%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP380-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.I1gZon2alg true
% Computer : n004.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 Oct 2 04:36:20 PM UTC 2025
% Result : Unsatisfiable 188.57s 27.71s
% Output : Refutation 188.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP380-1 : TPTP v9.2.0. Released v2.5.0.
% 0.05/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.I1gZon2alg true
% 0.10/0.31 % Computer : n004.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Oct 1 14:12:23 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Running portfolio for 300 s
% 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in FO mode
% 0.46/0.58 % Total configuration time : 435
% 0.46/0.58 % Estimated wc time : 1092
% 0.46/0.58 % Estimated cpu time (7 cpus) : 156.0
% 0.50/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.50/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.50/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.50/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 188.57/27.71 % Solved by fo/fo1_av.sh.
% 188.57/27.71 % done 19991 iterations in 26.944s
% 188.57/27.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 188.57/27.71 % SZS output start Refutation
% 188.57/27.71 thf(sk_c8_type, type, sk_c8: $i).
% 188.57/27.71 thf(sk_c3_type, type, sk_c3: $i).
% 188.57/27.71 thf(sk_c5_type, type, sk_c5: $i).
% 188.57/27.71 thf(sk_c9_type, type, sk_c9: $i).
% 188.57/27.71 thf(identity_type, type, identity: $i).
% 188.57/27.71 thf(multiply_type, type, multiply: $i > $i > $i).
% 188.57/27.71 thf(sk_c10_type, type, sk_c10: $i).
% 188.57/27.71 thf(sk_c2_type, type, sk_c2: $i).
% 188.57/27.71 thf(inverse_type, type, inverse: $i > $i).
% 188.57/27.71 thf(sk_c4_type, type, sk_c4: $i).
% 188.57/27.71 thf(sk_c1_type, type, sk_c1: $i).
% 188.57/27.71 thf(sk_c11_type, type, sk_c11: $i).
% 188.57/27.71 thf(prove_this_2, conjecture,
% 188.57/27.71 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.71 ( ( inverse @ sk_c11 ) = ( sk_c10 ) ) ))).
% 188.57/27.71 thf(zf_stmt_0, negated_conjecture,
% 188.57/27.71 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.71 ( ( inverse @ sk_c11 ) = ( sk_c10 ) )),
% 188.57/27.71 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 188.57/27.71 thf(zip_derived_cl4, plain,
% 188.57/27.71 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.71 inference('cnf', [status(esa)], [zf_stmt_0])).
% 188.57/27.71 thf(zip_derived_cl56, plain,
% 188.57/27.71 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.71 inference('split', [status(esa)], [zip_derived_cl4])).
% 188.57/27.71 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 188.57/27.71 thf(zip_derived_cl1, plain,
% 188.57/27.71 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.71 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.71 thf(zip_derived_cl174, plain,
% 188.57/27.71 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 188.57/27.71 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.71 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 188.57/27.71 thf(zip_derived_cl1, plain,
% 188.57/27.71 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.71 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.71 thf(associativity, axiom,
% 188.57/27.71 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 188.57/27.71 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 188.57/27.71 thf(zip_derived_cl2, plain,
% 188.57/27.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.71 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.71 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.71 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.71 thf(zip_derived_cl193, plain,
% 188.57/27.71 (![X0 : $i, X1 : $i]:
% 188.57/27.71 ((multiply @ identity @ X0)
% 188.57/27.71 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.71 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 188.57/27.71 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 188.57/27.71 thf(zip_derived_cl0, plain,
% 188.57/27.71 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.71 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.71 thf(zip_derived_cl195, plain,
% 188.57/27.71 (![X0 : $i, X1 : $i]:
% 188.57/27.71 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.71 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.71 thf(zip_derived_cl432, plain,
% 188.57/27.71 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity)))
% 188.57/27.71 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.71 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl195])).
% 188.57/27.71 thf(zip_derived_cl2, plain,
% 188.57/27.71 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.71 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.71 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.71 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.71 thf(zip_derived_cl518, plain,
% 188.57/27.71 ((![X0 : $i]:
% 188.57/27.71 ((multiply @ sk_c3 @ X0)
% 188.57/27.71 = (multiply @ (inverse @ sk_c11) @ (multiply @ identity @ X0))))
% 188.57/27.71 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.71 inference('s_sup+', [status(thm)], [zip_derived_cl432, zip_derived_cl2])).
% 188.57/27.71 thf(zip_derived_cl0, plain,
% 188.57/27.71 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.71 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.71 thf(zip_derived_cl523, plain,
% 188.57/27.71 ((![X0 : $i]:
% 188.57/27.71 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 188.57/27.71 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.71 inference('demod', [status(thm)], [zip_derived_cl518, zip_derived_cl0])).
% 188.57/27.71 thf(zip_derived_cl1, plain,
% 188.57/27.71 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.71 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.71 thf(zip_derived_cl1498, plain,
% 188.57/27.71 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl523, zip_derived_cl1])).
% 188.57/27.72 thf(prove_this_1, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_1, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 188.57/27.72 thf(zip_derived_cl3, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 188.57/27.72 | ((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_1])).
% 188.57/27.72 thf(zip_derived_cl55, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(prove_this_3, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_2, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 188.57/27.72 thf(zip_derived_cl5, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 188.57/27.72 | ((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_2])).
% 188.57/27.72 thf(zip_derived_cl58, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl5])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl439, plain,
% 188.57/27.72 ((((sk_c10) = (multiply @ (inverse @ sk_c4) @ sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl579, plain,
% 188.57/27.72 ((((sk_c9) = (multiply @ (inverse @ (inverse @ sk_c4)) @ sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl439, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl7462, plain,
% 188.57/27.72 ((((sk_c9) = (multiply @ (inverse @ (inverse @ sk_c4)) @ identity)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1519, zip_derived_cl579])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl430, plain,
% 188.57/27.72 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl7465, plain,
% 188.57/27.72 ((((sk_c9) = (sk_c4)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl7462, zip_derived_cl430])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(prove_this_11, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 188.57/27.72 thf(zf_stmt_3, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 188.57/27.72 thf(zip_derived_cl13, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_3])).
% 188.57/27.72 thf(zip_derived_cl74, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl13])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl437, plain,
% 188.57/27.72 ((((sk_c9) = (multiply @ (inverse @ sk_c10) @ sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl4541, plain,
% 188.57/27.72 ((((sk_c9) = (multiply @ (inverse @ identity) @ sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1519, zip_derived_cl437])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl429, plain,
% 188.57/27.72 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl4609, plain,
% 188.57/27.72 ((((sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl4541, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl8194, plain,
% 188.57/27.72 ((((sk_c4) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl7465, zip_derived_cl4609])).
% 188.57/27.72 thf(prove_this_4, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_4, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 188.57/27.72 thf(zip_derived_cl6, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_4])).
% 188.57/27.72 thf(zip_derived_cl60, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl6])).
% 188.57/27.72 thf(zip_derived_cl8473, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl8194, zip_derived_cl60])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl8510, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl8473, zip_derived_cl1519])).
% 188.57/27.72 thf(zip_derived_cl60, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl6])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl175, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl436, plain,
% 188.57/27.72 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl566, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c4 @ X0)
% 188.57/27.72 = (multiply @ (inverse @ sk_c10) @ (multiply @ identity @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl436, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl571, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl566, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl1607, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl571, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl175, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl330, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ identity @ X0)
% 188.57/27.72 = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl331, plain,
% 188.57/27.72 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl330, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1633, plain,
% 188.57/27.72 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1607, zip_derived_cl331])).
% 188.57/27.72 thf(zip_derived_cl55, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl208, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c10 @ X0)
% 188.57/27.72 = (multiply @ sk_c3 @ (multiply @ sk_c11 @ X0))))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl486, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c11 @ X0)
% 188.57/27.72 = (multiply @ (inverse @ sk_c3) @ (multiply @ sk_c10 @ X0))))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl208, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl4722, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity)
% 188.57/27.72 = (multiply @ (inverse @ sk_c3) @ sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1633, zip_derived_cl486])).
% 188.57/27.72 thf(zip_derived_cl55, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl438, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c3) @ sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl4730, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl4722, zip_derived_cl438])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl571, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl566, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl4553, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ identity) @ X0)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1519, zip_derived_cl571])).
% 188.57/27.72 thf(zip_derived_cl429, plain,
% 188.57/27.72 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl4613, plain,
% 188.57/27.72 ((![X0 : $i]: ((multiply @ sk_c4 @ X0) = (X0)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl4553, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl7465, plain,
% 188.57/27.72 ((((sk_c9) = (sk_c4)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl7462, zip_derived_cl430])).
% 188.57/27.72 thf(prove_this_13, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 188.57/27.72 thf(zf_stmt_5, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 188.57/27.72 thf(zip_derived_cl15, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 188.57/27.72 | ((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_5])).
% 188.57/27.72 thf('0', plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl15])).
% 188.57/27.72 thf(prove_this_23, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_6, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 188.57/27.72 thf(zip_derived_cl25, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 188.57/27.72 | ((multiply @ sk_c1 @ sk_c2) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_6])).
% 188.57/27.72 thf('1', plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl25])).
% 188.57/27.72 thf(prove_this_33, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 188.57/27.72 thf(zf_stmt_7, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 188.57/27.72 thf(zip_derived_cl35, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_7])).
% 188.57/27.72 thf('2', plain,
% 188.57/27.72 ((((inverse @ sk_c1) = (sk_c2))) |
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl35])).
% 188.57/27.72 thf(prove_this_43, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_8, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 188.57/27.72 thf(zip_derived_cl45, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 188.57/27.72 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_8])).
% 188.57/27.72 thf('3', plain,
% 188.57/27.72 ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))) |
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl45])).
% 188.57/27.72 thf(prove_this_12, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 188.57/27.72 thf(zf_stmt_9, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 188.57/27.72 thf(zip_derived_cl14, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))
% 188.57/27.72 | ((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_9])).
% 188.57/27.72 thf('4', plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl14])).
% 188.57/27.72 thf(prove_this_32, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 188.57/27.72 thf(zf_stmt_10, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 188.57/27.72 thf(zip_derived_cl34, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_10])).
% 188.57/27.72 thf('5', plain,
% 188.57/27.72 ((((inverse @ sk_c1) = (sk_c2))) | (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl34])).
% 188.57/27.72 thf(prove_this_42, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_11, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 188.57/27.72 thf(zip_derived_cl44, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))
% 188.57/27.72 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_11])).
% 188.57/27.72 thf('6', plain,
% 188.57/27.72 ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))) |
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl44])).
% 188.57/27.72 thf(prove_this_31, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 188.57/27.72 thf(zf_stmt_12, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 188.57/27.72 thf(zip_derived_cl33, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 188.57/27.72 | ((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_12])).
% 188.57/27.72 thf(zip_derived_cl114, plain,
% 188.57/27.72 ((((inverse @ sk_c1) = (sk_c2))) <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl33])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl214, plain,
% 188.57/27.72 ((((multiply @ sk_c2 @ sk_c1) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl448, plain,
% 188.57/27.72 ((((sk_c1) = (multiply @ (inverse @ sk_c2) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl214, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl833, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c1 @ X0)
% 188.57/27.72 = (multiply @ (inverse @ sk_c2) @ (multiply @ identity @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl448, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl837, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c2) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl833, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl2929, plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl837, zip_derived_cl1])).
% 188.57/27.72 thf(prove_this_21, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_13, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 188.57/27.72 thf(zip_derived_cl23, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c1 @ sk_c2) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_13])).
% 188.57/27.72 thf(zip_derived_cl94, plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl23])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl173, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl435, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c10) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl9563, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ identity) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl435])).
% 188.57/27.72 thf(zip_derived_cl429, plain,
% 188.57/27.72 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl9648, plain,
% 188.57/27.72 ((((sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl9563, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl173, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl326, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ identity @ X0)
% 188.57/27.72 = (multiply @ sk_c10 @ (multiply @ sk_c11 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl327, plain,
% 188.57/27.72 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c11 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl433, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c11 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl327, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl1179, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c10) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl433, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl327, plain,
% 188.57/27.72 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c11 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1220, plain,
% 188.57/27.72 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1179, zip_derived_cl327])).
% 188.57/27.72 thf(zip_derived_cl174, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl327, plain,
% 188.57/27.72 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c11 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl326, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl373, plain,
% 188.57/27.72 ((((sk_c3) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl327])).
% 188.57/27.72 thf(zip_derived_cl1249, plain,
% 188.57/27.72 ((((sk_c3) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1220, zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl373, plain,
% 188.57/27.72 ((((sk_c3) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl327])).
% 188.57/27.72 thf(prove_this_51, conjecture,
% 188.57/27.72 (~( ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 188.57/27.72 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 188.57/27.72 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ X5 ) != ( X6 ) ) |
% 188.57/27.72 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 188.57/27.72 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ X3 ) != ( X4 ) ) |
% 188.57/27.72 ( ( multiply @ X3 @ X4 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) != ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_14, negated_conjecture,
% 188.57/27.72 (( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 188.57/27.72 ( ( inverse @ X7 ) != ( X8 ) ) |
% 188.57/27.72 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ X5 ) != ( X6 ) ) |
% 188.57/27.72 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 188.57/27.72 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ X3 ) != ( X4 ) ) |
% 188.57/27.72 ( ( multiply @ X3 @ X4 ) != ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) != ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) != ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 188.57/27.72 thf(zip_derived_cl53, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X0) != (X2))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11))
% 188.57/27.72 | ((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 188.57/27.72 | ((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 188.57/27.72 | ((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c10 @ sk_c9) != (sk_c11))
% 188.57/27.72 | ((inverse @ sk_c11) != (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_14])).
% 188.57/27.72 thf(zip_derived_cl157, plain,
% 188.57/27.72 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11))))
% 188.57/27.72 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl379, plain,
% 188.57/27.72 ((![X0 : $i, X1 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0))
% 188.57/27.72 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl373, zip_derived_cl157])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl382, plain,
% 188.57/27.72 ((![X0 : $i, X1 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0))
% 188.57/27.72 | ((sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl379, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl388, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0))))
% 188.57/27.72 <= ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl382])).
% 188.57/27.72 thf(zip_derived_cl397, plain,
% 188.57/27.72 (((((sk_c10) != (identity))
% 188.57/27.72 | ((sk_c3) != (sk_c11))
% 188.57/27.72 | ((inverse @ sk_c10) != (sk_c11))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl388])).
% 188.57/27.72 thf(zip_derived_cl413, plain,
% 188.57/27.72 ((((sk_c3) != (sk_c11))) <= (~ (((sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl397])).
% 188.57/27.72 thf(zip_derived_cl1704, plain,
% 188.57/27.72 ((((sk_c10) != (sk_c11)))
% 188.57/27.72 <= (~ (((sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1249, zip_derived_cl413])).
% 188.57/27.72 thf(zip_derived_cl9608, plain,
% 188.57/27.72 ((((identity) != (sk_c11)))
% 188.57/27.72 <= (~ (((sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl1704])).
% 188.57/27.72 thf(zip_derived_cl37004, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl9648, zip_derived_cl9608])).
% 188.57/27.72 thf('7', plain,
% 188.57/27.72 ((((sk_c3) = (sk_c11))) | ~ (((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl37004])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl1498, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl523, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl56, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl4])).
% 188.57/27.72 thf(zip_derived_cl155, plain,
% 188.57/27.72 ((![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10))))
% 188.57/27.72 <= ((![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl163, plain,
% 188.57/27.72 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c3 @ sk_c11) != (sk_c10))))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl155])).
% 188.57/27.72 thf(zip_derived_cl164, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl163])).
% 188.57/27.72 thf(zip_derived_cl1520, plain,
% 188.57/27.72 ((((identity) != (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1498, zip_derived_cl164])).
% 188.57/27.72 thf(zip_derived_cl9602, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl1520])).
% 188.57/27.72 thf('8', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))) |
% 188.57/27.72 ~ (((inverse @ sk_c1) = (sk_c2))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl9602])).
% 188.57/27.72 thf(prove_this_22, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_15, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 188.57/27.72 thf(zip_derived_cl24, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))
% 188.57/27.72 | ((multiply @ sk_c1 @ sk_c2) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_15])).
% 188.57/27.72 thf('9', plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl24])).
% 188.57/27.72 thf(zip_derived_cl436, plain,
% 188.57/27.72 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl435, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c10) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl569, plain,
% 188.57/27.72 ((((sk_c11) = (sk_c4)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl436, zip_derived_cl435])).
% 188.57/27.72 thf(zip_derived_cl373, plain,
% 188.57/27.72 ((((sk_c3) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl327])).
% 188.57/27.72 thf(zip_derived_cl58, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl5])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl211, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c9 @ X0)
% 188.57/27.72 = (multiply @ sk_c4 @ (multiply @ sk_c10 @ X0))))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl509, plain,
% 188.57/27.72 ((((multiply @ sk_c9 @ identity) = (multiply @ sk_c4 @ sk_c3)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl373, zip_derived_cl211])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl534, plain,
% 188.57/27.72 ((((identity)
% 188.57/27.72 = (multiply @ (inverse @ sk_c9) @ (multiply @ sk_c4 @ sk_c3))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl509, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl595, plain,
% 188.57/27.72 ((((identity)
% 188.57/27.72 = (multiply @ (inverse @ sk_c9) @ (multiply @ sk_c11 @ sk_c3))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl569, zip_derived_cl534])).
% 188.57/27.72 thf(zip_derived_cl174, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl598, plain,
% 188.57/27.72 ((((identity) = (multiply @ (inverse @ sk_c9) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl595, zip_derived_cl174])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl600, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ identity @ X0)
% 188.57/27.72 = (multiply @ (inverse @ sk_c9) @ (multiply @ identity @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl598, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl604, plain,
% 188.57/27.72 ((![X0 : $i]: ((X0) = (multiply @ (inverse @ sk_c9) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl600, zip_derived_cl0, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl621, plain,
% 188.57/27.72 ((((sk_c9) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl604, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl439, plain,
% 188.57/27.72 ((((sk_c10) = (multiply @ (inverse @ sk_c4) @ sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl679, plain,
% 188.57/27.72 ((((sk_c10) = (multiply @ (inverse @ sk_c4) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl621, zip_derived_cl439])).
% 188.57/27.72 thf(zip_derived_cl569, plain,
% 188.57/27.72 ((((sk_c11) = (sk_c4)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl436, zip_derived_cl435])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl373, plain,
% 188.57/27.72 ((((sk_c3) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl327])).
% 188.57/27.72 thf(zip_derived_cl693, plain,
% 188.57/27.72 ((((sk_c10) = (sk_c3)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl679, zip_derived_cl569, zip_derived_cl54,
% 188.57/27.72 zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl55, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl737, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl693, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl173, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl760, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl737, zip_derived_cl173])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl154, plain,
% 188.57/27.72 ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10))))
% 188.57/27.72 <= ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl223, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10))))
% 188.57/27.72 <= ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl154])).
% 188.57/27.72 thf(zip_derived_cl226, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10))))
% 188.57/27.72 <= ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl223])).
% 188.57/27.72 thf(zip_derived_cl228, plain,
% 188.57/27.72 (((((sk_c10) != (identity))
% 188.57/27.72 | ((multiply @ sk_c11 @ identity) != (sk_c10))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl226])).
% 188.57/27.72 thf(zip_derived_cl236, plain,
% 188.57/27.72 ((((sk_c10) != (identity))) <= (~ (((sk_c10) = (identity))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl228])).
% 188.57/27.72 thf(zip_derived_cl952, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((sk_c10) = (identity))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl760, zip_derived_cl236])).
% 188.57/27.72 thf('10', plain,
% 188.57/27.72 ((((sk_c10) = (identity))) | ~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl952])).
% 188.57/27.72 thf('11', plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl13])).
% 188.57/27.72 thf('12', plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl23])).
% 188.57/27.72 thf('13', plain,
% 188.57/27.72 ((((inverse @ sk_c1) = (sk_c2))) |
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl33])).
% 188.57/27.72 thf(prove_this_41, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_16, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 188.57/27.72 thf(zip_derived_cl43, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_16])).
% 188.57/27.72 thf('14', plain,
% 188.57/27.72 ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))) |
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl43])).
% 188.57/27.72 thf(zip_derived_cl56, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl4])).
% 188.57/27.72 thf(zip_derived_cl388, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0))))
% 188.57/27.72 <= ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl382])).
% 188.57/27.72 thf(zip_derived_cl398, plain,
% 188.57/27.72 (((((sk_c11) != (identity))
% 188.57/27.72 | ((sk_c3) != (sk_c3))
% 188.57/27.72 | ((inverse @ sk_c10) != (sk_c3))))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl388])).
% 188.57/27.72 thf(zip_derived_cl404, plain,
% 188.57/27.72 (((((inverse @ sk_c10) != (sk_c3)) | ((sk_c11) != (identity))))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl398])).
% 188.57/27.72 thf('15', plain,
% 188.57/27.72 (~ (((inverse @ sk_c10) = (sk_c3))) |
% 188.57/27.72 ~
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11))) | ~ (((sk_c11) = (identity)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl404])).
% 188.57/27.72 thf(zip_derived_cl1220, plain,
% 188.57/27.72 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1179, zip_derived_cl327])).
% 188.57/27.72 thf(zip_derived_cl621, plain,
% 188.57/27.72 ((((sk_c9) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl604, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl74, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl13])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl250, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c11 @ X0)
% 188.57/27.72 = (multiply @ sk_c10 @ (multiply @ sk_c9 @ X0))))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl826, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c11 @ X0)
% 188.57/27.72 = (multiply @ sk_c10 @ (multiply @ identity @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl621, zip_derived_cl250])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl827, plain,
% 188.57/27.72 ((![X0 : $i]: ((multiply @ sk_c11 @ X0) = (multiply @ sk_c10 @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl826, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl16061, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1220, zip_derived_cl827])).
% 188.57/27.72 thf(zip_derived_cl1498, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl523, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl174, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl328, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ identity @ X0)
% 188.57/27.72 = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl329, plain,
% 188.57/27.72 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl328, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1518, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ sk_c11 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1498, zip_derived_cl329])).
% 188.57/27.72 thf(zip_derived_cl16065, plain,
% 188.57/27.72 ((((sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl16061, zip_derived_cl1518])).
% 188.57/27.72 thf(zip_derived_cl410, plain,
% 188.57/27.72 ((((inverse @ sk_c10) != (sk_c3)))
% 188.57/27.72 <= (~ (((inverse @ sk_c10) = (sk_c3))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl404])).
% 188.57/27.72 thf(zip_derived_cl16273, plain,
% 188.57/27.72 ((((inverse @ sk_c11) != (sk_c3)))
% 188.57/27.72 <= (~ (((inverse @ sk_c10) = (sk_c3))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl16065, zip_derived_cl410])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl16065, plain,
% 188.57/27.72 ((((sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl16061, zip_derived_cl1518])).
% 188.57/27.72 thf(zip_derived_cl1249, plain,
% 188.57/27.72 ((((sk_c3) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1220, zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl16065, plain,
% 188.57/27.72 ((((sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl16061, zip_derived_cl1518])).
% 188.57/27.72 thf(zip_derived_cl16387, plain,
% 188.57/27.72 ((((sk_c11) != (sk_c11)))
% 188.57/27.72 <= (~ (((inverse @ sk_c10) = (sk_c3))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl16273, zip_derived_cl54, zip_derived_cl16065,
% 188.57/27.72 zip_derived_cl1249, zip_derived_cl16065])).
% 188.57/27.72 thf('16', plain,
% 188.57/27.72 (~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 (((inverse @ sk_c10) = (sk_c3))) |
% 188.57/27.72 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 ~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl16387])).
% 188.57/27.72 thf(zip_derived_cl55, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl164, plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl163])).
% 188.57/27.72 thf(zip_derived_cl209, plain,
% 188.57/27.72 ((((sk_c10) != (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl164])).
% 188.57/27.72 thf('17', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl209])).
% 188.57/27.72 thf(zip_derived_cl1249, plain,
% 188.57/27.72 ((((sk_c3) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1220, zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl438, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c3) @ sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl1705, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c10) @ sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1249, zip_derived_cl438])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl1725, plain,
% 188.57/27.72 ((((sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl1705, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl56, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl4])).
% 188.57/27.72 thf(zip_derived_cl226, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10))))
% 188.57/27.72 <= ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl223])).
% 188.57/27.72 thf(zip_derived_cl229, plain,
% 188.57/27.72 (((((sk_c11) != (identity)) | ((multiply @ sk_c3 @ identity) != (sk_c10))))
% 188.57/27.72 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl226])).
% 188.57/27.72 thf(zip_derived_cl238, plain,
% 188.57/27.72 ((((sk_c11) != (identity))) <= (~ (((sk_c11) = (identity))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl229])).
% 188.57/27.72 thf(zip_derived_cl6055, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((sk_c11) = (identity))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1725, zip_derived_cl238])).
% 188.57/27.72 thf('18', plain,
% 188.57/27.72 ((((sk_c11) = (identity))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl6055])).
% 188.57/27.72 thf('19', plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))) |
% 188.57/27.72 ~
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 188.57/27.72 ~ (((sk_c10) = (sk_c11)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl382])).
% 188.57/27.72 thf(zip_derived_cl693, plain,
% 188.57/27.72 ((((sk_c10) = (sk_c3)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl679, zip_derived_cl569, zip_derived_cl54,
% 188.57/27.72 zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl438, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c3) @ sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl748, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c10) @ sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl693, zip_derived_cl438])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl766, plain,
% 188.57/27.72 ((((sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl748, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl760, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl737, zip_derived_cl173])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl155, plain,
% 188.57/27.72 ((![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10))))
% 188.57/27.72 <= ((![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl162, plain,
% 188.57/27.72 (((((sk_c10) != (sk_c11)) | ((multiply @ sk_c11 @ sk_c11) != (sk_c10))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl155])).
% 188.57/27.72 thf(zip_derived_cl172, plain,
% 188.57/27.72 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl162])).
% 188.57/27.72 thf(zip_derived_cl942, plain,
% 188.57/27.72 ((((identity) != (sk_c11)))
% 188.57/27.72 <= (~ (((sk_c10) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl760, zip_derived_cl172])).
% 188.57/27.72 thf(zip_derived_cl2984, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((sk_c10) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl766, zip_derived_cl942])).
% 188.57/27.72 thf('20', plain,
% 188.57/27.72 ((((sk_c10) = (sk_c11))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl2984])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl1607, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl571, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl60, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl6])).
% 188.57/27.72 thf(zip_derived_cl74, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl13])).
% 188.57/27.72 thf(zip_derived_cl154, plain,
% 188.57/27.72 ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10))))
% 188.57/27.72 <= ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl251, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((sk_c11) != (sk_c10))
% 188.57/27.72 | ((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10))))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl154])).
% 188.57/27.72 thf(zip_derived_cl254, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10))))
% 188.57/27.72 <= ((![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl251])).
% 188.57/27.72 thf(zip_derived_cl258, plain,
% 188.57/27.72 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c4 @ sk_c10) != (sk_c10))))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl254])).
% 188.57/27.72 thf(zip_derived_cl264, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) != (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl258])).
% 188.57/27.72 thf(zip_derived_cl1636, plain,
% 188.57/27.72 ((((identity) != (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1607, zip_derived_cl264])).
% 188.57/27.72 thf(zip_derived_cl4576, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1519, zip_derived_cl1636])).
% 188.57/27.72 thf('21', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10)))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10))) | ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl4576])).
% 188.57/27.72 thf(zip_derived_cl766, plain,
% 188.57/27.72 ((((sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl748, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl760, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl737, zip_derived_cl173])).
% 188.57/27.72 thf(zip_derived_cl693, plain,
% 188.57/27.72 ((((sk_c10) = (sk_c3)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl679, zip_derived_cl569, zip_derived_cl54,
% 188.57/27.72 zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl621, plain,
% 188.57/27.72 ((((sk_c9) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl604, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl158, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl662, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ identity) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl621, zip_derived_cl158])).
% 188.57/27.72 thf(zip_derived_cl373, plain,
% 188.57/27.72 ((((sk_c3) = (multiply @ sk_c10 @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl174, zip_derived_cl327])).
% 188.57/27.72 thf(zip_derived_cl691, plain,
% 188.57/27.72 ((((sk_c3) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl662, zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl759, plain,
% 188.57/27.72 ((((sk_c10) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl693, zip_derived_cl691])).
% 188.57/27.72 thf(zip_derived_cl996, plain,
% 188.57/27.72 ((((identity) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl760, zip_derived_cl759])).
% 188.57/27.72 thf(zip_derived_cl2987, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl766, zip_derived_cl996])).
% 188.57/27.72 thf('22', plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl2987])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl387, plain,
% 188.57/27.72 ((![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11))))
% 188.57/27.72 <= ((![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl382])).
% 188.57/27.72 thf(zip_derived_cl390, plain,
% 188.57/27.72 (((((sk_c10) != (identity))
% 188.57/27.72 | ((multiply @ sk_c11 @ identity) != (sk_c11))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl387])).
% 188.57/27.72 thf(zip_derived_cl435, plain,
% 188.57/27.72 ((((sk_c11) = (multiply @ (inverse @ sk_c10) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl433, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c11 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl327, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl1181, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity) = (sk_c11)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl435, zip_derived_cl433])).
% 188.57/27.72 thf(zip_derived_cl3102, plain,
% 188.57/27.72 (((((sk_c10) != (identity)) | ((sk_c11) != (sk_c11))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl390, zip_derived_cl1181])).
% 188.57/27.72 thf(zip_derived_cl3103, plain,
% 188.57/27.72 ((((sk_c10) != (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl3102])).
% 188.57/27.72 thf(zip_derived_cl4591, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1519, zip_derived_cl3103])).
% 188.57/27.72 thf('23', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl4591])).
% 188.57/27.72 thf('24', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))) |
% 188.57/27.72 ~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 ~ (((sk_c10) = (sk_c11))) |
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (sk_c10))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl251])).
% 188.57/27.72 thf(zip_derived_cl1249, plain,
% 188.57/27.72 ((((sk_c3) = (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl1220, zip_derived_cl373])).
% 188.57/27.72 thf(zip_derived_cl56, plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl4])).
% 188.57/27.72 thf(zip_derived_cl1695, plain,
% 188.57/27.72 ((((inverse @ sk_c10) = (sk_c11)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1249, zip_derived_cl56])).
% 188.57/27.72 thf(zip_derived_cl412, plain,
% 188.57/27.72 ((((inverse @ sk_c10) != (sk_c11)))
% 188.57/27.72 <= (~ (((inverse @ sk_c10) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl397])).
% 188.57/27.72 thf(zip_derived_cl48711, plain,
% 188.57/27.72 ((((sk_c11) != (sk_c11)))
% 188.57/27.72 <= (~ (((inverse @ sk_c10) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1695, zip_derived_cl412])).
% 188.57/27.72 thf('25', plain,
% 188.57/27.72 ((((inverse @ sk_c10) = (sk_c11))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl48711])).
% 188.57/27.72 thf('26', plain,
% 188.57/27.72 (~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c10) = (sk_c11))) | ~ (((sk_c3) = (sk_c11))) |
% 188.57/27.72 ~
% 188.57/27.72 (![X0 : $i]:
% 188.57/27.72 (((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c3) != (X0))
% 188.57/27.72 | ((inverse @ sk_c10) != (X0)))) |
% 188.57/27.72 ~ (((sk_c10) = (identity)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl397])).
% 188.57/27.72 thf(zip_derived_cl58, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl5])).
% 188.57/27.72 thf(zip_derived_cl60, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl6])).
% 188.57/27.72 thf(zip_derived_cl156, plain,
% 188.57/27.72 ((![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9))))
% 188.57/27.72 <= ((![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl168, plain,
% 188.57/27.72 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c4 @ sk_c10) != (sk_c9))))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl156])).
% 188.57/27.72 thf(zip_derived_cl170, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) != (sk_c9)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl168])).
% 188.57/27.72 thf(zip_derived_cl212, plain,
% 188.57/27.72 ((((sk_c9) != (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl170])).
% 188.57/27.72 thf('27', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9)))) |
% 188.57/27.72 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl212])).
% 188.57/27.72 thf(zip_derived_cl1181, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity) = (sk_c11)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl435, zip_derived_cl433])).
% 188.57/27.72 thf(zip_derived_cl157, plain,
% 188.57/27.72 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11))))
% 188.57/27.72 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl355, plain,
% 188.57/27.72 ((![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 (((multiply @ X1 @ X0) != (sk_c11))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 188.57/27.72 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 188.57/27.72 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('eq_res', [status(thm)], [zip_derived_cl157])).
% 188.57/27.72 thf(zip_derived_cl2572, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((multiply @ X0 @ identity) != (sk_c11))
% 188.57/27.72 | ((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ sk_c11) != (sk_c11))
% 188.57/27.72 | ((inverse @ sk_c11) != (identity))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1181, zip_derived_cl355])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl2630, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((multiply @ X0 @ identity) != (sk_c11))
% 188.57/27.72 | ((inverse @ X0) != (identity))
% 188.57/27.72 | ((sk_c10) != (sk_c11))
% 188.57/27.72 | ((sk_c10) != (sk_c11))
% 188.57/27.72 | ((sk_c10) != (identity))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl2572, zip_derived_cl0, zip_derived_cl54,
% 188.57/27.72 zip_derived_cl54])).
% 188.57/27.72 thf(zip_derived_cl2631, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((sk_c10) != (identity))
% 188.57/27.72 | ((sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X0) != (identity))
% 188.57/27.72 | ((multiply @ X0 @ identity) != (sk_c11))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl2630])).
% 188.57/27.72 thf('28', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((sk_c10) = (identity))) |
% 188.57/27.72 ~ (((sk_c10) = (sk_c11))) |
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl2631])).
% 188.57/27.72 thf('29', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))) |
% 188.57/27.72 ~ (((sk_c10) = (sk_c11))) | ~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c11 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl162])).
% 188.57/27.72 thf(zip_derived_cl9648, plain,
% 188.57/27.72 ((((sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl9563, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl172, plain,
% 188.57/27.72 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl162])).
% 188.57/27.72 thf(zip_derived_cl9535, plain,
% 188.57/27.72 ((((identity) != (sk_c11)))
% 188.57/27.72 <= (~ (((sk_c10) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl172])).
% 188.57/27.72 thf(zip_derived_cl37001, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((sk_c10) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl9648, zip_derived_cl9535])).
% 188.57/27.72 thf('30', plain,
% 188.57/27.72 ((((sk_c10) = (sk_c11))) | ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl37001])).
% 188.57/27.72 thf(zip_derived_cl9648, plain,
% 188.57/27.72 ((((sk_c11) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl9563, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl171, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c11) != (sk_c10)))
% 188.57/27.72 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl162])).
% 188.57/27.72 thf(zip_derived_cl36921, plain,
% 188.57/27.72 ((((multiply @ identity @ identity) != (sk_c10)))
% 188.57/27.72 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl9648, zip_derived_cl171])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl37041, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((multiply @ sk_c11 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl36921, zip_derived_cl0, zip_derived_cl3057])).
% 188.57/27.72 thf('31', plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10))) | ~ (((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl37041])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl3103, plain,
% 188.57/27.72 ((((sk_c10) != (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl3102])).
% 188.57/27.72 thf(zip_derived_cl9624, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl3103])).
% 188.57/27.72 thf('32', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X1 : $i]:
% 188.57/27.72 (((inverse @ X1) != (identity))
% 188.57/27.72 | ((multiply @ X1 @ identity) != (sk_c11)))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c1) = (sk_c2))) | ~ (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl9624])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl236, plain,
% 188.57/27.72 ((((sk_c10) != (identity))) <= (~ (((sk_c10) = (identity))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl228])).
% 188.57/27.72 thf(zip_derived_cl9545, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((sk_c10) = (identity))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl236])).
% 188.57/27.72 thf('33', plain,
% 188.57/27.72 ((((sk_c10) = (identity))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl9545])).
% 188.57/27.72 thf(zip_derived_cl94, plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl23])).
% 188.57/27.72 thf(zip_derived_cl114, plain,
% 188.57/27.72 ((((inverse @ sk_c1) = (sk_c2))) <= ((((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl33])).
% 188.57/27.72 thf(zip_derived_cl134, plain,
% 188.57/27.72 ((((multiply @ sk_c2 @ sk_c9) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl43])).
% 188.57/27.72 thf(zip_derived_cl154, plain,
% 188.57/27.72 ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10))))
% 188.57/27.72 <= ((![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl302, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((sk_c10) != (sk_c10))
% 188.57/27.72 | ((inverse @ X0) != (sk_c2))
% 188.57/27.72 | ((multiply @ X0 @ sk_c2) != (sk_c10))))
% 188.57/27.72 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))) &
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl154])).
% 188.57/27.72 thf(zip_derived_cl303, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 (((multiply @ X0 @ sk_c2) != (sk_c10)) | ((inverse @ X0) != (sk_c2))))
% 188.57/27.72 <= ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))) &
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl302])).
% 188.57/27.72 thf(zip_derived_cl310, plain,
% 188.57/27.72 (((((multiply @ sk_c1 @ sk_c2) != (sk_c10)) | ((sk_c2) != (sk_c2))))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10))) &
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl303])).
% 188.57/27.72 thf(zip_derived_cl311, plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) != (sk_c10)))
% 188.57/27.72 <= ((((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10))) &
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl310])).
% 188.57/27.72 thf(zip_derived_cl312, plain,
% 188.57/27.72 ((((sk_c10) != (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10))) &
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl311])).
% 188.57/27.72 thf('34', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10)))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c2 @ sk_c9) = (sk_c10))) |
% 188.57/27.72 ~ (((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl312])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl437, plain,
% 188.57/27.72 ((((sk_c9) = (multiply @ (inverse @ sk_c10) @ sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl9565, plain,
% 188.57/27.72 ((((sk_c9) = (multiply @ (inverse @ identity) @ sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl437])).
% 188.57/27.72 thf(zip_derived_cl429, plain,
% 188.57/27.72 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl9650, plain,
% 188.57/27.72 ((((sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl9565, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl3057, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2929, zip_derived_cl94])).
% 188.57/27.72 thf(zip_derived_cl54, plain,
% 188.57/27.72 ((((inverse @ sk_c11) = (sk_c10))) <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf(zip_derived_cl156, plain,
% 188.57/27.72 ((![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9))))
% 188.57/27.72 <= ((![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl165, plain,
% 188.57/27.72 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c11 @ sk_c10) != (sk_c9))))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl156])).
% 188.57/27.72 thf(zip_derived_cl167, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ sk_c10) != (sk_c9)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl165])).
% 188.57/27.72 thf(zip_derived_cl9533, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity) != (sk_c9)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl3057, zip_derived_cl167])).
% 188.57/27.72 thf(zip_derived_cl1181, plain,
% 188.57/27.72 ((((multiply @ sk_c11 @ identity) = (sk_c11)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl435, zip_derived_cl433])).
% 188.57/27.72 thf(zip_derived_cl9637, plain,
% 188.57/27.72 ((((sk_c11) != (sk_c9)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl9533, zip_derived_cl1181])).
% 188.57/27.72 thf(zip_derived_cl10668, plain,
% 188.57/27.72 ((((sk_c11) != (sk_c11)))
% 188.57/27.72 <= ((((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c1) = (sk_c2))) &
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10))
% 188.57/27.72 | ((multiply @ X4 @ sk_c10) != (sk_c9)))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl9650, zip_derived_cl9637])).
% 188.57/27.72 thf('35', plain,
% 188.57/27.72 (~
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9)))) |
% 188.57/27.72 ~ (((inverse @ sk_c1) = (sk_c2))) |
% 188.57/27.72 ~ (((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 ~ (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl10668])).
% 188.57/27.72 thf(prove_this_14, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) ) ))).
% 188.57/27.72 thf(zf_stmt_17, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c10 @ sk_c9 ) = ( sk_c11 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 188.57/27.72 thf(zip_derived_cl16, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_17])).
% 188.57/27.72 thf('36', plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl16])).
% 188.57/27.72 thf(prove_this_24, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_18, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 188.57/27.72 thf(zip_derived_cl26, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c1 @ sk_c2) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_18])).
% 188.57/27.72 thf('37', plain,
% 188.57/27.72 ((((multiply @ sk_c1 @ sk_c2) = (sk_c10))) |
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl26])).
% 188.57/27.72 thf(prove_this_34, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 188.57/27.72 thf(zf_stmt_19, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 188.57/27.72 thf(zip_derived_cl36, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_19])).
% 188.57/27.72 thf('38', plain,
% 188.57/27.72 ((((inverse @ sk_c1) = (sk_c2))) | (((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl36])).
% 188.57/27.72 thf(prove_this_44, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_20, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 188.57/27.72 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 188.57/27.72 thf(zip_derived_cl46, plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))
% 188.57/27.72 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_20])).
% 188.57/27.72 thf('39', plain,
% 188.57/27.72 ((((multiply @ sk_c2 @ sk_c9) = (sk_c10))) |
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl46])).
% 188.57/27.72 thf('40', plain,
% 188.57/27.72 (~ (((inverse @ sk_c11) = (sk_c10))) |
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 188.57/27.72 (((inverse @ X0) != (X2))
% 188.57/27.72 | ((multiply @ X1 @ X2) != (X0))
% 188.57/27.72 | ((inverse @ X1) != (X0))
% 188.57/27.72 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 188.57/27.72 | ((inverse @ X3) != (X2))
% 188.57/27.72 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 188.57/27.72 (![X4 : $i]:
% 188.57/27.72 (((inverse @ X4) != (sk_c10)) | ((multiply @ X4 @ sk_c10) != (sk_c9)))) |
% 188.57/27.72 (![X5 : $i]:
% 188.57/27.72 (((inverse @ X5) != (sk_c11))
% 188.57/27.72 | ((multiply @ X5 @ sk_c11) != (sk_c10)))) |
% 188.57/27.72 ~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 (![X6 : $i, X7 : $i]:
% 188.57/27.72 (((multiply @ X6 @ sk_c9) != (sk_c10))
% 188.57/27.72 | ((inverse @ X7) != (X6))
% 188.57/27.72 | ((multiply @ X7 @ X6) != (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf('41', plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl3])).
% 188.57/27.72 thf('42', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41'])).
% 188.57/27.72 thf('43', plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl4])).
% 188.57/27.72 thf('44', plain, ((((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '43'])).
% 188.57/27.72 thf('45', plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl5])).
% 188.57/27.72 thf('46', plain, ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '45'])).
% 188.57/27.72 thf(zip_derived_cl83945, plain, (((sk_c9) = (sk_c4))),
% 188.57/27.72 inference('simpl_trail', [status(thm)],
% 188.57/27.72 [zip_derived_cl7465, '42', '44', '46'])).
% 188.57/27.72 thf(zip_derived_cl4609, plain,
% 188.57/27.72 ((((sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl4541, zip_derived_cl429])).
% 188.57/27.72 thf('47', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41'])).
% 188.57/27.72 thf('48', plain, ((((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '43'])).
% 188.57/27.72 thf(prove_this_5, conjecture,
% 188.57/27.72 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_21, negated_conjecture,
% 188.57/27.72 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 188.57/27.72 thf(zip_derived_cl7, plain,
% 188.57/27.72 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 188.57/27.72 | ((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_21])).
% 188.57/27.72 thf('49', plain,
% 188.57/27.72 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 188.57/27.72 (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl7])).
% 188.57/27.72 thf(prove_this_6, conjecture,
% 188.57/27.72 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) ) ))).
% 188.57/27.72 thf(zf_stmt_22, negated_conjecture,
% 188.57/27.72 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 188.57/27.72 ( ( inverse @ sk_c11 ) = ( sk_c10 ) )),
% 188.57/27.72 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 188.57/27.72 thf(zip_derived_cl8, plain,
% 188.57/27.72 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('cnf', [status(esa)], [zf_stmt_22])).
% 188.57/27.72 thf('50', plain,
% 188.57/27.72 ((((inverse @ sk_c5) = (sk_c8))) | (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl8])).
% 188.57/27.72 thf('51', plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))) | (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl6])).
% 188.57/27.72 thf(zip_derived_cl64, plain,
% 188.57/27.72 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl8])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl176, plain,
% 188.57/27.72 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl195, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i]:
% 188.57/27.72 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl442, plain,
% 188.57/27.72 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity)))
% 188.57/27.72 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl176, zip_derived_cl195])).
% 188.57/27.72 thf(zip_derived_cl2, plain,
% 188.57/27.72 (![X0 : $i, X1 : $i, X2 : $i]:
% 188.57/27.72 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 188.57/27.72 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 188.57/27.72 inference('cnf', [status(esa)], [associativity])).
% 188.57/27.72 thf(zip_derived_cl723, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c5 @ X0)
% 188.57/27.72 = (multiply @ (inverse @ sk_c8) @ (multiply @ identity @ X0))))
% 188.57/27.72 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl2])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl727, plain,
% 188.57/27.72 ((![X0 : $i]:
% 188.57/27.72 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 188.57/27.72 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl723, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl1, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_inverse])).
% 188.57/27.72 thf(zip_derived_cl2261, plain,
% 188.57/27.72 ((((multiply @ sk_c5 @ sk_c8) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl727, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl62, plain,
% 188.57/27.72 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl7])).
% 188.57/27.72 thf(zip_derived_cl2309, plain,
% 188.57/27.72 ((((identity) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl2261, zip_derived_cl62])).
% 188.57/27.72 thf(zip_derived_cl1607, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 188.57/27.72 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl571, zip_derived_cl1])).
% 188.57/27.72 thf(zip_derived_cl58, plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl5])).
% 188.57/27.72 thf(zip_derived_cl1634, plain,
% 188.57/27.72 ((((identity) = (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1607, zip_derived_cl58])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl158, plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl4508, plain,
% 188.57/27.72 ((((multiply @ identity @ sk_c9) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1519, zip_derived_cl158])).
% 188.57/27.72 thf(zip_derived_cl0, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 188.57/27.72 inference('cnf', [status(esa)], [left_identity])).
% 188.57/27.72 thf(zip_derived_cl4595, plain,
% 188.57/27.72 ((((sk_c9) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl4508, zip_derived_cl0])).
% 188.57/27.72 thf(zip_derived_cl5585, plain,
% 188.57/27.72 ((((identity) != (sk_c11)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl1634, zip_derived_cl4595])).
% 188.57/27.72 thf(zip_derived_cl18175, plain,
% 188.57/27.72 ((((identity) != (identity)))
% 188.57/27.72 <= (~ (((multiply @ sk_c10 @ sk_c9) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c5) = (sk_c8))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl2309, zip_derived_cl5585])).
% 188.57/27.72 thf('52', plain,
% 188.57/27.72 ((((multiply @ sk_c10 @ sk_c9) = (sk_c11))) |
% 188.57/27.72 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 188.57/27.72 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 188.57/27.72 inference('simplify', [status(thm)], [zip_derived_cl18175])).
% 188.57/27.72 thf('53', plain, ((((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['49', '41', '50', '45', '51', '0', '1', '2', '3', '4', '5',
% 188.57/27.72 '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16',
% 188.57/27.72 '17', '18', '19', '20', '21', '22', '23', '24', '25', '26',
% 188.57/27.72 '27', '28', '29', '30', '31', '32', '33', '34', '35', '36',
% 188.57/27.72 '37', '38', '39', '40', '43', '52'])).
% 188.57/27.72 thf(zip_derived_cl83936, plain, (((sk_c9) = (sk_c11))),
% 188.57/27.72 inference('simpl_trail', [status(thm)],
% 188.57/27.72 [zip_derived_cl4609, '47', '48', '53'])).
% 188.57/27.72 thf(zip_derived_cl86155, plain, (((sk_c11) = (sk_c4))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl83945, zip_derived_cl83936])).
% 188.57/27.72 thf(zip_derived_cl97232, plain,
% 188.57/27.72 ((![X0 : $i]: ((multiply @ sk_c11 @ X0) = (X0)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl4613, zip_derived_cl86155])).
% 188.57/27.72 thf('54', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41'])).
% 188.57/27.72 thf('55', plain, ((((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '43'])).
% 188.57/27.72 thf('56', plain, ((((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '51'])).
% 188.57/27.72 thf(zip_derived_cl97233, plain,
% 188.57/27.72 (![X0 : $i]: ((multiply @ sk_c11 @ X0) = (X0))),
% 188.57/27.72 inference('simpl_trail', [status(thm)],
% 188.57/27.72 [zip_derived_cl97232, '54', '55', '56'])).
% 188.57/27.72 thf(zip_derived_cl98164, plain,
% 188.57/27.72 ((((identity) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl4730, zip_derived_cl97233])).
% 188.57/27.72 thf('57', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41'])).
% 188.57/27.72 thf('58', plain, ((((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '51'])).
% 188.57/27.72 thf(zip_derived_cl98165, plain, (((identity) = (sk_c11))),
% 188.57/27.72 inference('simpl_trail', [status(thm)], [zip_derived_cl98164, '57', '58'])).
% 188.57/27.72 thf(zip_derived_cl110307, plain,
% 188.57/27.72 ((((inverse @ identity) = (identity)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl8510, zip_derived_cl98165])).
% 188.57/27.72 thf(zip_derived_cl4609, plain,
% 188.57/27.72 ((((sk_c9) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)], [zip_derived_cl4541, zip_derived_cl429])).
% 188.57/27.72 thf(zip_derived_cl1634, plain,
% 188.57/27.72 ((((identity) = (sk_c9)))
% 188.57/27.72 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1607, zip_derived_cl58])).
% 188.57/27.72 thf(zip_derived_cl5590, plain,
% 188.57/27.72 ((((identity) = (sk_c11)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)],
% 188.57/27.72 [zip_derived_cl4609, zip_derived_cl1634])).
% 188.57/27.72 thf(zip_derived_cl159, plain,
% 188.57/27.72 ((((inverse @ sk_c11) != (sk_c10)))
% 188.57/27.72 <= (~ (((inverse @ sk_c11) = (sk_c10))))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl53])).
% 188.57/27.72 thf(zip_derived_cl18297, plain,
% 188.57/27.72 ((((inverse @ identity) != (sk_c10)))
% 188.57/27.72 <= (~ (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('s_sup-', [status(thm)],
% 188.57/27.72 [zip_derived_cl5590, zip_derived_cl159])).
% 188.57/27.72 thf(zip_derived_cl1519, plain,
% 188.57/27.72 ((((identity) = (sk_c10)))
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))))),
% 188.57/27.72 inference('s_sup+', [status(thm)], [zip_derived_cl1498, zip_derived_cl55])).
% 188.57/27.72 thf(zip_derived_cl18371, plain,
% 188.57/27.72 ((((inverse @ identity) != (identity)))
% 188.57/27.72 <= (~ (((inverse @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('demod', [status(thm)],
% 188.57/27.72 [zip_derived_cl18297, zip_derived_cl1519])).
% 188.57/27.72 thf('59', plain, (~ (((inverse @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40'])).
% 188.57/27.72 thf('60', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41'])).
% 188.57/27.72 thf('61', plain, ((((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '43'])).
% 188.57/27.72 thf('62', plain, ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '45'])).
% 188.57/27.72 thf('63', plain, ((((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 188.57/27.72 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 188.57/27.72 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 188.57/27.72 '32', '33', '34', '35', '36', '37', '38', '39', '40', '51'])).
% 188.57/27.72 thf('64', plain, ((((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['49', '41', '50', '45', '51', '0', '1', '2', '3', '4', '5',
% 188.57/27.72 '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16',
% 188.57/27.72 '17', '18', '19', '20', '21', '22', '23', '24', '25', '26',
% 188.57/27.72 '27', '28', '29', '30', '31', '32', '33', '34', '35', '36',
% 188.57/27.72 '37', '38', '39', '40', '43', '52'])).
% 188.57/27.72 thf(zip_derived_cl106513, plain, (((inverse @ identity) != (identity))),
% 188.57/27.72 inference('simpl_trail', [status(thm)],
% 188.57/27.72 [zip_derived_cl18371, '59', '60', '61', '62', '63', '64'])).
% 188.57/27.72 thf(zip_derived_cl110308, plain,
% 188.57/27.72 (($false)
% 188.57/27.72 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 188.57/27.72 (((inverse @ sk_c3) = (sk_c11))) &
% 188.57/27.72 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 188.57/27.72 (((inverse @ sk_c4) = (sk_c10))) &
% 188.57/27.72 (((multiply @ sk_c10 @ sk_c9) = (sk_c11))))),
% 188.57/27.72 inference('simplify_reflect-', [status(thm)],
% 188.57/27.72 [zip_derived_cl110307, zip_derived_cl106513])).
% 188.57/27.72 thf('65', plain,
% 188.57/27.72 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl45])).
% 188.57/27.72 thf('66', plain,
% 188.57/27.72 ((((inverse @ sk_c3) = (sk_c11))) |
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl44])).
% 188.57/27.72 thf('67', plain,
% 188.57/27.72 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl43])).
% 188.57/27.72 thf('68', plain,
% 188.57/27.72 ((((inverse @ sk_c4) = (sk_c10))) |
% 188.57/27.72 (((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 188.57/27.72 inference('split', [status(esa)], [zip_derived_cl46])).
% 188.57/27.72 thf('69', plain, ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '65', '4', '5', '66', '7', '8', '9', '10',
% 188.57/27.72 '11', '12', '13', '67', '15', '16', '17', '18', '19', '20',
% 188.57/27.72 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 188.57/27.72 '31', '32', '33', '34', '35', '36', '37', '38', '68', '40',
% 188.57/27.72 '41'])).
% 188.57/27.72 thf('70', plain, ((((inverse @ sk_c3) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '65', '4', '5', '66', '7', '8', '9', '10',
% 188.57/27.72 '11', '12', '13', '67', '15', '16', '17', '18', '19', '20',
% 188.57/27.72 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 188.57/27.72 '31', '32', '33', '34', '35', '36', '37', '38', '68', '40',
% 188.57/27.72 '43'])).
% 188.57/27.72 thf('71', plain, ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '65', '4', '5', '66', '7', '8', '9', '10',
% 188.57/27.72 '11', '12', '13', '67', '15', '16', '17', '18', '19', '20',
% 188.57/27.72 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 188.57/27.72 '31', '32', '33', '34', '35', '36', '37', '38', '68', '40',
% 188.57/27.72 '45'])).
% 188.57/27.72 thf('72', plain, ((((inverse @ sk_c4) = (sk_c10)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['0', '1', '2', '65', '4', '5', '66', '7', '8', '9', '10',
% 188.57/27.72 '11', '12', '13', '67', '15', '16', '17', '18', '19', '20',
% 188.57/27.72 '21', '22', '23', '24', '25', '26', '27', '28', '29', '30',
% 188.57/27.72 '31', '32', '33', '34', '35', '36', '37', '38', '68', '40',
% 188.57/27.72 '51'])).
% 188.57/27.72 thf('73', plain, ((((multiply @ sk_c10 @ sk_c9) = (sk_c11)))),
% 188.57/27.72 inference('sat_resolution*', [status(thm)],
% 188.57/27.72 ['49', '41', '50', '45', '51', '0', '1', '2', '65', '4', '5',
% 188.57/27.72 '66', '7', '8', '9', '10', '11', '12', '13', '67', '15',
% 188.57/27.72 '16', '17', '18', '19', '20', '21', '22', '23', '24', '25',
% 188.57/27.72 '26', '27', '28', '29', '30', '31', '32', '33', '34', '35',
% 188.57/27.72 '36', '37', '38', '68', '40', '43', '52'])).
% 188.57/27.72 thf(zip_derived_cl110309, plain, ($false),
% 188.57/27.72 inference('simpl_trail', [status(thm)],
% 188.57/27.72 [zip_derived_cl110308, '69', '70', '71', '72', '73'])).
% 188.57/27.72
% 188.57/27.72 % SZS output end Refutation
% 188.57/27.72
% 188.57/27.72
% 188.57/27.72 % Terminating...
% 188.57/27.78 % Runner terminated.
% 188.57/27.79 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------