TSTP Solution File: GRP247-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP247-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.K4fIqohbQX true
% Computer : n009.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 01:50:53 EDT 2023
% Result : Unsatisfiable 6.87s 1.57s
% Output : Refutation 6.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP247-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.K4fIqohbQX true
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 01:18:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.54/0.63 % Total configuration time : 435
% 0.54/0.63 % Estimated wc time : 1092
% 0.54/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 6.87/1.57 % Solved by fo/fo7.sh.
% 6.87/1.57 % done 2763 iterations in 0.785s
% 6.87/1.57 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.87/1.57 % SZS output start Refutation
% 6.87/1.57 thf(sk_c6_type, type, sk_c6: $i).
% 6.87/1.57 thf(sk_c8_type, type, sk_c8: $i).
% 6.87/1.57 thf(sk_c3_type, type, sk_c3: $i).
% 6.87/1.57 thf(sk_c7_type, type, sk_c7: $i).
% 6.87/1.57 thf(sk_c5_type, type, sk_c5: $i).
% 6.87/1.57 thf(identity_type, type, identity: $i).
% 6.87/1.57 thf(multiply_type, type, multiply: $i > $i > $i).
% 6.87/1.57 thf(sk_c9_type, type, sk_c9: $i).
% 6.87/1.57 thf(inverse_type, type, inverse: $i > $i).
% 6.87/1.57 thf(sk_c4_type, type, sk_c4: $i).
% 6.87/1.57 thf(sk_c2_type, type, sk_c2: $i).
% 6.87/1.57 thf(sk_c1_type, type, sk_c1: $i).
% 6.87/1.57 thf(prove_this_29, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_0, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 6.87/1.57 thf(zip_derived_cl31, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.87/1.57 thf(prove_this_35, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_1, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 6.87/1.57 thf(zip_derived_cl37, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_1])).
% 6.87/1.57 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(associativity, axiom,
% 6.87/1.57 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 6.87/1.57 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 6.87/1.57 thf(zip_derived_cl2, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.57 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.57 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.57 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.57 thf(zip_derived_cl109, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((multiply @ identity @ X0)
% 6.87/1.57 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 6.87/1.57 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl191, plain,
% 6.87/1.57 ((((sk_c7) = (multiply @ (inverse @ sk_c3) @ sk_c9))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl3241, plain,
% 6.87/1.57 ((((sk_c7) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl191])).
% 6.87/1.57 thf(zip_derived_cl3251, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((sk_c7) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl3241])).
% 6.87/1.57 thf(prove_this_30, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_2, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c3 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 6.87/1.57 thf(zip_derived_cl32, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_2])).
% 6.87/1.57 thf(prove_this_36, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_3, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 6.87/1.57 thf(zip_derived_cl38, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_3])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl192, plain,
% 6.87/1.57 ((((sk_c7) = (multiply @ (inverse @ sk_c3) @ sk_c9))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl5880, plain,
% 6.87/1.57 ((((sk_c7) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl192])).
% 6.87/1.57 thf(zip_derived_cl5890, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9))
% 6.87/1.57 | ((sk_c7) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl5880])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl5906, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ (inverse @ sk_c6) @ sk_c9))
% 6.87/1.57 | ((sk_c7) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl5890, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl8043, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((sk_c7) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((sk_c7) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl3251, zip_derived_cl5906])).
% 6.87/1.57 thf(zip_derived_cl8051, plain,
% 6.87/1.57 ((((sk_c7) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((sk_c8) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl8043])).
% 6.87/1.57 thf(prove_this_23, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 6.87/1.57 thf(zf_stmt_4, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 6.87/1.57 thf(zip_derived_cl25, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl67, plain,
% 6.87/1.57 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl176, plain,
% 6.87/1.57 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl141])).
% 6.87/1.57 thf(prove_this_17, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 6.87/1.57 thf(zf_stmt_5, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 6.87/1.57 thf(zip_derived_cl19, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_5])).
% 6.87/1.57 thf(zip_derived_cl582, plain,
% 6.87/1.57 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 6.87/1.57 = (sk_c7))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl176, zip_derived_cl19])).
% 6.87/1.57 thf(zip_derived_cl2, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.57 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.57 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.57 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl598, plain,
% 6.87/1.57 ((((identity) = (sk_c7))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.87/1.57 inference('demod', [status(thm)],
% 6.87/1.57 [zip_derived_cl582, zip_derived_cl2, zip_derived_cl0,
% 6.87/1.57 zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl599, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl598])).
% 6.87/1.57 thf(prove_this_24, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 6.87/1.57 thf(zf_stmt_6, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 6.87/1.57 thf(zip_derived_cl26, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_6])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl161, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl158, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl141, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl974, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.57 thf(zip_derived_cl161, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl1019, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.57 thf(zip_derived_cl1221, plain,
% 6.87/1.57 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c6 @ sk_c8) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1019])).
% 6.87/1.57 thf(prove_this_18, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 6.87/1.57 thf(zf_stmt_7, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 6.87/1.57 thf(zip_derived_cl20, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_7])).
% 6.87/1.57 thf(zip_derived_cl1744, plain,
% 6.87/1.57 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1221, zip_derived_cl20])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl1764, plain,
% 6.87/1.57 ((((identity) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c6 @ sk_c8) = (sk_c9)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl1744, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl1765, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl1764])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl1875, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ (inverse @ sk_c6) @ sk_c9))
% 6.87/1.57 | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1765, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl1908, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((identity) = (sk_c7))
% 6.87/1.57 | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl599, zip_derived_cl1875])).
% 6.87/1.57 thf(zip_derived_cl1913, plain,
% 6.87/1.57 ((((identity) = (sk_c7)) | ((sk_c8) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl1908])).
% 6.87/1.57 thf(zip_derived_cl8088, plain,
% 6.87/1.57 ((((identity) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((sk_c8) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((sk_c8) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl8051, zip_derived_cl1913])).
% 6.87/1.57 thf(zip_derived_cl8103, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((identity) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl8088])).
% 6.87/1.57 thf(zip_derived_cl974, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.57 thf(prove_this_20, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 6.87/1.57 thf(zf_stmt_8, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 6.87/1.57 thf(zip_derived_cl22, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_8])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl58, plain,
% 6.87/1.57 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl173, plain,
% 6.87/1.57 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl141])).
% 6.87/1.57 thf(prove_this_14, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 6.87/1.57 thf(zf_stmt_9, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 6.87/1.57 thf(zip_derived_cl16, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_9])).
% 6.87/1.57 thf(zip_derived_cl350, plain,
% 6.87/1.57 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 6.87/1.57 = (sk_c7))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl16])).
% 6.87/1.57 thf(zip_derived_cl2, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.57 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.57 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.57 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl366, plain,
% 6.87/1.57 ((((identity) = (sk_c7))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('demod', [status(thm)],
% 6.87/1.57 [zip_derived_cl350, zip_derived_cl2, zip_derived_cl0,
% 6.87/1.57 zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl367, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl366])).
% 6.87/1.57 thf(prove_this_32, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_10, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 6.87/1.57 thf(zip_derived_cl34, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_10])).
% 6.87/1.57 thf(zip_derived_cl377, plain,
% 6.87/1.57 ((((multiply @ sk_c3 @ identity) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl367, zip_derived_cl34])).
% 6.87/1.57 thf(zip_derived_cl382, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c3 @ identity) = (sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl377])).
% 6.87/1.57 thf(zip_derived_cl1024, plain,
% 6.87/1.57 ((((sk_c3) = (sk_c9)) | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl382])).
% 6.87/1.57 thf(prove_this_26, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_11, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 6.87/1.57 thf(zip_derived_cl28, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c3) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_11])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl70, plain,
% 6.87/1.57 ((((multiply @ sk_c9 @ sk_c3) = (identity))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl1072, plain,
% 6.87/1.57 ((((multiply @ sk_c9 @ sk_c9) = (identity))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c4) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1024, zip_derived_cl70])).
% 6.87/1.57 thf(zip_derived_cl1082, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl1072])).
% 6.87/1.57 thf(zip_derived_cl1019, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.57 thf(zip_derived_cl1945, plain,
% 6.87/1.57 ((((sk_c4) = (inverse @ sk_c9))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1082, zip_derived_cl1019])).
% 6.87/1.57 thf(prove_this_19, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 6.87/1.57 thf(zf_stmt_12, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 6.87/1.57 thf(zip_derived_cl21, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_12])).
% 6.87/1.57 thf(zip_derived_cl1019, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.57 thf(zip_derived_cl1216, plain,
% 6.87/1.57 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl1019])).
% 6.87/1.57 thf(prove_this_13, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 6.87/1.57 thf(zf_stmt_13, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 6.87/1.57 thf(zip_derived_cl15, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_13])).
% 6.87/1.57 thf(zip_derived_cl1686, plain,
% 6.87/1.57 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1216, zip_derived_cl15])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl1706, plain,
% 6.87/1.57 ((((identity) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl1686, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl1707, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl1706])).
% 6.87/1.57 thf(prove_this_31, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_14, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 6.87/1.57 thf(zip_derived_cl33, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c3 @ sk_c7) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_14])).
% 6.87/1.57 thf(zip_derived_cl1731, plain,
% 6.87/1.57 ((((multiply @ sk_c3 @ identity) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1707, zip_derived_cl33])).
% 6.87/1.57 thf(zip_derived_cl1738, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c3 @ identity) = (sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl1731])).
% 6.87/1.57 thf(zip_derived_cl974, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.57 thf(zip_derived_cl4016, plain,
% 6.87/1.57 ((((sk_c9) = (sk_c3)) | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1738, zip_derived_cl974])).
% 6.87/1.57 thf(prove_this_25, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c3 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_15, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c3 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 6.87/1.57 thf(zip_derived_cl27, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_15])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl90, plain,
% 6.87/1.57 ((((multiply @ sk_c9 @ sk_c3) = (identity))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl4051, plain,
% 6.87/1.57 ((((multiply @ sk_c9 @ sk_c9) = (identity))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c4 @ sk_c9) = (sk_c8)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl4016, zip_derived_cl90])).
% 6.87/1.57 thf(zip_derived_cl4078, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl4051])).
% 6.87/1.57 thf(zip_derived_cl6517, plain,
% 6.87/1.57 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1945, zip_derived_cl4078])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl6523, plain,
% 6.87/1.57 ((((identity) = (sk_c8))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl6517, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl6524, plain,
% 6.87/1.57 ((((multiply @ sk_c9 @ sk_c9) = (identity)) | ((identity) = (sk_c8)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl6523])).
% 6.87/1.57 thf(zip_derived_cl8322, plain,
% 6.87/1.57 ((((identity) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((identity) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((multiply @ sk_c9 @ sk_c9) = (identity)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl8103, zip_derived_cl6524])).
% 6.87/1.57 thf(zip_derived_cl8341, plain, (((identity) = (multiply @ sk_c9 @ sk_c9))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl8322])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl8398, plain,
% 6.87/1.57 (((sk_c9) = (multiply @ (inverse @ sk_c9) @ identity))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl8341, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl974, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.57 thf(zip_derived_cl8484, plain, (((sk_c9) = (inverse @ sk_c9))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl8398, zip_derived_cl974])).
% 6.87/1.57 thf(prove_this_8, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_16, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 6.87/1.57 thf(zip_derived_cl10, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_16])).
% 6.87/1.57 thf(zip_derived_cl8484, plain, (((sk_c9) = (inverse @ sk_c9))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl8398, zip_derived_cl974])).
% 6.87/1.57 thf(zip_derived_cl10, plain,
% 6.87/1.57 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_16])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl44, plain,
% 6.87/1.57 ((((multiply @ sk_c9 @ sk_c4) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl163, plain,
% 6.87/1.57 ((((sk_c4) = (multiply @ (inverse @ sk_c9) @ identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl141])).
% 6.87/1.57 thf(prove_this_7, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_17, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 6.87/1.57 thf(zip_derived_cl9, plain,
% 6.87/1.57 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_17])).
% 6.87/1.57 thf(zip_derived_cl217, plain,
% 6.87/1.57 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 6.87/1.57 = (sk_c8))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl163, zip_derived_cl9])).
% 6.87/1.57 thf(zip_derived_cl2, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.57 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.57 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.57 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl222, plain,
% 6.87/1.57 ((((identity) = (sk_c8))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('demod', [status(thm)],
% 6.87/1.57 [zip_derived_cl217, zip_derived_cl2, zip_derived_cl0,
% 6.87/1.57 zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl223, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9)) | ((identity) = (sk_c8)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl222])).
% 6.87/1.57 thf(zip_derived_cl223, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9)) | ((identity) = (sk_c8)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl222])).
% 6.87/1.57 thf(prove_this_10, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_18, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 6.87/1.57 thf(zip_derived_cl12, plain,
% 6.87/1.57 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_18])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl45, plain,
% 6.87/1.57 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl234, plain,
% 6.87/1.57 ((((multiply @ identity @ sk_c5) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl45])).
% 6.87/1.57 thf(zip_derived_cl241, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((multiply @ identity @ sk_c5) = (identity)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl234])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl291, plain,
% 6.87/1.57 ((((identity) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl241, zip_derived_cl0])).
% 6.87/1.57 thf(prove_this_21, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 6.87/1.57 thf(zf_stmt_19, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 6.87/1.57 thf(zip_derived_cl23, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_19])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl61, plain,
% 6.87/1.57 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl23, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl174, plain,
% 6.87/1.57 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl61, zip_derived_cl141])).
% 6.87/1.57 thf(prove_this_15, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 6.87/1.57 thf(zf_stmt_20, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 6.87/1.57 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 6.87/1.57 thf(zip_derived_cl17, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_20])).
% 6.87/1.57 thf(zip_derived_cl481, plain,
% 6.87/1.57 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 6.87/1.57 = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl17])).
% 6.87/1.57 thf(zip_derived_cl2, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.57 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.57 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.57 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl497, plain,
% 6.87/1.57 ((((identity) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (sk_c7))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (sk_c7)))),
% 6.87/1.57 inference('demod', [status(thm)],
% 6.87/1.57 [zip_derived_cl481, zip_derived_cl2, zip_derived_cl0,
% 6.87/1.57 zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl498, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl497])).
% 6.87/1.57 thf(zip_derived_cl511, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ sk_c8) != (identity)) | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('eq_fact', [status(thm)], [zip_derived_cl498])).
% 6.87/1.57 thf(zip_derived_cl517, plain,
% 6.87/1.57 ((((multiply @ identity @ sk_c8) != (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('sup-', [status(thm)], [zip_derived_cl291, zip_derived_cl511])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl522, plain,
% 6.87/1.57 ((((sk_c8) != (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((identity) = (sk_c7)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl517, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl223, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9)) | ((identity) = (sk_c8)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl222])).
% 6.87/1.57 thf(zip_derived_cl523, plain,
% 6.87/1.57 ((((identity) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl223])).
% 6.87/1.57 thf(zip_derived_cl45, plain,
% 6.87/1.57 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl171, plain,
% 6.87/1.57 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl974, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.57 thf(zip_derived_cl1005, plain,
% 6.87/1.57 ((((sk_c5) = (inverse @ sk_c8)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl171, zip_derived_cl974])).
% 6.87/1.57 thf(zip_derived_cl1019, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.57 thf(zip_derived_cl1, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.57 thf(zip_derived_cl1203, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1019, zip_derived_cl1])).
% 6.87/1.57 thf(zip_derived_cl223, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9)) | ((identity) = (sk_c8)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl222])).
% 6.87/1.57 thf(zip_derived_cl523, plain,
% 6.87/1.57 ((((identity) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('clc', [status(thm)], [zip_derived_cl522, zip_derived_cl223])).
% 6.87/1.57 thf(prove_this_9, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_21, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 6.87/1.57 thf(zip_derived_cl11, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_21])).
% 6.87/1.57 thf(zip_derived_cl525, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ sk_c8) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl523, zip_derived_cl11])).
% 6.87/1.57 thf(zip_derived_cl533, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c5 @ sk_c8) = (identity)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl525])).
% 6.87/1.57 thf(zip_derived_cl612, plain,
% 6.87/1.57 ((((multiply @ sk_c5 @ identity) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl223, zip_derived_cl533])).
% 6.87/1.57 thf(zip_derived_cl618, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((multiply @ sk_c5 @ identity) = (identity)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl612])).
% 6.87/1.57 thf(zip_derived_cl2, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.57 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.57 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.57 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.57 thf(zip_derived_cl689, plain,
% 6.87/1.57 (![X0 : $i]:
% 6.87/1.57 (((multiply @ identity @ X0)
% 6.87/1.57 = (multiply @ sk_c5 @ (multiply @ identity @ X0)))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl2])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl0, plain,
% 6.87/1.57 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.57 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.57 thf(zip_derived_cl697, plain,
% 6.87/1.57 (![X0 : $i]:
% 6.87/1.57 (((X0) = (multiply @ sk_c5 @ X0)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('demod', [status(thm)],
% 6.87/1.57 [zip_derived_cl689, zip_derived_cl0, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl1514, plain,
% 6.87/1.57 ((((inverse @ sk_c5) = (identity)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1203, zip_derived_cl697])).
% 6.87/1.57 thf(zip_derived_cl1590, plain,
% 6.87/1.57 ((((inverse @ (inverse @ sk_c8)) = (identity))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl1005, zip_derived_cl1514])).
% 6.87/1.57 thf(zip_derived_cl1594, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ (inverse @ sk_c8)) = (identity)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl1590])).
% 6.87/1.57 thf(prove_this_11, conjecture,
% 6.87/1.57 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_22, negated_conjecture,
% 6.87/1.57 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 6.87/1.57 thf(zip_derived_cl13, plain,
% 6.87/1.57 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_22])).
% 6.87/1.57 thf(prove_this_12, conjecture,
% 6.87/1.57 (~( ( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 6.87/1.57 thf(zf_stmt_23, negated_conjecture,
% 6.87/1.57 (( ( multiply @ sk_c6 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 6.87/1.57 thf(zip_derived_cl14, plain,
% 6.87/1.57 ((((multiply @ sk_c6 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_23])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl180, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ (inverse @ sk_c6) @ sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl141])).
% 6.87/1.57 thf(zip_derived_cl860, plain,
% 6.87/1.57 ((((sk_c8) = (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl180])).
% 6.87/1.57 thf(zip_derived_cl865, plain,
% 6.87/1.57 ((((inverse @ sk_c1) = (sk_c9)) | ((sk_c8) = (multiply @ sk_c9 @ sk_c9)))),
% 6.87/1.57 inference('simplify', [status(thm)], [zip_derived_cl860])).
% 6.87/1.57 thf(zip_derived_cl1019, plain,
% 6.87/1.57 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.57 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.57 thf(prove_this_37, conjecture,
% 6.87/1.57 (~( ( ( multiply @ X3 @ sk_c8 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ X3 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c8 ) ) ))).
% 6.87/1.57 thf(zf_stmt_24, negated_conjecture,
% 6.87/1.57 (( ( multiply @ X3 @ sk_c8 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ X3 ) != ( sk_c9 ) ) | ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ X1 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( inverse @ X6 ) != ( sk_c9 ) ) | ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 6.87/1.57 ( ( multiply @ X5 @ sk_c8 ) != ( sk_c7 ) ) |
% 6.87/1.57 ( ( inverse @ X4 ) != ( sk_c9 ) ) |
% 6.87/1.57 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c8 ) )),
% 6.87/1.57 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 6.87/1.57 thf(zip_derived_cl39, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.87/1.57 (((multiply @ X0 @ sk_c8) != (sk_c9))
% 6.87/1.57 | ((inverse @ X0) != (sk_c9))
% 6.87/1.57 | ((inverse @ X1) != (sk_c8))
% 6.87/1.57 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X2) != (sk_c9))
% 6.87/1.57 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 6.87/1.57 | ((multiply @ X3 @ sk_c7) != (sk_c9))
% 6.87/1.57 | ((inverse @ X3) != (sk_c9))
% 6.87/1.57 | ((inverse @ X4) != (sk_c8))
% 6.87/1.57 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X5) != (sk_c9))
% 6.87/1.57 | ((multiply @ X5 @ sk_c9) != (sk_c8)))),
% 6.87/1.57 inference('cnf', [status(esa)], [zf_stmt_24])).
% 6.87/1.57 thf(zip_derived_cl1204, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.87/1.57 (((X0) != (sk_c9))
% 6.87/1.57 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 6.87/1.57 | ((inverse @ X1) != (sk_c9))
% 6.87/1.57 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X2) != (sk_c8))
% 6.87/1.57 | ((inverse @ X3) != (sk_c9))
% 6.87/1.57 | ((multiply @ X3 @ sk_c7) != (sk_c9))
% 6.87/1.57 | ((multiply @ X4 @ sk_c9) != (sk_c8))
% 6.87/1.57 | ((inverse @ X4) != (sk_c9))
% 6.87/1.57 | ((multiply @ X5 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X5) != (sk_c8))
% 6.87/1.57 | ((multiply @ (inverse @ X0) @ sk_c8) != (sk_c9)))),
% 6.87/1.57 inference('sup-', [status(thm)], [zip_derived_cl1019, zip_derived_cl39])).
% 6.87/1.57 thf(zip_derived_cl1432, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.57 (((multiply @ (inverse @ sk_c9) @ sk_c8) != (sk_c9))
% 6.87/1.57 | ((inverse @ X0) != (sk_c8))
% 6.87/1.57 | ((multiply @ X0 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X1) != (sk_c9))
% 6.87/1.57 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 6.87/1.57 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.57 | ((inverse @ X2) != (sk_c9))
% 6.87/1.57 | ((inverse @ X3) != (sk_c8))
% 6.87/1.57 | ((multiply @ X3 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X4) != (sk_c9))
% 6.87/1.57 | ((multiply @ X4 @ sk_c9) != (sk_c8)))),
% 6.87/1.57 inference('eq_res', [status(thm)], [zip_derived_cl1204])).
% 6.87/1.57 thf(zip_derived_cl1435, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.57 (((multiply @ (inverse @ sk_c9) @ (multiply @ sk_c9 @ sk_c9))
% 6.87/1.57 != (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.57 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 6.87/1.57 | ((inverse @ X0) != (sk_c9))
% 6.87/1.57 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X1) != (sk_c8))
% 6.87/1.57 | ((inverse @ X2) != (sk_c9))
% 6.87/1.57 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.57 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 6.87/1.57 | ((inverse @ X3) != (sk_c9))
% 6.87/1.57 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 6.87/1.57 | ((inverse @ X4) != (sk_c8)))),
% 6.87/1.57 inference('sup-', [status(thm)], [zip_derived_cl865, zip_derived_cl1432])).
% 6.87/1.57 thf(zip_derived_cl141, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i]:
% 6.87/1.57 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.57 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.57 thf(zip_derived_cl1437, plain,
% 6.87/1.57 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.57 (((sk_c9) != (sk_c9))
% 6.87/1.57 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c8))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X4) != (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)], [zip_derived_cl1435, zip_derived_cl141])).
% 6.87/1.58 thf(zip_derived_cl1438, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.58 (((inverse @ X4) != (sk_c8))
% 6.87/1.58 | ((multiply @ X4 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X1) != (sk_c8))
% 6.87/1.58 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl1437])).
% 6.87/1.58 thf(zip_derived_cl12229, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c8))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ (inverse @ sk_c8) @ sk_c8) != (sk_c7)))),
% 6.87/1.58 inference('sup-', [status(thm)], [zip_derived_cl1594, zip_derived_cl1438])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl12257, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c8))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((identity) != (sk_c7)))),
% 6.87/1.58 inference('demod', [status(thm)], [zip_derived_cl12229, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl12258, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (sk_c7))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X1) != (sk_c8))
% 6.87/1.58 | ((multiply @ X1 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((identity) != (sk_c8)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12257])).
% 6.87/1.58 thf(zip_derived_cl12259, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (sk_c7))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (identity))
% 6.87/1.58 | ((multiply @ X2 @ identity) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ identity) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((identity) != (sk_c8)))),
% 6.87/1.58 inference('local_rewriting', [status(thm)], [zip_derived_cl12258])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12293, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (sk_c7))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (identity))
% 6.87/1.58 | ((X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((identity) != (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12259, zip_derived_cl974, zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl12299, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((identity) != (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((X2) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9)))),
% 6.87/1.58 inference('sup-', [status(thm)], [zip_derived_cl523, zip_derived_cl12293])).
% 6.87/1.58 thf(zip_derived_cl12322, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (identity))
% 6.87/1.58 | ((X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((identity) != (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12299])).
% 6.87/1.58 thf(zip_derived_cl12350, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((X2) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X3) != (sk_c9)))),
% 6.87/1.58 inference('sup-', [status(thm)], [zip_derived_cl223, zip_derived_cl12322])).
% 6.87/1.58 thf(zip_derived_cl12352, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((inverse @ X3) != (sk_c9))
% 6.87/1.58 | ((multiply @ X3 @ sk_c9) != (identity))
% 6.87/1.58 | ((X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12350])).
% 6.87/1.58 thf(zip_derived_cl12353, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((inverse @ sk_c9) != (sk_c9))
% 6.87/1.58 | ((multiply @ X2 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl12352])).
% 6.87/1.58 thf(zip_derived_cl8484, plain, (((sk_c9) = (inverse @ sk_c9))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl8398, zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl12354, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((sk_c9) != (sk_c9))
% 6.87/1.58 | ((multiply @ X2 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12353, zip_derived_cl8484])).
% 6.87/1.58 thf(zip_derived_cl12355, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((multiply @ X2 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (identity))
% 6.87/1.58 | ((X1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12354])).
% 6.87/1.58 thf(zip_derived_cl12356, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((inverse @ identity) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c9)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl12355])).
% 6.87/1.58 thf(zip_derived_cl0, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.58 thf(zip_derived_cl141, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.58 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.58 thf(zip_derived_cl160, plain,
% 6.87/1.58 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl141])).
% 6.87/1.58 thf(zip_derived_cl141, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.58 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.58 thf(zip_derived_cl213, plain,
% 6.87/1.58 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl160, zip_derived_cl141])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl825, plain, (((inverse @ identity) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl213, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl12357, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((identity) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c9)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12356, zip_derived_cl825])).
% 6.87/1.58 thf(zip_derived_cl12358, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((inverse @ X1) != (sk_c9))
% 6.87/1.58 | ((multiply @ X1 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12357])).
% 6.87/1.58 thf(zip_derived_cl12362, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((sk_c9) != (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ sk_c9 @ sk_c9) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12358])).
% 6.87/1.58 thf(zip_derived_cl8341, plain, (((identity) = (multiply @ sk_c9 @ sk_c9))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl8322])).
% 6.87/1.58 thf(zip_derived_cl12391, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((sk_c9) != (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((identity) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12362, zip_derived_cl8341])).
% 6.87/1.58 thf(zip_derived_cl12392, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((inverse @ X0) != (sk_c9))
% 6.87/1.58 | ((multiply @ X0 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12391])).
% 6.87/1.58 thf(zip_derived_cl12423, plain,
% 6.87/1.58 ((((sk_c9) != (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9))
% 6.87/1.58 | ((multiply @ sk_c4 @ sk_c9) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)], [zip_derived_cl10, zip_derived_cl12392])).
% 6.87/1.58 thf(zip_derived_cl12454, plain,
% 6.87/1.58 ((((multiply @ sk_c4 @ sk_c9) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12423])).
% 6.87/1.58 thf(zip_derived_cl10, plain,
% 6.87/1.58 ((((inverse @ sk_c4) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_16])).
% 6.87/1.58 thf(zip_derived_cl1203, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl1019, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl1518, plain,
% 6.87/1.58 ((((multiply @ sk_c4 @ sk_c9) = (identity))
% 6.87/1.58 | ((inverse @ sk_c1) = (sk_c9)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1203])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl1019, plain,
% 6.87/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl1432, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.58 (((multiply @ (inverse @ sk_c9) @ sk_c8) != (sk_c9))
% 6.87/1.58 | ((inverse @ X0) != (sk_c8))
% 6.87/1.58 | ((multiply @ X0 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c9))
% 6.87/1.58 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X3) != (sk_c8))
% 6.87/1.58 | ((multiply @ X3 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X4) != (sk_c9))
% 6.87/1.58 | ((multiply @ X4 @ sk_c9) != (sk_c8)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl1204])).
% 6.87/1.58 thf(zip_derived_cl8484, plain, (((sk_c9) = (inverse @ sk_c9))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl8398, zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl8505, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.58 (((multiply @ sk_c9 @ sk_c8) != (sk_c9))
% 6.87/1.58 | ((inverse @ X0) != (sk_c8))
% 6.87/1.58 | ((multiply @ X0 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c9))
% 6.87/1.58 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c9))
% 6.87/1.58 | ((inverse @ X2) != (sk_c9))
% 6.87/1.58 | ((inverse @ X3) != (sk_c8))
% 6.87/1.58 | ((multiply @ X3 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X4) != (sk_c9))
% 6.87/1.58 | ((multiply @ X4 @ sk_c9) != (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl1432, zip_derived_cl8484])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl12613, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.58 (((multiply @ (inverse @ sk_c1) @ sk_c8) != (inverse @ sk_c1))
% 6.87/1.58 | ((inverse @ X0) != (sk_c8))
% 6.87/1.58 | ((multiply @ X0 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (inverse @ sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ (inverse @ sk_c1)) != (sk_c8))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (inverse @ sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (inverse @ sk_c1))
% 6.87/1.58 | ((inverse @ X3) != (sk_c8))
% 6.87/1.58 | ((multiply @ X3 @ sk_c8) != (sk_c7))
% 6.87/1.58 | ((inverse @ X4) != (inverse @ sk_c1))
% 6.87/1.58 | ((multiply @ X4 @ (inverse @ sk_c1)) != (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8505, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl12475, zip_derived_cl12475])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(prove_this_2, conjecture,
% 6.87/1.58 (~( ( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.58 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.87/1.58 thf(zf_stmt_25, negated_conjecture,
% 6.87/1.58 (( ( inverse @ sk_c4 ) = ( sk_c9 ) ) |
% 6.87/1.58 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 6.87/1.58 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 6.87/1.58 thf(zip_derived_cl4, plain,
% 6.87/1.58 ((((inverse @ sk_c4) = (sk_c9)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_25])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl49, plain,
% 6.87/1.58 ((((multiply @ sk_c9 @ sk_c4) = (identity))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl141, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.58 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.58 thf(zip_derived_cl164, plain,
% 6.87/1.58 ((((sk_c4) = (multiply @ (inverse @ sk_c9) @ identity))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl49, zip_derived_cl141])).
% 6.87/1.58 thf(prove_this_1, conjecture,
% 6.87/1.58 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.58 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.87/1.58 thf(zf_stmt_26, negated_conjecture,
% 6.87/1.58 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c8 ) ) |
% 6.87/1.58 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 6.87/1.58 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 6.87/1.58 thf(zip_derived_cl3, plain,
% 6.87/1.58 ((((multiply @ sk_c4 @ sk_c9) = (sk_c8))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_26])).
% 6.87/1.58 thf(zip_derived_cl257, plain,
% 6.87/1.58 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 6.87/1.58 = (sk_c8))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl3])).
% 6.87/1.58 thf(zip_derived_cl2, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.58 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.58 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.58 thf(zip_derived_cl0, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl263, plain,
% 6.87/1.58 ((((identity) = (sk_c8))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl257, zip_derived_cl2, zip_derived_cl0,
% 6.87/1.58 zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl264, plain,
% 6.87/1.58 ((((multiply @ sk_c1 @ sk_c9) = (sk_c8)) | ((identity) = (sk_c8)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl263])).
% 6.87/1.58 thf(zip_derived_cl12475, plain, (((inverse @ sk_c1) = (sk_c9))),
% 6.87/1.58 inference('clc', [status(thm)], [zip_derived_cl12454, zip_derived_cl1518])).
% 6.87/1.58 thf(zip_derived_cl1203, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl1019, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl12528, plain,
% 6.87/1.58 ((((identity) = (sk_c8)) | ((identity) = (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl264, zip_derived_cl12475, zip_derived_cl1203])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12683, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X0) != (identity))
% 6.87/1.58 | ((X0) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((inverse @ X3) != (identity))
% 6.87/1.58 | ((X3) != (sk_c7))
% 6.87/1.58 | ((inverse @ X4) != (sk_c1))
% 6.87/1.58 | ((multiply @ X4 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12613, zip_derived_cl12604,
% 6.87/1.58 zip_derived_cl12529, zip_derived_cl974, zip_derived_cl12604,
% 6.87/1.58 zip_derived_cl12529, zip_derived_cl12529, zip_derived_cl974,
% 6.87/1.58 zip_derived_cl12604, zip_derived_cl12604,
% 6.87/1.58 zip_derived_cl12529, zip_derived_cl12604,
% 6.87/1.58 zip_derived_cl12604, zip_derived_cl12529,
% 6.87/1.58 zip_derived_cl12529, zip_derived_cl974, zip_derived_cl12604,
% 6.87/1.58 zip_derived_cl12604, zip_derived_cl12529])).
% 6.87/1.58 thf(zip_derived_cl12684, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.87/1.58 (((multiply @ X4 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X4) != (sk_c1))
% 6.87/1.58 | ((X3) != (sk_c7))
% 6.87/1.58 | ((inverse @ X3) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((X0) != (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12683])).
% 6.87/1.58 thf(zip_derived_cl12685, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((inverse @ X0) != (identity))
% 6.87/1.58 | ((X0) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c7) != (identity))
% 6.87/1.58 | ((inverse @ X3) != (sk_c1))
% 6.87/1.58 | ((multiply @ X3 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl12684])).
% 6.87/1.58 thf(zip_derived_cl498, plain,
% 6.87/1.58 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c7)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl497])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12656, plain,
% 6.87/1.58 ((((sk_c5) = (sk_c7)) | ((identity) = (sk_c7)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl498, zip_derived_cl12529, zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(prove_this_22, conjecture,
% 6.87/1.58 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.87/1.58 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 6.87/1.58 thf(zf_stmt_27, negated_conjecture,
% 6.87/1.58 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 6.87/1.58 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 6.87/1.58 thf(zip_derived_cl24, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_27])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl64, plain,
% 6.87/1.58 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 6.87/1.58 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl141, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.87/1.58 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 6.87/1.58 thf(zip_derived_cl175, plain,
% 6.87/1.58 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 6.87/1.58 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl141])).
% 6.87/1.58 thf(prove_this_16, conjecture,
% 6.87/1.58 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.87/1.58 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 6.87/1.58 thf(zf_stmt_28, negated_conjecture,
% 6.87/1.58 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.87/1.58 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c7 ) )),
% 6.87/1.58 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 6.87/1.58 thf(zip_derived_cl18, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_28])).
% 6.87/1.58 thf(zip_derived_cl627, plain,
% 6.87/1.58 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 6.87/1.58 = (sk_c7))
% 6.87/1.58 | ((inverse @ sk_c5) = (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl18])).
% 6.87/1.58 thf(zip_derived_cl2, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.87/1.58 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.87/1.58 inference('cnf', [status(esa)], [associativity])).
% 6.87/1.58 thf(zip_derived_cl0, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_identity])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl643, plain,
% 6.87/1.58 ((((identity) = (sk_c7))
% 6.87/1.58 | ((inverse @ sk_c5) = (sk_c8))
% 6.87/1.58 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl627, zip_derived_cl2, zip_derived_cl0,
% 6.87/1.58 zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl644, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (sk_c8)) | ((identity) = (sk_c7)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl643])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12658, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (identity)) | ((identity) = (sk_c7)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl644, zip_derived_cl12529])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl17, plain,
% 6.87/1.58 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7))
% 6.87/1.58 | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_20])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12648, plain,
% 6.87/1.58 ((((sk_c5) = (sk_c7)) | ((sk_c2) = (sk_c7)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl17, zip_derived_cl12529, zip_derived_cl974,
% 6.87/1.58 zip_derived_cl12529, zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl23, plain,
% 6.87/1.58 ((((multiply @ sk_c5 @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_19])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12650, plain,
% 6.87/1.58 ((((sk_c5) = (sk_c7)) | ((inverse @ sk_c2) = (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl23, zip_derived_cl12529, zip_derived_cl974,
% 6.87/1.58 zip_derived_cl12529])).
% 6.87/1.58 thf(zip_derived_cl12721, plain,
% 6.87/1.58 ((((inverse @ sk_c7) = (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((sk_c5) = (sk_c7)))),
% 6.87/1.58 inference('sup+', [status(thm)],
% 6.87/1.58 [zip_derived_cl12648, zip_derived_cl12650])).
% 6.87/1.58 thf(zip_derived_cl12724, plain,
% 6.87/1.58 ((((sk_c5) = (sk_c7)) | ((inverse @ sk_c7) = (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12721])).
% 6.87/1.58 thf(zip_derived_cl12724, plain,
% 6.87/1.58 ((((sk_c5) = (sk_c7)) | ((inverse @ sk_c7) = (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12721])).
% 6.87/1.58 thf(zip_derived_cl12685, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((inverse @ X0) != (identity))
% 6.87/1.58 | ((X0) != (sk_c7))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X2 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c7) != (identity))
% 6.87/1.58 | ((inverse @ X3) != (sk_c1))
% 6.87/1.58 | ((multiply @ X3 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl12684])).
% 6.87/1.58 thf(zip_derived_cl12824, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((identity) != (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((X3) != (sk_c7))
% 6.87/1.58 | ((inverse @ X3) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12724, zip_derived_cl12685])).
% 6.87/1.58 thf(zip_derived_cl12832, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((inverse @ X3) != (identity))
% 6.87/1.58 | ((X3) != (sk_c7))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12824])).
% 6.87/1.58 thf(zip_derived_cl13452, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((sk_c5) = (sk_c7))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c7) != (identity)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl12832])).
% 6.87/1.58 thf(zip_derived_cl13453, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((identity) != (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c1) != (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12724, zip_derived_cl13452])).
% 6.87/1.58 thf(zip_derived_cl13460, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((multiply @ X2 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13453])).
% 6.87/1.58 thf(zip_derived_cl13470, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12604, zip_derived_cl13460])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl1, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.87/1.58 inference('cnf', [status(esa)], [left_inverse])).
% 6.87/1.58 thf(zip_derived_cl12673, plain, (((multiply @ sk_c1 @ sk_c1) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl12604, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13485, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((identity) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13470, zip_derived_cl12673])).
% 6.87/1.58 thf(zip_derived_cl13486, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13485])).
% 6.87/1.58 thf(zip_derived_cl13504, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c7) != (sk_c1)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12604, zip_derived_cl13486])).
% 6.87/1.58 thf(zip_derived_cl13519, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((multiply @ sk_c1 @ sk_c7) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13504])).
% 6.87/1.58 thf(zip_derived_cl13539, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((multiply @ sk_c1 @ identity) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12658, zip_derived_cl13519])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl13542, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13539, zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl13543, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13542])).
% 6.87/1.58 thf(zip_derived_cl13663, plain,
% 6.87/1.58 ((((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12604, zip_derived_cl13543])).
% 6.87/1.58 thf(zip_derived_cl12673, plain, (((multiply @ sk_c1 @ sk_c1) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl12604, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13678, plain,
% 6.87/1.58 ((((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((sk_c5) = (sk_c7))
% 6.87/1.58 | ((identity) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13663, zip_derived_cl12673])).
% 6.87/1.58 thf(zip_derived_cl13679, plain,
% 6.87/1.58 ((((sk_c5) = (sk_c7)) | ((inverse @ sk_c5) = (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13678])).
% 6.87/1.58 thf(zip_derived_cl18, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c7)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_28])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl12649, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (identity)) | ((sk_c2) = (sk_c7)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl18, zip_derived_cl12529, zip_derived_cl12529,
% 6.87/1.58 zip_derived_cl974])).
% 6.87/1.58 thf(zip_derived_cl24, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 6.87/1.58 inference('cnf', [status(esa)], [zf_stmt_27])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12529, plain, (((identity) = (sk_c8))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl12528])).
% 6.87/1.58 thf(zip_derived_cl12651, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (identity)) | ((inverse @ sk_c2) = (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl24, zip_derived_cl12529, zip_derived_cl12529])).
% 6.87/1.58 thf(zip_derived_cl13027, plain,
% 6.87/1.58 ((((inverse @ sk_c7) = (identity))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity)))),
% 6.87/1.58 inference('sup+', [status(thm)],
% 6.87/1.58 [zip_derived_cl12649, zip_derived_cl12651])).
% 6.87/1.58 thf(zip_derived_cl13033, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (identity)) | ((inverse @ sk_c7) = (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13027])).
% 6.87/1.58 thf(zip_derived_cl13706, plain,
% 6.87/1.58 ((((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity))
% 6.87/1.58 | ((inverse @ sk_c5) = (identity)))),
% 6.87/1.58 inference('sup+', [status(thm)],
% 6.87/1.58 [zip_derived_cl13679, zip_derived_cl13033])).
% 6.87/1.58 thf(zip_derived_cl13718, plain, (((inverse @ sk_c5) = (identity))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13706])).
% 6.87/1.58 thf(zip_derived_cl1019, plain,
% 6.87/1.58 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl974, zip_derived_cl161])).
% 6.87/1.58 thf(zip_derived_cl13724, plain, (((sk_c5) = (inverse @ identity))),
% 6.87/1.58 inference('sup+', [status(thm)],
% 6.87/1.58 [zip_derived_cl13718, zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl825, plain, (((inverse @ identity) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl213, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13729, plain, (((sk_c5) = (identity))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13724, zip_derived_cl825])).
% 6.87/1.58 thf(zip_derived_cl13735, plain,
% 6.87/1.58 ((((identity) = (sk_c7)) | ((identity) = (sk_c7)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12656, zip_derived_cl13729])).
% 6.87/1.58 thf(zip_derived_cl13736, plain, (((identity) = (sk_c7))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13735])).
% 6.87/1.58 thf(zip_derived_cl13736, plain, (((identity) = (sk_c7))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13735])).
% 6.87/1.58 thf(zip_derived_cl974, plain,
% 6.87/1.58 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl161, zip_derived_cl158])).
% 6.87/1.58 thf(zip_derived_cl13736, plain, (((identity) = (sk_c7))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13735])).
% 6.87/1.58 thf(zip_derived_cl825, plain, (((inverse @ identity) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl213, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13758, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((inverse @ X0) != (identity))
% 6.87/1.58 | ((X0) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((X2) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((identity) != (identity))
% 6.87/1.58 | ((inverse @ X3) != (sk_c1))
% 6.87/1.58 | ((multiply @ X3 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl12685, zip_derived_cl13736,
% 6.87/1.58 zip_derived_cl13736, zip_derived_cl974, zip_derived_cl13736,
% 6.87/1.58 zip_derived_cl825])).
% 6.87/1.58 thf(zip_derived_cl13759, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.87/1.58 (((multiply @ X3 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X3) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((X0) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13758])).
% 6.87/1.58 thf(zip_derived_cl13771, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((inverse @ X0) != (identity))
% 6.87/1.58 | ((X0) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl13759])).
% 6.87/1.58 thf(zip_derived_cl12604, plain, (((inverse @ sk_c1) = (sk_c1))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl8484, zip_derived_cl12475, zip_derived_cl12475,
% 6.87/1.58 zip_derived_cl1019])).
% 6.87/1.58 thf(zip_derived_cl13772, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((inverse @ X0) != (identity))
% 6.87/1.58 | ((X0) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X2 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13771, zip_derived_cl12604])).
% 6.87/1.58 thf(zip_derived_cl13773, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.87/1.58 (((multiply @ X2 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X2) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((X0) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (identity)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13772])).
% 6.87/1.58 thf(zip_derived_cl13774, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((inverse @ identity) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('eq_res', [status(thm)], [zip_derived_cl13773])).
% 6.87/1.58 thf(zip_derived_cl825, plain, (((inverse @ identity) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl213, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13775, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((identity) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X1 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13774, zip_derived_cl825])).
% 6.87/1.58 thf(zip_derived_cl13776, plain,
% 6.87/1.58 (![X0 : $i, X1 : $i]:
% 6.87/1.58 (((multiply @ X1 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X1) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13775])).
% 6.87/1.58 thf(zip_derived_cl13778, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((multiply @ sk_c1 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12604, zip_derived_cl13776])).
% 6.87/1.58 thf(zip_derived_cl12673, plain, (((multiply @ sk_c1 @ sk_c1) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl12604, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13784, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((sk_c1) != (sk_c1))
% 6.87/1.58 | ((inverse @ X0) != (sk_c1))
% 6.87/1.58 | ((multiply @ X0 @ sk_c1) != (identity))
% 6.87/1.58 | ((identity) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13778, zip_derived_cl12673])).
% 6.87/1.58 thf(zip_derived_cl13785, plain,
% 6.87/1.58 (![X0 : $i]:
% 6.87/1.58 (((multiply @ X0 @ sk_c1) != (identity)) | ((inverse @ X0) != (sk_c1)))),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13784])).
% 6.87/1.58 thf(zip_derived_cl13792, plain,
% 6.87/1.58 ((((sk_c1) != (sk_c1)) | ((multiply @ sk_c1 @ sk_c1) != (identity)))),
% 6.87/1.58 inference('sup-', [status(thm)],
% 6.87/1.58 [zip_derived_cl12604, zip_derived_cl13785])).
% 6.87/1.58 thf(zip_derived_cl12673, plain, (((multiply @ sk_c1 @ sk_c1) = (identity))),
% 6.87/1.58 inference('sup+', [status(thm)], [zip_derived_cl12604, zip_derived_cl1])).
% 6.87/1.58 thf(zip_derived_cl13798, plain,
% 6.87/1.58 ((((sk_c1) != (sk_c1)) | ((identity) != (identity)))),
% 6.87/1.58 inference('demod', [status(thm)],
% 6.87/1.58 [zip_derived_cl13792, zip_derived_cl12673])).
% 6.87/1.58 thf(zip_derived_cl13799, plain, ($false),
% 6.87/1.58 inference('simplify', [status(thm)], [zip_derived_cl13798])).
% 6.87/1.58
% 6.87/1.58 % SZS output end Refutation
% 6.87/1.58
% 6.87/1.58
% 6.87/1.58 % Terminating...
% 7.27/1.67 % Runner terminated.
% 7.27/1.68 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------