TSTP Solution File: GRP312-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP312-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.tLzVj4tQqD true
% Computer : n010.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 01:51:09 EDT 2023
% Result : Unsatisfiable 30.17s 4.90s
% Output : Refutation 30.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP312-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.tLzVj4tQqD true
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 20:03:04 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in FO mode
% 0.22/0.66 % Total configuration time : 435
% 0.22/0.66 % Estimated wc time : 1092
% 0.22/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.73 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 30.17/4.90 % Solved by fo/fo1_av.sh.
% 30.17/4.90 % done 4560 iterations in 4.092s
% 30.17/4.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 30.17/4.90 % SZS output start Refutation
% 30.17/4.90 thf(sk_c9_type, type, sk_c9: $i).
% 30.17/4.90 thf(sk_c10_type, type, sk_c10: $i).
% 30.17/4.90 thf(sk_c7_type, type, sk_c7: $i).
% 30.17/4.90 thf(sk_c6_type, type, sk_c6: $i).
% 30.17/4.90 thf(sk_c5_type, type, sk_c5: $i).
% 30.17/4.90 thf(identity_type, type, identity: $i).
% 30.17/4.90 thf(multiply_type, type, multiply: $i > $i > $i).
% 30.17/4.90 thf(sk_c12_type, type, sk_c12: $i).
% 30.17/4.90 thf(sk_c2_type, type, sk_c2: $i).
% 30.17/4.90 thf(inverse_type, type, inverse: $i > $i).
% 30.17/4.90 thf(sk_c4_type, type, sk_c4: $i).
% 30.17/4.90 thf(sk_c1_type, type, sk_c1: $i).
% 30.17/4.90 thf(sk_c8_type, type, sk_c8: $i).
% 30.17/4.90 thf(sk_c11_type, type, sk_c11: $i).
% 30.17/4.90 thf(sk_c3_type, type, sk_c3: $i).
% 30.17/4.90 thf(prove_this_64, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_0, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c3 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_64])).
% 30.17/4.90 thf(zip_derived_cl66, plain,
% 30.17/4.90 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_0])).
% 30.17/4.90 thf('0', plain,
% 30.17/4.90 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl66])).
% 30.17/4.90 thf(prove_this_4, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_1, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 30.17/4.90 thf(zip_derived_cl6, plain,
% 30.17/4.90 ((((inverse @ sk_c5) = (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_1])).
% 30.17/4.90 thf('1', plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.90 (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl6])).
% 30.17/4.90 thf(prove_this_14, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_2, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 30.17/4.90 thf(zip_derived_cl16, plain,
% 30.17/4.90 ((((inverse @ sk_c5) = (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_2])).
% 30.17/4.90 thf('2', plain,
% 30.17/4.90 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.90 (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl16])).
% 30.17/4.90 thf(prove_this_24, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.90 thf(zf_stmt_3, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 30.17/4.90 thf(zip_derived_cl26, plain,
% 30.17/4.90 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_3])).
% 30.17/4.90 thf('3', plain,
% 30.17/4.90 ((((inverse @ sk_c1) = (sk_c12))) | (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl26])).
% 30.17/4.90 thf(prove_this_34, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_4, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 30.17/4.90 thf(zip_derived_cl36, plain,
% 30.17/4.90 ((((inverse @ sk_c5) = (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_4])).
% 30.17/4.90 thf('4', plain,
% 30.17/4.90 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.90 (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl36])).
% 30.17/4.90 thf(prove_this_44, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_5, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 30.17/4.90 thf(zip_derived_cl46, plain,
% 30.17/4.90 ((((inverse @ sk_c5) = (sk_c11)) | ((inverse @ sk_c2) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_5])).
% 30.17/4.90 thf('5', plain,
% 30.17/4.90 ((((inverse @ sk_c2) = (sk_c11))) | (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl46])).
% 30.17/4.90 thf(prove_this_1, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_6, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 30.17/4.90 thf(zip_derived_cl3, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_6])).
% 30.17/4.90 thf('6', plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(prove_this_2, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_7, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 30.17/4.90 thf(zip_derived_cl4, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_7])).
% 30.17/4.90 thf('7', plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl4])).
% 30.17/4.90 thf(prove_this_3, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_8, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 30.17/4.90 thf(zip_derived_cl5, plain,
% 30.17/4.90 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_8])).
% 30.17/4.90 thf('8', plain,
% 30.17/4.90 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl5])).
% 30.17/4.90 thf(prove_this_5, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_9, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 30.17/4.90 thf(zip_derived_cl7, plain,
% 30.17/4.90 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_9])).
% 30.17/4.90 thf('9', plain,
% 30.17/4.90 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl7])).
% 30.17/4.90 thf(prove_this_6, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_10, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 30.17/4.90 thf(zip_derived_cl8, plain,
% 30.17/4.90 ((((inverse @ sk_c6) = (sk_c9))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_10])).
% 30.17/4.90 thf('10', plain,
% 30.17/4.90 ((((inverse @ sk_c6) = (sk_c9))) |
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl8])).
% 30.17/4.90 thf(prove_this_12, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_11, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 30.17/4.90 thf(zip_derived_cl14, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))
% 30.17/4.90 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_11])).
% 30.17/4.90 thf('11', plain,
% 30.17/4.90 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl14])).
% 30.17/4.90 thf(prove_this_22, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.90 thf(zf_stmt_12, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 30.17/4.90 thf(zip_derived_cl24, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12)) | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_12])).
% 30.17/4.90 thf('12', plain,
% 30.17/4.90 ((((inverse @ sk_c1) = (sk_c12))) | (((inverse @ sk_c4) = (sk_c12)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl24])).
% 30.17/4.90 thf(prove_this_32, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_13, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 30.17/4.90 thf(zip_derived_cl34, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))
% 30.17/4.90 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_13])).
% 30.17/4.90 thf('13', plain,
% 30.17/4.90 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl34])).
% 30.17/4.90 thf(prove_this_42, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_14, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 30.17/4.90 thf(zip_derived_cl44, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12)) | ((inverse @ sk_c2) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_14])).
% 30.17/4.90 thf('14', plain,
% 30.17/4.90 ((((inverse @ sk_c2) = (sk_c11))) | (((inverse @ sk_c4) = (sk_c12)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl44])).
% 30.17/4.90 thf(prove_this_52, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) ) ))).
% 30.17/4.90 thf(zf_stmt_15, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_52])).
% 30.17/4.90 thf(zip_derived_cl54, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))
% 30.17/4.90 | ((multiply @ sk_c3 @ sk_c11) = (sk_c12)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_15])).
% 30.17/4.90 thf('15', plain,
% 30.17/4.90 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl54])).
% 30.17/4.90 thf(prove_this_62, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_16, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c4 ) = ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c3 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_62])).
% 30.17/4.90 thf(zip_derived_cl64, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12)) | ((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_16])).
% 30.17/4.90 thf('16', plain,
% 30.17/4.90 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c4) = (sk_c12)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl64])).
% 30.17/4.90 thf(prove_this_41, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_17, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 30.17/4.90 thf(zip_derived_cl43, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.90 | ((inverse @ sk_c2) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_17])).
% 30.17/4.90 thf(zip_derived_cl154, plain,
% 30.17/4.90 ((((inverse @ sk_c2) = (sk_c11))) <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl43])).
% 30.17/4.90 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(zip_derived_cl313, plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c2) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(associativity, axiom,
% 30.17/4.90 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 30.17/4.90 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 30.17/4.90 thf(zip_derived_cl2, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.90 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.90 thf(zip_derived_cl257, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i]:
% 30.17/4.90 ((multiply @ identity @ X0)
% 30.17/4.90 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 30.17/4.90 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl259, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i]:
% 30.17/4.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl683, plain,
% 30.17/4.90 ((((sk_c2) = (multiply @ (inverse @ sk_c11) @ identity)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl313, zip_derived_cl259])).
% 30.17/4.90 thf(zip_derived_cl2, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.90 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.90 thf(zip_derived_cl722, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ sk_c2 @ X0)
% 30.17/4.90 = (multiply @ (inverse @ sk_c11) @ (multiply @ identity @ X0))))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl683, zip_derived_cl2])).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl726, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl722, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(zip_derived_cl1351, plain,
% 30.17/4.90 ((((multiply @ sk_c2 @ sk_c11) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl726, zip_derived_cl1])).
% 30.17/4.90 thf(prove_this_31, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_18, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 30.17/4.90 thf(zip_derived_cl33, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_18])).
% 30.17/4.90 thf(zip_derived_cl134, plain,
% 30.17/4.90 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl33])).
% 30.17/4.90 thf(zip_derived_cl1369, plain,
% 30.17/4.90 ((((identity) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)],
% 30.17/4.90 [zip_derived_cl1351, zip_derived_cl134])).
% 30.17/4.90 thf(zip_derived_cl76, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl4])).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(zip_derived_cl241, plain,
% 30.17/4.90 ((((multiply @ sk_c12 @ sk_c4) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl74, plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c12) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(zip_derived_cl2, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.90 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.90 thf(zip_derived_cl272, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ sk_c10 @ X0)
% 30.17/4.90 = (multiply @ sk_c11 @ (multiply @ sk_c12 @ X0))))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl2])).
% 30.17/4.90 thf(zip_derived_cl755, plain,
% 30.17/4.90 ((((multiply @ sk_c10 @ sk_c4) = (multiply @ sk_c11 @ identity)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl241, zip_derived_cl272])).
% 30.17/4.90 thf(zip_derived_cl4289, plain,
% 30.17/4.90 ((((multiply @ identity @ sk_c4) = (multiply @ sk_c11 @ identity)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)],
% 30.17/4.90 [zip_derived_cl1369, zip_derived_cl755])).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl1351, plain,
% 30.17/4.90 ((((multiply @ sk_c2 @ sk_c11) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl726, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl313, plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c2) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl154, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl2, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.90 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.90 thf(zip_derived_cl644, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ identity @ X0)
% 30.17/4.90 = (multiply @ sk_c11 @ (multiply @ sk_c2 @ X0))))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl313, zip_derived_cl2])).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl645, plain,
% 30.17/4.90 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c2 @ X0))))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl644, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl1368, plain,
% 30.17/4.90 ((((sk_c11) = (multiply @ sk_c11 @ identity)))
% 30.17/4.90 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)],
% 30.17/4.90 [zip_derived_cl1351, zip_derived_cl645])).
% 30.17/4.90 thf(zip_derived_cl4294, plain,
% 30.17/4.90 ((((sk_c4) = (sk_c11)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('demod', [status(thm)],
% 30.17/4.90 [zip_derived_cl4289, zip_derived_cl0, zip_derived_cl1368])).
% 30.17/4.90 thf(zip_derived_cl76, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl4])).
% 30.17/4.90 thf(zip_derived_cl75, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(prove_this_71, conjecture,
% 30.17/4.90 (~( ( ( multiply @ X8 @ X3 ) != ( X9 ) ) |
% 30.17/4.90 ( ( inverse @ X9 ) != ( X3 ) ) | ( ( inverse @ X8 ) != ( X9 ) ) |
% 30.17/4.90 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ X7 ) != ( X3 ) ) |
% 30.17/4.90 ( ( multiply @ X7 @ X3 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ X2 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ X2 @ sk_c11 ) != ( sk_c10 ) ) |
% 30.17/4.90 ( ( inverse @ X1 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ X1 @ sk_c12 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ X6 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ X6 @ sk_c11 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ X5 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ X5 @ sk_c11 ) != ( sk_c10 ) ) |
% 30.17/4.90 ( ( inverse @ X4 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ X4 @ sk_c12 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) != ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_19, negated_conjecture,
% 30.17/4.90 (( ( multiply @ X8 @ X3 ) != ( X9 ) ) | ( ( inverse @ X9 ) != ( X3 ) ) |
% 30.17/4.90 ( ( inverse @ X8 ) != ( X9 ) ) |
% 30.17/4.90 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ X7 ) != ( X3 ) ) |
% 30.17/4.90 ( ( multiply @ X7 @ X3 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ X2 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ X2 @ sk_c11 ) != ( sk_c10 ) ) |
% 30.17/4.90 ( ( inverse @ X1 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ X1 @ sk_c12 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ X6 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ X6 @ sk_c11 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( inverse @ X5 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ X5 @ sk_c11 ) != ( sk_c10 ) ) |
% 30.17/4.90 ( ( inverse @ X4 ) != ( sk_c12 ) ) |
% 30.17/4.90 ( ( multiply @ X4 @ sk_c12 ) != ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) != ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_71])).
% 30.17/4.90 thf(zip_derived_cl73, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i,
% 30.17/4.90 X7 : $i, X8 : $i]:
% 30.17/4.90 (((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X0) != (X2))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12))
% 30.17/4.90 | ((inverse @ X4) != (sk_c11))
% 30.17/4.90 | ((multiply @ X4 @ sk_c11) != (sk_c10))
% 30.17/4.90 | ((inverse @ X5) != (sk_c12))
% 30.17/4.90 | ((multiply @ X5 @ sk_c12) != (sk_c11))
% 30.17/4.90 | ((inverse @ X6) != (sk_c11))
% 30.17/4.90 | ((multiply @ X6 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10))
% 30.17/4.90 | ((inverse @ X8) != (sk_c12))
% 30.17/4.90 | ((multiply @ X8 @ sk_c12) != (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) != (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_19])).
% 30.17/4.90 thf(zip_derived_cl219, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12))))
% 30.17/4.90 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.90 thf(zip_derived_cl294, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c12))
% 30.17/4.90 | ((sk_c11) != (X0))
% 30.17/4.90 | ((inverse @ sk_c4) != (X0))
% 30.17/4.90 | ((multiply @ sk_c12 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12))))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl219])).
% 30.17/4.90 thf(zip_derived_cl333, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c12))
% 30.17/4.90 | ((sk_c11) != (X0))
% 30.17/4.90 | ((inverse @ sk_c4) != (X0))))
% 30.17/4.90 <= ((![X0 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c12))
% 30.17/4.90 | ((sk_c11) != (X0))
% 30.17/4.90 | ((inverse @ sk_c4) != (X0)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl294])).
% 30.17/4.90 thf(zip_derived_cl335, plain,
% 30.17/4.90 (((((sk_c12) != (sk_c12)) | ((sk_c11) != (sk_c4)) | ((sk_c12) != (sk_c4))))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (![X0 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c12))
% 30.17/4.90 | ((sk_c11) != (X0))
% 30.17/4.90 | ((inverse @ sk_c4) != (X0)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl333])).
% 30.17/4.90 thf(zip_derived_cl342, plain,
% 30.17/4.90 (((((sk_c12) != (sk_c4)) | ((sk_c11) != (sk_c4))))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (![X0 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c12))
% 30.17/4.90 | ((sk_c11) != (X0))
% 30.17/4.90 | ((inverse @ sk_c4) != (X0)))))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl335])).
% 30.17/4.90 thf(zip_derived_cl345, plain,
% 30.17/4.90 ((((sk_c11) != (sk_c4))) <= (~ (((sk_c11) = (sk_c4))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl342])).
% 30.17/4.90 thf(zip_derived_cl4993, plain,
% 30.17/4.90 ((((sk_c11) != (sk_c11)))
% 30.17/4.90 <= (~ (((sk_c11) = (sk_c4))) &
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup-', [status(thm)],
% 30.17/4.90 [zip_derived_cl4294, zip_derived_cl345])).
% 30.17/4.90 thf('17', plain,
% 30.17/4.90 ((((sk_c11) = (sk_c4))) | ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.90 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.90 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.90 ~ (((inverse @ sk_c2) = (sk_c11)))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl4993])).
% 30.17/4.90 thf(zip_derived_cl75, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(zip_derived_cl241, plain,
% 30.17/4.90 ((((multiply @ sk_c12 @ sk_c4) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl2, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.90 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.90 thf(zip_derived_cl618, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ identity @ X0)
% 30.17/4.90 = (multiply @ sk_c12 @ (multiply @ sk_c4 @ X0))))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl241, zip_derived_cl2])).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl619, plain,
% 30.17/4.90 ((![X0 : $i]: ((X0) = (multiply @ sk_c12 @ (multiply @ sk_c4 @ X0))))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl618, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl651, plain,
% 30.17/4.90 ((((sk_c12) = (multiply @ sk_c12 @ sk_c11)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl619])).
% 30.17/4.90 thf(zip_derived_cl259, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i]:
% 30.17/4.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl686, plain,
% 30.17/4.90 ((((sk_c11) = (multiply @ (inverse @ sk_c12) @ sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl651, zip_derived_cl259])).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(zip_derived_cl708, plain,
% 30.17/4.90 ((((sk_c11) = (identity)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.90 thf(prove_this_61, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_20, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c3 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_61])).
% 30.17/4.90 thf(zip_derived_cl63, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.90 | ((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_20])).
% 30.17/4.90 thf(zip_derived_cl194, plain,
% 30.17/4.90 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl63])).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(zip_derived_cl371, plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl259, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i]:
% 30.17/4.90 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl684, plain,
% 30.17/4.90 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity)))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl371, zip_derived_cl259])).
% 30.17/4.90 thf(zip_derived_cl2, plain,
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.90 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.90 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.90 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.90 thf(zip_derived_cl728, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ sk_c3 @ X0)
% 30.17/4.90 = (multiply @ (inverse @ sk_c11) @ (multiply @ identity @ X0))))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl684, zip_derived_cl2])).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl733, plain,
% 30.17/4.90 ((![X0 : $i]:
% 30.17/4.90 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl728, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl1, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.90 thf(zip_derived_cl1520, plain,
% 30.17/4.90 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl733, zip_derived_cl1])).
% 30.17/4.90 thf(prove_this_51, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) ) ))).
% 30.17/4.90 thf(zf_stmt_21, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 30.17/4.90 thf(zip_derived_cl53, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.90 | ((multiply @ sk_c3 @ sk_c11) = (sk_c12)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_21])).
% 30.17/4.90 thf(zip_derived_cl174, plain,
% 30.17/4.90 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl53])).
% 30.17/4.90 thf(zip_derived_cl1541, plain,
% 30.17/4.90 ((((identity) = (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)],
% 30.17/4.90 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.90 thf(zip_derived_cl4294, plain,
% 30.17/4.90 ((((sk_c4) = (sk_c11)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('demod', [status(thm)],
% 30.17/4.90 [zip_derived_cl4289, zip_derived_cl0, zip_derived_cl1368])).
% 30.17/4.90 thf(zip_derived_cl344, plain,
% 30.17/4.90 ((((sk_c12) != (sk_c4))) <= (~ (((sk_c12) = (sk_c4))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl342])).
% 30.17/4.90 thf(zip_derived_cl4992, plain,
% 30.17/4.90 ((((sk_c12) != (sk_c11)))
% 30.17/4.90 <= (~ (((sk_c12) = (sk_c4))) &
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.90 inference('s_sup-', [status(thm)],
% 30.17/4.90 [zip_derived_cl4294, zip_derived_cl344])).
% 30.17/4.90 thf(zip_derived_cl5809, plain,
% 30.17/4.90 ((((identity) != (sk_c11)))
% 30.17/4.90 <= (~ (((sk_c12) = (sk_c4))) &
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))) &
% 30.17/4.90 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup-', [status(thm)],
% 30.17/4.90 [zip_derived_cl1541, zip_derived_cl4992])).
% 30.17/4.90 thf(zip_derived_cl5823, plain,
% 30.17/4.90 ((((identity) != (identity)))
% 30.17/4.90 <= (~ (((sk_c12) = (sk_c4))) &
% 30.17/4.90 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.90 (((inverse @ sk_c2) = (sk_c11))) &
% 30.17/4.90 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup-', [status(thm)],
% 30.17/4.90 [zip_derived_cl708, zip_derived_cl5809])).
% 30.17/4.90 thf('18', plain,
% 30.17/4.90 ((((sk_c12) = (sk_c4))) | ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.90 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.90 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.90 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 30.17/4.90 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.90 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.90 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl5823])).
% 30.17/4.90 thf(zip_derived_cl1541, plain,
% 30.17/4.90 ((((identity) = (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('s_sup+', [status(thm)],
% 30.17/4.90 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.90 thf(zip_derived_cl75, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(zip_derived_cl76, plain,
% 30.17/4.90 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl4])).
% 30.17/4.90 thf(zip_derived_cl74, plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c12) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(zip_derived_cl219, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12))))
% 30.17/4.90 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.90 thf(zip_derived_cl293, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c12))
% 30.17/4.90 | ((sk_c10) != (X0))
% 30.17/4.90 | ((inverse @ sk_c11) != (X0))
% 30.17/4.90 | ((multiply @ sk_c12 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12))))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl219])).
% 30.17/4.90 thf(zip_derived_cl296, plain,
% 30.17/4.90 ((![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12))))
% 30.17/4.90 <= ((![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl293])).
% 30.17/4.90 thf(zip_derived_cl299, plain,
% 30.17/4.90 (((((sk_c12) != (sk_c12)) | ((multiply @ sk_c4 @ sk_c12) != (sk_c12))))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl296])).
% 30.17/4.90 thf(zip_derived_cl305, plain,
% 30.17/4.90 ((((multiply @ sk_c4 @ sk_c12) != (sk_c12)))
% 30.17/4.90 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl299])).
% 30.17/4.90 thf(zip_derived_cl307, plain,
% 30.17/4.90 ((((sk_c11) != (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl305])).
% 30.17/4.90 thf(zip_derived_cl3841, plain,
% 30.17/4.90 ((((sk_c11) != (identity)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)],
% 30.17/4.90 [zip_derived_cl1541, zip_derived_cl307])).
% 30.17/4.90 thf(zip_derived_cl708, plain,
% 30.17/4.90 ((((sk_c11) = (identity)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl3894, plain,
% 30.17/4.90 ((((identity) != (identity)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl3841, zip_derived_cl708])).
% 30.17/4.90 thf('19', plain,
% 30.17/4.90 (~
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c12))
% 30.17/4.90 | ((multiply @ X1 @ sk_c12) != (sk_c12)))) |
% 30.17/4.90 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.90 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.90 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.90 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12)))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl3894])).
% 30.17/4.90 thf(zip_derived_cl708, plain,
% 30.17/4.90 ((((sk_c11) = (identity)))
% 30.17/4.90 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.90 thf(zip_derived_cl74, plain,
% 30.17/4.90 ((((multiply @ sk_c11 @ sk_c12) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.90 thf(zip_derived_cl1378, plain,
% 30.17/4.90 ((((multiply @ identity @ sk_c12) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('s_sup+', [status(thm)], [zip_derived_cl708, zip_derived_cl74])).
% 30.17/4.90 thf(zip_derived_cl0, plain,
% 30.17/4.90 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.90 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.90 thf(zip_derived_cl1432, plain,
% 30.17/4.90 ((((sk_c12) = (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.90 inference('demod', [status(thm)], [zip_derived_cl1378, zip_derived_cl0])).
% 30.17/4.90 thf(zip_derived_cl174, plain,
% 30.17/4.90 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl53])).
% 30.17/4.90 thf(zip_derived_cl194, plain,
% 30.17/4.90 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl63])).
% 30.17/4.90 thf(zip_derived_cl215, plain,
% 30.17/4.90 ((![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 30.17/4.90 <= ((![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.90 thf(zip_derived_cl375, plain,
% 30.17/4.90 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c3 @ sk_c11) != (sk_c10))))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.90 (![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl215])).
% 30.17/4.90 thf(zip_derived_cl378, plain,
% 30.17/4.90 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 30.17/4.90 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.90 (![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl375])).
% 30.17/4.90 thf(zip_derived_cl563, plain,
% 30.17/4.90 ((((sk_c12) != (sk_c10)))
% 30.17/4.90 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.90 (![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl378])).
% 30.17/4.90 thf(zip_derived_cl1566, plain,
% 30.17/4.90 ((((sk_c12) != (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.90 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.90 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.90 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.90 (![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)],
% 30.17/4.90 [zip_derived_cl1432, zip_derived_cl563])).
% 30.17/4.90 thf('20', plain,
% 30.17/4.90 (~
% 30.17/4.90 (![X7 : $i]:
% 30.17/4.90 (((inverse @ X7) != (sk_c11))
% 30.17/4.90 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 30.17/4.90 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.90 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.90 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.90 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.90 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12)))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl1566])).
% 30.17/4.90 thf(prove_this_33, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_22, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c2 @ sk_c11 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 30.17/4.90 thf(zip_derived_cl35, plain,
% 30.17/4.90 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 30.17/4.90 | ((multiply @ sk_c2 @ sk_c11) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_22])).
% 30.17/4.90 thf('21', plain,
% 30.17/4.90 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.90 (((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl35])).
% 30.17/4.90 thf(prove_this_43, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) ) ))).
% 30.17/4.90 thf(zf_stmt_23, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.90 ( ( inverse @ sk_c2 ) = ( sk_c11 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 30.17/4.90 thf(zip_derived_cl45, plain,
% 30.17/4.90 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 30.17/4.90 | ((inverse @ sk_c2) = (sk_c11)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_23])).
% 30.17/4.90 thf('22', plain,
% 30.17/4.90 ((((inverse @ sk_c2) = (sk_c11))) |
% 30.17/4.90 (((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl45])).
% 30.17/4.90 thf(zip_derived_cl82, plain,
% 30.17/4.90 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl7])).
% 30.17/4.90 thf(zip_derived_cl84, plain,
% 30.17/4.90 ((((inverse @ sk_c6) = (sk_c9))) <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl8])).
% 30.17/4.90 thf(zip_derived_cl82, plain,
% 30.17/4.90 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl7])).
% 30.17/4.90 thf(zip_derived_cl219, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12))))
% 30.17/4.90 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.90 thf(zip_derived_cl353, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i]:
% 30.17/4.90 (((inverse @ X0) != (sk_c9))
% 30.17/4.90 | ((sk_c12) != (X0))
% 30.17/4.90 | ((inverse @ sk_c6) != (X0))
% 30.17/4.90 | ((multiply @ sk_c9 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X1) != (sk_c9))
% 30.17/4.90 | ((multiply @ X1 @ sk_c9) != (sk_c12))))
% 30.17/4.90 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 30.17/4.90 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl219])).
% 30.17/4.90 thf(zip_derived_cl470, plain,
% 30.17/4.90 ((![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12))))
% 30.17/4.90 <= ((![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c9))
% 30.17/4.90 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl353])).
% 30.17/4.90 thf(zip_derived_cl475, plain,
% 30.17/4.90 (((((sk_c9) != (sk_c9)) | ((multiply @ sk_c6 @ sk_c9) != (sk_c12))))
% 30.17/4.90 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c9))
% 30.17/4.90 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl470])).
% 30.17/4.90 thf(zip_derived_cl481, plain,
% 30.17/4.90 ((((multiply @ sk_c6 @ sk_c9) != (sk_c12)))
% 30.17/4.90 <= ((((inverse @ sk_c6) = (sk_c9))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c9))
% 30.17/4.90 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl475])).
% 30.17/4.90 thf(zip_derived_cl497, plain,
% 30.17/4.90 ((((sk_c12) != (sk_c12)))
% 30.17/4.90 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 30.17/4.90 (((inverse @ sk_c6) = (sk_c9))) &
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c9))
% 30.17/4.90 | ((multiply @ X1 @ sk_c9) != (sk_c12)))))),
% 30.17/4.90 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl481])).
% 30.17/4.90 thf('23', plain,
% 30.17/4.90 (~
% 30.17/4.90 (![X1 : $i]:
% 30.17/4.90 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12)))) |
% 30.17/4.90 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 30.17/4.90 ~ (((inverse @ sk_c6) = (sk_c9)))),
% 30.17/4.90 inference('simplify', [status(thm)], [zip_derived_cl497])).
% 30.17/4.90 thf(prove_this_8, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_24, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 30.17/4.90 thf(zip_derived_cl10, plain,
% 30.17/4.90 ((((inverse @ sk_c8) = (sk_c7))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_24])).
% 30.17/4.90 thf(zip_derived_cl88, plain,
% 30.17/4.90 ((((inverse @ sk_c8) = (sk_c7))) <= ((((inverse @ sk_c8) = (sk_c7))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl10])).
% 30.17/4.90 thf(prove_this_9, conjecture,
% 30.17/4.90 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_25, negated_conjecture,
% 30.17/4.90 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 30.17/4.90 thf(zip_derived_cl11, plain,
% 30.17/4.90 ((((inverse @ sk_c7) = (sk_c9))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_25])).
% 30.17/4.90 thf(zip_derived_cl90, plain,
% 30.17/4.90 ((((inverse @ sk_c7) = (sk_c9))) <= ((((inverse @ sk_c7) = (sk_c9))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl11])).
% 30.17/4.90 thf(prove_this_10, conjecture,
% 30.17/4.90 (~( ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) ) ))).
% 30.17/4.90 thf(zf_stmt_26, negated_conjecture,
% 30.17/4.90 (( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 30.17/4.90 ( ( multiply @ sk_c11 @ sk_c12 ) = ( sk_c10 ) )),
% 30.17/4.90 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 30.17/4.90 thf(zip_derived_cl12, plain,
% 30.17/4.90 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))
% 30.17/4.90 | ((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.90 inference('cnf', [status(esa)], [zf_stmt_26])).
% 30.17/4.90 thf(zip_derived_cl92, plain,
% 30.17/4.90 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)))
% 30.17/4.90 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))))),
% 30.17/4.90 inference('split', [status(esa)], [zip_derived_cl12])).
% 30.17/4.90 thf(zip_derived_cl219, plain,
% 30.17/4.90 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12))))
% 30.17/4.90 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.90 (((inverse @ X0) != (X2))
% 30.17/4.90 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.90 | ((inverse @ X1) != (X0))
% 30.17/4.90 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.90 | ((inverse @ X3) != (X2))
% 30.17/4.90 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl423, plain,
% 30.17/4.91 ((![X0 : $i, X1 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0))
% 30.17/4.91 | ((multiply @ sk_c9 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X1) != (sk_c9))
% 30.17/4.91 | ((multiply @ X1 @ sk_c9) != (sk_c12))))
% 30.17/4.91 <= ((((multiply @ sk_c8 @ sk_c9) = (sk_c7))) &
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl92, zip_derived_cl219])).
% 30.17/4.91 thf(zip_derived_cl585, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0))))
% 30.17/4.91 <= ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl423])).
% 30.17/4.91 thf(zip_derived_cl591, plain,
% 30.17/4.91 (((((sk_c9) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (sk_c7))
% 30.17/4.91 | ((inverse @ sk_c8) != (sk_c7))))
% 30.17/4.91 <= ((((inverse @ sk_c7) = (sk_c9))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl90, zip_derived_cl585])).
% 30.17/4.91 thf(zip_derived_cl597, plain,
% 30.17/4.91 ((((inverse @ sk_c8) != (sk_c7)))
% 30.17/4.91 <= ((((inverse @ sk_c7) = (sk_c9))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl591])).
% 30.17/4.91 thf(zip_derived_cl598, plain,
% 30.17/4.91 ((((sk_c7) != (sk_c7)))
% 30.17/4.91 <= ((((inverse @ sk_c8) = (sk_c7))) &
% 30.17/4.91 (((inverse @ sk_c7) = (sk_c9))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl597])).
% 30.17/4.91 thf('24', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0)))) |
% 30.17/4.91 ~ (((inverse @ sk_c7) = (sk_c9))) | ~ (((inverse @ sk_c8) = (sk_c7)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl598])).
% 30.17/4.91 thf(prove_this_25, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_27, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c12 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 30.17/4.91 thf(zip_derived_cl27, plain,
% 30.17/4.91 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))
% 30.17/4.91 | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_27])).
% 30.17/4.91 thf('25', plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 (((multiply @ sk_c6 @ sk_c9) = (sk_c12)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl27])).
% 30.17/4.91 thf(prove_this_26, conjecture,
% 30.17/4.91 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_28, negated_conjecture,
% 30.17/4.91 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 30.17/4.91 thf(zip_derived_cl28, plain,
% 30.17/4.91 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_28])).
% 30.17/4.91 thf('26', plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) | (((inverse @ sk_c6) = (sk_c9)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl28])).
% 30.17/4.91 thf(prove_this_27, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_29, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c12 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 30.17/4.91 thf(zip_derived_cl29, plain,
% 30.17/4.91 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))
% 30.17/4.91 | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_29])).
% 30.17/4.91 thf('27', plain,
% 30.17/4.91 ((((multiply @ sk_c9 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl29])).
% 30.17/4.91 thf(prove_this_28, conjecture,
% 30.17/4.91 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_30, negated_conjecture,
% 30.17/4.91 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 30.17/4.91 thf(zip_derived_cl30, plain,
% 30.17/4.91 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_30])).
% 30.17/4.91 thf('28', plain,
% 30.17/4.91 ((((inverse @ sk_c8) = (sk_c7))) | (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl30])).
% 30.17/4.91 thf(prove_this_29, conjecture,
% 30.17/4.91 (~( ( ( inverse @ sk_c7 ) = ( sk_c9 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_31, negated_conjecture,
% 30.17/4.91 (( ( inverse @ sk_c7 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 30.17/4.91 thf(zip_derived_cl31, plain,
% 30.17/4.91 ((((inverse @ sk_c7) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_31])).
% 30.17/4.91 thf('29', plain,
% 30.17/4.91 ((((inverse @ sk_c7) = (sk_c9))) | (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl31])).
% 30.17/4.91 thf(prove_this_30, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_32, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 30.17/4.91 thf(zip_derived_cl32, plain,
% 30.17/4.91 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_32])).
% 30.17/4.91 thf('30', plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 (((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl32])).
% 30.17/4.91 thf(zip_derived_cl80, plain,
% 30.17/4.91 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl6])).
% 30.17/4.91 thf(zip_derived_cl1432, plain,
% 30.17/4.91 ((((sk_c12) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl1378, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl78, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl5])).
% 30.17/4.91 thf(zip_derived_cl259, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i]:
% 30.17/4.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl690, plain,
% 30.17/4.91 ((((sk_c11) = (multiply @ (inverse @ sk_c5) @ sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl78, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl1568, plain,
% 30.17/4.91 ((((sk_c11) = (multiply @ (inverse @ sk_c5) @ sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1432, zip_derived_cl690])).
% 30.17/4.91 thf(zip_derived_cl708, plain,
% 30.17/4.91 ((((sk_c11) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl1575, plain,
% 30.17/4.91 ((((identity) = (multiply @ (inverse @ sk_c5) @ sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl1568, zip_derived_cl708])).
% 30.17/4.91 thf(zip_derived_cl1688, plain,
% 30.17/4.91 ((((identity) = (multiply @ sk_c11 @ sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl1575])).
% 30.17/4.91 thf(zip_derived_cl708, plain,
% 30.17/4.91 ((((sk_c11) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl1689, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl1688, zip_derived_cl708, zip_derived_cl0])).
% 30.17/4.91 thf(prove_this_21, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_33, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c1 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 30.17/4.91 thf(zip_derived_cl23, plain,
% 30.17/4.91 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.91 | ((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_33])).
% 30.17/4.91 thf(zip_derived_cl114, plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf(zip_derived_cl1, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.91 thf(zip_derived_cl261, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c1) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl1707, plain,
% 30.17/4.91 ((((multiply @ identity @ sk_c1) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1689, zip_derived_cl261])).
% 30.17/4.91 thf(zip_derived_cl261, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c1) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl259, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i]:
% 30.17/4.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl688, plain,
% 30.17/4.91 ((((sk_c1) = (multiply @ (inverse @ sk_c12) @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl241, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c4) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl259, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i]:
% 30.17/4.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl687, plain,
% 30.17/4.91 ((((sk_c4) = (multiply @ (inverse @ sk_c12) @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl241, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl768, plain,
% 30.17/4.91 ((((sk_c4) = (sk_c1)))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl687])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl1752, plain,
% 30.17/4.91 ((((sk_c4) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl1707, zip_derived_cl768, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl768, plain,
% 30.17/4.91 ((((sk_c4) = (sk_c1)))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl687])).
% 30.17/4.91 thf(zip_derived_cl114, plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf(zip_derived_cl333, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0))))
% 30.17/4.91 <= ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl294])).
% 30.17/4.91 thf(zip_derived_cl340, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (sk_c1))
% 30.17/4.91 | ((inverse @ sk_c4) != (sk_c1))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl333])).
% 30.17/4.91 thf(zip_derived_cl343, plain,
% 30.17/4.91 (((((inverse @ sk_c4) != (sk_c1)) | ((sk_c11) != (sk_c1))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl340])).
% 30.17/4.91 thf(zip_derived_cl347, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c1))) <= (~ (((sk_c11) = (sk_c1))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl343])).
% 30.17/4.91 thf(zip_derived_cl938, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c4)))
% 30.17/4.91 <= (~ (((sk_c11) = (sk_c1))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl768, zip_derived_cl347])).
% 30.17/4.91 thf(zip_derived_cl1904, plain,
% 30.17/4.91 ((((sk_c11) != (identity)))
% 30.17/4.91 <= (~ (((sk_c11) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1752, zip_derived_cl938])).
% 30.17/4.91 thf(zip_derived_cl708, plain,
% 30.17/4.91 ((((sk_c11) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl1937, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= (~ (((sk_c11) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl1904, zip_derived_cl708])).
% 30.17/4.91 thf('31', plain,
% 30.17/4.91 ((((sk_c11) = (sk_c1))) | ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((inverse @ sk_c5) = (sk_c11))) | ~ (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl1937])).
% 30.17/4.91 thf(zip_derived_cl1752, plain,
% 30.17/4.91 ((((sk_c4) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl1707, zip_derived_cl768, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl768, plain,
% 30.17/4.91 ((((sk_c4) = (sk_c1)))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl687])).
% 30.17/4.91 thf(zip_derived_cl76, plain,
% 30.17/4.91 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl4])).
% 30.17/4.91 thf(zip_derived_cl346, plain,
% 30.17/4.91 ((((inverse @ sk_c4) != (sk_c1))) <= (~ (((inverse @ sk_c4) = (sk_c1))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl343])).
% 30.17/4.91 thf(zip_derived_cl348, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c1)))
% 30.17/4.91 <= (~ (((inverse @ sk_c4) = (sk_c1))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl346])).
% 30.17/4.91 thf(zip_derived_cl939, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c4)))
% 30.17/4.91 <= (~ (((inverse @ sk_c4) = (sk_c1))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl768, zip_derived_cl348])).
% 30.17/4.91 thf(zip_derived_cl1905, plain,
% 30.17/4.91 ((((sk_c12) != (identity)))
% 30.17/4.91 <= (~ (((inverse @ sk_c4) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1752, zip_derived_cl939])).
% 30.17/4.91 thf(zip_derived_cl1689, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl1688, zip_derived_cl708, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl1939, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= (~ (((inverse @ sk_c4) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl1905, zip_derived_cl1689])).
% 30.17/4.91 thf('32', plain,
% 30.17/4.91 ((((inverse @ sk_c4) = (sk_c1))) | ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c5) = (sk_c11))) | ~ (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl1939])).
% 30.17/4.91 thf('33', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0)))) |
% 30.17/4.91 ~ (((inverse @ sk_c4) = (sk_c1))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12))) | ~ (((sk_c11) = (sk_c1)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl343])).
% 30.17/4.91 thf('34', plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0)))) |
% 30.17/4.91 ~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))) |
% 30.17/4.91 ~
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl294])).
% 30.17/4.91 thf(zip_derived_cl1689, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl1688, zip_derived_cl708, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl307, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl305])).
% 30.17/4.91 thf(zip_derived_cl1715, plain,
% 30.17/4.91 ((((sk_c11) != (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1689, zip_derived_cl307])).
% 30.17/4.91 thf(zip_derived_cl708, plain,
% 30.17/4.91 ((((sk_c11) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl1761, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl1715, zip_derived_cl708])).
% 30.17/4.91 thf('35', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))) |
% 30.17/4.91 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl1761])).
% 30.17/4.91 thf(zip_derived_cl78, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl5])).
% 30.17/4.91 thf(zip_derived_cl80, plain,
% 30.17/4.91 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl6])).
% 30.17/4.91 thf(zip_derived_cl215, plain,
% 30.17/4.91 ((![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 30.17/4.91 <= ((![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl227, plain,
% 30.17/4.91 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c5 @ sk_c11) != (sk_c10))))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl215])).
% 30.17/4.91 thf(zip_derived_cl230, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) != (sk_c10)))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl227])).
% 30.17/4.91 thf(zip_derived_cl310, plain,
% 30.17/4.91 ((((sk_c10) != (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl230])).
% 30.17/4.91 thf('36', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 30.17/4.91 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl310])).
% 30.17/4.91 thf('37', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12)))) |
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c9)) | ((multiply @ X1 @ sk_c9) != (sk_c12)))) |
% 30.17/4.91 ~ (((multiply @ sk_c8 @ sk_c9) = (sk_c7))) |
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c7) != (X0))
% 30.17/4.91 | ((inverse @ sk_c8) != (X0)))) |
% 30.17/4.91 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c12)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl423])).
% 30.17/4.91 thf(zip_derived_cl651, plain,
% 30.17/4.91 ((((sk_c12) = (multiply @ sk_c12 @ sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl619])).
% 30.17/4.91 thf(zip_derived_cl298, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c11) != (sk_c12)))
% 30.17/4.91 <= (~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl293])).
% 30.17/4.91 thf(zip_derived_cl656, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c12)))
% 30.17/4.91 <= (~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl651, zip_derived_cl298])).
% 30.17/4.91 thf('38', plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl656])).
% 30.17/4.91 thf(prove_this_53, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.91 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_34, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.91 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_53])).
% 30.17/4.91 thf(zip_derived_cl55, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 30.17/4.91 | ((multiply @ sk_c3 @ sk_c11) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_34])).
% 30.17/4.91 thf('39', plain,
% 30.17/4.91 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl55])).
% 30.17/4.91 thf(prove_this_63, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) ))).
% 30.17/4.91 thf(zf_stmt_35, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c5 @ sk_c11 ) = ( sk_c10 ) ) |
% 30.17/4.91 ( ( inverse @ sk_c3 ) = ( sk_c11 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_63])).
% 30.17/4.91 thf(zip_derived_cl65, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))
% 30.17/4.91 | ((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_35])).
% 30.17/4.91 thf('40', plain,
% 30.17/4.91 ((((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl65])).
% 30.17/4.91 thf(zip_derived_cl1432, plain,
% 30.17/4.91 ((((sk_c12) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl1378, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl78, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl5])).
% 30.17/4.91 thf(zip_derived_cl80, plain,
% 30.17/4.91 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl6])).
% 30.17/4.91 thf(zip_derived_cl216, plain,
% 30.17/4.91 ((![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12))))
% 30.17/4.91 <= ((![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl232, plain,
% 30.17/4.91 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c5 @ sk_c11) != (sk_c12))))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl80, zip_derived_cl216])).
% 30.17/4.91 thf(zip_derived_cl235, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) != (sk_c12)))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl232])).
% 30.17/4.91 thf(zip_derived_cl311, plain,
% 30.17/4.91 ((((sk_c10) != (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl78, zip_derived_cl235])).
% 30.17/4.91 thf(zip_derived_cl1564, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1432, zip_derived_cl311])).
% 30.17/4.91 thf('41', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))) |
% 30.17/4.91 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl1564])).
% 30.17/4.91 thf(zip_derived_cl75, plain,
% 30.17/4.91 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.91 thf(zip_derived_cl76, plain,
% 30.17/4.91 ((((inverse @ sk_c4) = (sk_c12))) <= ((((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl4])).
% 30.17/4.91 thf(zip_derived_cl214, plain,
% 30.17/4.91 ((![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11))))
% 30.17/4.91 <= ((![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl221, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c12)) | ((multiply @ sk_c4 @ sk_c12) != (sk_c11))))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl214])).
% 30.17/4.91 thf(zip_derived_cl225, plain,
% 30.17/4.91 ((((multiply @ sk_c4 @ sk_c12) != (sk_c11)))
% 30.17/4.91 <= ((((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl221])).
% 30.17/4.91 thf(zip_derived_cl284, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl225])).
% 30.17/4.91 thf('42', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))) |
% 30.17/4.91 ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl284])).
% 30.17/4.91 thf('43', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c4) != (X0)))) |
% 30.17/4.91 ~ (((sk_c12) = (sk_c4))) | ~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((sk_c11) = (sk_c4)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl342])).
% 30.17/4.91 thf('44', plain,
% 30.17/4.91 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12)))) |
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))) |
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl688, plain,
% 30.17/4.91 ((((sk_c1) = (multiply @ (inverse @ sk_c12) @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl2, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.91 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.91 thf(zip_derived_cl766, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c1 @ X0)
% 30.17/4.91 = (multiply @ (inverse @ sk_c12) @ (multiply @ identity @ X0))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl688, zip_derived_cl2])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl770, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c12) @ X0)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl766, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl1, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.91 thf(zip_derived_cl1648, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl770, zip_derived_cl1])).
% 30.17/4.91 thf(prove_this_11, conjecture,
% 30.17/4.91 (~( ( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.91 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) ) ))).
% 30.17/4.91 thf(zf_stmt_36, negated_conjecture,
% 30.17/4.91 (( ( multiply @ sk_c4 @ sk_c12 ) = ( sk_c11 ) ) |
% 30.17/4.91 ( ( multiply @ sk_c1 @ sk_c12 ) = ( sk_c11 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 30.17/4.91 thf(zip_derived_cl13, plain,
% 30.17/4.91 ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))
% 30.17/4.91 | ((multiply @ sk_c1 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_36])).
% 30.17/4.91 thf(zip_derived_cl94, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl13])).
% 30.17/4.91 thf(zip_derived_cl1663, plain,
% 30.17/4.91 ((((identity) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl1648, zip_derived_cl94])).
% 30.17/4.91 thf(zip_derived_cl298, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c11) != (sk_c12)))
% 30.17/4.91 <= (~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl293])).
% 30.17/4.91 thf(zip_derived_cl6703, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ identity) != (sk_c12)))
% 30.17/4.91 <= (~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1663, zip_derived_cl298])).
% 30.17/4.91 thf(zip_derived_cl1648, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl770, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl261, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c1) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl2, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.91 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.91 thf(zip_derived_cl641, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ identity @ X0)
% 30.17/4.91 = (multiply @ sk_c12 @ (multiply @ sk_c1 @ X0))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl2])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl642, plain,
% 30.17/4.91 ((![X0 : $i]: ((X0) = (multiply @ sk_c12 @ (multiply @ sk_c1 @ X0))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl641, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl1662, plain,
% 30.17/4.91 ((((sk_c12) = (multiply @ sk_c12 @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1648, zip_derived_cl642])).
% 30.17/4.91 thf(zip_derived_cl6782, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c12)))
% 30.17/4.91 <= (~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl6703, zip_derived_cl1662])).
% 30.17/4.91 thf('45', plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl6782])).
% 30.17/4.91 thf(zip_derived_cl1369, plain,
% 30.17/4.91 ((((identity) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1351, zip_derived_cl134])).
% 30.17/4.91 thf(zip_derived_cl261, plain,
% 30.17/4.91 ((((multiply @ sk_c12 @ sk_c1) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl272, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c10 @ X0)
% 30.17/4.91 = (multiply @ sk_c11 @ (multiply @ sk_c12 @ X0))))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl2])).
% 30.17/4.91 thf(zip_derived_cl756, plain,
% 30.17/4.91 ((((multiply @ sk_c10 @ sk_c1) = (multiply @ sk_c11 @ identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl272])).
% 30.17/4.91 thf(zip_derived_cl4347, plain,
% 30.17/4.91 ((((multiply @ identity @ sk_c1) = (multiply @ sk_c11 @ identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1369, zip_derived_cl756])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl1368, plain,
% 30.17/4.91 ((((sk_c11) = (multiply @ sk_c11 @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1351, zip_derived_cl645])).
% 30.17/4.91 thf(zip_derived_cl4351, plain,
% 30.17/4.91 ((((sk_c1) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl4347, zip_derived_cl0, zip_derived_cl1368])).
% 30.17/4.91 thf(zip_derived_cl347, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c1))) <= (~ (((sk_c11) = (sk_c1))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl343])).
% 30.17/4.91 thf(zip_derived_cl5684, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c11)))
% 30.17/4.91 <= (~ (((sk_c11) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl4351, zip_derived_cl347])).
% 30.17/4.91 thf('46', plain,
% 30.17/4.91 ((((sk_c11) = (sk_c1))) | ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c2) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl5684])).
% 30.17/4.91 thf(zip_derived_cl174, plain,
% 30.17/4.91 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl53])).
% 30.17/4.91 thf(zip_derived_cl194, plain,
% 30.17/4.91 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl63])).
% 30.17/4.91 thf(zip_derived_cl216, plain,
% 30.17/4.91 ((![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12))))
% 30.17/4.91 <= ((![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl374, plain,
% 30.17/4.91 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c3 @ sk_c11) != (sk_c12))))
% 30.17/4.91 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl216])).
% 30.17/4.91 thf(zip_derived_cl377, plain,
% 30.17/4.91 ((((multiply @ sk_c3 @ sk_c11) != (sk_c12)))
% 30.17/4.91 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl374])).
% 30.17/4.91 thf(zip_derived_cl562, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl377])).
% 30.17/4.91 thf('47', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X6 : $i]:
% 30.17/4.91 (((inverse @ X6) != (sk_c11))
% 30.17/4.91 | ((multiply @ X6 @ sk_c11) != (sk_c12)))) |
% 30.17/4.91 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl562])).
% 30.17/4.91 thf(zip_derived_cl1663, plain,
% 30.17/4.91 ((((identity) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl1648, zip_derived_cl94])).
% 30.17/4.91 thf(zip_derived_cl74, plain,
% 30.17/4.91 ((((multiply @ sk_c11 @ sk_c12) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl3])).
% 30.17/4.91 thf(zip_derived_cl6683, plain,
% 30.17/4.91 ((((multiply @ identity @ sk_c12) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl1663, zip_derived_cl74])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl6775, plain,
% 30.17/4.91 ((((sk_c12) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl6683, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl563, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl174, zip_derived_cl378])).
% 30.17/4.91 thf(zip_derived_cl6893, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl6775, zip_derived_cl563])).
% 30.17/4.91 thf(zip_derived_cl1541, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.91 thf(zip_derived_cl1541, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.91 thf(zip_derived_cl6913, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl6893, zip_derived_cl1541, zip_derived_cl1541])).
% 30.17/4.91 thf('48', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X7 : $i]:
% 30.17/4.91 (((inverse @ X7) != (sk_c11))
% 30.17/4.91 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 30.17/4.91 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl6913])).
% 30.17/4.91 thf(zip_derived_cl1541, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.91 thf(zip_derived_cl1648, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl770, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl114, plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf(zip_derived_cl296, plain,
% 30.17/4.91 ((![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12))))
% 30.17/4.91 <= ((![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl293])).
% 30.17/4.91 thf(zip_derived_cl304, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c12)) | ((multiply @ sk_c1 @ sk_c12) != (sk_c12))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl296])).
% 30.17/4.91 thf(zip_derived_cl306, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) != (sk_c12)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl304])).
% 30.17/4.91 thf(zip_derived_cl1665, plain,
% 30.17/4.91 ((((identity) != (sk_c12)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1648, zip_derived_cl306])).
% 30.17/4.91 thf(zip_derived_cl6542, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1541, zip_derived_cl1665])).
% 30.17/4.91 thf('49', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))) |
% 30.17/4.91 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl6542])).
% 30.17/4.91 thf(zip_derived_cl4351, plain,
% 30.17/4.91 ((((sk_c1) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl4347, zip_derived_cl0, zip_derived_cl1368])).
% 30.17/4.91 thf(zip_derived_cl1541, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.91 thf(zip_derived_cl114, plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf(zip_derived_cl214, plain,
% 30.17/4.91 ((![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11))))
% 30.17/4.91 <= ((![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl264, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c12)) | ((multiply @ sk_c1 @ sk_c12) != (sk_c11))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl214])).
% 30.17/4.91 thf(zip_derived_cl265, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) != (sk_c11)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl264])).
% 30.17/4.91 thf(zip_derived_cl3834, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ identity) != (sk_c11)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1541, zip_derived_cl265])).
% 30.17/4.91 thf(zip_derived_cl770, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c12) @ X0)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl766, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl688, plain,
% 30.17/4.91 ((((sk_c1) = (multiply @ (inverse @ sk_c12) @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl1652, plain,
% 30.17/4.91 ((((sk_c1) = (multiply @ sk_c1 @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl770, zip_derived_cl688])).
% 30.17/4.91 thf(zip_derived_cl3888, plain,
% 30.17/4.91 ((((sk_c1) != (sk_c11)))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl3834, zip_derived_cl1652])).
% 30.17/4.91 thf(zip_derived_cl5703, plain,
% 30.17/4.91 ((((sk_c11) != (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))) &
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl4351, zip_derived_cl3888])).
% 30.17/4.91 thf('50', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X8 : $i]:
% 30.17/4.91 (((inverse @ X8) != (sk_c12))
% 30.17/4.91 | ((multiply @ X8 @ sk_c12) != (sk_c11)))) |
% 30.17/4.91 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl5703])).
% 30.17/4.91 thf('51', plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl13])).
% 30.17/4.91 thf('52', plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf('53', plain,
% 30.17/4.91 ((((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl33])).
% 30.17/4.91 thf('54', plain,
% 30.17/4.91 ((((inverse @ sk_c2) = (sk_c11))) |
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl43])).
% 30.17/4.91 thf('55', plain,
% 30.17/4.91 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl53])).
% 30.17/4.91 thf('56', plain,
% 30.17/4.91 ((((inverse @ sk_c3) = (sk_c11))) |
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl63])).
% 30.17/4.91 thf(zip_derived_cl84, plain,
% 30.17/4.91 ((((inverse @ sk_c6) = (sk_c9))) <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl8])).
% 30.17/4.91 thf(zip_derived_cl1, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.91 thf(zip_derived_cl243, plain,
% 30.17/4.91 ((((multiply @ sk_c9 @ sk_c6) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl84, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl259, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i]:
% 30.17/4.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl693, plain,
% 30.17/4.91 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl243, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl2, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.91 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.91 thf(zip_derived_cl814, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c6 @ X0)
% 30.17/4.91 = (multiply @ (inverse @ sk_c9) @ (multiply @ identity @ X0))))
% 30.17/4.91 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl693, zip_derived_cl2])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl817, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c6 @ X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 30.17/4.91 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl814, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl1, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.91 thf(zip_derived_cl1851, plain,
% 30.17/4.91 ((((multiply @ sk_c6 @ sk_c9) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl817, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl82, plain,
% 30.17/4.91 ((((multiply @ sk_c6 @ sk_c9) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl7])).
% 30.17/4.91 thf(zip_derived_cl1865, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl1851, zip_derived_cl82])).
% 30.17/4.91 thf(zip_derived_cl80, plain,
% 30.17/4.91 ((((inverse @ sk_c5) = (sk_c11))) <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl6])).
% 30.17/4.91 thf(zip_derived_cl1, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.91 thf(zip_derived_cl242, plain,
% 30.17/4.91 ((((multiply @ sk_c11 @ sk_c5) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl259, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i]:
% 30.17/4.91 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl257, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl682, plain,
% 30.17/4.91 ((((sk_c5) = (multiply @ (inverse @ sk_c11) @ identity)))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl242, zip_derived_cl259])).
% 30.17/4.91 thf(zip_derived_cl2, plain,
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i]:
% 30.17/4.91 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 30.17/4.91 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 30.17/4.91 inference('cnf', [status(esa)], [associativity])).
% 30.17/4.91 thf(zip_derived_cl717, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c5 @ X0)
% 30.17/4.91 = (multiply @ (inverse @ sk_c11) @ (multiply @ identity @ X0))))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl682, zip_derived_cl2])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl720, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl717, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl1, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_inverse])).
% 30.17/4.91 thf(zip_derived_cl1266, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (identity)))
% 30.17/4.91 <= ((((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl720, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl78, plain,
% 30.17/4.91 ((((multiply @ sk_c5 @ sk_c11) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl5])).
% 30.17/4.91 thf(zip_derived_cl1301, plain,
% 30.17/4.91 ((((identity) = (sk_c10)))
% 30.17/4.91 <= ((((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl1266, zip_derived_cl78])).
% 30.17/4.91 thf(zip_derived_cl708, plain,
% 30.17/4.91 ((((sk_c11) = (identity)))
% 30.17/4.91 <= ((((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl686, zip_derived_cl1])).
% 30.17/4.91 thf(zip_derived_cl220, plain,
% 30.17/4.91 ((((multiply @ sk_c11 @ sk_c12) != (sk_c10)))
% 30.17/4.91 <= (~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl1383, plain,
% 30.17/4.91 ((((multiply @ identity @ sk_c12) != (sk_c10)))
% 30.17/4.91 <= (~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl708, zip_derived_cl220])).
% 30.17/4.91 thf(zip_derived_cl0, plain,
% 30.17/4.91 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 30.17/4.91 inference('cnf', [status(esa)], [left_identity])).
% 30.17/4.91 thf(zip_derived_cl1433, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c10)))
% 30.17/4.91 <= (~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))))),
% 30.17/4.91 inference('demod', [status(thm)], [zip_derived_cl1383, zip_derived_cl0])).
% 30.17/4.91 thf(zip_derived_cl2162, plain,
% 30.17/4.91 ((((sk_c12) != (identity)))
% 30.17/4.91 <= (~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1301, zip_derived_cl1433])).
% 30.17/4.91 thf(zip_derived_cl11177, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= (~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c4) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11))) &
% 30.17/4.91 (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c6) = (sk_c9))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1865, zip_derived_cl2162])).
% 30.17/4.91 thf('57', plain,
% 30.17/4.91 (~ (((inverse @ sk_c4) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c6 @ sk_c9) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c5) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c4 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c5 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c6) = (sk_c9))) |
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl11177])).
% 30.17/4.91 thf(prove_this_54, conjecture,
% 30.17/4.91 (~( ( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.91 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) ) ))).
% 30.17/4.91 thf(zf_stmt_37, negated_conjecture,
% 30.17/4.91 (( ( inverse @ sk_c5 ) = ( sk_c11 ) ) |
% 30.17/4.91 ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c12 ) )),
% 30.17/4.91 inference('cnf.neg', [status(esa)], [prove_this_54])).
% 30.17/4.91 thf(zip_derived_cl56, plain,
% 30.17/4.91 ((((inverse @ sk_c5) = (sk_c11))
% 30.17/4.91 | ((multiply @ sk_c3 @ sk_c11) = (sk_c12)))),
% 30.17/4.91 inference('cnf', [status(esa)], [zf_stmt_37])).
% 30.17/4.91 thf('58', plain,
% 30.17/4.91 ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 (((inverse @ sk_c5) = (sk_c11)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl56])).
% 30.17/4.91 thf(zip_derived_cl1663, plain,
% 30.17/4.91 ((((identity) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('s_sup+', [status(thm)], [zip_derived_cl1648, zip_derived_cl94])).
% 30.17/4.91 thf(zip_derived_cl1541, plain,
% 30.17/4.91 ((((identity) = (sk_c12)))
% 30.17/4.91 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup+', [status(thm)],
% 30.17/4.91 [zip_derived_cl1520, zip_derived_cl174])).
% 30.17/4.91 thf(zip_derived_cl4351, plain,
% 30.17/4.91 ((((sk_c1) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('demod', [status(thm)],
% 30.17/4.91 [zip_derived_cl4347, zip_derived_cl0, zip_derived_cl1368])).
% 30.17/4.91 thf(zip_derived_cl114, plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf(zip_derived_cl471, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c12) != (X0))
% 30.17/4.91 | ((inverse @ sk_c6) != (X0))))
% 30.17/4.91 <= ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c12) != (X0))
% 30.17/4.91 | ((inverse @ sk_c6) != (X0)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl353])).
% 30.17/4.91 thf(zip_derived_cl490, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c9))
% 30.17/4.91 | ((sk_c12) != (sk_c1))
% 30.17/4.91 | ((inverse @ sk_c6) != (sk_c1))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c9))
% 30.17/4.91 | ((sk_c12) != (X0))
% 30.17/4.91 | ((inverse @ sk_c6) != (X0)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl471])).
% 30.17/4.91 thf(zip_derived_cl533, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c1))) <= (~ (((sk_c12) = (sk_c1))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl490])).
% 30.17/4.91 thf(zip_derived_cl5690, plain,
% 30.17/4.91 ((((sk_c12) != (sk_c11)))
% 30.17/4.91 <= (~ (((sk_c12) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl4351, zip_derived_cl533])).
% 30.17/4.91 thf(zip_derived_cl6362, plain,
% 30.17/4.91 ((((identity) != (sk_c11)))
% 30.17/4.91 <= (~ (((sk_c12) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1541, zip_derived_cl5690])).
% 30.17/4.91 thf(zip_derived_cl6774, plain,
% 30.17/4.91 ((((identity) != (identity)))
% 30.17/4.91 <= (~ (((sk_c12) = (sk_c1))) &
% 30.17/4.91 (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) &
% 30.17/4.91 (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) &
% 30.17/4.91 (((inverse @ sk_c2) = (sk_c11))) &
% 30.17/4.91 (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) &
% 30.17/4.91 (((inverse @ sk_c3) = (sk_c11))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl1663, zip_derived_cl6362])).
% 30.17/4.91 thf('59', plain,
% 30.17/4.91 ((((sk_c12) = (sk_c1))) | ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 ~ (((inverse @ sk_c2) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c2 @ sk_c11) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12))) |
% 30.17/4.91 ~ (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~ (((multiply @ sk_c11 @ sk_c12) = (sk_c10))) |
% 30.17/4.91 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl6774])).
% 30.17/4.91 thf(zip_derived_cl114, plain,
% 30.17/4.91 ((((inverse @ sk_c1) = (sk_c12))) <= ((((inverse @ sk_c1) = (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl23])).
% 30.17/4.91 thf(zip_derived_cl94, plain,
% 30.17/4.91 ((((multiply @ sk_c1 @ sk_c12) = (sk_c11)))
% 30.17/4.91 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl13])).
% 30.17/4.91 thf(zip_derived_cl219, plain,
% 30.17/4.91 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12))))
% 30.17/4.91 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl73])).
% 30.17/4.91 thf(zip_derived_cl435, plain,
% 30.17/4.91 ((![X0 : $i, X1 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0))
% 30.17/4.91 | ((multiply @ sk_c12 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12))))
% 30.17/4.91 <= ((((multiply @ sk_c1 @ sk_c12) = (sk_c11))) &
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl219])).
% 30.17/4.91 thf(zip_derived_cl1333, plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0))))
% 30.17/4.91 <= ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0)))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl435])).
% 30.17/4.91 thf(zip_derived_cl1340, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c12)) | ((sk_c11) != (sk_c1)) | ((sk_c12) != (sk_c1))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0)))))),
% 30.17/4.91 inference('s_sup-', [status(thm)],
% 30.17/4.91 [zip_derived_cl114, zip_derived_cl1333])).
% 30.17/4.91 thf(zip_derived_cl1344, plain,
% 30.17/4.91 (((((sk_c12) != (sk_c1)) | ((sk_c11) != (sk_c1))))
% 30.17/4.91 <= ((((inverse @ sk_c1) = (sk_c12))) &
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0)))))),
% 30.17/4.91 inference('simplify', [status(thm)], [zip_derived_cl1340])).
% 30.17/4.91 thf('60', plain,
% 30.17/4.91 (~
% 30.17/4.91 (![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0)))) |
% 30.17/4.91 ~ (((sk_c12) = (sk_c1))) | ~ (((sk_c11) = (sk_c1))) |
% 30.17/4.91 ~ (((inverse @ sk_c1) = (sk_c12)))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl1344])).
% 30.17/4.91 thf('61', plain,
% 30.17/4.91 ((![X0 : $i]:
% 30.17/4.91 (((inverse @ X0) != (sk_c12))
% 30.17/4.91 | ((sk_c11) != (X0))
% 30.17/4.91 | ((inverse @ sk_c1) != (X0)))) |
% 30.17/4.91 ~ (((multiply @ sk_c12 @ sk_c11) = (sk_c12))) |
% 30.17/4.91 (![X1 : $i]:
% 30.17/4.91 (((inverse @ X1) != (sk_c12))
% 30.17/4.91 | ((multiply @ X1 @ sk_c12) != (sk_c12)))) |
% 30.17/4.91 ~ (((multiply @ sk_c1 @ sk_c12) = (sk_c11))) |
% 30.17/4.91 ~
% 30.17/4.91 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 30.17/4.91 (((inverse @ X0) != (X2))
% 30.17/4.91 | ((multiply @ X1 @ X2) != (X0))
% 30.17/4.91 | ((inverse @ X1) != (X0))
% 30.17/4.91 | ((multiply @ X2 @ sk_c11) != (sk_c12))
% 30.17/4.91 | ((inverse @ X3) != (X2))
% 30.17/4.91 | ((multiply @ X3 @ X2) != (sk_c12))))),
% 30.17/4.91 inference('split', [status(esa)], [zip_derived_cl435])).
% 30.17/4.91 thf(zip_derived_cl30447, plain, ($false),
% 30.17/4.91 inference('sat_resolution*', [status(thm)],
% 30.17/4.91 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 30.17/4.91 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 30.17/4.91 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 30.17/4.91 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 30.17/4.91 '42', '43', '44', '45', '46', '47', '48', '49', '50', '51',
% 30.17/4.91 '52', '53', '54', '55', '56', '57', '58', '59', '60', '61'])).
% 30.17/4.91
% 30.17/4.91 % SZS output end Refutation
% 30.17/4.91
% 30.17/4.91
% 30.17/4.91 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 30.17/4.91 % Terminating...
% 30.50/4.99 % Runner terminated.
% 30.50/5.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------