TSTP Solution File: GRP273-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP273-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sXTsSHPdKY true
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:59 EDT 2023
% Result : Timeout 288.08s 41.97s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP273-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.sXTsSHPdKY true
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 20:15:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.64 % Total configuration time : 435
% 0.22/0.64 % Estimated wc time : 1092
% 0.22/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 288.08/41.97 % Solved by fo/fo1_av.sh.
% 288.08/41.97 % done 23777 iterations in 41.168s
% 288.08/41.97 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 288.08/41.97 % SZS output start Refutation
% 288.08/41.97 thf(sk_c5_type, type, sk_c5: $i).
% 288.08/41.97 thf(sk_c10_type, type, sk_c10: $i).
% 288.08/41.97 thf(sk_c7_type, type, sk_c7: $i).
% 288.08/41.97 thf(sk_c9_type, type, sk_c9: $i).
% 288.08/41.97 thf(sk_c4_type, type, sk_c4: $i).
% 288.08/41.97 thf(identity_type, type, identity: $i).
% 288.08/41.97 thf(multiply_type, type, multiply: $i > $i > $i).
% 288.08/41.97 thf(sk_c11_type, type, sk_c11: $i).
% 288.08/41.97 thf(sk_c2_type, type, sk_c2: $i).
% 288.08/41.97 thf(inverse_type, type, inverse: $i > $i).
% 288.08/41.97 thf(sk_c3_type, type, sk_c3: $i).
% 288.08/41.97 thf(sk_c6_type, type, sk_c6: $i).
% 288.08/41.97 thf(sk_c8_type, type, sk_c8: $i).
% 288.08/41.97 thf(sk_c1_type, type, sk_c1: $i).
% 288.08/41.97 thf(prove_this_41, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.97 thf(zf_stmt_0, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 288.08/41.97 thf(zip_derived_cl43, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 288.08/41.97 | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_0])).
% 288.08/41.97 thf('0', plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.97 thf(prove_this_50, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.97 thf(zf_stmt_1, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_50])).
% 288.08/41.97 thf(zip_derived_cl52, plain,
% 288.08/41.97 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_1])).
% 288.08/41.97 thf('1', plain,
% 288.08/41.97 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl52])).
% 288.08/41.97 thf(prove_this_47, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.97 thf(zf_stmt_2, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_47])).
% 288.08/41.97 thf(zip_derived_cl49, plain,
% 288.08/41.97 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))
% 288.08/41.97 | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_2])).
% 288.08/41.97 thf('2', plain,
% 288.08/41.97 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl49])).
% 288.08/41.97 thf(prove_this_48, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.97 thf(zf_stmt_3, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_48])).
% 288.08/41.97 thf(zip_derived_cl50, plain,
% 288.08/41.97 ((((inverse @ sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_3])).
% 288.08/41.97 thf('3', plain,
% 288.08/41.97 ((((inverse @ sk_c7) = (sk_c6))) | (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl50])).
% 288.08/41.97 thf(prove_this_4, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_4, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 288.08/41.97 thf(zip_derived_cl6, plain,
% 288.08/41.97 ((((inverse @ sk_c4) = (sk_c10))
% 288.08/41.97 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_4])).
% 288.08/41.97 thf('4', plain,
% 288.08/41.97 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.97 (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl6])).
% 288.08/41.97 thf(prove_this_14, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_5, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 288.08/41.97 thf(zip_derived_cl16, plain,
% 288.08/41.97 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_5])).
% 288.08/41.97 thf('5', plain,
% 288.08/41.97 ((((inverse @ sk_c1) = (sk_c11))) | (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl16])).
% 288.08/41.97 thf(prove_this_24, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_6, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 288.08/41.97 thf(zip_derived_cl26, plain,
% 288.08/41.97 ((((inverse @ sk_c4) = (sk_c10))
% 288.08/41.97 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_6])).
% 288.08/41.97 thf('6', plain,
% 288.08/41.97 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.97 (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl26])).
% 288.08/41.97 thf(prove_this_1, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_7, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 288.08/41.97 thf(zip_derived_cl3, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 288.08/41.97 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_7])).
% 288.08/41.97 thf(zip_derived_cl55, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.97 thf(prove_this_2, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_8, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 288.08/41.97 thf(zip_derived_cl4, plain,
% 288.08/41.97 ((((inverse @ sk_c3) = (sk_c11))
% 288.08/41.97 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_8])).
% 288.08/41.97 thf(zip_derived_cl56, plain,
% 288.08/41.97 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl4])).
% 288.08/41.97 thf(prove_this_51, conjecture,
% 288.08/41.97 (~( ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 288.08/41.97 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 288.08/41.97 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( inverse @ X5 ) != ( X6 ) ) |
% 288.08/41.97 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 288.08/41.97 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 288.08/41.97 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c11 @ sk_c9 ) != ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_9, negated_conjecture,
% 288.08/41.97 (( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 288.08/41.97 ( ( inverse @ X7 ) != ( X8 ) ) |
% 288.08/41.97 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( inverse @ X5 ) != ( X6 ) ) |
% 288.08/41.97 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 288.08/41.97 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 288.08/41.97 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c11 @ sk_c9 ) != ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 288.08/41.97 thf(zip_derived_cl53, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 288.08/41.97 (((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X0) != (X2))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11))
% 288.08/41.97 | ((inverse @ X4) != (sk_c10))
% 288.08/41.97 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 288.08/41.97 | ((inverse @ X5) != (sk_c11))
% 288.08/41.97 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 288.08/41.97 | ((inverse @ X6) != (sk_c9))
% 288.08/41.97 | ((multiply @ X6 @ sk_c9) != (sk_c11))
% 288.08/41.97 | ((multiply @ sk_c11 @ sk_c9) != (sk_c10))
% 288.08/41.97 | ((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_9])).
% 288.08/41.97 thf(zip_derived_cl154, plain,
% 288.08/41.97 ((![X7 : $i]:
% 288.08/41.97 (((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 288.08/41.97 <= ((![X7 : $i]:
% 288.08/41.97 (((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.97 thf(zip_derived_cl160, plain,
% 288.08/41.97 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c3 @ sk_c11) != (sk_c10))))
% 288.08/41.97 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.97 (![X7 : $i]:
% 288.08/41.97 (((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl154])).
% 288.08/41.97 thf(zip_derived_cl164, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 288.08/41.97 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.97 (![X7 : $i]:
% 288.08/41.97 (((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.97 inference('simplify', [status(thm)], [zip_derived_cl160])).
% 288.08/41.97 thf(zip_derived_cl224, plain,
% 288.08/41.97 ((((sk_c10) != (sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.97 (![X7 : $i]:
% 288.08/41.97 (((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl164])).
% 288.08/41.97 thf('7', plain,
% 288.08/41.97 (~
% 288.08/41.97 (![X7 : $i]:
% 288.08/41.97 (((inverse @ X7) != (sk_c11))
% 288.08/41.97 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 288.08/41.97 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 288.08/41.97 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.97 inference('simplify', [status(thm)], [zip_derived_cl224])).
% 288.08/41.97 thf(prove_this_5, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_10, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 288.08/41.97 thf(zip_derived_cl7, plain,
% 288.08/41.97 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 288.08/41.97 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_10])).
% 288.08/41.97 thf(zip_derived_cl62, plain,
% 288.08/41.97 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl7])).
% 288.08/41.97 thf(prove_this_6, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_11, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 288.08/41.97 thf(zip_derived_cl8, plain,
% 288.08/41.97 ((((inverse @ sk_c5) = (sk_c8))
% 288.08/41.97 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_11])).
% 288.08/41.97 thf(zip_derived_cl64, plain,
% 288.08/41.97 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl8])).
% 288.08/41.97 thf(zip_derived_cl62, plain,
% 288.08/41.97 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl7])).
% 288.08/41.97 thf(zip_derived_cl158, plain,
% 288.08/41.97 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.97 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.97 thf(zip_derived_cl291, plain,
% 288.08/41.97 ((![X0 : $i, X1 : $i]:
% 288.08/41.97 (((inverse @ X0) != (sk_c8))
% 288.08/41.97 | ((sk_c11) != (X0))
% 288.08/41.97 | ((inverse @ sk_c5) != (X0))
% 288.08/41.97 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X1) != (sk_c8))
% 288.08/41.97 | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 288.08/41.97 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl158])).
% 288.08/41.97 thf(zip_derived_cl416, plain,
% 288.08/41.97 ((![X1 : $i]:
% 288.08/41.97 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 288.08/41.97 <= ((![X1 : $i]:
% 288.08/41.97 (((inverse @ X1) != (sk_c8))
% 288.08/41.97 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl291])).
% 288.08/41.97 thf(zip_derived_cl422, plain,
% 288.08/41.97 (((((sk_c8) != (sk_c8)) | ((multiply @ sk_c5 @ sk_c8) != (sk_c11))))
% 288.08/41.97 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.97 (![X1 : $i]:
% 288.08/41.97 (((inverse @ X1) != (sk_c8))
% 288.08/41.97 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl416])).
% 288.08/41.97 thf(zip_derived_cl426, plain,
% 288.08/41.97 ((((multiply @ sk_c5 @ sk_c8) != (sk_c11)))
% 288.08/41.97 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.97 (![X1 : $i]:
% 288.08/41.97 (((inverse @ X1) != (sk_c8))
% 288.08/41.97 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 288.08/41.97 inference('simplify', [status(thm)], [zip_derived_cl422])).
% 288.08/41.97 thf(zip_derived_cl428, plain,
% 288.08/41.97 ((((sk_c11) != (sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.97 (![X1 : $i]:
% 288.08/41.97 (((inverse @ X1) != (sk_c8))
% 288.08/41.97 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl426])).
% 288.08/41.97 thf('8', plain,
% 288.08/41.97 (~
% 288.08/41.97 (![X1 : $i]:
% 288.08/41.97 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11)))) |
% 288.08/41.97 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 288.08/41.97 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 288.08/41.97 inference('simplify', [status(thm)], [zip_derived_cl428])).
% 288.08/41.97 thf(prove_this_31, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_12, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 288.08/41.97 thf(zip_derived_cl33, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 288.08/41.97 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_12])).
% 288.08/41.97 thf('9', plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl33])).
% 288.08/41.97 thf(prove_this_32, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_13, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 288.08/41.97 thf(zip_derived_cl34, plain,
% 288.08/41.97 ((((inverse @ sk_c3) = (sk_c11))
% 288.08/41.97 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_13])).
% 288.08/41.97 thf('10', plain,
% 288.08/41.97 ((((inverse @ sk_c3) = (sk_c11))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl34])).
% 288.08/41.97 thf(prove_this_33, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_14, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 288.08/41.97 thf(zip_derived_cl35, plain,
% 288.08/41.97 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 288.08/41.97 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_14])).
% 288.08/41.97 thf('11', plain,
% 288.08/41.97 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl35])).
% 288.08/41.97 thf(prove_this_37, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_15, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 288.08/41.97 thf(zip_derived_cl39, plain,
% 288.08/41.97 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))
% 288.08/41.97 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_15])).
% 288.08/41.97 thf('12', plain,
% 288.08/41.97 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl39])).
% 288.08/41.97 thf(prove_this_38, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_16, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_38])).
% 288.08/41.97 thf(zip_derived_cl40, plain,
% 288.08/41.97 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_16])).
% 288.08/41.97 thf('13', plain,
% 288.08/41.97 ((((inverse @ sk_c7) = (sk_c6))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl40])).
% 288.08/41.97 thf(prove_this_39, conjecture,
% 288.08/41.97 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_17, negated_conjecture,
% 288.08/41.97 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_39])).
% 288.08/41.97 thf(zip_derived_cl41, plain,
% 288.08/41.97 ((((inverse @ sk_c6) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_17])).
% 288.08/41.97 thf('14', plain,
% 288.08/41.97 ((((inverse @ sk_c6) = (sk_c8))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl41])).
% 288.08/41.97 thf(prove_this_40, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_18, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_40])).
% 288.08/41.97 thf(zip_derived_cl42, plain,
% 288.08/41.97 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 288.08/41.97 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_18])).
% 288.08/41.97 thf('15', plain,
% 288.08/41.97 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl42])).
% 288.08/41.97 thf(zip_derived_cl54, plain,
% 288.08/41.97 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.97 thf(prove_this_11, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 288.08/41.97 thf(zf_stmt_19, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 288.08/41.97 thf(zip_derived_cl13, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 288.08/41.97 | ((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_19])).
% 288.08/41.97 thf(zip_derived_cl74, plain,
% 288.08/41.97 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl13])).
% 288.08/41.97 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 288.08/41.97 thf(zip_derived_cl1, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.97 thf(zip_derived_cl183, plain,
% 288.08/41.97 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 288.08/41.97 thf(associativity, axiom,
% 288.08/41.97 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 288.08/41.97 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 288.08/41.97 thf(zip_derived_cl2, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.97 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.97 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.97 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.97 thf(zip_derived_cl451, plain,
% 288.08/41.97 ((![X0 : $i]:
% 288.08/41.97 ((multiply @ identity @ X0)
% 288.08/41.97 = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl2])).
% 288.08/41.97 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl452, plain,
% 288.08/41.97 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl451, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl480, plain,
% 288.08/41.97 ((((sk_c11) = (multiply @ sk_c11 @ sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl452])).
% 288.08/41.97 thf(zip_derived_cl1, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.97 thf(zip_derived_cl2, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.97 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.97 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.97 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.97 thf(zip_derived_cl200, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i]:
% 288.08/41.97 ((multiply @ identity @ X0)
% 288.08/41.97 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl202, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i]:
% 288.08/41.97 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl543, plain,
% 288.08/41.97 ((((sk_c10) = (multiply @ (inverse @ sk_c11) @ sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl480, zip_derived_cl202])).
% 288.08/41.97 thf(zip_derived_cl1, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.97 thf(zip_derived_cl567, plain,
% 288.08/41.97 ((((sk_c10) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl543, zip_derived_cl1])).
% 288.08/41.97 thf(prove_this_21, conjecture,
% 288.08/41.97 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 288.08/41.97 thf(zf_stmt_20, negated_conjecture,
% 288.08/41.97 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 288.08/41.97 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) )),
% 288.08/41.97 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 288.08/41.97 thf(zip_derived_cl23, plain,
% 288.08/41.97 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 288.08/41.97 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.97 inference('cnf', [status(esa)], [zf_stmt_20])).
% 288.08/41.97 thf(zip_derived_cl94, plain,
% 288.08/41.97 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl23])).
% 288.08/41.97 thf(zip_derived_cl202, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i]:
% 288.08/41.97 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl545, plain,
% 288.08/41.97 ((((sk_c9) = (multiply @ (inverse @ sk_c11) @ sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl202])).
% 288.08/41.97 thf(zip_derived_cl706, plain,
% 288.08/41.97 ((((sk_c9) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl567, zip_derived_cl545])).
% 288.08/41.97 thf(zip_derived_cl183, plain,
% 288.08/41.97 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 288.08/41.97 thf(zip_derived_cl202, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i]:
% 288.08/41.97 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl542, plain,
% 288.08/41.97 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl202])).
% 288.08/41.97 thf(zip_derived_cl714, plain,
% 288.08/41.97 ((((sk_c9) = (sk_c1)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl542])).
% 288.08/41.97 thf(zip_derived_cl114, plain,
% 288.08/41.97 ((((multiply @ sk_c2 @ sk_c9) = (sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl33])).
% 288.08/41.97 thf(zip_derived_cl815, plain,
% 288.08/41.97 ((((multiply @ sk_c2 @ sk_c1) = (sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl714, zip_derived_cl114])).
% 288.08/41.97 thf(zip_derived_cl134, plain,
% 288.08/41.97 ((((inverse @ sk_c2) = (sk_c9))) <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.97 thf(zip_derived_cl1, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.97 thf(zip_derived_cl269, plain,
% 288.08/41.97 ((((multiply @ sk_c9 @ sk_c2) = (identity)))
% 288.08/41.97 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl1])).
% 288.08/41.97 thf(zip_derived_cl2, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.97 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.97 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.97 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.97 thf(zip_derived_cl476, plain,
% 288.08/41.97 ((![X0 : $i]:
% 288.08/41.97 ((multiply @ identity @ X0)
% 288.08/41.97 = (multiply @ sk_c9 @ (multiply @ sk_c2 @ X0))))
% 288.08/41.97 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl269, zip_derived_cl2])).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl477, plain,
% 288.08/41.97 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c2 @ X0))))
% 288.08/41.97 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl476, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl1085, plain,
% 288.08/41.97 ((((sk_c1) = (multiply @ sk_c9 @ sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl815, zip_derived_cl477])).
% 288.08/41.97 thf(zip_derived_cl714, plain,
% 288.08/41.97 ((((sk_c9) = (sk_c1)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl542])).
% 288.08/41.97 thf(zip_derived_cl452, plain,
% 288.08/41.97 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl451, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl202, plain,
% 288.08/41.97 (![X0 : $i, X1 : $i]:
% 288.08/41.97 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.97 thf(zip_derived_cl540, plain,
% 288.08/41.97 ((![X0 : $i]:
% 288.08/41.97 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl452, zip_derived_cl202])).
% 288.08/41.97 thf(zip_derived_cl1, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.97 thf(zip_derived_cl868, plain,
% 288.08/41.97 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 288.08/41.97 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl540, zip_derived_cl1])).
% 288.08/41.97 thf(zip_derived_cl1090, plain,
% 288.08/41.97 ((((sk_c1) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)],
% 288.08/41.97 [zip_derived_cl1085, zip_derived_cl714, zip_derived_cl868])).
% 288.08/41.97 thf(zip_derived_cl74, plain,
% 288.08/41.97 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl13])).
% 288.08/41.97 thf(zip_derived_cl1159, plain,
% 288.08/41.97 ((((inverse @ identity) = (sk_c11)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl1090, zip_derived_cl74])).
% 288.08/41.97 thf(zip_derived_cl1090, plain,
% 288.08/41.97 ((((sk_c1) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)],
% 288.08/41.97 [zip_derived_cl1085, zip_derived_cl714, zip_derived_cl868])).
% 288.08/41.97 thf(zip_derived_cl54, plain,
% 288.08/41.97 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.97 thf(zip_derived_cl1158, plain,
% 288.08/41.97 ((((multiply @ identity @ sk_c11) = (sk_c10)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('s_sup+', [status(thm)], [zip_derived_cl1090, zip_derived_cl54])).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl567, plain,
% 288.08/41.97 ((((sk_c10) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl543, zip_derived_cl1])).
% 288.08/41.97 thf(zip_derived_cl1194, plain,
% 288.08/41.97 ((((sk_c11) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)],
% 288.08/41.97 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.97 thf(zip_derived_cl25309, plain,
% 288.08/41.97 ((((inverse @ identity) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)],
% 288.08/41.97 [zip_derived_cl1159, zip_derived_cl1194])).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl158, plain,
% 288.08/41.97 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.97 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.97 thf(zip_derived_cl231, plain,
% 288.08/41.97 ((![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.97 (((inverse @ X1) != (X0))
% 288.08/41.97 | ((X0) != (X1))
% 288.08/41.97 | ((inverse @ identity) != (X1))
% 288.08/41.97 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X2) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ X0) != (sk_c11))))
% 288.08/41.97 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl158])).
% 288.08/41.97 thf(zip_derived_cl840, plain,
% 288.08/41.97 ((![X0 : $i, X1 : $i]:
% 288.08/41.97 (((multiply @ X1 @ X0) != (sk_c11))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ identity) != (X0))
% 288.08/41.97 | ((inverse @ X0) != (X0))))
% 288.08/41.97 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('eq_res', [status(thm)], [zip_derived_cl231])).
% 288.08/41.97 thf(zip_derived_cl2071, plain,
% 288.08/41.97 ((![X0 : $i]:
% 288.08/41.97 (((X0) != (sk_c11))
% 288.08/41.97 | ((inverse @ identity) != (X0))
% 288.08/41.97 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ identity) != (X0))
% 288.08/41.97 | ((inverse @ X0) != (X0))))
% 288.08/41.97 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl840])).
% 288.08/41.97 thf(zip_derived_cl2155, plain,
% 288.08/41.97 ((![X0 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X0))
% 288.08/41.97 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ identity) != (X0))
% 288.08/41.97 | ((X0) != (sk_c11))))
% 288.08/41.97 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('simplify', [status(thm)], [zip_derived_cl2071])).
% 288.08/41.97 thf(zip_derived_cl25329, plain,
% 288.08/41.97 (((((identity) != (identity))
% 288.08/41.97 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((identity) != (identity))
% 288.08/41.97 | ((identity) != (sk_c11))))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.97 | ((inverse @ X3) != (X2))
% 288.08/41.97 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.97 inference('s_sup-', [status(thm)],
% 288.08/41.97 [zip_derived_cl25309, zip_derived_cl2155])).
% 288.08/41.97 thf(zip_derived_cl567, plain,
% 288.08/41.97 ((((sk_c10) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.97 inference('demod', [status(thm)], [zip_derived_cl543, zip_derived_cl1])).
% 288.08/41.97 thf(zip_derived_cl0, plain,
% 288.08/41.97 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.97 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.97 thf(zip_derived_cl1194, plain,
% 288.08/41.97 ((((sk_c11) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)],
% 288.08/41.97 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.97 thf(zip_derived_cl1194, plain,
% 288.08/41.97 ((((sk_c11) = (identity)))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.97 inference('demod', [status(thm)],
% 288.08/41.97 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.97 thf(zip_derived_cl25686, plain,
% 288.08/41.97 (((((identity) != (identity))
% 288.08/41.97 | ((identity) != (identity))
% 288.08/41.97 | ((identity) != (identity))
% 288.08/41.97 | ((identity) != (identity))))
% 288.08/41.97 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.97 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.97 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.97 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.97 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.97 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.97 (((inverse @ X0) != (X2))
% 288.08/41.97 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.97 | ((inverse @ X1) != (X0))
% 288.08/41.97 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl25329, zip_derived_cl567, zip_derived_cl0,
% 288.08/41.98 zip_derived_cl1194, zip_derived_cl1194])).
% 288.08/41.98 thf('16', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl25686])).
% 288.08/41.98 thf('17', plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl7])).
% 288.08/41.98 thf(prove_this_15, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_21, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 288.08/41.98 thf(zip_derived_cl17, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 288.08/41.98 | ((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_21])).
% 288.08/41.98 thf('18', plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl17])).
% 288.08/41.98 thf(prove_this_25, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_22, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 288.08/41.98 thf(zip_derived_cl27, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 288.08/41.98 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_22])).
% 288.08/41.98 thf('19', plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl27])).
% 288.08/41.98 thf('20', plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl4])).
% 288.08/41.98 thf(prove_this_12, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_23, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 288.08/41.98 thf(zip_derived_cl14, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_23])).
% 288.08/41.98 thf('21', plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) | (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl14])).
% 288.08/41.98 thf(prove_this_22, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_24, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 288.08/41.98 thf(zip_derived_cl24, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11))
% 288.08/41.98 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_24])).
% 288.08/41.98 thf('22', plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl24])).
% 288.08/41.98 thf(zip_derived_cl815, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c1) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl714, zip_derived_cl114])).
% 288.08/41.98 thf(zip_derived_cl2, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.98 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl230, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 288.08/41.98 (((inverse @ X3) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ (multiply @ X1 @ X0)) != (X3))
% 288.08/41.98 | ((inverse @ (multiply @ X2 @ X1)) != (X3))
% 288.08/41.98 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X4) != (X0))
% 288.08/41.98 | ((multiply @ X4 @ X0) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl2, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl1083, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0))
% 288.08/41.98 | ((multiply @ sk_c1 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X2) != (sk_c1))
% 288.08/41.98 | ((multiply @ X2 @ sk_c1) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl230])).
% 288.08/41.98 thf(zip_derived_cl567, plain,
% 288.08/41.98 ((((sk_c10) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl543, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl542, plain,
% 288.08/41.98 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl540, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl452, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl870, plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ identity) = (sk_c1)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl542, zip_derived_cl540])).
% 288.08/41.98 thf(zip_derived_cl1088, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0))
% 288.08/41.98 | ((sk_c1) != (sk_c11))
% 288.08/41.98 | ((inverse @ X2) != (sk_c1))
% 288.08/41.98 | ((multiply @ X2 @ sk_c1) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1083, zip_derived_cl567, zip_derived_cl870])).
% 288.08/41.98 thf('23', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 288.08/41.98 ~ (((sk_c11) = (sk_c1))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c1)) | ((multiply @ X1 @ sk_c1) != (sk_c11)))) |
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl1088])).
% 288.08/41.98 thf(zip_derived_cl54, plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.98 thf(zip_derived_cl74, plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl13])).
% 288.08/41.98 thf(zip_derived_cl154, plain,
% 288.08/41.98 ((![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 288.08/41.98 <= ((![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl179, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c1 @ sk_c11) != (sk_c10))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl154])).
% 288.08/41.98 thf(zip_derived_cl180, plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) != (sk_c10)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl179])).
% 288.08/41.98 thf(zip_derived_cl213, plain,
% 288.08/41.98 ((((sk_c10) != (sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl180])).
% 288.08/41.98 thf('24', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl213])).
% 288.08/41.98 thf(zip_derived_cl64, plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl8])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl186, plain,
% 288.08/41.98 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl2, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.98 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.98 thf(zip_derived_cl467, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ identity @ X0)
% 288.08/41.98 = (multiply @ sk_c8 @ (multiply @ sk_c5 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl186, zip_derived_cl2])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl468, plain,
% 288.08/41.98 ((![X0 : $i]: ((X0) = (multiply @ sk_c8 @ (multiply @ sk_c5 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl467, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl552, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl468, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl1231, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl552, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl62, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl7])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl542, plain,
% 288.08/41.98 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl5508, plain,
% 288.08/41.98 ((((sk_c1) = (multiply @ (inverse @ identity) @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1263, zip_derived_cl542])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl536, plain,
% 288.08/41.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl5582, plain,
% 288.08/41.98 ((((sk_c1) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl5508, zip_derived_cl536])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl74, plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl13])).
% 288.08/41.98 thf(zip_derived_cl54, plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl233, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c1) != (X0))
% 288.08/41.98 | ((multiply @ sk_c11 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c11))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl237, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c1) != (X0))))
% 288.08/41.98 <= ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c1) != (X0)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl233])).
% 288.08/41.98 thf(zip_derived_cl261, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c11)) | ((sk_c10) != (sk_c1)) | ((sk_c11) != (sk_c1))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c1) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl237])).
% 288.08/41.98 thf(zip_derived_cl267, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c1)) | ((sk_c10) != (sk_c1))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c1) != (X0)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl261])).
% 288.08/41.98 thf(zip_derived_cl276, plain,
% 288.08/41.98 ((((sk_c11) != (sk_c1))) <= (~ (((sk_c11) = (sk_c1))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl267])).
% 288.08/41.98 thf(zip_derived_cl5498, plain,
% 288.08/41.98 ((((identity) != (sk_c1)))
% 288.08/41.98 <= (~ (((sk_c11) = (sk_c1))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1263, zip_derived_cl276])).
% 288.08/41.98 thf(zip_derived_cl224815, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((sk_c11) = (sk_c1))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl5582, zip_derived_cl5498])).
% 288.08/41.98 thf('25', plain,
% 288.08/41.98 ((((sk_c11) = (sk_c1))) | ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl224815])).
% 288.08/41.98 thf(zip_derived_cl25309, plain,
% 288.08/41.98 ((((inverse @ identity) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1159, zip_derived_cl1194])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl23071, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl1088])).
% 288.08/41.98 thf(zip_derived_cl23074, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ identity @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ sk_c2) != (X0))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl23071])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl23092, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ sk_c2) != (X0))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0)))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl23074, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl25438, plain,
% 288.08/41.98 (((((identity) != (sk_c1))
% 288.08/41.98 | ((sk_c11) != (identity))
% 288.08/41.98 | ((inverse @ sk_c2) != (identity))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl25309, zip_derived_cl23092])).
% 288.08/41.98 thf(zip_derived_cl1090, plain,
% 288.08/41.98 ((((sk_c1) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1085, zip_derived_cl714, zip_derived_cl868])).
% 288.08/41.98 thf(zip_derived_cl1194, plain,
% 288.08/41.98 ((((sk_c11) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.98 thf(zip_derived_cl714, plain,
% 288.08/41.98 ((((sk_c9) = (sk_c1)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl542])).
% 288.08/41.98 thf(zip_derived_cl269, plain,
% 288.08/41.98 ((((multiply @ sk_c9 @ sk_c2) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl550, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl269, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl832, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ sk_c1) @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl714, zip_derived_cl550])).
% 288.08/41.98 thf(zip_derived_cl74, plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl13])).
% 288.08/41.98 thf(zip_derived_cl839, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ sk_c11 @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl832, zip_derived_cl74])).
% 288.08/41.98 thf(zip_derived_cl868, plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl540, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl452, plain,
% 288.08/41.98 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl451, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl880, plain,
% 288.08/41.98 ((((sk_c11) = (multiply @ sk_c11 @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl868, zip_derived_cl452])).
% 288.08/41.98 thf(zip_derived_cl14438, plain,
% 288.08/41.98 ((((sk_c2) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl839, zip_derived_cl880])).
% 288.08/41.98 thf(zip_derived_cl1194, plain,
% 288.08/41.98 ((((sk_c11) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.98 thf(zip_derived_cl25309, plain,
% 288.08/41.98 ((((inverse @ identity) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1159, zip_derived_cl1194])).
% 288.08/41.98 thf(zip_derived_cl25859, plain,
% 288.08/41.98 (((((identity) != (identity))
% 288.08/41.98 | ((identity) != (identity))
% 288.08/41.98 | ((identity) != (identity))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl25438, zip_derived_cl1090, zip_derived_cl1194,
% 288.08/41.98 zip_derived_cl14438, zip_derived_cl1194, zip_derived_cl25309])).
% 288.08/41.98 thf('26', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (X0))
% 288.08/41.98 | ((inverse @ (multiply @ X1 @ sk_c2)) != (X0)))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl25859])).
% 288.08/41.98 thf(zip_derived_cl25309, plain,
% 288.08/41.98 ((((inverse @ identity) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1159, zip_derived_cl1194])).
% 288.08/41.98 thf(zip_derived_cl183, plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl450, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c1))
% 288.08/41.98 | ((identity) != (X0))
% 288.08/41.98 | ((inverse @ sk_c11) != (X0))
% 288.08/41.98 | ((multiply @ sk_c1 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c1) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl183, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl1663, plain,
% 288.08/41.98 ((![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c1)) | ((multiply @ X1 @ sk_c1) != (sk_c11))))
% 288.08/41.98 <= ((![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c1) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl450])).
% 288.08/41.98 thf(zip_derived_cl25457, plain,
% 288.08/41.98 (((((identity) != (sk_c1)) | ((multiply @ identity @ sk_c1) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c1) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl25309, zip_derived_cl1663])).
% 288.08/41.98 thf(zip_derived_cl1090, plain,
% 288.08/41.98 ((((sk_c1) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1085, zip_derived_cl714, zip_derived_cl868])).
% 288.08/41.98 thf(zip_derived_cl1090, plain,
% 288.08/41.98 ((((sk_c1) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1085, zip_derived_cl714, zip_derived_cl868])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl1194, plain,
% 288.08/41.98 ((((sk_c11) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.98 thf(zip_derived_cl25892, plain,
% 288.08/41.98 (((((identity) != (identity)) | ((identity) != (identity))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c1))
% 288.08/41.98 | ((multiply @ X1 @ sk_c1) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl25457, zip_derived_cl1090, zip_derived_cl1090,
% 288.08/41.98 zip_derived_cl0, zip_derived_cl1194])).
% 288.08/41.98 thf('27', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c1)) | ((multiply @ X1 @ sk_c1) != (sk_c11)))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl25892])).
% 288.08/41.98 thf(zip_derived_cl25309, plain,
% 288.08/41.98 ((((inverse @ identity) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1159, zip_derived_cl1194])).
% 288.08/41.98 thf(zip_derived_cl157, plain,
% 288.08/41.98 ((![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9))))
% 288.08/41.98 <= ((![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl25466, plain,
% 288.08/41.98 (((((identity) != (sk_c10)) | ((multiply @ identity @ sk_c10) != (sk_c9))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl25309, zip_derived_cl157])).
% 288.08/41.98 thf(zip_derived_cl567, plain,
% 288.08/41.98 ((((sk_c10) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl543, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl567, plain,
% 288.08/41.98 ((((sk_c10) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl543, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl714, plain,
% 288.08/41.98 ((((sk_c9) = (sk_c1)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl542])).
% 288.08/41.98 thf(zip_derived_cl1090, plain,
% 288.08/41.98 ((((sk_c1) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1085, zip_derived_cl714, zip_derived_cl868])).
% 288.08/41.98 thf(zip_derived_cl25910, plain,
% 288.08/41.98 (((((identity) != (identity)) | ((identity) != (identity))))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl25466, zip_derived_cl567, zip_derived_cl567,
% 288.08/41.98 zip_derived_cl0, zip_derived_cl714, zip_derived_cl1090])).
% 288.08/41.98 thf('28', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9)))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl25910])).
% 288.08/41.98 thf(prove_this_3, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_25, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 288.08/41.98 thf(zip_derived_cl5, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 288.08/41.98 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_25])).
% 288.08/41.98 thf('29', plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl5])).
% 288.08/41.98 thf(prove_this_13, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_26, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 288.08/41.98 thf(zip_derived_cl15, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 288.08/41.98 | ((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_26])).
% 288.08/41.98 thf('30', plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl15])).
% 288.08/41.98 thf(prove_this_23, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_27, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 288.08/41.98 thf(zip_derived_cl25, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 288.08/41.98 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_27])).
% 288.08/41.98 thf('31', plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl25])).
% 288.08/41.98 thf('32', plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl23])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl56, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl4])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl184, plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl544, plain,
% 288.08/41.98 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl184, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl5509, plain,
% 288.08/41.98 ((((sk_c3) = (multiply @ (inverse @ identity) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1263, zip_derived_cl544])).
% 288.08/41.98 thf(zip_derived_cl536, plain,
% 288.08/41.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl5583, plain,
% 288.08/41.98 ((((sk_c3) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl5509, zip_derived_cl536])).
% 288.08/41.98 thf(zip_derived_cl60, plain,
% 288.08/41.98 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl6])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl185, plain,
% 288.08/41.98 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl2, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.98 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.98 thf(zip_derived_cl457, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ identity @ X0)
% 288.08/41.98 = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl185, zip_derived_cl2])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl458, plain,
% 288.08/41.98 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl457, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl546, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl458, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl1115, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl546, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl58, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl5])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl56, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl4])).
% 288.08/41.98 thf(zip_derived_cl155, plain,
% 288.08/41.98 ((![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9)) | ((multiply @ X6 @ sk_c9) != (sk_c11))))
% 288.08/41.98 <= ((![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl165, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c9)) | ((multiply @ sk_c3 @ sk_c9) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl155])).
% 288.08/41.98 thf(zip_derived_cl193, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c9) != (sk_c11)))
% 288.08/41.98 <= (~ (((multiply @ sk_c3 @ sk_c9) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl165])).
% 288.08/41.98 thf(zip_derived_cl3843, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ identity) != (sk_c11)))
% 288.08/41.98 <= (~ (((multiply @ sk_c3 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1127, zip_derived_cl193])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl537, plain,
% 288.08/41.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl534, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl202, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl3441, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl537, zip_derived_cl534])).
% 288.08/41.98 thf(zip_derived_cl151989, plain,
% 288.08/41.98 ((((sk_c3) != (sk_c11)))
% 288.08/41.98 <= (~ (((multiply @ sk_c3 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl3843, zip_derived_cl3441])).
% 288.08/41.98 thf(zip_derived_cl225465, plain,
% 288.08/41.98 ((((identity) != (sk_c11)))
% 288.08/41.98 <= (~ (((multiply @ sk_c3 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl5583, zip_derived_cl151989])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl225762, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((multiply @ sk_c3 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl225465, zip_derived_cl1263])).
% 288.08/41.98 thf('33', plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c3) = (sk_c11))) | ~ (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl225762])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl194, plain,
% 288.08/41.98 ((((sk_c11) != (sk_c9))) <= (~ (((sk_c11) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl165])).
% 288.08/41.98 thf(zip_derived_cl3844, plain,
% 288.08/41.98 ((((sk_c11) != (identity)))
% 288.08/41.98 <= (~ (((sk_c11) = (sk_c9))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1127, zip_derived_cl194])).
% 288.08/41.98 thf(zip_derived_cl152003, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((sk_c11) = (sk_c9))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1263, zip_derived_cl3844])).
% 288.08/41.98 thf('34', plain,
% 288.08/41.98 ((((sk_c11) = (sk_c9))) | ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl152003])).
% 288.08/41.98 thf(prove_this_42, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.98 thf(zf_stmt_28, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 288.08/41.98 thf(zip_derived_cl44, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_28])).
% 288.08/41.98 thf('35', plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl44])).
% 288.08/41.98 thf(prove_this_43, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.98 thf(zf_stmt_29, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 288.08/41.98 thf(zip_derived_cl45, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_29])).
% 288.08/41.98 thf('36', plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl45])).
% 288.08/41.98 thf(prove_this_46, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.98 thf(zf_stmt_30, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 288.08/41.98 thf(zip_derived_cl48, plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_30])).
% 288.08/41.98 thf('37', plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8))) | (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl48])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl550, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl269, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl2, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.98 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.98 thf(zip_derived_cl661, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c2 @ X0)
% 288.08/41.98 = (multiply @ (inverse @ sk_c9) @ (multiply @ identity @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl550, zip_derived_cl2])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl664, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl661, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl1495, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl664, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl134, plain,
% 288.08/41.98 ((((inverse @ sk_c2) = (sk_c9))) <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.98 thf(zip_derived_cl155, plain,
% 288.08/41.98 ((![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9)) | ((multiply @ X6 @ sk_c9) != (sk_c11))))
% 288.08/41.98 <= ((![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl273, plain,
% 288.08/41.98 (((((sk_c9) != (sk_c9)) | ((multiply @ sk_c2 @ sk_c9) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl155])).
% 288.08/41.98 thf(zip_derived_cl275, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) != (sk_c11)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl273])).
% 288.08/41.98 thf(zip_derived_cl1509, plain,
% 288.08/41.98 ((((identity) != (sk_c11)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1495, zip_derived_cl275])).
% 288.08/41.98 thf(zip_derived_cl38566, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1263, zip_derived_cl1509])).
% 288.08/41.98 thf('38', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9)) | ((multiply @ X6 @ sk_c9) != (sk_c11)))) |
% 288.08/41.98 ~ (((inverse @ sk_c5) = (sk_c8))) | ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl38566])).
% 288.08/41.98 thf(prove_this_36, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_31, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 288.08/41.98 thf(zip_derived_cl38, plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_31])).
% 288.08/41.98 thf('39', plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8))) |
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl38])).
% 288.08/41.98 thf(prove_this_35, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_32, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 288.08/41.98 thf(zip_derived_cl37, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 288.08/41.98 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_32])).
% 288.08/41.98 thf('40', plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl37])).
% 288.08/41.98 thf(prove_this_45, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.98 thf(zf_stmt_33, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_45])).
% 288.08/41.98 thf(zip_derived_cl47, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_33])).
% 288.08/41.98 thf('41', plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl47])).
% 288.08/41.98 thf(prove_this_34, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_34, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 288.08/41.98 thf(zip_derived_cl36, plain,
% 288.08/41.98 ((((inverse @ sk_c4) = (sk_c10))
% 288.08/41.98 | ((multiply @ sk_c2 @ sk_c9) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_34])).
% 288.08/41.98 thf('42', plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl36])).
% 288.08/41.98 thf(prove_this_44, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.98 thf(zf_stmt_35, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 288.08/41.98 thf(zip_derived_cl46, plain,
% 288.08/41.98 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_35])).
% 288.08/41.98 thf('43', plain,
% 288.08/41.98 ((((inverse @ sk_c4) = (sk_c10))) | (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl46])).
% 288.08/41.98 thf(zip_derived_cl114, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl33])).
% 288.08/41.98 thf(zip_derived_cl275, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) != (sk_c11)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl273])).
% 288.08/41.98 thf(zip_derived_cl398, plain,
% 288.08/41.98 ((((sk_c11) != (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9))
% 288.08/41.98 | ((multiply @ X6 @ sk_c9) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl275])).
% 288.08/41.98 thf('44', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9)) | ((multiply @ X6 @ sk_c9) != (sk_c11)))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl398])).
% 288.08/41.98 thf('45', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9)) | ((multiply @ X6 @ sk_c9) != (sk_c11)))) |
% 288.08/41.98 ~ (((sk_c11) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c3 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl165])).
% 288.08/41.98 thf(zip_derived_cl664, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl661, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl550, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl269, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl1497, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ sk_c2 @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl664, zip_derived_cl550])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl235, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 (((multiply @ X1 @ X0) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 288.08/41.98 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('eq_res', [status(thm)], [zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl1519, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((multiply @ X0 @ identity) != (sk_c11))
% 288.08/41.98 | ((inverse @ X0) != (identity))
% 288.08/41.98 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ sk_c2) != (sk_c2))
% 288.08/41.98 | ((inverse @ sk_c2) != (identity))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1497, zip_derived_cl235])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl134, plain,
% 288.08/41.98 ((((inverse @ sk_c2) = (sk_c9))) <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.98 thf(zip_derived_cl134, plain,
% 288.08/41.98 ((((inverse @ sk_c2) = (sk_c9))) <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.98 thf(zip_derived_cl1525, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((multiply @ X0 @ identity) != (sk_c11))
% 288.08/41.98 | ((inverse @ X0) != (identity))
% 288.08/41.98 | ((sk_c10) != (sk_c11))
% 288.08/41.98 | ((sk_c9) != (sk_c2))
% 288.08/41.98 | ((sk_c9) != (identity))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1519, zip_derived_cl0, zip_derived_cl134,
% 288.08/41.98 zip_derived_cl134])).
% 288.08/41.98 thf('46', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 288.08/41.98 ~ (((sk_c10) = (sk_c11))) | ~ (((sk_c9) = (identity))) |
% 288.08/41.98 ~ (((sk_c9) = (sk_c2))) | ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl1525])).
% 288.08/41.98 thf(zip_derived_cl1495, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl664, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl114, plain,
% 288.08/41.98 ((((multiply @ sk_c2 @ sk_c9) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl33])).
% 288.08/41.98 thf(zip_derived_cl1508, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1495, zip_derived_cl114])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl545, plain,
% 288.08/41.98 ((((sk_c9) = (multiply @ (inverse @ sk_c11) @ sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl630, plain,
% 288.08/41.98 ((((sk_c10) = (multiply @ (inverse @ (inverse @ sk_c11)) @ sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl545, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl3862, plain,
% 288.08/41.98 ((((sk_c10) = (multiply @ (inverse @ (inverse @ sk_c11)) @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1127, zip_derived_cl630])).
% 288.08/41.98 thf(zip_derived_cl537, plain,
% 288.08/41.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl3881, plain,
% 288.08/41.98 ((((sk_c10) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl3862, zip_derived_cl537])).
% 288.08/41.98 thf(zip_derived_cl184, plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl2, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 288.08/41.98 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 288.08/41.98 inference('cnf', [status(esa)], [associativity])).
% 288.08/41.98 thf(zip_derived_cl454, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ identity @ X0)
% 288.08/41.98 = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl184, zip_derived_cl2])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl455, plain,
% 288.08/41.98 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl454, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl541, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl455, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl1, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_inverse])).
% 288.08/41.98 thf(zip_derived_cl1014, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl541, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl164, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl160])).
% 288.08/41.98 thf(zip_derived_cl1031, plain,
% 288.08/41.98 ((((identity) != (sk_c10)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1014, zip_derived_cl164])).
% 288.08/41.98 thf(zip_derived_cl4017, plain,
% 288.08/41.98 ((((identity) != (sk_c11)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl3881, zip_derived_cl1031])).
% 288.08/41.98 thf(zip_derived_cl159717, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1508, zip_derived_cl4017])).
% 288.08/41.98 thf('47', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl159717])).
% 288.08/41.98 thf(zip_derived_cl3881, plain,
% 288.08/41.98 ((((sk_c10) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl3862, zip_derived_cl537])).
% 288.08/41.98 thf(zip_derived_cl60, plain,
% 288.08/41.98 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl6])).
% 288.08/41.98 thf(zip_derived_cl154, plain,
% 288.08/41.98 ((![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 288.08/41.98 <= ((![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl161, plain,
% 288.08/41.98 (((((sk_c10) != (sk_c11)) | ((multiply @ sk_c4 @ sk_c11) != (sk_c10))))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl154])).
% 288.08/41.98 thf(zip_derived_cl182, plain,
% 288.08/41.98 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl161])).
% 288.08/41.98 thf(zip_derived_cl3977, plain,
% 288.08/41.98 ((((sk_c11) != (sk_c11)))
% 288.08/41.98 <= (~ (((sk_c10) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl3881, zip_derived_cl182])).
% 288.08/41.98 thf('48', plain,
% 288.08/41.98 ((((sk_c10) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl3977])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl550, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl269, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl3861, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ identity) @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1127, zip_derived_cl550])).
% 288.08/41.98 thf(zip_derived_cl536, plain,
% 288.08/41.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl3880, plain,
% 288.08/41.98 ((((sk_c2) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl3861, zip_derived_cl536])).
% 288.08/41.98 thf(zip_derived_cl134, plain,
% 288.08/41.98 ((((inverse @ sk_c2) = (sk_c9))) <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.98 thf(zip_derived_cl58, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl5])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl249, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c10))
% 288.08/41.98 | ((sk_c9) != (X0))
% 288.08/41.98 | ((inverse @ sk_c4) != (X0))
% 288.08/41.98 | ((multiply @ sk_c10 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c10))
% 288.08/41.98 | ((multiply @ X1 @ sk_c10) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl355, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c10))
% 288.08/41.98 | ((sk_c9) != (X0))
% 288.08/41.98 | ((inverse @ sk_c4) != (X0))))
% 288.08/41.98 <= ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c10))
% 288.08/41.98 | ((sk_c9) != (X0))
% 288.08/41.98 | ((inverse @ sk_c4) != (X0)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl249])).
% 288.08/41.98 thf(zip_derived_cl372, plain,
% 288.08/41.98 (((((sk_c9) != (sk_c10))
% 288.08/41.98 | ((sk_c9) != (sk_c2))
% 288.08/41.98 | ((inverse @ sk_c4) != (sk_c2))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c10))
% 288.08/41.98 | ((sk_c9) != (X0))
% 288.08/41.98 | ((inverse @ sk_c4) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl355])).
% 288.08/41.98 thf(zip_derived_cl413, plain,
% 288.08/41.98 ((((sk_c9) != (sk_c2))) <= (~ (((sk_c9) = (sk_c2))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl372])).
% 288.08/41.98 thf(zip_derived_cl154938, plain,
% 288.08/41.98 ((((sk_c9) != (identity)))
% 288.08/41.98 <= (~ (((sk_c9) = (sk_c2))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl3880, zip_derived_cl413])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl155126, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((sk_c9) = (sk_c2))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl154938, zip_derived_cl1127])).
% 288.08/41.98 thf('49', plain,
% 288.08/41.98 ((((sk_c9) = (sk_c2))) | ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl155126])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl550, plain,
% 288.08/41.98 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl269, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl235, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i]:
% 288.08/41.98 (((multiply @ X1 @ X0) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 288.08/41.98 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('eq_res', [status(thm)], [zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl949, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((multiply @ X0 @ identity) != (sk_c11))
% 288.08/41.98 | ((inverse @ X0) != (identity))
% 288.08/41.98 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ (inverse @ sk_c9)) != (sk_c2))
% 288.08/41.98 | ((inverse @ sk_c2) != (identity))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl550, zip_derived_cl235])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl134, plain,
% 288.08/41.98 ((((inverse @ sk_c2) = (sk_c9))) <= ((((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl43])).
% 288.08/41.98 thf(zip_derived_cl992, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((multiply @ X0 @ identity) != (sk_c11))
% 288.08/41.98 | ((inverse @ X0) != (identity))
% 288.08/41.98 | ((sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ (inverse @ sk_c9)) != (sk_c2))
% 288.08/41.98 | ((sk_c9) != (identity))))
% 288.08/41.98 <= ((((inverse @ sk_c2) = (sk_c9))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl949, zip_derived_cl0, zip_derived_cl134])).
% 288.08/41.98 thf(zip_derived_cl19615, plain,
% 288.08/41.98 ((((sk_c9) != (identity))) <= (~ (((sk_c9) = (identity))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl992])).
% 288.08/41.98 thf(zip_derived_cl19618, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((sk_c9) = (identity))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1127, zip_derived_cl19615])).
% 288.08/41.98 thf('50', plain,
% 288.08/41.98 ((((sk_c9) = (identity))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl19618])).
% 288.08/41.98 thf(zip_derived_cl58, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl5])).
% 288.08/41.98 thf(zip_derived_cl60, plain,
% 288.08/41.98 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl6])).
% 288.08/41.98 thf(zip_derived_cl157, plain,
% 288.08/41.98 ((![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9))))
% 288.08/41.98 <= ((![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl170, plain,
% 288.08/41.98 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c4 @ sk_c10) != (sk_c9))))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl157])).
% 288.08/41.98 thf(zip_derived_cl173, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) != (sk_c9)))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl170])).
% 288.08/41.98 thf(zip_derived_cl251, plain,
% 288.08/41.98 ((((sk_c9) != (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10))
% 288.08/41.98 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl173])).
% 288.08/41.98 thf('51', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9)))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl251])).
% 288.08/41.98 thf(zip_derived_cl1014, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl541, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl55, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.98 thf(zip_derived_cl1030, plain,
% 288.08/41.98 ((((identity) = (sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1014, zip_derived_cl55])).
% 288.08/41.98 thf(zip_derived_cl1127, plain,
% 288.08/41.98 ((((identity) = (sk_c9)))
% 288.08/41.98 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1115, zip_derived_cl58])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl159, plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c9) != (sk_c10)))
% 288.08/41.98 <= (~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl5480, plain,
% 288.08/41.98 ((((multiply @ identity @ sk_c9) != (sk_c10)))
% 288.08/41.98 <= (~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1263, zip_derived_cl159])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl5570, plain,
% 288.08/41.98 ((((sk_c9) != (sk_c10)))
% 288.08/41.98 <= (~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl5480, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl6563, plain,
% 288.08/41.98 ((((identity) != (sk_c10)))
% 288.08/41.98 <= (~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1127, zip_derived_cl5570])).
% 288.08/41.98 thf(zip_derived_cl266575, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 288.08/41.98 (((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1030, zip_derived_cl6563])).
% 288.08/41.98 thf('52', plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 288.08/41.98 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl266575])).
% 288.08/41.98 thf(zip_derived_cl56, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl4])).
% 288.08/41.98 thf(zip_derived_cl542, plain,
% 288.08/41.98 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl578, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (identity))
% 288.08/41.98 | ((sk_c1) != (X0))
% 288.08/41.98 | ((inverse @ (inverse @ sk_c11)) != (X0))
% 288.08/41.98 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl542, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl0, plain,
% 288.08/41.98 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 288.08/41.98 inference('cnf', [status(esa)], [left_identity])).
% 288.08/41.98 thf(zip_derived_cl581, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (identity))
% 288.08/41.98 | ((sk_c1) != (X0))
% 288.08/41.98 | ((inverse @ (inverse @ sk_c11)) != (X0))
% 288.08/41.98 | ((sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl578, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl3773, plain,
% 288.08/41.98 ((![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11))))
% 288.08/41.98 <= ((![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl581])).
% 288.08/41.98 thf(zip_derived_cl3778, plain,
% 288.08/41.98 (((((sk_c11) != (identity)) | ((multiply @ sk_c3 @ identity) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl3773])).
% 288.08/41.98 thf(zip_derived_cl544, plain,
% 288.08/41.98 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl184, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl541, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl455, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl1018, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ identity) = (sk_c3)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl544, zip_derived_cl541])).
% 288.08/41.98 thf(zip_derived_cl3786, plain,
% 288.08/41.98 (((((sk_c11) != (identity)) | ((sk_c3) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl3778, zip_derived_cl1018])).
% 288.08/41.98 thf('53', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (identity))
% 288.08/41.98 | ((multiply @ X1 @ identity) != (sk_c11)))) |
% 288.08/41.98 ~ (((sk_c11) = (sk_c3))) | ~ (((identity) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl3786])).
% 288.08/41.98 thf(zip_derived_cl5583, plain,
% 288.08/41.98 ((((sk_c3) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl5509, zip_derived_cl536])).
% 288.08/41.98 thf(zip_derived_cl56, plain,
% 288.08/41.98 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl4])).
% 288.08/41.98 thf(zip_derived_cl55, plain,
% 288.08/41.98 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 288.08/41.98 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl3])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl234, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c3) != (X0))
% 288.08/41.98 | ((multiply @ sk_c11 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c11))
% 288.08/41.98 | ((multiply @ X1 @ sk_c11) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl314, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c3) != (X0))))
% 288.08/41.98 <= ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c3) != (X0)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl234])).
% 288.08/41.98 thf(zip_derived_cl317, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c11)) | ((sk_c10) != (sk_c3)) | ((sk_c11) != (sk_c3))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c3) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl314])).
% 288.08/41.98 thf(zip_derived_cl324, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c3)) | ((sk_c10) != (sk_c3))))
% 288.08/41.98 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c11))
% 288.08/41.98 | ((sk_c10) != (X0))
% 288.08/41.98 | ((inverse @ sk_c3) != (X0)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl317])).
% 288.08/41.98 thf(zip_derived_cl325, plain,
% 288.08/41.98 ((((sk_c11) != (sk_c3))) <= (~ (((sk_c11) = (sk_c3))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl324])).
% 288.08/41.98 thf(zip_derived_cl225215, plain,
% 288.08/41.98 ((((sk_c11) != (identity)))
% 288.08/41.98 <= (~ (((sk_c11) = (sk_c3))) &
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl5583, zip_derived_cl325])).
% 288.08/41.98 thf(zip_derived_cl1263, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl62])).
% 288.08/41.98 thf(zip_derived_cl225492, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((sk_c11) = (sk_c3))) &
% 288.08/41.98 (((inverse @ sk_c3) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl225215, zip_derived_cl1263])).
% 288.08/41.98 thf('54', plain,
% 288.08/41.98 ((((sk_c11) = (sk_c3))) | ~ (((inverse @ sk_c3) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl225492])).
% 288.08/41.98 thf('55', plain,
% 288.08/41.98 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl8])).
% 288.08/41.98 thf(prove_this_16, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 288.08/41.98 thf(zf_stmt_36, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 288.08/41.98 thf(zip_derived_cl18, plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c11)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_36])).
% 288.08/41.98 thf('56', plain,
% 288.08/41.98 ((((inverse @ sk_c1) = (sk_c11))) | (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl18])).
% 288.08/41.98 thf(prove_this_26, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_37, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c11 @ sk_c9 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 288.08/41.98 thf(zip_derived_cl28, plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8))
% 288.08/41.98 | ((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_37])).
% 288.08/41.98 thf('57', plain,
% 288.08/41.98 ((((multiply @ sk_c11 @ sk_c9) = (sk_c10))) |
% 288.08/41.98 (((inverse @ sk_c5) = (sk_c8)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl28])).
% 288.08/41.98 thf(zip_derived_cl1194, plain,
% 288.08/41.98 ((((sk_c11) = (identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('demod', [status(thm)],
% 288.08/41.98 [zip_derived_cl1158, zip_derived_cl0, zip_derived_cl567])).
% 288.08/41.98 thf(zip_derived_cl62, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl7])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl551, plain,
% 288.08/41.98 ((((sk_c8) = (multiply @ (inverse @ sk_c5) @ sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl62, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl1581, plain,
% 288.08/41.98 ((((sk_c8) = (multiply @ (inverse @ sk_c5) @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1194, zip_derived_cl551])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl2262, plain,
% 288.08/41.98 ((((identity) = (multiply @ (inverse @ (inverse @ sk_c5)) @ sk_c8)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1581, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl202, plain,
% 288.08/41.98 (![X0 : $i, X1 : $i]:
% 288.08/41.98 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 288.08/41.98 thf(zip_derived_cl2429, plain,
% 288.08/41.98 ((((sk_c8)
% 288.08/41.98 = (multiply @ (inverse @ (inverse @ (inverse @ sk_c5))) @ identity)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl2262, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl537, plain,
% 288.08/41.98 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl202])).
% 288.08/41.98 thf(zip_derived_cl3443, plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8)))
% 288.08/41.98 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl2429, zip_derived_cl537])).
% 288.08/41.98 thf(zip_derived_cl62, plain,
% 288.08/41.98 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl7])).
% 288.08/41.98 thf(zip_derived_cl840, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((multiply @ X1 @ X0) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ identity) != (X0))
% 288.08/41.98 | ((inverse @ X0) != (X0))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('eq_res', [status(thm)], [zip_derived_cl231])).
% 288.08/41.98 thf(zip_derived_cl2128, plain,
% 288.08/41.98 (((((sk_c11) != (sk_c11))
% 288.08/41.98 | ((inverse @ sk_c5) != (sk_c8))
% 288.08/41.98 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ identity) != (sk_c8))
% 288.08/41.98 | ((inverse @ sk_c8) != (sk_c8))))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl840])).
% 288.08/41.98 thf(zip_derived_cl2213, plain,
% 288.08/41.98 (((((inverse @ sk_c8) != (sk_c8))
% 288.08/41.98 | ((inverse @ identity) != (sk_c8))
% 288.08/41.98 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ sk_c5) != (sk_c8))))
% 288.08/41.98 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl2128])).
% 288.08/41.98 thf(zip_derived_cl60567, plain,
% 288.08/41.98 ((((inverse @ sk_c5) != (sk_c8))) <= (~ (((inverse @ sk_c5) = (sk_c8))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl2213])).
% 288.08/41.98 thf(zip_derived_cl144397, plain,
% 288.08/41.98 ((((sk_c8) != (sk_c8)))
% 288.08/41.98 <= (~ (((inverse @ sk_c5) = (sk_c8))) &
% 288.08/41.98 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c1) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c11 @ sk_c9) = (sk_c10))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl3443, zip_derived_cl60567])).
% 288.08/41.98 thf('58', plain,
% 288.08/41.98 ((((inverse @ sk_c5) = (sk_c8))) |
% 288.08/41.98 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 288.08/41.98 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl144397])).
% 288.08/41.98 thf(zip_derived_cl1508, plain,
% 288.08/41.98 ((((identity) = (sk_c11)))
% 288.08/41.98 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup+', [status(thm)],
% 288.08/41.98 [zip_derived_cl1495, zip_derived_cl114])).
% 288.08/41.98 thf(zip_derived_cl185, plain,
% 288.08/41.98 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl456, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c4))
% 288.08/41.98 | ((identity) != (X0))
% 288.08/41.98 | ((inverse @ sk_c10) != (X0))
% 288.08/41.98 | ((multiply @ sk_c4 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c4))
% 288.08/41.98 | ((multiply @ X1 @ sk_c4) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl185, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl1115, plain,
% 288.08/41.98 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 288.08/41.98 inference('s_sup+', [status(thm)], [zip_derived_cl546, zip_derived_cl1])).
% 288.08/41.98 thf(zip_derived_cl1753, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c4))
% 288.08/41.98 | ((identity) != (X0))
% 288.08/41.98 | ((inverse @ sk_c10) != (X0))
% 288.08/41.98 | ((identity) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c4))
% 288.08/41.98 | ((multiply @ X1 @ sk_c4) != (sk_c11))))
% 288.08/41.98 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('demod', [status(thm)], [zip_derived_cl456, zip_derived_cl1115])).
% 288.08/41.98 thf(zip_derived_cl1756, plain,
% 288.08/41.98 ((((identity) != (sk_c11))) <= (~ (((identity) = (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl1753])).
% 288.08/41.98 thf(zip_derived_cl38211, plain,
% 288.08/41.98 ((((identity) != (identity)))
% 288.08/41.98 <= (~ (((identity) = (sk_c11))) &
% 288.08/41.98 (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) &
% 288.08/41.98 (((inverse @ sk_c2) = (sk_c9))))),
% 288.08/41.98 inference('s_sup-', [status(thm)],
% 288.08/41.98 [zip_derived_cl1508, zip_derived_cl1756])).
% 288.08/41.98 thf('59', plain,
% 288.08/41.98 ((((identity) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c11))) |
% 288.08/41.98 ~ (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl38211])).
% 288.08/41.98 thf(prove_this_49, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 288.08/41.98 thf(zf_stmt_38, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_49])).
% 288.08/41.98 thf(zip_derived_cl51, plain,
% 288.08/41.98 ((((inverse @ sk_c6) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_38])).
% 288.08/41.98 thf('60', plain,
% 288.08/41.98 ((((inverse @ sk_c6) = (sk_c8))) | (((inverse @ sk_c2) = (sk_c9)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl51])).
% 288.08/41.98 thf(prove_this_8, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_39, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 288.08/41.98 thf(zip_derived_cl10, plain,
% 288.08/41.98 ((((inverse @ sk_c7) = (sk_c6))
% 288.08/41.98 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_39])).
% 288.08/41.98 thf(zip_derived_cl68, plain,
% 288.08/41.98 ((((inverse @ sk_c7) = (sk_c6))) <= ((((inverse @ sk_c7) = (sk_c6))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl10])).
% 288.08/41.98 thf(prove_this_9, conjecture,
% 288.08/41.98 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_40, negated_conjecture,
% 288.08/41.98 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 288.08/41.98 thf(zip_derived_cl11, plain,
% 288.08/41.98 ((((inverse @ sk_c6) = (sk_c8))
% 288.08/41.98 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_40])).
% 288.08/41.98 thf(zip_derived_cl70, plain,
% 288.08/41.98 ((((inverse @ sk_c6) = (sk_c8))) <= ((((inverse @ sk_c6) = (sk_c8))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl11])).
% 288.08/41.98 thf(prove_this_10, conjecture,
% 288.08/41.98 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 288.08/41.98 thf(zf_stmt_41, negated_conjecture,
% 288.08/41.98 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 288.08/41.98 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 288.08/41.98 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 288.08/41.98 thf(zip_derived_cl12, plain,
% 288.08/41.98 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 288.08/41.98 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 288.08/41.98 inference('cnf', [status(esa)], [zf_stmt_41])).
% 288.08/41.98 thf(zip_derived_cl72, plain,
% 288.08/41.98 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)))
% 288.08/41.98 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl12])).
% 288.08/41.98 thf(zip_derived_cl158, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11))))
% 288.08/41.98 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl311, plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0))
% 288.08/41.98 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X1) != (sk_c8))
% 288.08/41.98 | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 288.08/41.98 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) &
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl158])).
% 288.08/41.98 thf(zip_derived_cl1293, plain,
% 288.08/41.98 ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0))))
% 288.08/41.98 <= ((![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0)))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl311])).
% 288.08/41.98 thf(zip_derived_cl1300, plain,
% 288.08/41.98 (((((sk_c8) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (sk_c6))
% 288.08/41.98 | ((inverse @ sk_c7) != (sk_c6))))
% 288.08/41.98 <= ((((inverse @ sk_c6) = (sk_c8))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl1293])).
% 288.08/41.98 thf(zip_derived_cl1304, plain,
% 288.08/41.98 ((((inverse @ sk_c7) != (sk_c6)))
% 288.08/41.98 <= ((((inverse @ sk_c6) = (sk_c8))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0)))))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl1300])).
% 288.08/41.98 thf(zip_derived_cl29927, plain,
% 288.08/41.98 ((((sk_c6) != (sk_c6)))
% 288.08/41.98 <= ((((inverse @ sk_c7) = (sk_c6))) &
% 288.08/41.98 (((inverse @ sk_c6) = (sk_c8))) &
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0)))))),
% 288.08/41.98 inference('s_sup-', [status(thm)], [zip_derived_cl68, zip_derived_cl1304])).
% 288.08/41.98 thf('61', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0)))) |
% 288.08/41.98 ~ (((inverse @ sk_c6) = (sk_c8))) | ~ (((inverse @ sk_c7) = (sk_c6)))),
% 288.08/41.98 inference('simplify', [status(thm)], [zip_derived_cl29927])).
% 288.08/41.98 thf('62', plain,
% 288.08/41.98 (~
% 288.08/41.98 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 288.08/41.98 (![X0 : $i]:
% 288.08/41.98 (((inverse @ X0) != (sk_c8))
% 288.08/41.98 | ((sk_c6) != (X0))
% 288.08/41.98 | ((inverse @ sk_c7) != (X0)))) |
% 288.08/41.98 ~ (((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 288.08/41.98 ~ (((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 288.08/41.98 (![X1 : $i]:
% 288.08/41.98 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11))))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl311])).
% 288.08/41.98 thf('63', plain,
% 288.08/41.98 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 288.08/41.98 (((inverse @ X0) != (X2))
% 288.08/41.98 | ((multiply @ X1 @ X2) != (X0))
% 288.08/41.98 | ((inverse @ X1) != (X0))
% 288.08/41.98 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 288.08/41.98 | ((inverse @ X3) != (X2))
% 288.08/41.98 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 288.08/41.98 (![X7 : $i]:
% 288.08/41.98 (((inverse @ X7) != (sk_c11))
% 288.08/41.98 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 288.08/41.98 (![X6 : $i]:
% 288.08/41.98 (((inverse @ X6) != (sk_c9)) | ((multiply @ X6 @ sk_c9) != (sk_c11)))) |
% 288.08/41.98 (![X4 : $i]:
% 288.08/41.98 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9)))) |
% 288.08/41.98 ~ (((multiply @ sk_c11 @ sk_c9) = (sk_c10)))),
% 288.08/41.98 inference('split', [status(esa)], [zip_derived_cl53])).
% 288.08/41.98 thf(zip_derived_cl274433, plain, ($false),
% 288.08/41.98 inference('sat_resolution*', [status(thm)],
% 288.08/41.98 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 288.08/41.98 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 288.08/41.98 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 288.08/41.98 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 288.08/41.98 '42', '43', '44', '45', '46', '47', '48', '49', '50', '51',
% 288.08/41.98 '52', '53', '54', '55', '56', '57', '58', '59', '60', '61',
% 288.08/41.98 '62', '63'])).
% 288.08/41.98
% 288.08/41.98 % SZS output end Refutation
% 288.08/41.98
% 288.08/41.98
% 288.08/41.98 % Terminating...
% 289.53/42.06 % Runner terminated.
% 289.53/42.06 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------