012', plain, 5.30/5.53 (h3(op1(e10, e13)) = op2(h3(e10), e22)) | ~ (e20 = op2(e23, e22)) | 5.30/5.53 ~ (op2(e20, e22) = e22) | ~ (op2(e22, e22) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['2011'])). 5.30/5.53 tff('2013', plain, (e22 = op2(e22, e20)) <= ((e22 = op2(e22, e20))), 5.30/5.53 inference('split', [status(esa)], ['1456'])). 5.30/5.53 tff('2014', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('2015', plain, (op1(e13, e10) = e13) <= ((op1(e13, e10) = e13)), 5.30/5.53 inference('split', [status(esa)], ['23'])). 5.30/5.53 tff('2016', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2017', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2018', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2019', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2020', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2021', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2022', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2023', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('2024', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2025', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2026', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2027', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2028', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['2016', '2017', '2018', '2019', '2020', '2021', '2022', 5.30/5.53 '2023', '2024', '2025', '2026', '2027'])). 5.30/5.53 tff('2029', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['2028'])). 5.30/5.53 tff('2030', plain, 5.30/5.53 (op2(e22, h3(e10)) != h3(op1(e13, e10))) 5.30/5.53 <= (~ (op2(e22, h3(e10)) = h3(op1(e13, e10)))), 5.30/5.53 inference('split', [status(esa)], ['2029'])). 5.30/5.53 tff('2031', plain, 5.30/5.53 (op2(e22, h3(e10)) != h3(e13)) 5.30/5.53 <= (~ (op2(e22, h3(e10)) = h3(op1(e13, e10))) & (op1(e13, e10) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['2015', '2030'])). 5.30/5.53 tff('2032', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2033', plain, 5.30/5.53 (op2(e22, h3(e10)) != e22) 5.30/5.53 <= (~ (op2(e22, h3(e10)) = h3(op1(e13, e10))) & (op1(e13, e10) = e13)), 5.30/5.53 inference('demod', [status(thm)], ['2031', '2032'])). 5.30/5.53 tff('2034', plain, 5.30/5.53 (op2(e22, e20) != e22) 5.30/5.53 <= (~ (op2(e22, h3(e10)) = h3(op1(e13, e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e13, e10) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['2014', '2033'])). 5.30/5.53 tff('2035', plain, 5.30/5.53 (e22 != e22) 5.30/5.53 <= (~ (op2(e22, h3(e10)) = h3(op1(e13, e10))) & 5.30/5.53 (e22 = op2(e22, e20)) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e13, e10) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['2013', '2034'])). 5.30/5.53 tff('2036', plain, 5.30/5.53 (op2(e22, h3(e10)) = h3(op1(e13, e10))) | ~ (op1(e13, e10) = e13) | 5.30/5.53 ~ (e20 = op2(e23, e22)) | ~ (e22 = op2(e22, e20)) | 5.30/5.53 ~ (op2(e22, e22) = e21), inference('simplify', [status(thm)], ['2035'])). 5.30/5.53 tff('2037', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('2038', plain, (h3(e12) = e23) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1451', '1861'])). 5.30/5.53 tff('2039', plain, (op1(e13, e12) = e10) <= ((op1(e13, e12) = e10)), 5.30/5.53 inference('split', [status(esa)], ['311'])). 5.30/5.53 tff('2040', plain, 5.30/5.53 (h3(op1(e13, e12)) != op2(e22, h3(e12))) 5.30/5.53 <= (~ (h3(op1(e13, e12)) = op2(e22, h3(e12)))), 5.30/5.53 inference('split', [status(esa)], ['215'])). 5.30/5.53 tff('2041', plain, 5.30/5.53 (h3(e10) != op2(e22, h3(e12))) 5.30/5.53 <= (~ (h3(op1(e13, e12)) = op2(e22, h3(e12))) & (op1(e13, e12) = e10)), 5.30/5.53 inference('sup-', [status(thm)], ['2039', '2040'])). 5.30/5.53 tff('2042', plain, 5.30/5.53 (h3(e10) != op2(e22, e23)) 5.30/5.53 <= (~ (h3(op1(e13, e12)) = op2(e22, h3(e12))) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e13, e12) = e10)), 5.30/5.53 inference('sup-', [status(thm)], ['2038', '2041'])). 5.30/5.53 tff('2043', plain, op2(e22, e23) = e20, 5.30/5.53 inference('demod', [status(thm)], ['110', '111', '112'])). 5.30/5.53 tff('2044', plain, 5.30/5.53 (h3(e10) != e20) 5.30/5.53 <= (~ (h3(op1(e13, e12)) = op2(e22, h3(e12))) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e13, e12) = e10)), 5.30/5.53 inference('demod', [status(thm)], ['2042', '2043'])). 5.30/5.53 tff('2045', plain, 5.30/5.53 (e20 != e20) 5.30/5.53 <= (~ (h3(op1(e13, e12)) = op2(e22, h3(e12))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (op1(e13, e12) = e10)), 5.30/5.53 inference('sup-', [status(thm)], ['2037', '2044'])). 5.30/5.53 tff('2046', plain, 5.30/5.53 (h3(op1(e13, e12)) = op2(e22, h3(e12))) | ~ (op1(e13, e12) = e10) | 5.30/5.53 ~ (e20 = op2(e23, e22)) | ~ (op2(e22, e22) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['2045'])). 5.30/5.53 tff('2047', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('2048', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2049', plain, (h3(e10) != e20) <= (~ (h3(e10) = e20)), 5.30/5.53 inference('split', [status(esa)], ['2048'])). 5.30/5.53 tff('2050', plain, 5.30/5.53 (e20 != e20) 5.30/5.53 <= (~ (h3(e10) = e20) & (e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2047', '2049'])). 5.30/5.53 tff('2051', plain, 5.30/5.53 (h3(e10) = e20) | ~ (e20 = op2(e23, e22)) | ~ (op2(e22, e22) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['2050'])). 5.30/5.53 tff('2052', plain, 5.30/5.53 (op2(e21, e22) = e23) | (op2(e21, e22) = e20) | (e21 = op2(e21, e22)) | 5.30/5.53 (op2(e21, e22) = e22), inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2053', plain, 5.30/5.53 (op2(e21, e20) = e20 5.30/5.53 | op2(e21, e21) = e20 5.30/5.53 | op2(e21, e22) = e20 5.30/5.53 | e20 = op2(e21, e23)), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('2054', plain, 5.30/5.53 (e20 = op2(e21, e20)) | (op2(e21, e22) = e20) | (e20 = op2(e21, e23)) | 5.30/5.53 (e20 = op2(e21, e21)), inference('split', [status(esa)], ['2053'])). 5.30/5.53 tff('2055', plain, (e20 = op2(e21, e23)) <= ((e20 = op2(e21, e23))), 5.30/5.53 inference('split', [status(esa)], ['190'])). 5.30/5.53 tff('2056', plain, op2(e21, e23) != op2(e22, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2057', plain, op2(e22, e23) = e20, 5.30/5.53 inference('demod', [status(thm)], ['110', '111', '112'])). 5.30/5.53 tff('2058', plain, op2(e21, e23) != e20, 5.30/5.53 inference('demod', [status(thm)], ['2056', '2057'])). 5.30/5.53 tff('2059', plain, (e20 != e20) <= ((e20 = op2(e21, e23))), 5.30/5.53 inference('sup-', [status(thm)], ['2055', '2058'])). 5.30/5.53 tff('2060', plain, ~ (e20 = op2(e21, e23)), 5.30/5.53 inference('simplify', [status(thm)], ['2059'])). 5.30/5.53 tff('2061', plain, 5.30/5.53 (e20 = op2(e20, e22) 5.30/5.53 | op2(e23, e22) = e20 5.30/5.53 | op2(e22, e22) = e20 5.30/5.53 | e20 = op2(e21, e22)), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('2062', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2063', plain, 5.30/5.53 (e20 = op2(e20, e22) 5.30/5.53 | op2(e23, e22) = e20 5.30/5.53 | h3(e11) = e20 5.30/5.53 | e20 = op2(e21, e22)), 5.30/5.53 inference('demod', [status(thm)], ['2061', '2062'])). 5.30/5.53 tff('2064', plain, 5.30/5.53 (e20 = op2(e23, e22)) | (op2(e21, e22) = e20) | (op2(e20, e22) = e20) | 5.30/5.53 (h3(e11) = e20), inference('split', [status(esa)], ['2063'])). 5.30/5.53 tff('2065', plain, (op2(e20, e22) = e20) <= ((op2(e20, e22) = e20)), 5.30/5.53 inference('split', [status(esa)], ['1607'])). 5.30/5.53 tff('2066', plain, (op2(e20, e21) = e20) <= ((op2(e20, e21) = e20)), 5.30/5.53 inference('split', [status(esa)], ['1498'])). 5.30/5.53 tff('2067', plain, op2(e20, e21) != op2(e20, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2068', plain, (e20 != op2(e20, e22)) <= ((op2(e20, e21) = e20)), 5.30/5.53 inference('sup-', [status(thm)], ['2066', '2067'])). 5.30/5.53 tff('2069', plain, 5.30/5.53 (e20 != e20) <= ((op2(e20, e21) = e20) & (op2(e20, e22) = e20)), 5.30/5.53 inference('sup-', [status(thm)], ['2065', '2068'])). 5.30/5.53 tff('2070', plain, ~ (op2(e20, e22) = e20) | ~ (op2(e20, e21) = e20), 5.30/5.53 inference('simplify', [status(thm)], ['2069'])). 5.30/5.53 tff('2071', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2072', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2073', plain, 5.30/5.53 (op2(e20, op2(e20, e22)) = e20 5.30/5.53 | op2(e22, op2(e22, e22)) = e22 5.30/5.53 | e23 = op2(e23, op2(e23, e22)) 5.30/5.53 | e21 = op2(e21, op2(e21, e22))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.53 tff('2074', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2075', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2076', plain, 5.30/5.53 (op2(e20, op2(e20, e22)) = e20 5.30/5.53 | h3(e12) = e22 5.30/5.53 | e23 = op2(e23, op2(e23, e22)) 5.30/5.53 | e21 = op2(e21, op2(e21, e22))), 5.30/5.53 inference('demod', [status(thm)], ['2073', '2074', '2075'])). 5.30/5.53 tff('2077', plain, 5.30/5.53 (op2(e20, op2(e20, e22)) = e20) <= ((op2(e20, op2(e20, e22)) = e20)), 5.30/5.53 inference('split', [status(esa)], ['2076'])). 5.30/5.53 tff('2078', plain, 5.30/5.53 (op2(e20, e22) = e20) 5.30/5.53 <= ((op2(e20, e22) = e22) & (op2(e20, op2(e20, e22)) = e20)), 5.30/5.53 inference('sup+', [status(thm)], ['2072', '2077'])). 5.30/5.53 tff('2079', plain, 5.30/5.53 (e22 = e20) <= ((op2(e20, e22) = e22) & (op2(e20, op2(e20, e22)) = e20)), 5.30/5.53 inference('sup+', [status(thm)], ['2071', '2078'])). 5.30/5.53 tff('2080', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('2081', plain, 5.30/5.53 ~ (op2(e20, op2(e20, e22)) = e20) | ~ (op2(e20, e22) = e22), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2079', '2080'])). 5.30/5.53 tff('2082', plain, (op2(e20, e22) = e23) <= ((op2(e20, e22) = e23)), 5.30/5.53 inference('split', [status(esa)], ['179'])). 5.30/5.53 tff('2083', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2084', plain, 5.30/5.53 (e23 = e22) <= ((op2(e20, e22) = e23) & (op2(e20, e22) = e22)), 5.30/5.53 inference('sup+', [status(thm)], ['2082', '2083'])). 5.30/5.53 tff('2085', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('2086', plain, ~ (op2(e20, e22) = e23) | ~ (op2(e20, e22) = e22), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2084', '2085'])). 5.30/5.53 tff('2087', plain, (op2(e21, e22) = e20) <= ((op2(e21, e22) = e20)), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2088', plain, (op2(e21, e22) = e22) <= ((op2(e21, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2089', plain, 5.30/5.53 (e20 = e22) <= ((op2(e21, e22) = e20) & (op2(e21, e22) = e22)), 5.30/5.53 inference('sup+', [status(thm)], ['2087', '2088'])). 5.30/5.53 tff('2090', plain, e22 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('2091', plain, ~ (op2(e21, e22) = e22) | ~ (op2(e21, e22) = e20), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2089', '2090'])). 5.30/5.53 tff('2092', plain, 5.30/5.53 (e23 = op2(e23, op2(e23, e22))) | (e21 = op2(e21, op2(e21, e22))) | 5.30/5.53 (h3(e12) = e22) | (op2(e20, op2(e20, e22)) = e20), 5.30/5.53 inference('split', [status(esa)], ['2076'])). 5.30/5.53 tff('2093', plain, 5.30/5.53 (e23 = op2(e22, e22) 5.30/5.53 | op2(e23, e22) = e23 5.30/5.53 | op2(e21, e22) = e23 5.30/5.53 | op2(e20, e22) = e23), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('2094', plain, 5.30/5.53 (op2(e21, e22) = e23) | (e23 = op2(e23, e22)) | (op2(e22, e22) = e23) | 5.30/5.53 (op2(e20, e22) = e23), inference('split', [status(esa)], ['2093'])). 5.30/5.53 tff('2095', plain, op2(e21, e21) = h2(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax15])). 5.30/5.53 tff('2096', plain, (op2(e21, e21) = e21) <= ((op2(e21, e21) = e21)), 5.30/5.53 inference('split', [status(esa)], ['1530'])). 5.30/5.53 tff('2097', plain, (h2(e11) = e21) <= ((op2(e21, e21) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['2095', '2096'])). 5.30/5.53 tff('2098', plain, (op2(e21, e22) = e20) <= ((op2(e21, e22) = e20)), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2099', plain, 5.30/5.53 (op2(e20, op2(e20, e22)) = e20 5.30/5.53 | op2(e22, op2(e22, e22)) = e22 5.30/5.53 | e23 = op2(e23, op2(e23, e22)) 5.30/5.53 | e21 = op2(e21, op2(e21, e22))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_65])). 5.30/5.53 tff('2100', plain, 5.30/5.53 (e21 = op2(e21, op2(e21, e22))) <= ((e21 = op2(e21, op2(e21, e22)))), 5.30/5.53 inference('split', [status(esa)], ['2099'])). 5.30/5.53 tff('2101', plain, 5.30/5.53 (e21 = op2(e21, e20)) 5.30/5.53 <= ((op2(e21, e22) = e20) & (e21 = op2(e21, op2(e21, e22)))), 5.30/5.53 inference('sup+', [status(thm)], ['2098', '2100'])). 5.30/5.53 tff('2102', plain, op2(e21, e21) != op2(e21, e20), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2103', plain, op2(e21, e21) = h2(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax15])). 5.30/5.53 tff('2104', plain, h2(e11) != op2(e21, e20), 5.30/5.53 inference('demod', [status(thm)], ['2102', '2103'])). 5.30/5.53 tff('2105', plain, 5.30/5.53 (h2(e11) != e21) 5.30/5.53 <= ((op2(e21, e22) = e20) & (e21 = op2(e21, op2(e21, e22)))), 5.30/5.53 inference('sup-', [status(thm)], ['2101', '2104'])). 5.30/5.53 tff('2106', plain, 5.30/5.53 (e21 != e21) 5.30/5.53 <= ((op2(e21, e22) = e20) & 5.30/5.53 (op2(e21, e21) = e21) & 5.30/5.53 (e21 = op2(e21, op2(e21, e22)))), 5.30/5.53 inference('sup-', [status(thm)], ['2097', '2105'])). 5.30/5.53 tff('2107', plain, 5.30/5.53 ~ (e21 = op2(e21, op2(e21, e22))) | ~ (op2(e21, e22) = e20) | 5.30/5.53 ~ (op2(e21, e21) = e21), inference('simplify', [status(thm)], ['2106'])). 5.30/5.53 tff('2108', plain, (op2(e21, e22) = e20) <= ((op2(e21, e22) = e20)), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2109', plain, (op2(e21, e22) = e23) <= ((op2(e21, e22) = e23)), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2110', plain, 5.30/5.53 (e20 = e23) <= ((op2(e21, e22) = e20) & (op2(e21, e22) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['2108', '2109'])). 5.30/5.53 tff('2111', plain, e23 != e20, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('2112', plain, ~ (op2(e21, e22) = e20) | ~ (op2(e21, e22) = e23), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2110', '2111'])). 5.30/5.53 tff('2113', plain, e21 = op2(e23, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax13])). 5.30/5.53 tff('2114', plain, (e23 = op2(e23, e22)) <= ((e23 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('2115', plain, 5.30/5.53 (e23 = op2(e23, op2(e23, e22))) <= ((e23 = op2(e23, op2(e23, e22)))), 5.30/5.53 inference('split', [status(esa)], ['2099'])). 5.30/5.53 tff('2116', plain, 5.30/5.53 (e23 = op2(e23, e23)) 5.30/5.53 <= ((e23 = op2(e23, e22)) & (e23 = op2(e23, op2(e23, e22)))), 5.30/5.53 inference('sup+', [status(thm)], ['2114', '2115'])). 5.30/5.53 tff('2117', plain, 5.30/5.53 (e23 = e21) <= ((e23 = op2(e23, e22)) & (e23 = op2(e23, op2(e23, e22)))), 5.30/5.53 inference('sup+', [status(thm)], ['2113', '2116'])). 5.30/5.53 tff('2118', plain, e21 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('2119', plain, 5.30/5.53 ~ (e23 = op2(e23, e22)) | ~ (e23 = op2(e23, op2(e23, e22))), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2117', '2118'])). 5.30/5.53 tff('2120', plain, (e22 = op2(e21, e23)) <= ((e22 = op2(e21, e23))), 5.30/5.53 inference('split', [status(esa)], ['190'])). 5.30/5.53 tff('2121', plain, (e13 = op1(e11, e12)) <= ((e13 = op1(e11, e12))), 5.30/5.53 inference('split', [status(esa)], ['548'])). 5.30/5.53 tff('2122', plain, 5.30/5.53 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1449', '1450'])). 5.30/5.53 tff('2123', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2124', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2125', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2126', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2127', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2128', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2129', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2130', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('2131', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2132', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2133', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2134', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2135', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['2123', '2124', '2125', '2126', '2127', '2128', '2129', 5.30/5.53 '2130', '2131', '2132', '2133', '2134'])). 5.30/5.53 tff('2136', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e12) != e23 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['2135'])). 5.30/5.53 tff('2137', plain, 5.30/5.53 (op2(h3(e11), h3(e12)) != h3(op1(e11, e12))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12)))), 5.30/5.53 inference('split', [status(esa)], ['2136'])). 5.30/5.53 tff('2138', plain, 5.30/5.53 (op2(h3(e11), e23) != h3(op1(e11, e12))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) & 5.30/5.53 (op2(e22, e21) = e23) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2122', '2137'])). 5.30/5.53 tff('2139', plain, (h3(e11) = e21) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['162', '163'])). 5.30/5.53 tff('2140', plain, 5.30/5.53 (op2(e21, e23) != h3(op1(e11, e12))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) & 5.30/5.53 (op2(e22, e21) = e23) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2138', '2139'])). 5.30/5.53 tff('2141', plain, (op2(e22, e21) = e23), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['1453', '1455', '1462', '1463', '1467', '1471', '1473', 5.30/5.53 '1475', '1477', '1479', '1481', '1483', '1485', '1487', 5.30/5.53 '1489', '1491', '1493', '1495', '1497', '1503', '1505', 5.30/5.53 '1507', '1509', '1511', '1513', '1515', '1517', '1519', 5.30/5.53 '1521', '1523', '1528', '1547', '1549', '1563', '1574', 5.30/5.53 '1579', '1581', '1588', '1590', '1591', '1598', '1606', 5.30/5.53 '1612', '1613', '1618', '1624', '1628', '1634', '1636', 5.30/5.53 '1638', '1645', '1650', '1655', '1657', '1663', '1668', 5.30/5.53 '1673', '1678', '1683', '1688', '1690', '1695', '1700', 5.30/5.53 '1705', '1707', '1712', '1714', '1719', '1721', '1726', 5.30/5.53 '1731', '1736', '1741', '1746', '1751', '1756', '1761', 5.30/5.53 '1762', '1770', '1775', '1783', '1791', '1796', '1804', 5.30/5.53 '1816', '1818', '1823', '1825', '1830', '1838', '1839', 5.30/5.53 '1846', '1852', '1857', '1859', '1860'])). 5.30/5.53 tff('2142', plain, 5.30/5.53 (op2(e21, e23) != h3(op1(e11, e12))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['2140', '2141'])). 5.30/5.53 tff('2143', plain, 5.30/5.53 (op2(e21, e23) != h3(e13)) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e13 = op1(e11, e12))), 5.30/5.53 inference('sup-', [status(thm)], ['2121', '2142'])). 5.30/5.53 tff('2144', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2145', plain, 5.30/5.53 (op2(e21, e23) != e22) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e13 = op1(e11, e12))), 5.30/5.53 inference('demod', [status(thm)], ['2143', '2144'])). 5.30/5.53 tff('2146', plain, 5.30/5.53 (e22 != e22) 5.30/5.53 <= (~ (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) & 5.30/5.53 (op2(e22, e22) = e21) & 5.30/5.53 (e22 = op2(e21, e23)) & 5.30/5.53 (e13 = op1(e11, e12))), 5.30/5.53 inference('sup-', [status(thm)], ['2120', '2145'])). 5.30/5.53 tff('2147', plain, 5.30/5.53 (op2(h3(e11), h3(e12)) = h3(op1(e11, e12))) | ~ (e13 = op1(e11, e12)) | 5.30/5.53 ~ (e22 = op2(e21, e23)) | ~ (op2(e22, e22) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['2146'])). 5.30/5.53 tff('2148', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.53 inference('split', [status(esa)], ['64'])). 5.30/5.53 tff('2149', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('2150', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e12) != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2151', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2152', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2153', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2154', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2155', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2156', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2157', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('2158', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2159', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2160', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2161', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2162', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e12) != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['2150', '2151', '2152', '2153', '2154', '2155', '2156', 5.30/5.53 '2157', '2158', '2159', '2160', '2161'])). 5.30/5.53 tff('2163', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['2162'])). 5.30/5.53 tff('2164', plain, 5.30/5.53 (op2(h3(e11), h3(e11)) != h3(op1(e11, e11))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11)))), 5.30/5.53 inference('split', [status(esa)], ['2163'])). 5.30/5.53 tff('2165', plain, 5.30/5.53 (op2(e21, h3(e11)) != h3(op1(e11, e11))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) & (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2149', '2164'])). 5.30/5.53 tff('2166', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('2167', plain, op2(e21, e21) = h2(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax15])). 5.30/5.53 tff('2168', plain, 5.30/5.53 (h2(e11) != h3(op1(e11, e11))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) & (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2165', '2166', '2167'])). 5.30/5.53 tff('2169', plain, (h2(e11) = e21) <= ((op2(e21, e21) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['2095', '2096'])). 5.30/5.53 tff('2170', plain, (h2(e11) = e23) <= ((op2(e21, e21) = e23)), 5.30/5.53 inference('sup+', [status(thm)], ['1529', '1531'])). 5.30/5.53 tff('2171', plain, (op2(e22, e21) = e23) <= ((op2(e22, e21) = e23)), 5.30/5.53 inference('split', [status(esa)], ['273'])). 5.30/5.53 tff('2172', plain, op2(e22, e21) != op2(e21, e21), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2173', plain, op2(e21, e21) = h2(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax15])). 5.30/5.53 tff('2174', plain, op2(e22, e21) != h2(e11), 5.30/5.53 inference('demod', [status(thm)], ['2172', '2173'])). 5.30/5.53 tff('2175', plain, (e23 != h2(e11)) <= ((op2(e22, e21) = e23)), 5.30/5.53 inference('sup-', [status(thm)], ['2171', '2174'])). 5.30/5.53 tff('2176', plain, 5.30/5.53 (e23 != e23) <= ((op2(e22, e21) = e23) & (op2(e21, e21) = e23)), 5.30/5.53 inference('sup-', [status(thm)], ['2170', '2175'])). 5.30/5.53 tff('2177', plain, ~ (op2(e21, e21) = e23) | ~ (op2(e22, e21) = e23), 5.30/5.53 inference('simplify', [status(thm)], ['2176'])). 5.30/5.53 tff('2178', plain, 5.30/5.53 (op2(e21, e21) = e21) | (op2(e21, e21) = e23) | (e22 = op2(e21, e21)) | 5.30/5.53 (e20 = op2(e21, e21)), inference('split', [status(esa)], ['1530'])). 5.30/5.53 tff('2179', plain, (op2(e21, e21) = e21), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['1453', '1455', '1462', '1463', '1467', '1471', '1473', 5.30/5.53 '1475', '1477', '1479', '1481', '1483', '1485', '1487', 5.30/5.53 '1489', '1491', '1493', '1495', '1497', '1503', '1505', 5.30/5.53 '1507', '1509', '1511', '1513', '1515', '1517', '1519', 5.30/5.53 '1521', '1523', '1528', '1547', '1549', '1563', '1574', 5.30/5.53 '1579', '1581', '1588', '1590', '1591', '1598', '1606', 5.30/5.53 '1612', '1613', '1618', '1624', '1628', '1634', '1636', 5.30/5.53 '1638', '1645', '1650', '1655', '1657', '1663', '1668', 5.30/5.53 '1673', '1678', '1683', '1688', '1690', '1695', '1700', 5.30/5.53 '1705', '1707', '1712', '1714', '1719', '1721', '1726', 5.30/5.53 '1731', '1736', '1741', '1746', '1751', '1756', '1761', 5.30/5.53 '1762', '1770', '1775', '1783', '1791', '1796', '1804', 5.30/5.53 '1816', '1818', '1823', '1825', '1830', '1838', '1839', 5.30/5.53 '1846', '1852', '1857', '1859', '1860', '2177', '2178'])). 5.30/5.53 tff('2180', plain, h2(e11) = e21, 5.30/5.53 inference('simpl_trail', [status(thm)], ['2169', '2179'])). 5.30/5.53 tff('2181', plain, 5.30/5.53 (e21 != h3(op1(e11, e11))) 5.30/5.53 <= (~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) & (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2168', '2180'])). 5.30/5.53 tff('2182', plain, 5.30/5.53 (e21 != h3(e11)) 5.30/5.53 <= (~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) & 5.30/5.53 (e11 = op1(e11, e11)) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2148', '2181'])). 5.30/5.53 tff('2183', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('2184', plain, 5.30/5.53 (e21 != e21) 5.30/5.53 <= (~ (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) & 5.30/5.53 (e11 = op1(e11, e11)) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2182', '2183'])). 5.30/5.53 tff('2185', plain, 5.30/5.53 (op2(h3(e11), h3(e11)) = h3(op1(e11, e11))) | ~ (e11 = op1(e11, e11)) | 5.30/5.53 ~ (h3(e11) = e21), inference('simplify', [status(thm)], ['2184'])). 5.30/5.53 tff('2186', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.53 inference('split', [status(esa)], ['480'])). 5.30/5.53 tff('2187', plain, 5.30/5.53 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['272', '274'])). 5.30/5.53 tff('2188', plain, (op2(e22, e21) = e23), 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['1453', '1455', '1462', '1463', '1467', '1471', '1473', 5.30/5.53 '1475', '1477', '1479', '1481', '1483', '1485', '1487', 5.30/5.53 '1489', '1491', '1493', '1495', '1497', '1503', '1505', 5.30/5.53 '1507', '1509', '1511', '1513', '1515', '1517', '1519', 5.30/5.53 '1521', '1523', '1528', '1547', '1549', '1563', '1574', 5.30/5.53 '1579', '1581', '1588', '1590', '1591', '1598', '1606', 5.30/5.53 '1612', '1613', '1618', '1624', '1628', '1634', '1636', 5.30/5.53 '1638', '1645', '1650', '1655', '1657', '1663', '1668', 5.30/5.53 '1673', '1678', '1683', '1688', '1690', '1695', '1700', 5.30/5.53 '1705', '1707', '1712', '1714', '1719', '1721', '1726', 5.30/5.53 '1731', '1736', '1741', '1746', '1751', '1756', '1761', 5.30/5.53 '1762', '1770', '1775', '1783', '1791', '1796', '1804', 5.30/5.53 '1816', '1818', '1823', '1825', '1830', '1838', '1839', 5.30/5.53 '1846', '1852', '1857', '1859', '1860'])). 5.30/5.53 tff('2189', plain, (h3(e12) = e23) <= ((h3(e11) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['2187', '2188'])). 5.30/5.53 tff('2190', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | e22 != h3(e13) 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2191', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2192', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2193', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2194', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2195', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2196', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2197', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('2198', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2199', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2200', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2201', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2202', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2203', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | e22 != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['2190', '2191', '2192', '2193', '2194', '2195', '2196', 5.30/5.53 '2197', '2198', '2199', '2200', '2201', '2202'])). 5.30/5.53 tff('2204', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['2203'])). 5.30/5.53 tff('2205', plain, 5.30/5.53 (op2(h3(e12), h3(e11)) != h3(op1(e12, e11))) 5.30/5.53 <= (~ (op2(h3(e12), h3(e11)) = h3(op1(e12, e11)))), 5.30/5.53 inference('split', [status(esa)], ['2204'])). 5.30/5.53 tff('2206', plain, 5.30/5.53 (op2(e23, h3(e11)) != h3(op1(e12, e11))) 5.30/5.53 <= (~ (op2(h3(e12), h3(e11)) = h3(op1(e12, e11))) & (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2189', '2205'])). 5.30/5.53 tff('2207', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('2208', plain, e22 = op2(e23, e21), 5.30/5.53 inference('demod', [status(thm)], ['92', '93'])). 5.30/5.53 tff('2209', plain, 5.30/5.53 (e22 != h3(op1(e12, e11))) 5.30/5.53 <= (~ (op2(h3(e12), h3(e11)) = h3(op1(e12, e11))) & (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2206', '2207', '2208'])). 5.30/5.53 tff('2210', plain, 5.30/5.53 (e22 != h3(e13)) 5.30/5.53 <= (~ (op2(h3(e12), h3(e11)) = h3(op1(e12, e11))) & 5.30/5.53 (e13 = op1(e12, e11)) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2186', '2209'])). 5.30/5.53 tff('2211', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2212', plain, 5.30/5.53 (e22 != e22) 5.30/5.53 <= (~ (op2(h3(e12), h3(e11)) = h3(op1(e12, e11))) & 5.30/5.53 (e13 = op1(e12, e11)) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2210', '2211'])). 5.30/5.53 tff('2213', plain, 5.30/5.53 (op2(h3(e12), h3(e11)) = h3(op1(e12, e11))) | ~ (e13 = op1(e12, e11)) | 5.30/5.53 ~ (h3(e11) = e21), inference('simplify', [status(thm)], ['2212'])). 5.30/5.53 tff('2214', plain, (op1(e12, e12) = e11) <= ((op1(e12, e12) = e11)), 5.30/5.53 inference('split', [status(esa)], ['44'])). 5.30/5.53 tff('2215', plain, 5.30/5.53 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['272', '274'])). 5.30/5.53 tff('2216', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2217', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2218', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2219', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2220', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2221', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2222', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2223', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('2224', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2225', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2226', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2227', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2228', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['2216', '2217', '2218', '2219', '2220', '2221', '2222', 5.30/5.53 '2223', '2224', '2225', '2226', '2227'])). 5.30/5.53 tff('2229', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | e23 != h3(e11) 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['2228'])). 5.30/5.53 tff('2230', plain, 5.30/5.53 (op2(h3(e12), h3(e12)) != h3(op1(e12, e12))) 5.30/5.53 <= (~ (op2(h3(e12), h3(e12)) = h3(op1(e12, e12)))), 5.30/5.53 inference('split', [status(esa)], ['2229'])). 5.30/5.53 tff('2231', plain, 5.30/5.53 (op2(e23, h3(e12)) != h3(op1(e12, e12))) 5.30/5.53 <= (~ (op2(h3(e12), h3(e12)) = h3(op1(e12, e12))) & 5.30/5.53 (op2(e22, e21) = e23) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2215', '2230'])). 5.30/5.53 tff('2232', plain, 5.30/5.53 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['272', '274'])). 5.30/5.53 tff('2233', plain, e21 = op2(e23, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax13])). 5.30/5.53 tff('2234', plain, 5.30/5.53 (e21 != h3(op1(e12, e12))) 5.30/5.53 <= (~ (op2(h3(e12), h3(e12)) = h3(op1(e12, e12))) & 5.30/5.53 (op2(e22, e21) = e23) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2231', '2232', '2233'])). 5.30/5.53 tff('2235', plain, 5.30/5.53 (e21 != h3(e11)) 5.30/5.53 <= (~ (op2(h3(e12), h3(e12)) = h3(op1(e12, e12))) & 5.30/5.53 (op2(e22, e21) = e23) & 5.30/5.53 (op1(e12, e12) = e11) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2214', '2234'])). 5.30/5.53 tff('2236', plain, (h3(e11) = e21) <= ((h3(e11) = e21)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('2237', plain, 5.30/5.53 (e21 != e21) 5.30/5.53 <= (~ (op2(h3(e12), h3(e12)) = h3(op1(e12, e12))) & 5.30/5.53 (op2(e22, e21) = e23) & 5.30/5.53 (op1(e12, e12) = e11) & 5.30/5.53 (h3(e11) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2235', '2236'])). 5.30/5.53 tff('2238', plain, 5.30/5.53 (op2(h3(e12), h3(e12)) = h3(op1(e12, e12))) | ~ (op1(e12, e12) = e11) | 5.30/5.53 ~ (h3(e11) = e21) | ~ (op2(e22, e21) = e23), 5.30/5.53 inference('simplify', [status(thm)], ['2237'])). 5.30/5.53 tff('2239', plain, 5.30/5.53 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['272', '274'])). 5.30/5.53 tff('2240', plain, (h3(e12) = e22) <= ((h3(e12) = e22)), 5.30/5.53 inference('split', [status(esa)], ['2076'])). 5.30/5.53 tff('2241', plain, 5.30/5.53 (e23 = e22) 5.30/5.53 <= ((op2(e22, e21) = e23) & (h3(e11) = e21) & (h3(e12) = e22)), 5.30/5.53 inference('sup+', [status(thm)], ['2239', '2240'])). 5.30/5.53 tff('2242', plain, e22 != e23, inference('cnf', [status(esa)], [ax8])). 5.30/5.53 tff('2243', plain, 5.30/5.53 ~ (h3(e12) = e22) | ~ (h3(e11) = e21) | ~ (op2(e22, e21) = e23), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2241', '2242'])). 5.30/5.53 tff('2244', plain, 5.30/5.53 (h3(e12) = e23) <= ((op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['272', '274'])). 5.30/5.53 tff('2245', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e11) != e22 5.30/5.53 | h3(e12) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2246', plain, (h3(e12) != e23) <= (~ (h3(e12) = e23)), 5.30/5.53 inference('split', [status(esa)], ['2245'])). 5.30/5.53 tff('2247', plain, 5.30/5.53 (e23 != e23) 5.30/5.53 <= (~ (h3(e12) = e23) & (op2(e22, e21) = e23) & (h3(e11) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2244', '2246'])). 5.30/5.53 tff('2248', plain, 5.30/5.53 (h3(e12) = e23) | ~ (h3(e11) = e21) | ~ (op2(e22, e21) = e23), 5.30/5.53 inference('simplify', [status(thm)], ['2247'])). 5.30/5.53 tff('2249', plain, 5.30/5.53 (e22 = op2(e22, e23) 5.30/5.53 | e22 = op2(e23, e23) 5.30/5.53 | op2(e21, e23) = e22 5.30/5.53 | op2(e20, e23) = e22), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('2250', plain, 5.30/5.53 (e22 = op2(e21, e23)) | (op2(e20, e23) = e22) | (op2(e23, e23) = e22) | 5.30/5.53 (e22 = op2(e22, e23)), inference('split', [status(esa)], ['2249'])). 5.30/5.53 tff('2251', plain, 5.30/5.53 (op2(e20, e23) = e21 5.30/5.53 | e23 = op2(e20, e23) 5.30/5.53 | op2(e20, e23) = e22 5.30/5.53 | e20 = op2(e20, e23)), 5.30/5.53 inference('cnf', [status(esa)], [ax3])). 5.30/5.53 tff('2252', plain, 5.30/5.53 (e23 = op2(e20, e23)) | (op2(e20, e23) = e22) | (op2(e20, e23) = e21) | 5.30/5.53 (e20 = op2(e20, e23)), inference('split', [status(esa)], ['2251'])). 5.30/5.53 tff('2253', plain, 5.30/5.53 (op2(e20, e22) = e21 5.30/5.53 | e21 = op2(e22, e22) 5.30/5.53 | op2(e23, e22) = e21 5.30/5.53 | e21 = op2(e21, e22)), 5.30/5.53 inference('cnf', [status(esa)], [ax4])). 5.30/5.53 tff('2254', plain, 5.30/5.53 (op2(e22, e22) = e21) | (e21 = op2(e20, e22)) | (e21 = op2(e21, e22)) | 5.30/5.53 (e21 = op2(e23, e22)), inference('split', [status(esa)], ['2253'])). 5.30/5.53 tff('2255', plain, 5.30/5.53 (h3(e11) = e21) | (e21 = op2(e20, e22)) | (e21 = op2(e23, e22)) | 5.30/5.53 (e21 = op2(e21, e22)), inference('split', [status(esa)], ['167'])). 5.30/5.53 tff('2256', plain, (e21 = op2(e23, e22)) <= ((e21 = op2(e23, e22))), 5.30/5.53 inference('split', [status(esa)], ['142'])). 5.30/5.53 tff('2257', plain, op2(e23, e22) != op2(e23, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2258', plain, e21 = op2(e23, e23), 5.30/5.53 inference('cnf', [status(esa)], [ax13])). 5.30/5.53 tff('2259', plain, op2(e23, e22) != e21, 5.30/5.53 inference('demod', [status(thm)], ['2257', '2258'])). 5.30/5.53 tff('2260', plain, (e21 != e21) <= ((e21 = op2(e23, e22))), 5.30/5.53 inference('sup-', [status(thm)], ['2256', '2259'])). 5.30/5.53 tff('2261', plain, ~ (e21 = op2(e23, e22)), 5.30/5.53 inference('simplify', [status(thm)], ['2260'])). 5.30/5.53 tff('2262', plain, (h2(e11) = e21) <= ((op2(e21, e21) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['2095', '2096'])). 5.30/5.53 tff('2263', plain, (e21 = op2(e21, e22)) <= ((e21 = op2(e21, e22))), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2264', plain, op2(e21, e22) != op2(e21, e21), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2265', plain, op2(e21, e21) = h2(e11), 5.30/5.53 inference('cnf', [status(esa)], [ax15])). 5.30/5.53 tff('2266', plain, op2(e21, e22) != h2(e11), 5.30/5.53 inference('demod', [status(thm)], ['2264', '2265'])). 5.30/5.53 tff('2267', plain, (e21 != h2(e11)) <= ((e21 = op2(e21, e22))), 5.30/5.53 inference('sup-', [status(thm)], ['2263', '2266'])). 5.30/5.53 tff('2268', plain, 5.30/5.53 (e21 != e21) <= ((e21 = op2(e21, e22)) & (op2(e21, e21) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2262', '2267'])). 5.30/5.53 tff('2269', plain, ~ (e21 = op2(e21, e22)) | ~ (op2(e21, e21) = e21), 5.30/5.53 inference('simplify', [status(thm)], ['2268'])). 5.30/5.53 tff('2270', plain, ~ ( zip_tseitin_20) | (e22 = op2(e22, e20)), 5.30/5.53 inference('split', [status(esa)], ['1454'])). 5.30/5.53 tff('2271', plain, 5.30/5.53 (op2(e20, e22) = e22) | (h3(e11) = e22) | (op2(e23, e22) = e22) | 5.30/5.53 (op2(e21, e22) = e22), inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2272', plain, ~ (e23 = op2(e22, e20)) | ~ (e21 = op2(e22, e20)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1671', '1672'])). 5.30/5.53 tff('2273', plain, (e22 = h3(e11)) <= ((h3(e11) = e22)), 5.30/5.53 inference('split', [status(esa)], ['269'])). 5.30/5.53 tff('2274', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2275', plain, h3(e11) != op2(e20, e22), 5.30/5.53 inference('demod', [status(thm)], ['169', '170'])). 5.30/5.53 tff('2276', plain, (h3(e11) != e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2274', '2275'])). 5.30/5.53 tff('2277', plain, (e22 != e22) <= ((op2(e20, e22) = e22) & (h3(e11) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2273', '2276'])). 5.30/5.53 tff('2278', plain, ~ (h3(e11) = e22) | ~ (op2(e20, e22) = e22), 5.30/5.53 inference('simplify', [status(thm)], ['2277'])). 5.30/5.53 tff('2279', plain, (h3(e11) = e22) <= ((e22 = op2(e22, e22))), 5.30/5.53 inference('sup+', [status(thm)], ['106', '107'])). 5.30/5.53 tff('2280', plain, (h3(e11) != e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2274', '2275'])). 5.30/5.53 tff('2281', plain, 5.30/5.53 (e22 != e22) <= ((e22 = op2(e22, e22)) & (op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2279', '2280'])). 5.30/5.53 tff('2282', plain, ~ (e22 = op2(e22, e22)) | ~ (op2(e20, e22) = e22), 5.30/5.53 inference('simplify', [status(thm)], ['2281'])). 5.30/5.53 tff('2283', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2284', plain, (op2(e20, e23) = e22) <= ((op2(e20, e23) = e22)), 5.30/5.53 inference('split', [status(esa)], ['137'])). 5.30/5.53 tff('2285', plain, op2(e20, e23) != op2(e20, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2286', plain, (e22 != op2(e20, e22)) <= ((op2(e20, e23) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2284', '2285'])). 5.30/5.53 tff('2287', plain, 5.30/5.53 (e22 != e22) <= ((op2(e20, e23) = e22) & (op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2283', '2286'])). 5.30/5.53 tff('2288', plain, ~ (op2(e20, e23) = e22) | ~ (op2(e20, e22) = e22), 5.30/5.53 inference('simplify', [status(thm)], ['2287'])). 5.30/5.53 tff('2289', plain, (op2(e21, e22) = e22) <= ((op2(e21, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['188'])). 5.30/5.53 tff('2290', plain, (op2(e20, e22) = e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('split', [status(esa)], ['1601'])). 5.30/5.53 tff('2291', plain, op2(e21, e22) != op2(e20, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax6])). 5.30/5.53 tff('2292', plain, (op2(e21, e22) != e22) <= ((op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2290', '2291'])). 5.30/5.53 tff('2293', plain, 5.30/5.53 (e22 != e22) <= ((op2(e21, e22) = e22) & (op2(e20, e22) = e22)), 5.30/5.53 inference('sup-', [status(thm)], ['2289', '2292'])). 5.30/5.53 tff('2294', plain, ~ (op2(e21, e22) = e22) | ~ (op2(e20, e22) = e22), 5.30/5.53 inference('simplify', [status(thm)], ['2293'])). 5.30/5.53 tff('2295', plain, (op2(e23, e20) = e23) <= ((op2(e23, e20) = e23)), 5.30/5.53 inference('split', [status(esa)], ['144'])). 5.30/5.53 tff('2296', plain, 5.30/5.53 (e20 = h3(e10)) <= ((e20 = op2(e23, e22)) & (op2(e22, e22) = e21)), 5.30/5.53 inference('sup+', [status(thm)], ['1864', '1865'])). 5.30/5.53 tff('2297', plain, (h3(e12) = e23) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1451', '1861'])). 5.30/5.53 tff('2298', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), h3(e13)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(h3(e13), h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(h3(e13), h3(e12)) 5.30/5.53 | op2(h3(e13), h3(e13)) != h3(op1(e13, e13)) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | op2(h3(e13), h3(e11)) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), h3(e13)) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), h3(e13))), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_66])). 5.30/5.53 tff('2299', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2300', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2301', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2302', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2303', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2304', plain, h3(e11) = op2(e22, e22), 5.30/5.53 inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2305', plain, op1(e13, e13) = e11, 5.30/5.53 inference('cnf', [status(esa)], [ax12])). 5.30/5.53 tff('2306', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2307', plain, h3(e12) = op2(e22, h3(e11)), 5.30/5.53 inference('demod', [status(thm)], ['209', '210'])). 5.30/5.53 tff('2308', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2309', plain, h3(e13) = e22, inference('cnf', [status(esa)], [ax16])). 5.30/5.53 tff('2310', plain, 5.30/5.53 (h3(op1(e10, e10)) != op2(h3(e10), h3(e10)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | h3(e11) != h3(e11) 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e11, e13)) != op2(h3(e11), e22)), 5.30/5.53 inference('demod', [status(thm)], 5.30/5.53 ['2298', '2299', '2300', '2301', '2302', '2303', '2304', 5.30/5.53 '2305', '2306', '2307', '2308', '2309'])). 5.30/5.53 tff('2311', plain, 5.30/5.53 (h3(op1(e11, e13)) != op2(h3(e11), e22) 5.30/5.53 | op2(h3(e12), h3(e12)) != h3(op1(e12, e12)) 5.30/5.53 | h3(op1(e12, e13)) != op2(h3(e12), e22) 5.30/5.53 | h3(e12) != h3(op1(e13, e11)) 5.30/5.53 | h3(e10) != e23 5.30/5.53 | h3(e12) != e22 5.30/5.53 | h3(e11) != e21 5.30/5.53 | h3(e10) != e20 5.30/5.53 | h3(op1(e13, e12)) != op2(e22, h3(e12)) 5.30/5.53 | op2(e22, h3(e10)) != h3(op1(e13, e10)) 5.30/5.53 | op2(h3(e12), h3(e11)) != h3(op1(e12, e11)) 5.30/5.53 | h3(op1(e12, e10)) != op2(h3(e12), h3(e10)) 5.30/5.53 | op2(h3(e11), h3(e12)) != h3(op1(e11, e12)) 5.30/5.53 | op2(h3(e11), h3(e11)) != h3(op1(e11, e11)) 5.30/5.53 | h3(op1(e11, e10)) != op2(h3(e11), h3(e10)) 5.30/5.53 | h3(op1(e10, e13)) != op2(h3(e10), e22) 5.30/5.53 | op2(h3(e10), h3(e12)) != h3(op1(e10, e12)) 5.30/5.53 | op2(h3(e10), h3(e11)) != h3(op1(e10, e11)) 5.30/5.53 | h3(op1(e10, e10)) != op2(h3(e10), h3(e10))), 5.30/5.53 inference('simplify', [status(thm)], ['2310'])). 5.30/5.53 tff('2312', plain, 5.30/5.53 (h3(op1(e12, e10)) != op2(h3(e12), h3(e10))) 5.30/5.53 <= (~ (h3(op1(e12, e10)) = op2(h3(e12), h3(e10)))), 5.30/5.53 inference('split', [status(esa)], ['2311'])). 5.30/5.53 tff('2313', plain, 5.30/5.53 (h3(op1(e12, e10)) != op2(e23, h3(e10))) 5.30/5.53 <= (~ (h3(op1(e12, e10)) = op2(h3(e12), h3(e10))) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2297', '2312'])). 5.30/5.53 tff('2314', plain, 5.30/5.53 (e12 = op1(e12, e10) 5.30/5.53 | op1(e12, e11) = e12 5.30/5.53 | e12 = op1(e12, e12) 5.30/5.53 | e12 = op1(e12, e13)), 5.30/5.53 inference('cnf', [status(esa)], [ax2])). 5.30/5.53 tff('2315', plain, e12 != op1(e12, e12), 5.30/5.53 inference('simpl_trail', [status(thm)], ['651', '930'])). 5.30/5.53 tff('2316', plain, (e12 != op1(e12, e11)) <= ((op1(e13, e11) = e12)), 5.30/5.53 inference('sup-', [status(thm)], ['297', '298'])). 5.30/5.53 tff('2317', plain, (op1(e13, e11) = e12), 5.30/5.53 inference('sat_resolution*', [status(thm)], ['284', '289', '290'])). 5.30/5.53 tff('2318', plain, e12 != op1(e12, e11), 5.30/5.53 inference('simpl_trail', [status(thm)], ['2316', '2317'])). 5.30/5.53 tff('2319', plain, (e12 = op1(e12, e10) | e12 = op1(e12, e13)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2314', '2315', '2318'])). 5.30/5.53 tff('2320', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.53 inference('split', [status(esa)], ['51'])). 5.30/5.53 tff('2321', plain, 5.30/5.53 ((e12 = e10 | e12 = op1(e12, e10))) <= ((op1(e12, e13) = e10)), 5.30/5.53 inference('sup+', [status(thm)], ['2319', '2320'])). 5.30/5.53 tff('2322', plain, e10 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2323', plain, (e12 = op1(e12, e10)) <= ((op1(e12, e13) = e10)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2321', '2322'])). 5.30/5.53 tff('2324', plain, (op1(e12, e13) = e10), 5.30/5.53 inference('sat_resolution*', [status(thm)], ['2002', '1420', '1376'])). 5.30/5.53 tff('2325', plain, e12 = op1(e12, e10), 5.30/5.53 inference('simpl_trail', [status(thm)], ['2323', '2324'])). 5.30/5.53 tff('2326', plain, (h3(e12) = e23) <= ((op2(e22, e22) = e21)), 5.30/5.53 inference('simpl_trail', [status(thm)], ['1451', '1861'])). 5.30/5.53 tff('2327', plain, 5.30/5.53 (e23 != op2(e23, h3(e10))) 5.30/5.53 <= (~ (h3(op1(e12, e10)) = op2(h3(e12), h3(e10))) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('demod', [status(thm)], ['2313', '2325', '2326'])). 5.30/5.53 tff('2328', plain, 5.30/5.53 (e23 != op2(e23, e20)) 5.30/5.53 <= (~ (h3(op1(e12, e10)) = op2(h3(e12), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2296', '2327'])). 5.30/5.53 tff('2329', plain, 5.30/5.53 (e23 != e23) 5.30/5.53 <= (~ (h3(op1(e12, e10)) = op2(h3(e12), h3(e10))) & 5.30/5.53 (e20 = op2(e23, e22)) & 5.30/5.53 (op2(e23, e20) = e23) & 5.30/5.53 (op2(e22, e22) = e21)), 5.30/5.53 inference('sup-', [status(thm)], ['2295', '2328'])). 5.30/5.53 tff('2330', plain, 5.30/5.53 (h3(op1(e12, e10)) = op2(h3(e12), h3(e10))) | ~ (op2(e23, e20) = e23) | 5.30/5.53 ~ (op2(e22, e22) = e21) | ~ (e20 = op2(e23, e22)), 5.30/5.53 inference('simplify', [status(thm)], ['2329'])). 5.30/5.53 tff('2331', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.53 inference('split', [status(esa)], ['480'])). 5.30/5.53 tff('2332', plain, 5.30/5.53 (op1(e12, e11) = e12) 5.30/5.53 <= ((op1(e12, e12) = e11) & (op1(e12, op1(e12, e12)) = e12)), 5.30/5.53 inference('sup+', [status(thm)], ['293', '295'])). 5.30/5.53 tff('2333', plain, 5.30/5.53 (e13 = e12) 5.30/5.53 <= ((e13 = op1(e12, e11)) & 5.30/5.53 (op1(e12, e12) = e11) & 5.30/5.53 (op1(e12, op1(e12, e12)) = e12)), 5.30/5.53 inference('sup+', [status(thm)], ['2331', '2332'])). 5.30/5.53 tff('2334', plain, e12 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2335', plain, 5.30/5.53 ~ (op1(e12, op1(e12, e12)) = e12) | ~ (op1(e12, e12) = e11) | 5.30/5.53 ~ (e13 = op1(e12, e11)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2333', '2334'])). 5.30/5.53 tff('2336', plain, (op1(e10, e12) = e12) <= ((op1(e10, e12) = e12)), 5.30/5.53 inference('split', [status(esa)], ['71'])). 5.30/5.53 tff('2337', plain, (e11 = op1(e10, e12)) <= ((e11 = op1(e10, e12))), 5.30/5.53 inference('split', [status(esa)], ['350'])). 5.30/5.53 tff('2338', plain, 5.30/5.53 (e11 = e12) <= ((op1(e10, e12) = e12) & (e11 = op1(e10, e12))), 5.30/5.53 inference('sup+', [status(thm)], ['2336', '2337'])). 5.30/5.53 tff('2339', plain, e11 != e12, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2340', plain, ~ (e11 = op1(e10, e12)) | ~ (op1(e10, e12) = e12), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2338', '2339'])). 5.30/5.53 tff('2341', plain, (e13 = op1(e10, e11)) <= ((e13 = op1(e10, e11))), 5.30/5.53 inference('split', [status(esa)], ['8'])). 5.30/5.53 tff('2342', plain, (op1(e10, e13) = e13) <= ((op1(e10, e13) = e13)), 5.30/5.53 inference('split', [status(esa)], ['326'])). 5.30/5.53 tff('2343', plain, op1(e10, e11) != op1(e10, e13), 5.30/5.53 inference('cnf', [status(esa)], [ax5])). 5.30/5.53 tff('2344', plain, (op1(e10, e11) != e13) <= ((op1(e10, e13) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['2342', '2343'])). 5.30/5.53 tff('2345', plain, 5.30/5.53 (e13 != e13) <= ((op1(e10, e13) = e13) & (e13 = op1(e10, e11))), 5.30/5.53 inference('sup-', [status(thm)], ['2341', '2344'])). 5.30/5.53 tff('2346', plain, ~ (e13 = op1(e10, e11)) | ~ (op1(e10, e13) = e13), 5.30/5.53 inference('simplify', [status(thm)], ['2345'])). 5.30/5.53 tff('2347', plain, (op1(e11, e12) = e11) <= ((op1(e11, e12) = e11)), 5.30/5.53 inference('split', [status(esa)], ['58'])). 5.30/5.53 tff('2348', plain, (op1(e11, e12) != e11) <= ((e11 = op1(e11, e11))), 5.30/5.53 inference('sup-', [status(thm)], ['1233', '1234'])). 5.30/5.53 tff('2349', plain, 5.30/5.53 (e11 != e11) <= ((op1(e11, e12) = e11) & (e11 = op1(e11, e11))), 5.30/5.53 inference('sup-', [status(thm)], ['2347', '2348'])). 5.30/5.53 tff('2350', plain, ~ (e11 = op1(e11, e11)) | ~ (op1(e11, e12) = e11), 5.30/5.53 inference('simplify', [status(thm)], ['2349'])). 5.30/5.53 tff('2351', plain, (op1(e11, e11) = e13) <= ((op1(e11, e11) = e13)), 5.30/5.53 inference('split', [status(esa)], ['519'])). 5.30/5.53 tff('2352', plain, (e11 = op1(e11, e11)) <= ((e11 = op1(e11, e11))), 5.30/5.53 inference('split', [status(esa)], ['64'])). 5.30/5.53 tff('2353', plain, 5.30/5.53 (e11 = e13) <= ((op1(e11, e11) = e13) & (e11 = op1(e11, e11))), 5.30/5.53 inference('sup+', [status(thm)], ['2351', '2352'])). 5.30/5.53 tff('2354', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2355', plain, ~ (e11 = op1(e11, e11)) | ~ (op1(e11, e11) = e13), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2353', '2354'])). 5.30/5.53 tff('2356', plain, (op1(e11, e10) = e13) <= ((op1(e11, e10) = e13)), 5.30/5.53 inference('split', [status(esa)], ['802'])). 5.30/5.53 tff('2357', plain, (e10 = op1(e11, e12)) <= ((e10 = op1(e11, e12))), 5.30/5.53 inference('split', [status(esa)], ['548'])). 5.30/5.53 tff('2358', plain, 5.30/5.53 (e11 = op1(e11, op1(e11, e12))) <= ((e11 = op1(e11, op1(e11, e12)))), 5.30/5.53 inference('split', [status(esa)], ['294'])). 5.30/5.53 tff('2359', plain, 5.30/5.53 (e11 = op1(e11, e10)) 5.30/5.53 <= ((e10 = op1(e11, e12)) & (e11 = op1(e11, op1(e11, e12)))), 5.30/5.53 inference('sup+', [status(thm)], ['2357', '2358'])). 5.30/5.53 tff('2360', plain, 5.30/5.53 (e11 = e13) 5.30/5.53 <= ((op1(e11, e10) = e13) & 5.30/5.53 (e10 = op1(e11, e12)) & 5.30/5.53 (e11 = op1(e11, op1(e11, e12)))), 5.30/5.53 inference('sup+', [status(thm)], ['2356', '2359'])). 5.30/5.53 tff('2361', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2362', plain, 5.30/5.53 ~ (e11 = op1(e11, op1(e11, e12))) | ~ (e10 = op1(e11, e12)) | 5.30/5.53 ~ (op1(e11, e10) = e13), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2360', '2361'])). 5.30/5.53 tff('2363', plain, (op1(e10, e11) = e10) <= ((op1(e10, e11) = e10)), 5.30/5.53 inference('split', [status(esa)], ['8'])). 5.30/5.53 tff('2364', plain, 5.30/5.53 (e10 = op1(e10, op1(e10, e11))) <= ((e10 = op1(e10, op1(e10, e11)))), 5.30/5.53 inference('split', [status(esa)], ['354'])). 5.30/5.53 tff('2365', plain, 5.30/5.53 (e10 = op1(e10, e10)) 5.30/5.53 <= ((op1(e10, e11) = e10) & (e10 = op1(e10, op1(e10, e11)))), 5.30/5.53 inference('sup+', [status(thm)], ['2363', '2364'])). 5.30/5.53 tff('2366', plain, op1(e10, e11) != op1(e10, e10), 5.30/5.53 inference('cnf', [status(esa)], [ax5])). 5.30/5.53 tff('2367', plain, 5.30/5.53 (op1(e10, e11) != e10) 5.30/5.53 <= ((op1(e10, e11) = e10) & (e10 = op1(e10, op1(e10, e11)))), 5.30/5.53 inference('sup-', [status(thm)], ['2365', '2366'])). 5.30/5.53 tff('2368', plain, (op1(e10, e11) = e10) <= ((op1(e10, e11) = e10)), 5.30/5.53 inference('split', [status(esa)], ['8'])). 5.30/5.53 tff('2369', plain, 5.30/5.53 (e10 != e10) <= ((op1(e10, e11) = e10) & (e10 = op1(e10, op1(e10, e11)))), 5.30/5.53 inference('demod', [status(thm)], ['2367', '2368'])). 5.30/5.53 tff('2370', plain, 5.30/5.53 ~ (e10 = op1(e10, op1(e10, e11))) | ~ (op1(e10, e11) = e10), 5.30/5.53 inference('simplify', [status(thm)], ['2369'])). 5.30/5.53 tff('2371', plain, 5.30/5.53 ~ (e13 = op1(e13, op1(e13, e12))) | ~ (e13 = op1(e13, e12)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['307', '308'])). 5.30/5.53 tff('2372', plain, ~ (e11 = op1(e11, e11)) | ~ (e11 = op1(e12, e11)), 5.30/5.53 inference('simplify', [status(thm)], ['320'])). 5.30/5.53 tff('2373', plain, 5.30/5.53 (e10 = op1(e11, e10)) | (e10 = op1(e11, e11)) | (op1(e11, e13) = e10) | 5.30/5.53 (e10 = op1(e11, e12)), inference('split', [status(esa)], ['366'])). 5.30/5.53 tff('2374', plain, ~ (op1(e12, e10) = e13) | ~ (e13 = op1(e12, e12)), 5.30/5.53 inference('simplify', [status(thm)], ['379'])). 5.30/5.53 tff('2375', plain, ~ (e12 = op1(e12, e11)) | ~ (e11 = op1(e12, e11)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['384', '385'])). 5.30/5.53 tff('2376', plain, ~ (e10 = op1(e11, e10)) | ~ (e10 = op1(e13, e10)), 5.30/5.53 inference('simplify', [status(thm)], ['493'])). 5.30/5.53 tff('2377', plain, 5.30/5.53 (op1(e11, e11) = e13) | (op1(e11, e10) = e13) | (e13 = op1(e11, e12)) | 5.30/5.53 (op1(e11, e13) = e13), inference('split', [status(esa)], ['516'])). 5.30/5.53 tff('2378', plain, ~ (e13 = op1(e12, e11)) | ~ (op1(e11, e11) = e13), 5.30/5.53 inference('simplify', [status(thm)], ['523'])). 5.30/5.53 tff('2379', plain, 5.30/5.53 (e13 = op1(e12, e12)) | (e13 = op1(e13, e12)) | (e13 = op1(e10, e12)) | 5.30/5.53 (e13 = op1(e11, e12)), inference('split', [status(esa)], ['554'])). 5.30/5.53 tff('2380', plain, 5.30/5.53 (e13 = op1(e12, e12)) | (e13 = op1(e12, e11)) | (op1(e12, e10) = e13) | 5.30/5.53 (e13 = op1(e12, e13)), inference('split', [status(esa)], ['645'])). 5.30/5.53 tff('2381', plain, ~ (op1(e12, e12) = e11) | ~ (e13 = op1(e12, e12)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['967', '968'])). 5.30/5.53 tff('2382', plain, 5.30/5.53 (e11 = op1(e12, e11)) | (op1(e12, e12) = e11) | (op1(e12, e13) = e11) | 5.30/5.53 (op1(e12, e10) = e11), inference('split', [status(esa)], ['975'])). 5.30/5.53 tff('2383', plain, 5.30/5.53 (e11 = op1(e12, e11)) | (e11 = op1(e11, e11)) | (op1(e13, e11) = e11) | 5.30/5.53 (e11 = op1(e10, e11)), inference('split', [status(esa)], ['1046'])). 5.30/5.53 tff('2384', plain, 5.30/5.53 ~ (op1(e11, op1(e11, e13)) = e11) | ~ (op1(e11, e13) = e10) | 5.30/5.53 ~ (op1(e11, e12) = e11), inference('simplify', [status(thm)], ['1055'])). 5.30/5.53 tff('2385', plain, 5.30/5.53 (e11 = op1(e12, e11)) | (e13 = op1(e12, e11)) | (e12 = op1(e12, e11)) | 5.30/5.53 (op1(e12, e11) = e10), inference('split', [status(esa)], ['480'])). 5.30/5.53 tff('2386', plain, 5.30/5.53 (op1(e11, e12) = e11) | (e11 = op1(e11, e11)) | (op1(e11, e13) = e11) | 5.30/5.53 (e11 = op1(e11, e10)), inference('split', [status(esa)], ['1098'])). 5.30/5.53 tff('2387', plain, ~ (op1(e13, e10) = e13) | ~ (op1(e11, e10) = e13), 5.30/5.53 inference('simplify', [status(thm)], ['1130'])). 5.30/5.53 tff('2388', plain, 5.30/5.53 (op1(e11, e11) = e13) | (e11 = op1(e11, e11)) | (e10 = op1(e11, e11)) | 5.30/5.53 (e12 = op1(e11, e11)), inference('split', [status(esa)], ['64'])). 5.30/5.53 tff('2389', plain, ~ (e13 = op1(e13, e11)) | ~ (op1(e11, e11) = e13), 5.30/5.53 inference('simplify', [status(thm)], ['1159'])). 5.30/5.53 tff('2390', plain, 5.30/5.53 ~ (e10 = op1(e11, e11)) | ~ (op1(e11, op1(e11, e11)) = e11) | 5.30/5.53 ~ (op1(e11, e12) = e11), inference('simplify', [status(thm)], ['1167'])). 5.30/5.53 tff('2391', plain, 5.30/5.53 (op1(e11, e12) = e11) | (e10 = op1(e11, e12)) | (e12 = op1(e11, e12)) | 5.30/5.53 (e13 = op1(e11, e12)), inference('split', [status(esa)], ['548'])). 5.30/5.53 tff('2392', plain, 5.30/5.53 (e10 = op1(e11, e10)) | (op1(e11, e10) = e13) | (e12 = op1(e11, e10)) | 5.30/5.53 (e11 = op1(e11, e10)), inference('split', [status(esa)], ['333'])). 5.30/5.53 tff('2393', plain, 5.30/5.53 (e10 = op1(e13, e10)) | (op1(e13, e10) = e13) | (op1(e13, e10) = e12), 5.30/5.53 inference('split', [status(esa)], ['23'])). 5.30/5.53 tff('2394', plain, (op1(e11, e12) = e11) | ~ ( zip_tseitin_3), 5.30/5.53 inference('split', [status(esa)], ['1307'])). 5.30/5.53 tff('2395', plain, ~ (e12 = op1(e11, e12)) | ~ (e10 = op1(e11, e12)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1338', '1339'])). 5.30/5.53 tff('2396', plain, ~ (e12 = op1(e11, e12)) | ~ (op1(e11, e12) = e11), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['1343', '1344'])). 5.30/5.53 tff('2397', plain, ~ (op1(e13, e10) = e13) | ~ (e13 = op1(e13, e12)), 5.30/5.53 inference('simplify', [status(thm)], ['714'])). 5.30/5.53 tff('2398', plain, ~ (e11 = op1(e11, e10)) | ~ (op1(e11, e12) = e11), 5.30/5.53 inference('simplify', [status(thm)], ['780'])). 5.30/5.53 tff('2399', plain, 5.30/5.53 (op1(e11, e12) = e11) | (op1(e12, e12) = e11) | (e11 = op1(e13, e12)) | 5.30/5.53 (e11 = op1(e10, e12)), inference('split', [status(esa)], ['786'])). 5.30/5.53 tff('2400', plain, 5.30/5.53 (e10 = op1(e10, e11) 5.30/5.53 | op1(e13, e11) = e10 5.30/5.53 | e10 = op1(e12, e11) 5.30/5.53 | op1(e11, e11) = e10), 5.30/5.53 inference('cnf', [status(esa)], [ax2])). 5.30/5.53 tff('2401', plain, 5.30/5.53 (op1(e10, e11) = e10) | (e10 = op1(e11, e11)) | (e10 = op1(e13, e11)) | 5.30/5.53 (op1(e12, e11) = e10), inference('split', [status(esa)], ['2400'])). 5.30/5.53 tff('2402', plain, (op1(e12, e11) = e10) <= ((op1(e12, e11) = e10)), 5.30/5.53 inference('split', [status(esa)], ['525'])). 5.30/5.53 tff('2403', plain, (op1(e12, e13) = e10) <= ((op1(e12, e13) = e10)), 5.30/5.53 inference('split', [status(esa)], ['51'])). 5.30/5.53 tff('2404', plain, op1(e12, e13) != op1(e12, e11), 5.30/5.53 inference('cnf', [status(esa)], [ax5])). 5.30/5.53 tff('2405', plain, (e10 != op1(e12, e11)) <= ((op1(e12, e13) = e10)), 5.30/5.53 inference('sup-', [status(thm)], ['2403', '2404'])). 5.30/5.53 tff('2406', plain, 5.30/5.53 (e10 != e10) <= ((op1(e12, e11) = e10) & (op1(e12, e13) = e10)), 5.30/5.53 inference('sup-', [status(thm)], ['2402', '2405'])). 5.30/5.53 tff('2407', plain, ~ (op1(e12, e11) = e10) | ~ (op1(e12, e13) = e10), 5.30/5.53 inference('simplify', [status(thm)], ['2406'])). 5.30/5.53 tff('2408', plain, (op1(e10, e10) != e10 | ~ zip_tseitin_12), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_8])). 5.30/5.53 tff('2409', plain, ~ (e10 = op1(e10, e10)) | ~ ( zip_tseitin_12), 5.30/5.53 inference('split', [status(esa)], ['2408'])). 5.30/5.53 tff('2410', plain, (e10 != op1(e11, e11) | ~ zip_tseitin_12), 5.30/5.53 inference('cnf', [status(esa)], [zf_stmt_8])). 5.30/5.53 tff('2411', plain, ~ (e10 = op1(e11, e11)) | ~ ( zip_tseitin_12), 5.30/5.53 inference('split', [status(esa)], ['2410'])). 5.30/5.53 tff('2412', plain, (e13 = op1(e12, e12)) <= ((e13 = op1(e12, e12))), 5.30/5.53 inference('split', [status(esa)], ['44'])). 5.30/5.53 tff('2413', plain, 5.30/5.53 (op1(e13, e12) = e13) 5.30/5.53 <= ((op1(e13, e11) = e12) & (op1(e13, op1(e13, e11)) = e13)), 5.30/5.53 inference('sup+', [status(thm)], ['15', '17'])). 5.30/5.53 tff('2414', plain, op1(e12, e12) != op1(e13, e12), 5.30/5.53 inference('cnf', [status(esa)], [ax5])). 5.30/5.53 tff('2415', plain, 5.30/5.53 (op1(e12, e12) != e13) 5.30/5.53 <= ((op1(e13, e11) = e12) & (op1(e13, op1(e13, e11)) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['2413', '2414'])). 5.30/5.53 tff('2416', plain, 5.30/5.53 (e13 != e13) 5.30/5.53 <= ((e13 = op1(e12, e12)) & 5.30/5.53 (op1(e13, e11) = e12) & 5.30/5.53 (op1(e13, op1(e13, e11)) = e13)), 5.30/5.53 inference('sup-', [status(thm)], ['2412', '2415'])). 5.30/5.53 tff('2417', plain, 5.30/5.53 ~ (op1(e13, op1(e13, e11)) = e13) | ~ (e13 = op1(e12, e12)) | 5.30/5.53 ~ (op1(e13, e11) = e12), inference('simplify', [status(thm)], ['2416'])). 5.30/5.53 tff('2418', plain, 5.30/5.53 ( zip_tseitin_3) | ( zip_tseitin_12) | ( zip_tseitin_8) | 5.30/5.53 ( zip_tseitin_15) | ( zip_tseitin_5) | ( zip_tseitin_11) | 5.30/5.53 ( zip_tseitin_0) | ( zip_tseitin_7) | ( zip_tseitin_4) | 5.30/5.53 ( zip_tseitin_10) | ( zip_tseitin_2) | ( zip_tseitin_6) | 5.30/5.53 ( zip_tseitin_14) | ( zip_tseitin_13) | ( zip_tseitin_1) | 5.30/5.53 ( zip_tseitin_9), inference('split', [status(esa)], ['728'])). 5.30/5.53 tff('2419', plain, (e11 = op1(e12, e11)) | ~ ( zip_tseitin_3), 5.30/5.53 inference('split', [status(esa)], ['1181'])). 5.30/5.53 tff('2420', plain, (e11 = op1(e12, e11)) <= ((e11 = op1(e12, e11))), 5.30/5.53 inference('split', [status(esa)], ['0'])). 5.30/5.53 tff('2421', plain, (e13 = op1(e12, e11)) <= ((e13 = op1(e12, e11))), 5.30/5.53 inference('split', [status(esa)], ['480'])). 5.30/5.53 tff('2422', plain, 5.30/5.53 (e13 = e11) <= ((e13 = op1(e12, e11)) & (e11 = op1(e12, e11))), 5.30/5.53 inference('sup+', [status(thm)], ['2420', '2421'])). 5.30/5.53 tff('2423', plain, e11 != e13, inference('cnf', [status(esa)], [ax7])). 5.30/5.53 tff('2424', plain, ~ (e13 = op1(e12, e11)) | ~ (e11 = op1(e12, e11)), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2422', '2423'])). 5.30/5.53 tff('2425', plain, 5.30/5.53 (e13 = op1(e10, e11) 5.30/5.53 | op1(e11, e11) = e13 5.30/5.53 | e13 = op1(e13, e11) 5.30/5.53 | op1(e12, e11) = e13), 5.30/5.53 inference('cnf', [status(esa)], [ax2])). 5.30/5.53 tff('2426', plain, 5.30/5.53 (op1(e11, e11) = e13) | (e13 = op1(e12, e11)) | (e13 = op1(e13, e11)) | 5.30/5.53 (e13 = op1(e10, e11)), inference('split', [status(esa)], ['2425'])). 5.30/5.53 tff('2427', plain, (op1(e11, e11) = e13) <= ((op1(e11, e11) = e13)), 5.30/5.53 inference('split', [status(esa)], ['519'])). 5.30/5.53 tff('2428', plain, 5.30/5.53 (op1(e11, op1(e11, e11)) = e11) <= ((op1(e11, op1(e11, e11)) = e11)), 5.30/5.53 inference('split', [status(esa)], ['354'])). 5.30/5.53 tff('2429', plain, 5.30/5.53 (op1(e11, e13) = e11) 5.30/5.53 <= ((op1(e11, e11) = e13) & (op1(e11, op1(e11, e11)) = e11)), 5.30/5.53 inference('sup+', [status(thm)], ['2427', '2428'])). 5.30/5.53 tff('2430', plain, op1(e11, e13) != e11, 5.30/5.53 inference('demod', [status(thm)], ['506', '507'])). 5.30/5.53 tff('2431', plain, 5.30/5.53 ~ (op1(e11, op1(e11, e11)) = e11) | ~ (op1(e11, e11) = e13), 5.30/5.53 inference('simplify_reflect-', [status(thm)], ['2429', '2430'])). 5.30/5.53 tff('2432', plain, 5.30/5.53 (op1(e11, op1(e11, e11)) = e11) | (op1(e13, op1(e13, e11)) = e13) | 5.30/5.53 (e12 = op1(e12, op1(e12, e11))) | (e10 = op1(e10, op1(e10, e11))), 5.30/5.53 inference('split', [status(esa)], ['354'])). 5.30/5.53 tff('2433', plain, $false, 5.30/5.53 inference('sat_resolution*', [status(thm)], 5.30/5.53 ['7', '9', '28', '30', '36', '41', '43', '45', '56', '63', 5.30/5.53 '70', '79', '85', '87', '89', '91', '100', '104', '120', 5.30/5.53 '135', '141', '149', '150', '161', '174', '176', '178', 5.30/5.53 '185', '187', '196', '198', '216', '234', '264', '1443', 5.30/5.53 '1889', '1918', '1945', '1976', '2012', '2036', '2046', 5.30/5.53 '2051', '2052', '2054', '2060', '2064', '2070', '2081', 5.30/5.53 '2086', '2091', '2092', '2094', '2107', '2112', '2119', 5.30/5.53 '2147', '2185', '2213', '2238', '2243', '2248', '2250', 5.30/5.53 '2252', '2254', '2255', '2261', '2177', '2178', '2269', 5.30/5.53 '1453', '2270', '1462', '1463', '1467', '1471', '1521', 5.30/5.53 '1523', '1528', '1547', '1549', '1563', '1574', '1579', 5.30/5.53 '1581', '1590', '1612', '2271', '1618', '1624', '1628', 5.30/5.53 '1634', '1636', '1645', '1860', '1783', '1791', '1804', 5.30/5.53 '1816', '1818', '1838', '1839', '1846', '1852', '1857', 5.30/5.53 '1638', '1473', '1475', '1477', '1479', '1481', '1483', 5.30/5.53 '1485', '1487', '1489', '1491', '1493', '1495', '1591', 5.30/5.53 '1598', '1497', '1650', '1655', '1657', '1663', '1690', 5.30/5.53 '1825', '1668', '2272', '1796', '1695', '1700', '1705', 5.30/5.53 '1707', '1714', '1721', '1731', '1736', '1741', '1746', 5.30/5.53 '1751', '1756', '1761', '1823', '1762', '1770', '1775', 5.30/5.53 '1678', '1683', '1688', '1505', '1507', '1830', '1511', 5.30/5.53 '1726', '1712', '1719', '1513', '1515', '1517', '1519', 5.30/5.53 '1859', '1509', '1503', '1588', '2278', '2282', '2288', 5.30/5.53 '2294', '1606', '2330', '2335', '2340', '2346', '2350', 5.30/5.53 '2355', '2362', '2370', '1969', '284', '290', '292', '301', 5.30/5.53 '2371', '315', '2372', '332', '343', '349', '359', '365', 5.30/5.53 '2373', '373', '2374', '2375', '394', '399', '407', '413', 5.30/5.53 '415', '423', '425', '434', '441', '448', '462', '467', 5.30/5.53 '475', '477', '487', '2376', '504', '515', '2377', '2378', 5.30/5.53 '533', '534', '547', '553', '2379', '562', '568', '573', 5.30/5.53 '574', '580', '581', '589', '595', '597', '601', '606', 5.30/5.53 '612', '618', '627', '633', '634', '642', '644', '2380', 5.30/5.53 '932', '938', '943', '949', '954', '959', '964', '2381', 5.30/5.53 '974', '2382', '980', '986', '992', '998', '1004', '1010', 5.30/5.53 '1015', '1021', '1027', '1033', '1039', '1045', '2383', 5.30/5.53 '1050', '2384', '1063', '1064', '1071', '1077', '1082', 5.30/5.53 '1086', '1091', '2385', '1097', '2386', '1102', '1104', 5.30/5.53 '1107', '1113', '1119', '1125', '2387', '1132', '1139', 5.30/5.53 '1146', '2388', '1154', '2389', '2390', '1175', '1180', 5.30/5.53 '1184', '1187', '1193', '1199', '1204', '1209', '2391', 5.30/5.53 '1212', '1220', '1226', '1231', '1237', '1242', '1248', 5.30/5.53 '1254', '1261', '1265', '2392', '1271', '1276', '1281', 5.30/5.53 '1286', '1288', '1290', '1297', '2393', '1304', '2394', 5.30/5.53 '1313', '1318', '1323', '1328', '1335', '2395', '2396', 5.30/5.53 '1347', '1349', '658', '660', '1351', '674', '679', '1352', 5.30/5.53 '1353', '1354', '693', '699', '706', '711', '2397', '1355', 5.30/5.53 '723', '1356', '727', '777', '2398', '1360', '1361', '2399', 5.30/5.53 '1363', '1364', '1365', '1366', '807', '1367', '1368', 5.30/5.53 '1369', '816', '1371', '1372', '1373', '832', '1374', '1375', 5.30/5.53 '842', '857', '1378', '868', '874', '1381', '1382', '1383', 5.30/5.53 '1384', '898', '1386', '910', '1387', '922', '1388', '1389', 5.30/5.53 '1390', '1391', '1397', '1401', '1407', '1415', '849', 5.30/5.53 '1421', '2007', '1066', '540', '2401', '289', '2002', '1420', 5.30/5.53 '1376', '2407', '2409', '2411', '2417', '668', '2418', '735', 5.30/5.53 '741', '743', '745', '751', '753', '1359', '762', '767', 5.30/5.53 '769', '771', '450', '456', '1385', '1306', '2419', '2424', 5.30/5.53 '2426', '2431', '2432'])). 5.30/5.53 5.30/5.53 % SZS output end Refutation 5.30/5.53 5.30/5.54 % Zipperpin 1.5 exiting 5.30/5.54 EOF