TSTP Solution File: GRP250-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP250-1 : 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.A7jKeAMhVL true
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:54 EDT 2023
% Result : Unsatisfiable 8.70s 1.85s
% Output : Refutation 8.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP250-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.A7jKeAMhVL true
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 19:49:31 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.16/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.16/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.16/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.16/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 8.70/1.85 % Solved by fo/fo1_av.sh.
% 8.70/1.85 % done 2200 iterations in 1.085s
% 8.70/1.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.70/1.85 % SZS output start Refutation
% 8.70/1.85 thf(sk_c6_type, type, sk_c6: $i).
% 8.70/1.85 thf(sk_c8_type, type, sk_c8: $i).
% 8.70/1.85 thf(sk_c3_type, type, sk_c3: $i).
% 8.70/1.85 thf(sk_c7_type, type, sk_c7: $i).
% 8.70/1.85 thf(sk_c5_type, type, sk_c5: $i).
% 8.70/1.85 thf(identity_type, type, identity: $i).
% 8.70/1.85 thf(multiply_type, type, multiply: $i > $i > $i).
% 8.70/1.85 thf(sk_c9_type, type, sk_c9: $i).
% 8.70/1.85 thf(inverse_type, type, inverse: $i > $i).
% 8.70/1.85 thf(sk_c4_type, type, sk_c4: $i).
% 8.70/1.85 thf(sk_c2_type, type, sk_c2: $i).
% 8.70/1.85 thf(sk_c1_type, type, sk_c1: $i).
% 8.70/1.85 thf(prove_this_12, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 8.70/1.85 thf(zf_stmt_0, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 8.70/1.85 thf(zip_derived_cl14, plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.70/1.85 thf('0', plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl14])).
% 8.70/1.85 thf(prove_this_11, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 8.70/1.85 thf(zf_stmt_1, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 8.70/1.85 thf(zip_derived_cl13, plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_1])).
% 8.70/1.85 thf('1', plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7))) | (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl13])).
% 8.70/1.85 thf(prove_this_9, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 8.70/1.85 thf(zf_stmt_2, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 8.70/1.85 thf(zip_derived_cl11, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_2])).
% 8.70/1.85 thf('2', plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl11])).
% 8.70/1.85 thf(prove_this_1, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_3, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 8.70/1.85 thf(zip_derived_cl3, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 8.70/1.85 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_3])).
% 8.70/1.85 thf(zip_derived_cl40, plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl3])).
% 8.70/1.85 thf(prove_this_7, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 8.70/1.85 thf(zf_stmt_4, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 8.70/1.85 thf(zip_derived_cl9, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_4])).
% 8.70/1.85 thf(zip_derived_cl52, plain,
% 8.70/1.85 ((((inverse @ sk_c1) = (sk_c9))) <= ((((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl9])).
% 8.70/1.85 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl134, plain,
% 8.70/1.85 ((((multiply @ sk_c9 @ sk_c1) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl1])).
% 8.70/1.85 thf(associativity, axiom,
% 8.70/1.85 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 8.70/1.85 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl213, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ sk_c9 @ (multiply @ sk_c1 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl2])).
% 8.70/1.85 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl214, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c1 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl213, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl226, plain,
% 8.70/1.85 ((((sk_c9) = (multiply @ sk_c9 @ sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl214])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl154, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl286, plain,
% 8.70/1.85 ((((sk_c8) = (multiply @ (inverse @ sk_c9) @ sk_c9)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl226, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl317, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl286, zip_derived_cl1])).
% 8.70/1.85 thf(prove_this_19, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_5, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 8.70/1.85 thf(zip_derived_cl21, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_5])).
% 8.70/1.85 thf(zip_derived_cl76, plain,
% 8.70/1.85 ((((inverse @ sk_c2) = (sk_c8))) <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl21])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl169, plain,
% 8.70/1.85 ((((multiply @ sk_c8 @ sk_c2) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl221, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ sk_c8 @ (multiply @ sk_c2 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl169, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl222, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c8 @ (multiply @ sk_c2 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl221, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl295, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl222, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl841, plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl295, zip_derived_cl1])).
% 8.70/1.85 thf(prove_this_13, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 8.70/1.85 thf(zf_stmt_6, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 8.70/1.85 thf(zip_derived_cl15, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 8.70/1.85 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_6])).
% 8.70/1.85 thf(zip_derived_cl64, plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl15])).
% 8.70/1.85 thf(zip_derived_cl857, plain,
% 8.70/1.85 ((((identity) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl841, zip_derived_cl64])).
% 8.70/1.85 thf(prove_this_5, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_7, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 8.70/1.85 thf(zip_derived_cl7, plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_7])).
% 8.70/1.85 thf(zip_derived_cl48, plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7))) <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl7])).
% 8.70/1.85 thf(prove_this_37, conjecture,
% 8.70/1.85 (~( ( ( multiply @ X3 @ sk_c8 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 8.70/1.85 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ X6 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 8.70/1.85 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_8, negated_conjecture,
% 8.70/1.85 (( ( multiply @ X3 @ sk_c8 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X3 ) != ( sk_c7 ) ) | ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 8.70/1.85 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ X6 ) != ( sk_c8 ) ) | ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 8.70/1.85 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 8.70/1.85 thf(zip_derived_cl39, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 8.70/1.85 (((multiply @ X0 @ sk_c8) != (sk_c7))
% 8.70/1.85 | ((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((inverse @ X1) != (sk_c8))
% 8.70/1.85 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 8.70/1.85 | ((inverse @ X2) != (sk_c9))
% 8.70/1.85 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 8.70/1.85 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8))
% 8.70/1.85 | ((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 8.70/1.85 | ((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_8])).
% 8.70/1.85 thf(zip_derived_cl113, plain,
% 8.70/1.85 ((![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8)) | ((multiply @ X4 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl127, plain,
% 8.70/1.85 (((((sk_c7) != (sk_c8)) | ((multiply @ sk_c6 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl113])).
% 8.70/1.85 thf(zip_derived_cl159, plain,
% 8.70/1.85 ((((sk_c7) != (sk_c8))) <= (~ (((sk_c7) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl127])).
% 8.70/1.85 thf(zip_derived_cl10362, plain,
% 8.70/1.85 ((((identity) != (sk_c8)))
% 8.70/1.85 <= (~ (((sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl857, zip_derived_cl159])).
% 8.70/1.85 thf(zip_derived_cl20166, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= (~ (((sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)],
% 8.70/1.85 [zip_derived_cl317, zip_derived_cl10362])).
% 8.70/1.85 thf('3', plain,
% 8.70/1.85 ((((sk_c7) = (sk_c8))) | ~ (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c1) = (sk_c9))) |
% 8.70/1.85 ~ (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c2) = (sk_c8)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl20166])).
% 8.70/1.85 thf(zip_derived_cl857, plain,
% 8.70/1.85 ((((identity) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl841, zip_derived_cl64])).
% 8.70/1.85 thf(prove_this_25, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_9, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 8.70/1.85 thf(zip_derived_cl27, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_9])).
% 8.70/1.85 thf(zip_derived_cl88, plain,
% 8.70/1.85 ((((inverse @ sk_c3) = (sk_c8))) <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl27])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl187, plain,
% 8.70/1.85 ((((multiply @ sk_c8 @ sk_c3) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl88, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl223, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ sk_c8 @ (multiply @ sk_c3 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl187, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl224, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c8 @ (multiply @ sk_c3 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl223, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl296, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl224, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl966, plain,
% 8.70/1.85 ((((multiply @ sk_c3 @ sk_c8) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl296, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl88, plain,
% 8.70/1.85 ((((inverse @ sk_c3) = (sk_c8))) <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl27])).
% 8.70/1.85 thf(zip_derived_cl117, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl188, plain,
% 8.70/1.85 (((((sk_c8) != (sk_c7)) | ((multiply @ sk_c3 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))) &
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl117])).
% 8.70/1.85 thf(zip_derived_cl193, plain,
% 8.70/1.85 ((((multiply @ sk_c3 @ sk_c8) != (sk_c7)))
% 8.70/1.85 <= (~ (((multiply @ sk_c3 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl188])).
% 8.70/1.85 thf(zip_derived_cl985, plain,
% 8.70/1.85 ((((identity) != (sk_c7)))
% 8.70/1.85 <= (~ (((multiply @ sk_c3 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl966, zip_derived_cl193])).
% 8.70/1.85 thf(zip_derived_cl10398, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= (~ (((multiply @ sk_c3 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl857, zip_derived_cl985])).
% 8.70/1.85 thf('4', plain,
% 8.70/1.85 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c2) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c3) = (sk_c8)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl10398])).
% 8.70/1.85 thf(prove_this_31, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_10, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 8.70/1.85 thf(zip_derived_cl33, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 8.70/1.85 | ((multiply @ sk_c3 @ sk_c7) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_10])).
% 8.70/1.85 thf(zip_derived_cl100, plain,
% 8.70/1.85 ((((multiply @ sk_c3 @ sk_c7) = (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c3 @ sk_c7) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl33])).
% 8.70/1.85 thf(zip_derived_cl88, plain,
% 8.70/1.85 ((((inverse @ sk_c3) = (sk_c8))) <= ((((inverse @ sk_c3) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl27])).
% 8.70/1.85 thf(zip_derived_cl114, plain,
% 8.70/1.85 ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8))))
% 8.70/1.85 <= ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl189, plain,
% 8.70/1.85 (((((multiply @ sk_c3 @ sk_c7) != (sk_c8)) | ((sk_c8) != (sk_c8))))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl88, zip_derived_cl114])).
% 8.70/1.85 thf(zip_derived_cl191, plain,
% 8.70/1.85 ((((multiply @ sk_c3 @ sk_c7) != (sk_c8)))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 8.70/1.85 thf(zip_derived_cl211, plain,
% 8.70/1.85 ((((sk_c8) != (sk_c8)))
% 8.70/1.85 <= ((((inverse @ sk_c3) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c3 @ sk_c7) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl191])).
% 8.70/1.85 thf('5', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8)))) |
% 8.70/1.85 ~ (((inverse @ sk_c3) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c3 @ sk_c7) = (sk_c8)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl211])).
% 8.70/1.85 thf(prove_this_4, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_11, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 8.70/1.85 thf(zip_derived_cl6, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_11])).
% 8.70/1.85 thf('6', plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl6])).
% 8.70/1.85 thf(prove_this_28, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_12, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 8.70/1.85 thf(zip_derived_cl30, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_12])).
% 8.70/1.85 thf('7', plain,
% 8.70/1.85 ((((inverse @ sk_c3) = (sk_c8))) | (((inverse @ sk_c5) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl30])).
% 8.70/1.85 thf(prove_this_34, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_13, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 8.70/1.85 thf(zip_derived_cl36, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_13])).
% 8.70/1.85 thf('8', plain,
% 8.70/1.85 ((((multiply @ sk_c3 @ sk_c7) = (sk_c8))) |
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl36])).
% 8.70/1.85 thf(prove_this_3, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_14, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 8.70/1.85 thf(zip_derived_cl5, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))
% 8.70/1.85 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.70/1.85 thf('9', plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl5])).
% 8.70/1.85 thf(zip_derived_cl41, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl3])).
% 8.70/1.85 thf(prove_this_2, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_15, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 8.70/1.85 thf(zip_derived_cl4, plain,
% 8.70/1.85 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_15])).
% 8.70/1.85 thf(zip_derived_cl42, plain,
% 8.70/1.85 ((((inverse @ sk_c4) = (sk_c9))) <= ((((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl4])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl135, plain,
% 8.70/1.85 ((((multiply @ sk_c9 @ sk_c4) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl42, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl215, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ sk_c9 @ (multiply @ sk_c4 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl216, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c9 @ (multiply @ sk_c4 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl215, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl229, plain,
% 8.70/1.85 ((((sk_c9) = (multiply @ sk_c9 @ sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl216])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl287, plain,
% 8.70/1.85 ((((sk_c8) = (multiply @ (inverse @ sk_c9) @ sk_c9)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl229, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl318, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl287, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl44, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl5])).
% 8.70/1.85 thf(zip_derived_cl46, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl6])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl136, plain,
% 8.70/1.85 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl217, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ sk_c8 @ (multiply @ sk_c5 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl218, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c8 @ (multiply @ sk_c5 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl217, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl246, plain,
% 8.70/1.85 ((((sk_c8) = (multiply @ sk_c8 @ sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl218])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl298, plain,
% 8.70/1.85 ((((sk_c7) = (multiply @ (inverse @ sk_c8) @ sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl324, plain,
% 8.70/1.85 ((((sk_c7) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl298, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl159, plain,
% 8.70/1.85 ((((sk_c7) != (sk_c8))) <= (~ (((sk_c7) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl127])).
% 8.70/1.85 thf(zip_derived_cl1699, plain,
% 8.70/1.85 ((((identity) != (sk_c8)))
% 8.70/1.85 <= (~ (((sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl324, zip_derived_cl159])).
% 8.70/1.85 thf(zip_derived_cl3607, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= (~ (((sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)],
% 8.70/1.85 [zip_derived_cl318, zip_derived_cl1699])).
% 8.70/1.85 thf('10', plain,
% 8.70/1.85 ((((sk_c7) = (sk_c8))) | ~ (((multiply @ sk_c4 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c4) = (sk_c9)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl3607])).
% 8.70/1.85 thf(zip_derived_cl318, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl287, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl48, plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7))) <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl7])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl137, plain,
% 8.70/1.85 ((((multiply @ sk_c7 @ sk_c6) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl219, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ identity @ X0)
% 8.70/1.85 = (multiply @ sk_c7 @ (multiply @ sk_c6 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl137, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl220, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c7 @ (multiply @ sk_c6 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl219, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl303, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c6 @ X0) = (multiply @ (inverse @ sk_c7) @ X0)))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl220, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl1058, plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c7) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl303, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl48, plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7))) <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl7])).
% 8.70/1.85 thf(zip_derived_cl114, plain,
% 8.70/1.85 ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8))))
% 8.70/1.85 <= ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl132, plain,
% 8.70/1.85 (((((multiply @ sk_c6 @ sk_c7) != (sk_c8)) | ((sk_c7) != (sk_c8))))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl114])).
% 8.70/1.85 thf(zip_derived_cl164, plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c7) != (sk_c8)))
% 8.70/1.85 <= (~ (((multiply @ sk_c6 @ sk_c7) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl132])).
% 8.70/1.85 thf(zip_derived_cl1165, plain,
% 8.70/1.85 ((((identity) != (sk_c8)))
% 8.70/1.85 <= (~ (((multiply @ sk_c6 @ sk_c7) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('s_sup-', [status(thm)],
% 8.70/1.85 [zip_derived_cl1058, zip_derived_cl164])).
% 8.70/1.85 thf(zip_derived_cl2484, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= (~ (((multiply @ sk_c6 @ sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('s_sup-', [status(thm)],
% 8.70/1.85 [zip_derived_cl318, zip_derived_cl1165])).
% 8.70/1.85 thf('11', plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c7) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c4) = (sk_c9))) |
% 8.70/1.85 ~ (((multiply @ sk_c4 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c6) = (sk_c7)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl2484])).
% 8.70/1.85 thf(prove_this_6, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_16, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 8.70/1.85 thf(zip_derived_cl8, plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7))
% 8.70/1.85 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_16])).
% 8.70/1.85 thf(zip_derived_cl50, plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c8) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c6 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl8])).
% 8.70/1.85 thf(zip_derived_cl48, plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7))) <= ((((inverse @ sk_c6) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl7])).
% 8.70/1.85 thf(zip_derived_cl117, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl143, plain,
% 8.70/1.85 (((((sk_c7) != (sk_c7)) | ((multiply @ sk_c6 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))) &
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl117])).
% 8.70/1.85 thf(zip_derived_cl144, plain,
% 8.70/1.85 ((((multiply @ sk_c6 @ sk_c8) != (sk_c7)))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))) &
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl143])).
% 8.70/1.85 thf(zip_derived_cl201, plain,
% 8.70/1.85 ((((sk_c7) != (sk_c7)))
% 8.70/1.85 <= ((((inverse @ sk_c6) = (sk_c7))) &
% 8.70/1.85 (((multiply @ sk_c6 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl50, zip_derived_cl144])).
% 8.70/1.85 thf('12', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7)))) |
% 8.70/1.85 ~ (((inverse @ sk_c6) = (sk_c7))) |
% 8.70/1.85 ~ (((multiply @ sk_c6 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl201])).
% 8.70/1.85 thf('13', plain,
% 8.70/1.85 ((((inverse @ sk_c6) = (sk_c7))) |
% 8.70/1.85 (((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl7])).
% 8.70/1.85 thf('14', plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 (((multiply @ sk_c6 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl8])).
% 8.70/1.85 thf('15', plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 (((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl3])).
% 8.70/1.85 thf('16', plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl4])).
% 8.70/1.85 thf(zip_derived_cl40, plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl3])).
% 8.70/1.85 thf(zip_derived_cl52, plain,
% 8.70/1.85 ((((inverse @ sk_c1) = (sk_c9))) <= ((((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl9])).
% 8.70/1.85 thf(zip_derived_cl112, plain,
% 8.70/1.85 ((![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9)) | ((multiply @ X5 @ sk_c9) != (sk_c8))))
% 8.70/1.85 <= ((![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl118, plain,
% 8.70/1.85 (((((sk_c9) != (sk_c9)) | ((multiply @ sk_c1 @ sk_c9) != (sk_c8))))
% 8.70/1.85 <= ((((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl112])).
% 8.70/1.85 thf(zip_derived_cl122, plain,
% 8.70/1.85 ((((multiply @ sk_c1 @ sk_c9) != (sk_c8)))
% 8.70/1.85 <= ((((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl118])).
% 8.70/1.85 thf(zip_derived_cl167, plain,
% 8.70/1.85 ((((sk_c8) != (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl40, zip_derived_cl122])).
% 8.70/1.85 thf('17', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9)) | ((multiply @ X5 @ sk_c9) != (sk_c8)))) |
% 8.70/1.85 ~ (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl167])).
% 8.70/1.85 thf('18', plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl9])).
% 8.70/1.85 thf(prove_this_8, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 8.70/1.85 thf(zf_stmt_17, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 8.70/1.85 thf(zip_derived_cl10, plain,
% 8.70/1.85 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_17])).
% 8.70/1.85 thf('19', plain,
% 8.70/1.85 ((((inverse @ sk_c4) = (sk_c9))) | (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl10])).
% 8.70/1.85 thf(zip_derived_cl41, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl3])).
% 8.70/1.85 thf(zip_derived_cl42, plain,
% 8.70/1.85 ((((inverse @ sk_c4) = (sk_c9))) <= ((((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl4])).
% 8.70/1.85 thf(zip_derived_cl112, plain,
% 8.70/1.85 ((![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9)) | ((multiply @ X5 @ sk_c9) != (sk_c8))))
% 8.70/1.85 <= ((![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl119, plain,
% 8.70/1.85 (((((sk_c9) != (sk_c9)) | ((multiply @ sk_c4 @ sk_c9) != (sk_c8))))
% 8.70/1.85 <= ((((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl42, zip_derived_cl112])).
% 8.70/1.85 thf(zip_derived_cl123, plain,
% 8.70/1.85 ((((multiply @ sk_c4 @ sk_c9) != (sk_c8)))
% 8.70/1.85 <= ((((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl119])).
% 8.70/1.85 thf(zip_derived_cl181, plain,
% 8.70/1.85 ((((sk_c8) != (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9))
% 8.70/1.85 | ((multiply @ X5 @ sk_c9) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl41, zip_derived_cl123])).
% 8.70/1.85 thf('20', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9)) | ((multiply @ X5 @ sk_c9) != (sk_c8)))) |
% 8.70/1.85 ~ (((inverse @ sk_c4) = (sk_c9))) |
% 8.70/1.85 ~ (((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl181])).
% 8.70/1.85 thf(prove_this_15, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 8.70/1.85 thf(zf_stmt_18, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 8.70/1.85 thf(zip_derived_cl17, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))
% 8.70/1.85 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_18])).
% 8.70/1.85 thf('21', plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl17])).
% 8.70/1.85 thf(prove_this_16, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 8.70/1.85 thf(zf_stmt_19, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 8.70/1.85 thf(zip_derived_cl18, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_19])).
% 8.70/1.85 thf('22', plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl18])).
% 8.70/1.85 thf(zip_derived_cl64, plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl15])).
% 8.70/1.85 thf(zip_derived_cl76, plain,
% 8.70/1.85 ((((inverse @ sk_c2) = (sk_c8))) <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl21])).
% 8.70/1.85 thf(zip_derived_cl113, plain,
% 8.70/1.85 ((![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8)) | ((multiply @ X4 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl172, plain,
% 8.70/1.85 (((((sk_c8) != (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl76, zip_derived_cl113])).
% 8.70/1.85 thf(zip_derived_cl175, plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) != (sk_c7)))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl172])).
% 8.70/1.85 thf(zip_derived_cl206, plain,
% 8.70/1.85 ((((sk_c7) != (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl175])).
% 8.70/1.85 thf('23', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8)) | ((multiply @ X4 @ sk_c8) != (sk_c7)))) |
% 8.70/1.85 ~ (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c2) = (sk_c8)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl206])).
% 8.70/1.85 thf(prove_this_21, conjecture,
% 8.70/1.85 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_20, negated_conjecture,
% 8.70/1.85 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 8.70/1.85 thf(zip_derived_cl23, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_20])).
% 8.70/1.85 thf('24', plain,
% 8.70/1.85 ((((inverse @ sk_c2) = (sk_c8))) |
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl23])).
% 8.70/1.85 thf(prove_this_22, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 8.70/1.85 thf(zf_stmt_21, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 8.70/1.85 thf(zip_derived_cl24, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_21])).
% 8.70/1.85 thf('25', plain,
% 8.70/1.85 ((((inverse @ sk_c2) = (sk_c8))) | (((inverse @ sk_c5) = (sk_c8)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl24])).
% 8.70/1.85 thf(zip_derived_cl44, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl5])).
% 8.70/1.85 thf(zip_derived_cl46, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl6])).
% 8.70/1.85 thf(zip_derived_cl113, plain,
% 8.70/1.85 ((![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8)) | ((multiply @ X4 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl126, plain,
% 8.70/1.85 (((((sk_c8) != (sk_c8)) | ((multiply @ sk_c5 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl113])).
% 8.70/1.85 thf(zip_derived_cl128, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) != (sk_c7)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl126])).
% 8.70/1.85 thf(zip_derived_cl196, plain,
% 8.70/1.85 ((((sk_c7) != (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8))
% 8.70/1.85 | ((multiply @ X4 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl44, zip_derived_cl128])).
% 8.70/1.85 thf('26', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8)) | ((multiply @ X4 @ sk_c8) != (sk_c7)))) |
% 8.70/1.85 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl196])).
% 8.70/1.85 thf(zip_derived_cl246, plain,
% 8.70/1.85 ((((sk_c8) = (multiply @ sk_c8 @ sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl218])).
% 8.70/1.85 thf(zip_derived_cl226, plain,
% 8.70/1.85 ((((sk_c9) = (multiply @ sk_c9 @ sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl214])).
% 8.70/1.85 thf(zip_derived_cl2, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.70/1.85 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.70/1.85 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.70/1.85 inference('cnf', [status(esa)], [associativity])).
% 8.70/1.85 thf(zip_derived_cl231, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c9 @ X0)
% 8.70/1.85 = (multiply @ sk_c9 @ (multiply @ sk_c8 @ X0))))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl226, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl260, plain,
% 8.70/1.85 ((((multiply @ sk_c9 @ sk_c7) = (multiply @ sk_c9 @ sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl246, zip_derived_cl231])).
% 8.70/1.85 thf(zip_derived_cl226, plain,
% 8.70/1.85 ((((sk_c9) = (multiply @ sk_c9 @ sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl40, zip_derived_cl214])).
% 8.70/1.85 thf(zip_derived_cl261, plain,
% 8.70/1.85 ((((multiply @ sk_c9 @ sk_c7) = (sk_c9)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl260, zip_derived_cl226])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl290, plain,
% 8.70/1.85 ((((sk_c7) = (multiply @ (inverse @ sk_c9) @ sk_c9)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl261, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl320, plain,
% 8.70/1.85 ((((sk_c7) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl159, plain,
% 8.70/1.85 ((((sk_c7) != (sk_c8))) <= (~ (((sk_c7) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl127])).
% 8.70/1.85 thf(zip_derived_cl1070, plain,
% 8.70/1.85 ((((identity) != (sk_c8)))
% 8.70/1.85 <= (~ (((sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl320, zip_derived_cl159])).
% 8.70/1.85 thf(zip_derived_cl317, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl286, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl1098, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= (~ (((sk_c7) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl1070, zip_derived_cl317])).
% 8.70/1.85 thf('27', plain,
% 8.70/1.85 ((((sk_c7) = (sk_c8))) | ~ (((inverse @ sk_c1) = (sk_c9))) |
% 8.70/1.85 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl1098])).
% 8.70/1.85 thf(zip_derived_cl320, plain,
% 8.70/1.85 ((((sk_c7) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl46, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl6])).
% 8.70/1.85 thf(zip_derived_cl114, plain,
% 8.70/1.85 ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8))))
% 8.70/1.85 <= ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl131, plain,
% 8.70/1.85 (((((multiply @ sk_c5 @ sk_c7) != (sk_c8)) | ((sk_c8) != (sk_c8))))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl114])).
% 8.70/1.85 thf(zip_derived_cl133, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c7) != (sk_c8)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl131])).
% 8.70/1.85 thf(zip_derived_cl1067, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ identity) != (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl320, zip_derived_cl133])).
% 8.70/1.85 thf(zip_derived_cl136, plain,
% 8.70/1.85 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl231, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c9 @ X0)
% 8.70/1.85 = (multiply @ sk_c9 @ (multiply @ sk_c8 @ X0))))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl226, zip_derived_cl2])).
% 8.70/1.85 thf(zip_derived_cl234, plain,
% 8.70/1.85 ((((multiply @ sk_c9 @ sk_c5) = (multiply @ sk_c9 @ identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl231])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl289, plain,
% 8.70/1.85 ((((sk_c5)
% 8.70/1.85 = (multiply @ (inverse @ sk_c9) @ (multiply @ sk_c9 @ identity))))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl319, plain,
% 8.70/1.85 ((((sk_c5) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl289, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl317, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl286, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl1095, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('demod', [status(thm)],
% 8.70/1.85 [zip_derived_cl1067, zip_derived_cl319, zip_derived_cl0,
% 8.70/1.85 zip_derived_cl317])).
% 8.70/1.85 thf('28', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8)))) |
% 8.70/1.85 ~ (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c1) = (sk_c9))) | ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl1095])).
% 8.70/1.85 thf(zip_derived_cl46, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl6])).
% 8.70/1.85 thf(zip_derived_cl117, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl142, plain,
% 8.70/1.85 (((((sk_c8) != (sk_c7)) | ((multiply @ sk_c5 @ sk_c8) != (sk_c7))))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7))
% 8.70/1.85 | ((multiply @ X0 @ sk_c8) != (sk_c7)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl46, zip_derived_cl117])).
% 8.70/1.85 thf('29', plain,
% 8.70/1.85 (~ (((sk_c7) = (sk_c8))) |
% 8.70/1.85 ~
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7)))) |
% 8.70/1.85 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl142])).
% 8.70/1.85 thf('30', plain,
% 8.70/1.85 (~ (((sk_c7) = (sk_c8))) | ~ (((multiply @ sk_c6 @ sk_c7) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c6) = (sk_c7))) |
% 8.70/1.85 ~
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl132])).
% 8.70/1.85 thf(zip_derived_cl169, plain,
% 8.70/1.85 ((((multiply @ sk_c8 @ sk_c2) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl299, plain,
% 8.70/1.85 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity)))
% 8.70/1.85 <= ((((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl169, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl136, plain,
% 8.70/1.85 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl46, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl297, plain,
% 8.70/1.85 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl411, plain,
% 8.70/1.85 ((((sk_c5) = (sk_c2)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) & (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl299, zip_derived_cl297])).
% 8.70/1.85 thf(zip_derived_cl317, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl286, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl64, plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ sk_c8) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c2 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl15])).
% 8.70/1.85 thf(zip_derived_cl330, plain,
% 8.70/1.85 ((((multiply @ sk_c2 @ identity) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl317, zip_derived_cl64])).
% 8.70/1.85 thf(zip_derived_cl1989, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ identity) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl411, zip_derived_cl330])).
% 8.70/1.85 thf(zip_derived_cl319, plain,
% 8.70/1.85 ((((sk_c5) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl289, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl0, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_identity])).
% 8.70/1.85 thf(zip_derived_cl1993, plain,
% 8.70/1.85 ((((identity) = (sk_c7)))
% 8.70/1.85 <= ((((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)],
% 8.70/1.85 [zip_derived_cl1989, zip_derived_cl319, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl218, plain,
% 8.70/1.85 ((![X0 : $i]: ((X0) = (multiply @ sk_c8 @ (multiply @ sk_c5 @ X0))))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl217, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl156, plain,
% 8.70/1.85 (![X0 : $i, X1 : $i]:
% 8.70/1.85 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 8.70/1.85 thf(zip_derived_cl294, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl700, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) = (identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl294, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl183, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c8) != (sk_c7)))
% 8.70/1.85 <= (~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl142])).
% 8.70/1.85 thf(zip_derived_cl714, plain,
% 8.70/1.85 ((((identity) != (sk_c7)))
% 8.70/1.85 <= (~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl700, zip_derived_cl183])).
% 8.70/1.85 thf(zip_derived_cl2052, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= (~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c1) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c2) = (sk_c8))))),
% 8.70/1.85 inference('s_sup-', [status(thm)],
% 8.70/1.85 [zip_derived_cl1993, zip_derived_cl714])).
% 8.70/1.85 thf('31', plain,
% 8.70/1.85 (~ (((multiply @ sk_c1 @ sk_c9) = (sk_c8))) |
% 8.70/1.85 ~ (((inverse @ sk_c1) = (sk_c9))) | ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c2 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c2) = (sk_c8))) |
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl2052])).
% 8.70/1.85 thf('32', plain,
% 8.70/1.85 (~ (((sk_c7) = (sk_c8))) | ~ (((multiply @ sk_c3 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c3) = (sk_c8))) |
% 8.70/1.85 ~
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl188])).
% 8.70/1.85 thf(prove_this_10, conjecture,
% 8.70/1.85 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.70/1.85 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 8.70/1.85 thf(zf_stmt_22, negated_conjecture,
% 8.70/1.85 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 8.70/1.85 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 8.70/1.85 thf(zip_derived_cl12, plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('cnf', [status(esa)], [zf_stmt_22])).
% 8.70/1.85 thf('33', plain,
% 8.70/1.85 ((((inverse @ sk_c5) = (sk_c8))) | (((inverse @ sk_c1) = (sk_c9)))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl12])).
% 8.70/1.85 thf(zip_derived_cl318, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl287, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl297, plain,
% 8.70/1.85 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl742, plain,
% 8.70/1.85 ((((sk_c5) = (multiply @ (inverse @ identity) @ identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl318, zip_derived_cl297])).
% 8.70/1.85 thf(zip_derived_cl1, plain,
% 8.70/1.85 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.70/1.85 inference('cnf', [status(esa)], [left_inverse])).
% 8.70/1.85 thf(zip_derived_cl753, plain,
% 8.70/1.85 ((((sk_c5) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl742, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl324, plain,
% 8.70/1.85 ((((sk_c7) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl298, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl133, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ sk_c7) != (sk_c8)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl131])).
% 8.70/1.85 thf(zip_derived_cl1696, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ identity) != (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)], [zip_derived_cl324, zip_derived_cl133])).
% 8.70/1.85 thf(zip_derived_cl297, plain,
% 8.70/1.85 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl294, plain,
% 8.70/1.85 ((![X0 : $i]:
% 8.70/1.85 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl218, zip_derived_cl156])).
% 8.70/1.85 thf(zip_derived_cl702, plain,
% 8.70/1.85 ((((multiply @ sk_c5 @ identity) = (sk_c5)))
% 8.70/1.85 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 8.70/1.85 inference('s_sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl294])).
% 8.70/1.85 thf(zip_derived_cl1723, plain,
% 8.70/1.85 ((((sk_c5) != (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl1696, zip_derived_cl702])).
% 8.70/1.85 thf(zip_derived_cl6709, plain,
% 8.70/1.85 ((((identity) != (sk_c8)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('s_sup-', [status(thm)],
% 8.70/1.85 [zip_derived_cl753, zip_derived_cl1723])).
% 8.70/1.85 thf(zip_derived_cl318, plain,
% 8.70/1.85 ((((sk_c8) = (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl287, zip_derived_cl1])).
% 8.70/1.85 thf(zip_derived_cl6753, plain,
% 8.70/1.85 ((((identity) != (identity)))
% 8.70/1.85 <= ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))) &
% 8.70/1.85 (((inverse @ sk_c4) = (sk_c9))) &
% 8.70/1.85 (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) &
% 8.70/1.85 (((inverse @ sk_c5) = (sk_c8))) &
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8))
% 8.70/1.85 | ((inverse @ X3) != (sk_c8)))))),
% 8.70/1.85 inference('demod', [status(thm)], [zip_derived_cl6709, zip_derived_cl318])).
% 8.70/1.85 thf('34', plain,
% 8.70/1.85 (~
% 8.70/1.85 (![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8)))) |
% 8.70/1.85 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 8.70/1.85 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c7))) |
% 8.70/1.85 ~ (((inverse @ sk_c4) = (sk_c9))) |
% 8.70/1.85 ~ (((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 8.70/1.85 inference('simplify', [status(thm)], [zip_derived_cl6753])).
% 8.70/1.85 thf('35', plain,
% 8.70/1.85 ((![X3 : $i]:
% 8.70/1.85 (((multiply @ X3 @ sk_c7) != (sk_c8)) | ((inverse @ X3) != (sk_c8)))) |
% 8.70/1.85 (![X0 : $i]:
% 8.70/1.85 (((inverse @ X0) != (sk_c7)) | ((multiply @ X0 @ sk_c8) != (sk_c7)))) |
% 8.70/1.85 (![X5 : $i]:
% 8.70/1.85 (((inverse @ X5) != (sk_c9)) | ((multiply @ X5 @ sk_c9) != (sk_c8)))) |
% 8.70/1.85 (![X4 : $i]:
% 8.70/1.85 (((inverse @ X4) != (sk_c8)) | ((multiply @ X4 @ sk_c8) != (sk_c7))))),
% 8.70/1.85 inference('split', [status(esa)], [zip_derived_cl39])).
% 8.70/1.85 thf(zip_derived_cl20173, plain, ($false),
% 8.70/1.85 inference('sat_resolution*', [status(thm)],
% 8.70/1.85 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 8.70/1.85 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 8.70/1.85 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 8.70/1.85 '32', '33', '34', '35'])).
% 8.70/1.85
% 8.70/1.85 % SZS output end Refutation
% 8.70/1.85
% 8.70/1.85
% 8.70/1.85 % Terminating...
% 9.09/1.96 % Runner terminated.
% 9.09/1.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------