TSTP Solution File: GRP260-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP260-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.GUcIcE40Av true
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:56 EDT 2023
% Result : Unsatisfiable 144.23s 21.34s
% Output : Refutation 144.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP260-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.GUcIcE40Av true
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 00:19:56 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.35 % Running portfolio for 300 s
% 0.20/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % Number of cores: 8
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.69 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 1.24/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.32/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.32/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.32/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 144.23/21.34 % Solved by fo/fo1_av.sh.
% 144.23/21.34 % done 12249 iterations in 20.561s
% 144.23/21.34 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 144.23/21.34 % SZS output start Refutation
% 144.23/21.34 thf(sk_c5_type, type, sk_c5: $i).
% 144.23/21.34 thf(sk_c10_type, type, sk_c10: $i).
% 144.23/21.34 thf(sk_c7_type, type, sk_c7: $i).
% 144.23/21.34 thf(sk_c9_type, type, sk_c9: $i).
% 144.23/21.34 thf(sk_c4_type, type, sk_c4: $i).
% 144.23/21.34 thf(identity_type, type, identity: $i).
% 144.23/21.34 thf(multiply_type, type, multiply: $i > $i > $i).
% 144.23/21.34 thf(sk_c11_type, type, sk_c11: $i).
% 144.23/21.34 thf(sk_c2_type, type, sk_c2: $i).
% 144.23/21.34 thf(inverse_type, type, inverse: $i > $i).
% 144.23/21.34 thf(sk_c3_type, type, sk_c3: $i).
% 144.23/21.34 thf(sk_c6_type, type, sk_c6: $i).
% 144.23/21.34 thf(sk_c8_type, type, sk_c8: $i).
% 144.23/21.34 thf(sk_c1_type, type, sk_c1: $i).
% 144.23/21.34 thf(prove_this_43, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_0, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 144.23/21.34 thf(zip_derived_cl45, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 144.23/21.34 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_0])).
% 144.23/21.34 thf('0', plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl45])).
% 144.23/21.34 thf(prove_this_31, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_1, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 144.23/21.34 thf(zip_derived_cl33, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 144.23/21.34 | ((inverse @ sk_c2) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_1])).
% 144.23/21.34 thf(zip_derived_cl114, plain,
% 144.23/21.34 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl33])).
% 144.23/21.34 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl212, plain,
% 144.23/21.34 ((((multiply @ sk_c10 @ sk_c2) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(associativity, axiom,
% 144.23/21.34 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 144.23/21.34 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl194, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((multiply @ identity @ X0)
% 144.23/21.34 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 144.23/21.34 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl506, plain,
% 144.23/21.34 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 144.23/21.34 thf(prove_this_4, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_2, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 144.23/21.34 thf(zip_derived_cl6, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_2])).
% 144.23/21.34 thf(zip_derived_cl60, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl179, plain,
% 144.23/21.34 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl505, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl584, plain,
% 144.23/21.34 ((((sk_c4) = (sk_c2)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl505])).
% 144.23/21.34 thf(prove_this_21, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 144.23/21.34 thf(zf_stmt_3, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 144.23/21.34 thf(zip_derived_cl23, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_3])).
% 144.23/21.34 thf(zip_derived_cl94, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl23])).
% 144.23/21.34 thf(zip_derived_cl623, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl584, zip_derived_cl94])).
% 144.23/21.34 thf(zip_derived_cl179, plain,
% 144.23/21.34 ((((multiply @ sk_c10 @ sk_c4) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl441, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ identity @ X0)
% 144.23/21.34 = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl442, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl441, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl504, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl1058, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl5828, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl623, zip_derived_cl1058])).
% 144.23/21.34 thf(prove_this_41, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_4, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 144.23/21.34 thf(zip_derived_cl43, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_4])).
% 144.23/21.34 thf(zip_derived_cl134, plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl43])).
% 144.23/21.34 thf(zip_derived_cl5829, plain,
% 144.23/21.34 ((((multiply @ identity @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl5828, zip_derived_cl134])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl5855, plain,
% 144.23/21.34 ((((sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl5829, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl60, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(prove_this_51, conjecture,
% 144.23/21.34 (~( ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 144.23/21.34 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 144.23/21.34 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ X5 ) != ( X6 ) ) |
% 144.23/21.34 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_5, negated_conjecture,
% 144.23/21.34 (( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 144.23/21.34 ( ( inverse @ X7 ) != ( X8 ) ) |
% 144.23/21.34 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ X5 ) != ( X6 ) ) |
% 144.23/21.34 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ X3 @ sk_c11 ) != ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 144.23/21.34 thf(zip_derived_cl53, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (X2))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))
% 144.23/21.34 | ((inverse @ X4) != (sk_c10))
% 144.23/21.34 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 144.23/21.34 | ((inverse @ X5) != (sk_c11))
% 144.23/21.34 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c9 @ sk_c11) != (sk_c10))
% 144.23/21.34 | ((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9))
% 144.23/21.34 | ((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_5])).
% 144.23/21.34 thf(zip_derived_cl154, plain,
% 144.23/21.34 ((![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 144.23/21.34 <= ((![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl161, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c11)) | ((multiply @ sk_c4 @ sk_c11) != (sk_c10))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl154])).
% 144.23/21.34 thf(zip_derived_cl176, plain,
% 144.23/21.34 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl161])).
% 144.23/21.34 thf(zip_derived_cl6036, plain,
% 144.23/21.34 ((((sk_c11) != (sk_c11)))
% 144.23/21.34 <= (~ (((sk_c10) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl5855, zip_derived_cl176])).
% 144.23/21.34 thf('1', plain,
% 144.23/21.34 ((((sk_c10) = (sk_c11))) | ~ (((inverse @ sk_c2) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl6036])).
% 144.23/21.34 thf(prove_this_3, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_6, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 144.23/21.34 thf(zip_derived_cl5, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_6])).
% 144.23/21.34 thf('2', plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl5])).
% 144.23/21.34 thf(prove_this_13, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_7, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 144.23/21.34 thf(zip_derived_cl15, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 144.23/21.34 | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_7])).
% 144.23/21.34 thf('3', plain,
% 144.23/21.34 ((((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl15])).
% 144.23/21.34 thf(zip_derived_cl506, plain,
% 144.23/21.34 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl582, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c2 @ X0)
% 144.23/21.34 = (multiply @ (inverse @ sk_c10) @ (multiply @ identity @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl506, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl586, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl1239, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl212, plain,
% 144.23/21.34 ((((multiply @ sk_c10 @ sk_c2) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl453, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ identity @ X0)
% 144.23/21.34 = (multiply @ sk_c10 @ (multiply @ sk_c2 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl454, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c2 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl453, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl1269, plain,
% 144.23/21.34 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1239, zip_derived_cl454])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl496, plain,
% 144.23/21.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl158, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl223, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 144.23/21.34 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('eq_res', [status(thm)], [zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl2836, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (X0))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl496, zip_derived_cl223])).
% 144.23/21.34 thf(zip_derived_cl3498, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c10) != (identity))
% 144.23/21.34 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (identity))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1269, zip_derived_cl2836])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl3589, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c10) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (identity))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl3498, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl3590, plain,
% 144.23/21.34 (((((inverse @ identity) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((inverse @ sk_c10) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl3589])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl494, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl196, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl2430, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl586, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl1241, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c2 @ (multiply @ sk_c10 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl72864, plain,
% 144.23/21.34 ((((inverse @ sk_c10) = (multiply @ sk_c2 @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl2430, zip_derived_cl1241])).
% 144.23/21.34 thf(zip_derived_cl586, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c2 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl582, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl506, plain,
% 144.23/21.34 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1243, plain,
% 144.23/21.34 ((((sk_c2) = (multiply @ sk_c2 @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl506])).
% 144.23/21.34 thf(zip_derived_cl73083, plain,
% 144.23/21.34 ((((inverse @ sk_c10) = (sk_c2))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl72864, zip_derived_cl1243])).
% 144.23/21.34 thf(zip_derived_cl139150, plain,
% 144.23/21.34 (((((inverse @ identity) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((sk_c2) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl3590, zip_derived_cl73083])).
% 144.23/21.34 thf('4', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 144.23/21.34 ~ (((identity) = (inverse @ (inverse @ identity)))) |
% 144.23/21.34 ~ (((inverse @ identity) = (identity))) | ~ (((sk_c10) = (sk_c11))) |
% 144.23/21.34 ~ (((sk_c2) = (identity))) | ~ (((inverse @ sk_c2) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl139150])).
% 144.23/21.34 thf(zip_derived_cl1239, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl586, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl94, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl23])).
% 144.23/21.34 thf(zip_derived_cl1270, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1239, zip_derived_cl94])).
% 144.23/21.34 thf(zip_derived_cl134, plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl43])).
% 144.23/21.34 thf(zip_derived_cl7163, plain,
% 144.23/21.34 ((((multiply @ identity @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1270, zip_derived_cl134])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl7189, plain,
% 144.23/21.34 ((((sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl7163, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl176, plain,
% 144.23/21.34 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl161])).
% 144.23/21.34 thf(zip_derived_cl7278, plain,
% 144.23/21.34 ((((sk_c11) != (sk_c11)))
% 144.23/21.34 <= (~ (((sk_c10) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl7189, zip_derived_cl176])).
% 144.23/21.34 thf('5', plain,
% 144.23/21.34 ((((sk_c10) = (sk_c11))) | ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl7278])).
% 144.23/21.34 thf(prove_this_11, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_8, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 144.23/21.34 thf(zip_derived_cl13, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 144.23/21.34 | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_8])).
% 144.23/21.34 thf(zip_derived_cl74, plain,
% 144.23/21.34 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl13])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl177, plain,
% 144.23/21.34 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl428, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ identity @ X0)
% 144.23/21.34 = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl429, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c1 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl428, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl500, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl429, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl807, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl500, zip_derived_cl1])).
% 144.23/21.34 thf(prove_this_1, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_9, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 144.23/21.34 thf(zip_derived_cl3, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_9])).
% 144.23/21.34 thf(zip_derived_cl54, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl819, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 144.23/21.34 thf(zip_derived_cl506, plain,
% 144.23/21.34 ((((sk_c2) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl212, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl957, plain,
% 144.23/21.34 ((((sk_c2) = (multiply @ (inverse @ identity) @ identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl819, zip_derived_cl506])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl973, plain,
% 144.23/21.34 ((((sk_c2) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl957, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl114, plain,
% 144.23/21.34 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl33])).
% 144.23/21.34 thf(zip_derived_cl1768, plain,
% 144.23/21.34 ((((inverse @ identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl973, zip_derived_cl114])).
% 144.23/21.34 thf(zip_derived_cl819, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 144.23/21.34 thf(zip_derived_cl1792, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1768, zip_derived_cl819])).
% 144.23/21.34 thf(prove_this_2, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_10, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 144.23/21.34 thf(zip_derived_cl4, plain,
% 144.23/21.34 ((((inverse @ sk_c3) = (sk_c11))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_10])).
% 144.23/21.34 thf(zip_derived_cl56, plain,
% 144.23/21.34 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl4])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl178, plain,
% 144.23/21.34 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl503, plain,
% 144.23/21.34 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl177, plain,
% 144.23/21.34 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl502, plain,
% 144.23/21.34 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl538, plain,
% 144.23/21.34 ((((sk_c1) = (sk_c3)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl503, zip_derived_cl502])).
% 144.23/21.34 thf(zip_derived_cl55, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl541, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl807, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl500, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl1138, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 144.23/21.34 thf(zip_derived_cl505, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1171, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ identity) @ identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1138, zip_derived_cl505])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl1196, plain,
% 144.23/21.34 ((((sk_c4) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1171, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl58, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl5])).
% 144.23/21.34 thf(zip_derived_cl1461, plain,
% 144.23/21.34 ((((multiply @ identity @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1196, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl1138, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1494, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1461, zip_derived_cl1138, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl134, plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl43])).
% 144.23/21.34 thf(zip_derived_cl1985, plain,
% 144.23/21.34 ((((multiply @ identity @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1494, zip_derived_cl134])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl178, plain,
% 144.23/21.34 ((((multiply @ sk_c11 @ sk_c3) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl56, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl431, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ identity @ X0)
% 144.23/21.34 = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl178, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl432, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c11 @ (multiply @ sk_c3 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl431, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl501, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl432, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl918, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl501, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl55, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl2001, plain,
% 144.23/21.34 ((((sk_c11) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1985, zip_derived_cl0, zip_derived_cl1001])).
% 144.23/21.34 thf(zip_derived_cl54, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl2110, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl2001, zip_derived_cl54])).
% 144.23/21.34 thf(zip_derived_cl502, plain,
% 144.23/21.34 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl177, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl500, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c11) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl429, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl809, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ identity) = (sk_c1)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl502, zip_derived_cl500])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl2183, plain,
% 144.23/21.34 ((((sk_c1) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl2110, zip_derived_cl809, zip_derived_cl1001])).
% 144.23/21.34 thf(zip_derived_cl54, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl499, plain,
% 144.23/21.34 ((((sk_c11) = (multiply @ (inverse @ sk_c1) @ sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl158, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl526, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c1)) != (X0))
% 144.23/21.34 | ((multiply @ sk_c10 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (sk_c10))
% 144.23/21.34 | ((multiply @ X1 @ sk_c10) != (sk_c11))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl499, zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl2868, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c1)) != (X0))))
% 144.23/21.34 <= ((![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl526])).
% 144.23/21.34 thf(zip_derived_cl2919, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (X0))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl2183, zip_derived_cl2868])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl2001, plain,
% 144.23/21.34 ((((sk_c11) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1985, zip_derived_cl0, zip_derived_cl1001])).
% 144.23/21.34 thf(zip_derived_cl2964, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (identity))
% 144.23/21.34 | ((identity) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (X0))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl2919, zip_derived_cl1001, zip_derived_cl2001])).
% 144.23/21.34 thf(zip_derived_cl3099, plain,
% 144.23/21.34 (((((identity) != (inverse @ (inverse @ identity)))
% 144.23/21.34 | ((inverse @ (inverse @ (inverse @ identity))) != (identity))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c10))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c1)) != (X0)))))),
% 144.23/21.34 inference('eq_res', [status(thm)], [zip_derived_cl2964])).
% 144.23/21.34 thf(zip_derived_cl3101, plain,
% 144.23/21.34 ((((identity) != (inverse @ (inverse @ identity))))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3099])).
% 144.23/21.34 thf(zip_derived_cl51507, plain,
% 144.23/21.34 ((((identity) != (inverse @ identity)))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1792, zip_derived_cl3101])).
% 144.23/21.34 thf(zip_derived_cl1792, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1768, zip_derived_cl819])).
% 144.23/21.34 thf(zip_derived_cl52060, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl51507, zip_derived_cl1792])).
% 144.23/21.34 thf('6', plain,
% 144.23/21.34 ((((identity) = (inverse @ (inverse @ identity)))) |
% 144.23/21.34 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl52060])).
% 144.23/21.34 thf(zip_derived_cl973, plain,
% 144.23/21.34 ((((sk_c2) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl957, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl94, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl23])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl516, plain,
% 144.23/21.34 ((((sk_c10) = (multiply @ (inverse @ sk_c2) @ sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl723, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c10 @ X0)
% 144.23/21.34 = (multiply @ (inverse @ sk_c2) @ (multiply @ sk_c9 @ X0))))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl516, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl2001, plain,
% 144.23/21.34 ((((sk_c11) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1985, zip_derived_cl0, zip_derived_cl1001])).
% 144.23/21.34 thf(zip_derived_cl54, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl206, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c10 @ X0)
% 144.23/21.34 = (multiply @ sk_c1 @ (multiply @ sk_c11 @ X0))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl54, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl158, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl566, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((inverse @ X1) != (multiply @ sk_c11 @ X0))
% 144.23/21.34 | ((multiply @ sk_c10 @ X0) != (X1))
% 144.23/21.34 | ((inverse @ sk_c1) != (X1))
% 144.23/21.34 | ((multiply @ (multiply @ sk_c11 @ X0) @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X2) != (multiply @ sk_c11 @ X0))
% 144.23/21.34 | ((multiply @ X2 @ (multiply @ sk_c11 @ X0)) != (sk_c11))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl206, zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl574, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((inverse @ X1) != (multiply @ sk_c11 @ X0))
% 144.23/21.34 | ((multiply @ sk_c10 @ X0) != (X1))
% 144.23/21.34 | ((inverse @ sk_c1) != (X1))
% 144.23/21.34 | ((multiply @ sk_c11 @ (multiply @ X0 @ sk_c10)) != (sk_c11))
% 144.23/21.34 | ((inverse @ X2) != (multiply @ sk_c11 @ X0))
% 144.23/21.34 | ((multiply @ X2 @ (multiply @ sk_c11 @ X0)) != (sk_c11))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl566, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl3816, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((inverse @ X1) != (multiply @ identity @ X0))
% 144.23/21.34 | ((multiply @ sk_c10 @ X0) != (X1))
% 144.23/21.34 | ((inverse @ sk_c1) != (X1))
% 144.23/21.34 | ((multiply @ identity @ (multiply @ X0 @ sk_c10)) != (identity))
% 144.23/21.34 | ((inverse @ X2) != (multiply @ identity @ X0))
% 144.23/21.34 | ((multiply @ X2 @ (multiply @ identity @ X0)) != (identity))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl2001, zip_derived_cl574])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl2183, plain,
% 144.23/21.34 ((((sk_c1) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl2110, zip_derived_cl809, zip_derived_cl1001])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl3827, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((inverse @ X1) != (X0))
% 144.23/21.34 | ((X0) != (X1))
% 144.23/21.34 | ((inverse @ identity) != (X1))
% 144.23/21.34 | ((multiply @ X0 @ identity) != (identity))
% 144.23/21.34 | ((inverse @ X2) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ X0) != (identity))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl3816, zip_derived_cl0, zip_derived_cl1001,
% 144.23/21.34 zip_derived_cl0, zip_derived_cl2183, zip_derived_cl1001,
% 144.23/21.34 zip_derived_cl0, zip_derived_cl0, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl3910, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X0) != (identity))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ identity) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (X0))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('eq_res', [status(thm)], [zip_derived_cl3827])).
% 144.23/21.34 thf(zip_derived_cl11039, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((multiply @ sk_c10 @ X0) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c2)) != (multiply @ sk_c9 @ X0))
% 144.23/21.34 | ((multiply @ (multiply @ sk_c9 @ X0) @ identity) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (multiply @ sk_c9 @ X0))
% 144.23/21.34 | ((inverse @ (multiply @ sk_c9 @ X0)) != (multiply @ sk_c9 @ X0))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl723, zip_derived_cl3910])).
% 144.23/21.34 thf(zip_derived_cl1058, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl58, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl5])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl134, plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl43])).
% 144.23/21.34 thf(zip_derived_cl4840, plain,
% 144.23/21.34 ((((multiply @ identity @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1072, zip_derived_cl134])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl4862, plain,
% 144.23/21.34 ((((sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl4840, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl2001, plain,
% 144.23/21.34 ((((sk_c11) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1985, zip_derived_cl0, zip_derived_cl1001])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl11076, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((X0) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c2)) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ identity) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (X0))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl11039, zip_derived_cl4862, zip_derived_cl2001,
% 144.23/21.34 zip_derived_cl0, zip_derived_cl1072, zip_derived_cl0,
% 144.23/21.34 zip_derived_cl1072, zip_derived_cl0, zip_derived_cl1072,
% 144.23/21.34 zip_derived_cl0, zip_derived_cl1072, zip_derived_cl0,
% 144.23/21.34 zip_derived_cl1072, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl12103, plain,
% 144.23/21.34 (((((inverse @ (inverse @ (inverse @ sk_c2)))
% 144.23/21.34 != (inverse @ (inverse @ sk_c2)))
% 144.23/21.34 | ((inverse @ identity) != (inverse @ (inverse @ sk_c2)))
% 144.23/21.34 | ((multiply @ (inverse @ (inverse @ sk_c2)) @ identity) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c2)) != (identity))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('eq_res', [status(thm)], [zip_derived_cl11076])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl497, plain,
% 144.23/21.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl12104, plain,
% 144.23/21.34 (((((inverse @ (inverse @ (inverse @ sk_c2)))
% 144.23/21.34 != (inverse @ (inverse @ sk_c2)))
% 144.23/21.34 | ((inverse @ identity) != (inverse @ (inverse @ sk_c2)))
% 144.23/21.34 | ((sk_c2) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ sk_c2)) != (identity))))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl12103, zip_derived_cl497])).
% 144.23/21.34 thf(zip_derived_cl12141, plain,
% 144.23/21.34 ((((sk_c2) != (identity))) <= (~ (((sk_c2) = (identity))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl12104])).
% 144.23/21.34 thf(zip_derived_cl12191, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((sk_c2) = (identity))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl973, zip_derived_cl12141])).
% 144.23/21.34 thf('7', plain,
% 144.23/21.34 ((((sk_c2) = (identity))) | ~ (((inverse @ sk_c2) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl12191])).
% 144.23/21.34 thf('8', plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(prove_this_14, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_11, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 144.23/21.34 thf(zip_derived_cl16, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_11])).
% 144.23/21.34 thf('9', plain,
% 144.23/21.34 ((((inverse @ sk_c1) = (sk_c11))) | (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl16])).
% 144.23/21.34 thf(prove_this_44, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_12, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_44])).
% 144.23/21.34 thf(zip_derived_cl46, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_12])).
% 144.23/21.34 thf('10', plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl46])).
% 144.23/21.34 thf(prove_this_10, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_13, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 144.23/21.34 thf(zip_derived_cl12, plain,
% 144.23/21.34 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_13])).
% 144.23/21.34 thf(zip_derived_cl72, plain,
% 144.23/21.34 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)))
% 144.23/21.34 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl12])).
% 144.23/21.34 thf(zip_derived_cl223, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X2) != (multiply @ X2 @ X0))
% 144.23/21.34 | ((inverse @ (multiply @ X2 @ X0)) != (X0))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('eq_res', [status(thm)], [zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl888, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((multiply @ X0 @ sk_c8) != (sk_c11))
% 144.23/21.34 | ((inverse @ X0) != (sk_c8))
% 144.23/21.34 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c7) != (sk_c6))
% 144.23/21.34 | ((inverse @ sk_c6) != (sk_c8))))
% 144.23/21.34 <= ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl223])).
% 144.23/21.34 thf('11', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 144.23/21.34 (![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11)))) |
% 144.23/21.34 ~ (((inverse @ sk_c6) = (sk_c8))) |
% 144.23/21.34 ~ (((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 144.23/21.34 ~ (((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c7) = (sk_c6)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl888])).
% 144.23/21.34 thf(prove_this_5, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_14, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 144.23/21.34 thf(zip_derived_cl7, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_14])).
% 144.23/21.34 thf(zip_derived_cl62, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl7])).
% 144.23/21.34 thf(prove_this_6, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_15, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c1 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 144.23/21.34 thf(zip_derived_cl8, plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_15])).
% 144.23/21.34 thf(zip_derived_cl64, plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl8])).
% 144.23/21.34 thf(zip_derived_cl62, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl7])).
% 144.23/21.34 thf(zip_derived_cl158, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl269, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c8))
% 144.23/21.34 | ((sk_c11) != (X0))
% 144.23/21.34 | ((inverse @ sk_c5) != (X0))
% 144.23/21.34 | ((multiply @ sk_c8 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (sk_c8))
% 144.23/21.34 | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl395, plain,
% 144.23/21.34 ((![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11))))
% 144.23/21.34 <= ((![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8))
% 144.23/21.34 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl269])).
% 144.23/21.34 thf(zip_derived_cl401, plain,
% 144.23/21.34 (((((sk_c8) != (sk_c8)) | ((multiply @ sk_c5 @ sk_c8) != (sk_c11))))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 144.23/21.34 (![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8))
% 144.23/21.34 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl395])).
% 144.23/21.34 thf(zip_derived_cl405, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) != (sk_c11)))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))) &
% 144.23/21.34 (![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8))
% 144.23/21.34 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl401])).
% 144.23/21.34 thf(zip_derived_cl407, plain,
% 144.23/21.34 ((((sk_c11) != (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))) &
% 144.23/21.34 (![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8))
% 144.23/21.34 | ((multiply @ X1 @ sk_c8) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl62, zip_derived_cl405])).
% 144.23/21.34 thf('12', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X1 : $i]:
% 144.23/21.34 (((inverse @ X1) != (sk_c8)) | ((multiply @ X1 @ sk_c8) != (sk_c11)))) |
% 144.23/21.34 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl407])).
% 144.23/21.34 thf('13', plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl13])).
% 144.23/21.34 thf(prove_this_12, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_16, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 144.23/21.34 thf(zip_derived_cl14, plain,
% 144.23/21.34 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_16])).
% 144.23/21.34 thf('14', plain,
% 144.23/21.34 ((((inverse @ sk_c3) = (sk_c11))) | (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl14])).
% 144.23/21.34 thf(prove_this_15, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_17, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 144.23/21.34 thf(zip_derived_cl17, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_17])).
% 144.23/21.34 thf('15', plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl17])).
% 144.23/21.34 thf(prove_this_16, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_18, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 144.23/21.34 thf(zip_derived_cl18, plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_18])).
% 144.23/21.34 thf('16', plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))) | (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl18])).
% 144.23/21.34 thf(prove_this_17, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_19, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c8 @ sk_c10 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 144.23/21.34 thf(zip_derived_cl19, plain,
% 144.23/21.34 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_19])).
% 144.23/21.34 thf('17', plain,
% 144.23/21.34 ((((multiply @ sk_c8 @ sk_c10) = (sk_c11))) |
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl19])).
% 144.23/21.34 thf(prove_this_18, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_20, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 144.23/21.34 thf(zip_derived_cl20, plain,
% 144.23/21.34 ((((inverse @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_20])).
% 144.23/21.34 thf('18', plain,
% 144.23/21.34 ((((inverse @ sk_c7) = (sk_c6))) | (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl20])).
% 144.23/21.34 thf(prove_this_19, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_21, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 144.23/21.34 thf(zip_derived_cl21, plain,
% 144.23/21.34 ((((inverse @ sk_c6) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_21])).
% 144.23/21.34 thf('19', plain,
% 144.23/21.34 ((((inverse @ sk_c6) = (sk_c8))) | (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl21])).
% 144.23/21.34 thf(prove_this_20, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 144.23/21.34 thf(zf_stmt_22, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 144.23/21.34 thf(zip_derived_cl22, plain,
% 144.23/21.34 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_22])).
% 144.23/21.34 thf('20', plain,
% 144.23/21.34 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))) |
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl22])).
% 144.23/21.34 thf(zip_derived_cl54, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl74, plain,
% 144.23/21.34 ((((inverse @ sk_c1) = (sk_c11))) <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl13])).
% 144.23/21.34 thf(zip_derived_cl154, plain,
% 144.23/21.34 ((![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 144.23/21.34 <= ((![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl173, plain,
% 144.23/21.34 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c1 @ sk_c11) != (sk_c10))))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl154])).
% 144.23/21.34 thf(zip_derived_cl174, plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) != (sk_c10)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl173])).
% 144.23/21.34 thf(zip_derived_cl207, plain,
% 144.23/21.34 ((((sk_c10) != (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl174])).
% 144.23/21.34 thf('21', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl207])).
% 144.23/21.34 thf(zip_derived_cl55, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf(zip_derived_cl56, plain,
% 144.23/21.34 ((((inverse @ sk_c3) = (sk_c11))) <= ((((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl4])).
% 144.23/21.34 thf(zip_derived_cl154, plain,
% 144.23/21.34 ((![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10))))
% 144.23/21.34 <= ((![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl160, plain,
% 144.23/21.34 (((((sk_c11) != (sk_c11)) | ((multiply @ sk_c3 @ sk_c11) != (sk_c10))))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl154])).
% 144.23/21.34 thf(zip_derived_cl164, plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) != (sk_c10)))
% 144.23/21.34 <= ((((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl160])).
% 144.23/21.34 thf(zip_derived_cl210, plain,
% 144.23/21.34 ((((sk_c10) != (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl164])).
% 144.23/21.34 thf('22', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 144.23/21.34 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl210])).
% 144.23/21.34 thf(zip_derived_cl1196, plain,
% 144.23/21.34 ((((sk_c4) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1171, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl60, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(zip_derived_cl1462, plain,
% 144.23/21.34 ((((inverse @ identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1196, zip_derived_cl60])).
% 144.23/21.34 thf(zip_derived_cl1138, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 144.23/21.34 thf(zip_derived_cl1495, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1462, zip_derived_cl1138])).
% 144.23/21.34 thf(zip_derived_cl497, plain,
% 144.23/21.34 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl158, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl219, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 (((inverse @ X1) != (X0))
% 144.23/21.34 | ((X0) != (X1))
% 144.23/21.34 | ((inverse @ identity) != (X1))
% 144.23/21.34 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X2) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ X0) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl729, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ identity) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (X0))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('eq_res', [status(thm)], [zip_derived_cl219])).
% 144.23/21.34 thf(zip_derived_cl2849, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ (inverse @ X0))) != (identity))
% 144.23/21.34 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ identity) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (identity))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl729])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl2863, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ (inverse @ X0))) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ identity) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (identity))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl2849, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl2864, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((inverse @ identity) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ (inverse @ X0))) != (identity))
% 144.23/21.34 | ((X0) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl2863])).
% 144.23/21.34 thf(zip_derived_cl3021, plain,
% 144.23/21.34 ((((inverse @ identity) != (identity)))
% 144.23/21.34 <= (~ (((inverse @ identity) = (identity))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl2864])).
% 144.23/21.34 thf(zip_derived_cl39954, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((inverse @ identity) = (identity))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1495, zip_derived_cl3021])).
% 144.23/21.34 thf('23', plain,
% 144.23/21.34 ((((inverse @ identity) = (identity))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl39954])).
% 144.23/21.34 thf(zip_derived_cl1495, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1462, zip_derived_cl1138])).
% 144.23/21.34 thf(zip_derived_cl3101, plain,
% 144.23/21.34 ((((identity) != (inverse @ (inverse @ identity))))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3099])).
% 144.23/21.34 thf(zip_derived_cl39959, plain,
% 144.23/21.34 ((((identity) != (inverse @ identity)))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1495, zip_derived_cl3101])).
% 144.23/21.34 thf(zip_derived_cl1495, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl1462, zip_derived_cl1138])).
% 144.23/21.34 thf(zip_derived_cl40516, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl39959, zip_derived_cl1495])).
% 144.23/21.34 thf('24', plain,
% 144.23/21.34 ((((identity) = (inverse @ (inverse @ identity)))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl40516])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl505, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1915, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ identity) @ identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1001, zip_derived_cl505])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl1944, plain,
% 144.23/21.34 ((((sk_c4) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1915, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl60, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(zip_derived_cl177, plain,
% 144.23/21.34 ((((multiply @ sk_c11 @ sk_c1) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl158, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl427, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((inverse @ X0) != (sk_c1))
% 144.23/21.34 | ((identity) != (X0))
% 144.23/21.34 | ((inverse @ sk_c11) != (X0))
% 144.23/21.34 | ((multiply @ sk_c1 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (sk_c1))
% 144.23/21.34 | ((multiply @ X1 @ sk_c1) != (sk_c11))))
% 144.23/21.34 <= ((((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl158])).
% 144.23/21.34 thf(zip_derived_cl1519, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 (((identity) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (sk_c1))
% 144.23/21.34 | ((inverse @ sk_c11) != (X0))))
% 144.23/21.34 <= ((![X0 : $i]:
% 144.23/21.34 (((identity) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (sk_c1))
% 144.23/21.34 | ((inverse @ sk_c11) != (X0)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl427])).
% 144.23/21.34 thf(zip_derived_cl1530, plain,
% 144.23/21.34 (((((identity) != (sk_c4))
% 144.23/21.34 | ((sk_c10) != (sk_c1))
% 144.23/21.34 | ((inverse @ sk_c11) != (sk_c4))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i]:
% 144.23/21.34 (((identity) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (sk_c1))
% 144.23/21.34 | ((inverse @ sk_c11) != (X0)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl1519])).
% 144.23/21.34 thf(zip_derived_cl41388, plain,
% 144.23/21.34 ((((identity) != (sk_c4))) <= (~ (((identity) = (sk_c4))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl1530])).
% 144.23/21.34 thf(zip_derived_cl41394, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((identity) = (sk_c4))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1944, zip_derived_cl41388])).
% 144.23/21.34 thf('25', plain,
% 144.23/21.34 ((((identity) = (sk_c4))) | ~ (((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl41394])).
% 144.23/21.34 thf(zip_derived_cl64, plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))) <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl8])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl180, plain,
% 144.23/21.34 ((((multiply @ sk_c8 @ sk_c5) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl512, plain,
% 144.23/21.34 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl180, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl2, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i]:
% 144.23/21.34 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 144.23/21.34 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 144.23/21.34 inference('cnf', [status(esa)], [associativity])).
% 144.23/21.34 thf(zip_derived_cl619, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c5 @ X0)
% 144.23/21.34 = (multiply @ (inverse @ sk_c8) @ (multiply @ identity @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl512, zip_derived_cl2])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl622, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c5 @ X0) = (multiply @ (inverse @ sk_c8) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl619, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl1342, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl622, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl62, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl7])).
% 144.23/21.34 thf(zip_derived_cl1356, plain,
% 144.23/21.34 ((((identity) = (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1342, zip_derived_cl62])).
% 144.23/21.34 thf(zip_derived_cl1001, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl918, zip_derived_cl55])).
% 144.23/21.34 thf(zip_derived_cl1072, plain,
% 144.23/21.34 ((((identity) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1058, zip_derived_cl58])).
% 144.23/21.34 thf(zip_derived_cl159, plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) != (sk_c10)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl4841, plain,
% 144.23/21.34 ((((multiply @ identity @ sk_c11) != (sk_c10)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1072, zip_derived_cl159])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl4863, plain,
% 144.23/21.34 ((((sk_c11) != (sk_c10)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl4841, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl4884, plain,
% 144.23/21.34 ((((sk_c11) != (identity)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1001, zip_derived_cl4863])).
% 144.23/21.34 thf(zip_derived_cl17517, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1356, zip_derived_cl4884])).
% 144.23/21.34 thf('26', plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 ~ (((inverse @ sk_c5) = (sk_c8))) |
% 144.23/21.34 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl17517])).
% 144.23/21.34 thf(zip_derived_cl1356, plain,
% 144.23/21.34 ((((identity) = (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1342, zip_derived_cl62])).
% 144.23/21.34 thf(zip_derived_cl1138, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl541, zip_derived_cl807])).
% 144.23/21.34 thf(zip_derived_cl176, plain,
% 144.23/21.34 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl161])).
% 144.23/21.34 thf(zip_derived_cl1142, plain,
% 144.23/21.34 ((((identity) != (sk_c11)))
% 144.23/21.34 <= (~ (((sk_c10) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1138, zip_derived_cl176])).
% 144.23/21.34 thf(zip_derived_cl8060, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((sk_c10) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c3) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1356, zip_derived_cl1142])).
% 144.23/21.34 thf('27', plain,
% 144.23/21.34 ((((sk_c10) = (sk_c11))) | ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 ~ (((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl8060])).
% 144.23/21.34 thf('28', plain,
% 144.23/21.34 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3])).
% 144.23/21.34 thf('29', plain,
% 144.23/21.34 ((((inverse @ sk_c3) = (sk_c11))) |
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl4])).
% 144.23/21.34 thf('30', plain,
% 144.23/21.34 ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl7])).
% 144.23/21.34 thf('31', plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))) |
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl8])).
% 144.23/21.34 thf(prove_this_45, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_23, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_45])).
% 144.23/21.34 thf(zip_derived_cl47, plain,
% 144.23/21.34 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 144.23/21.34 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_23])).
% 144.23/21.34 thf('32', plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 (((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl47])).
% 144.23/21.34 thf(prove_this_46, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_24, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 144.23/21.34 thf(zip_derived_cl48, plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))
% 144.23/21.34 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_24])).
% 144.23/21.34 thf('33', plain,
% 144.23/21.34 ((((inverse @ sk_c5) = (sk_c8))) |
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl48])).
% 144.23/21.34 thf(zip_derived_cl4862, plain,
% 144.23/21.34 ((((sk_c11) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl4840, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl176, plain,
% 144.23/21.34 ((((sk_c10) != (sk_c11))) <= (~ (((sk_c10) = (sk_c11))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl161])).
% 144.23/21.34 thf(zip_derived_cl5003, plain,
% 144.23/21.34 ((((sk_c11) != (sk_c11)))
% 144.23/21.34 <= (~ (((sk_c10) = (sk_c11))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c9 @ sk_c11) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl4862, zip_derived_cl176])).
% 144.23/21.34 thf('34', plain,
% 144.23/21.34 ((((sk_c10) = (sk_c11))) | ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl5003])).
% 144.23/21.34 thf(prove_this_24, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 144.23/21.34 thf(zf_stmt_25, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 144.23/21.34 thf(zip_derived_cl26, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))
% 144.23/21.34 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_25])).
% 144.23/21.34 thf('35', plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl26])).
% 144.23/21.34 thf(prove_this_34, conjecture,
% 144.23/21.34 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_26, negated_conjecture,
% 144.23/21.34 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_34])).
% 144.23/21.34 thf(zip_derived_cl36, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c2) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_26])).
% 144.23/21.34 thf('36', plain,
% 144.23/21.34 ((((inverse @ sk_c2) = (sk_c10))) | (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl36])).
% 144.23/21.34 thf(zip_derived_cl58, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl5])).
% 144.23/21.34 thf(zip_derived_cl60, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(zip_derived_cl155, plain,
% 144.23/21.34 ((![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9))))
% 144.23/21.34 <= ((![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl166, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c4 @ sk_c10) != (sk_c9))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl155])).
% 144.23/21.34 thf(zip_derived_cl169, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) != (sk_c9)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl166])).
% 144.23/21.34 thf(zip_derived_cl240, plain,
% 144.23/21.34 ((((sk_c9) != (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl58, zip_derived_cl169])).
% 144.23/21.34 thf('37', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9)))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl240])).
% 144.23/21.34 thf(prove_this_23, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 144.23/21.34 thf(zf_stmt_27, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( multiply @ sk_c2 @ sk_c10 ) = ( sk_c9 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 144.23/21.34 thf(zip_derived_cl25, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 144.23/21.34 | ((multiply @ sk_c2 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_27])).
% 144.23/21.34 thf('38', plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl25])).
% 144.23/21.34 thf(zip_derived_cl94, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) = (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl23])).
% 144.23/21.34 thf(zip_derived_cl114, plain,
% 144.23/21.34 ((((inverse @ sk_c2) = (sk_c10))) <= ((((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl33])).
% 144.23/21.34 thf(zip_derived_cl155, plain,
% 144.23/21.34 ((![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9))))
% 144.23/21.34 <= ((![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl213, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c10)) | ((multiply @ sk_c2 @ sk_c10) != (sk_c9))))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl114, zip_derived_cl155])).
% 144.23/21.34 thf(zip_derived_cl215, plain,
% 144.23/21.34 ((((multiply @ sk_c2 @ sk_c10) != (sk_c9)))
% 144.23/21.34 <= ((((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl213])).
% 144.23/21.34 thf(zip_derived_cl311, plain,
% 144.23/21.34 ((((sk_c9) != (sk_c9)))
% 144.23/21.34 <= ((((multiply @ sk_c2 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))) &
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10))
% 144.23/21.34 | ((multiply @ X6 @ sk_c10) != (sk_c9)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl94, zip_derived_cl215])).
% 144.23/21.34 thf('39', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9)))) |
% 144.23/21.34 ~ (((multiply @ sk_c2 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 ~ (((inverse @ sk_c2) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl311])).
% 144.23/21.34 thf(zip_derived_cl819, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 144.23/21.34 thf(zip_derived_cl505, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl956, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ identity) @ identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl819, zip_derived_cl505])).
% 144.23/21.34 thf(zip_derived_cl1, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_inverse])).
% 144.23/21.34 thf(zip_derived_cl972, plain,
% 144.23/21.34 ((((sk_c4) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl956, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl60, plain,
% 144.23/21.34 ((((inverse @ sk_c4) = (sk_c10))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl6])).
% 144.23/21.34 thf(zip_derived_cl1591, plain,
% 144.23/21.34 ((((inverse @ identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl972, zip_derived_cl60])).
% 144.23/21.34 thf(zip_derived_cl819, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 144.23/21.34 thf(zip_derived_cl1624, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1591, zip_derived_cl819])).
% 144.23/21.34 thf(zip_derived_cl3101, plain,
% 144.23/21.34 ((((identity) != (inverse @ (inverse @ identity))))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl3099])).
% 144.23/21.34 thf(zip_derived_cl44462, plain,
% 144.23/21.34 ((((identity) != (inverse @ identity)))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1624, zip_derived_cl3101])).
% 144.23/21.34 thf(zip_derived_cl1624, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1591, zip_derived_cl819])).
% 144.23/21.34 thf(zip_derived_cl44956, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((identity) = (inverse @ (inverse @ identity)))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl44462, zip_derived_cl1624])).
% 144.23/21.34 thf('40', plain,
% 144.23/21.34 ((((identity) = (inverse @ (inverse @ identity)))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) | ~ (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl44956])).
% 144.23/21.34 thf(zip_derived_cl1624, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1591, zip_derived_cl819])).
% 144.23/21.34 thf(zip_derived_cl3021, plain,
% 144.23/21.34 ((((inverse @ identity) != (identity)))
% 144.23/21.34 <= (~ (((inverse @ identity) = (identity))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl2864])).
% 144.23/21.34 thf(zip_derived_cl44460, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((inverse @ identity) = (identity))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1624, zip_derived_cl3021])).
% 144.23/21.34 thf('41', plain,
% 144.23/21.34 ((((inverse @ identity) = (identity))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) | ~ (((inverse @ sk_c4) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl44460])).
% 144.23/21.34 thf(zip_derived_cl972, plain,
% 144.23/21.34 ((((sk_c4) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl956, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl41388, plain,
% 144.23/21.34 ((((identity) != (sk_c4))) <= (~ (((identity) = (sk_c4))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl1530])).
% 144.23/21.34 thf(zip_derived_cl41393, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((identity) = (sk_c4))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl972, zip_derived_cl41388])).
% 144.23/21.34 thf('42', plain,
% 144.23/21.34 ((((identity) = (sk_c4))) | ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl41393])).
% 144.23/21.34 thf(zip_derived_cl1356, plain,
% 144.23/21.34 ((((identity) = (sk_c11)))
% 144.23/21.34 <= ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl1342, zip_derived_cl62])).
% 144.23/21.34 thf(zip_derived_cl819, plain,
% 144.23/21.34 ((((identity) = (sk_c10)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl807, zip_derived_cl54])).
% 144.23/21.34 thf(zip_derived_cl4863, plain,
% 144.23/21.34 ((((sk_c11) != (sk_c10)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl4841, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl4883, plain,
% 144.23/21.34 ((((sk_c11) != (identity)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl819, zip_derived_cl4863])).
% 144.23/21.34 thf(zip_derived_cl17491, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) &
% 144.23/21.34 (((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c5) = (sk_c8))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1356, zip_derived_cl4883])).
% 144.23/21.34 thf('43', plain,
% 144.23/21.34 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) |
% 144.23/21.34 ~ (((multiply @ sk_c4 @ sk_c10) = (sk_c9))) |
% 144.23/21.34 ~ (((multiply @ sk_c5 @ sk_c8) = (sk_c11))) |
% 144.23/21.34 ~ (((inverse @ sk_c5) = (sk_c8)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl17491])).
% 144.23/21.34 thf(prove_this_33, conjecture,
% 144.23/21.34 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 144.23/21.34 thf(zf_stmt_28, negated_conjecture,
% 144.23/21.34 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 144.23/21.34 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 144.23/21.34 inference('cnf.neg', [status(esa)], [prove_this_33])).
% 144.23/21.34 thf(zip_derived_cl35, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 144.23/21.34 | ((inverse @ sk_c2) = (sk_c10)))),
% 144.23/21.34 inference('cnf', [status(esa)], [zf_stmt_28])).
% 144.23/21.34 thf('44', plain,
% 144.23/21.34 ((((inverse @ sk_c2) = (sk_c10))) |
% 144.23/21.34 (((multiply @ sk_c4 @ sk_c10) = (sk_c9)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl35])).
% 144.23/21.34 thf(zip_derived_cl1792, plain,
% 144.23/21.34 ((((inverse @ identity) = (identity)))
% 144.23/21.34 <= ((((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl1768, zip_derived_cl819])).
% 144.23/21.34 thf(zip_derived_cl3021, plain,
% 144.23/21.34 ((((inverse @ identity) != (identity)))
% 144.23/21.34 <= (~ (((inverse @ identity) = (identity))))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl2864])).
% 144.23/21.34 thf(zip_derived_cl51505, plain,
% 144.23/21.34 ((((identity) != (identity)))
% 144.23/21.34 <= (~ (((inverse @ identity) = (identity))) &
% 144.23/21.34 (((multiply @ sk_c1 @ sk_c11) = (sk_c10))) &
% 144.23/21.34 (((inverse @ sk_c1) = (sk_c11))) &
% 144.23/21.34 (((inverse @ sk_c2) = (sk_c10))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1792, zip_derived_cl3021])).
% 144.23/21.34 thf('45', plain,
% 144.23/21.34 ((((inverse @ identity) = (identity))) |
% 144.23/21.34 ~ (((inverse @ sk_c2) = (sk_c10))) |
% 144.23/21.34 ~ (((inverse @ sk_c1) = (sk_c11))) |
% 144.23/21.34 ~ (((multiply @ sk_c1 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl51505])).
% 144.23/21.34 thf(zip_derived_cl1058, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ sk_c10) = (identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl442, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c10 @ (multiply @ sk_c4 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl441, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl1071, plain,
% 144.23/21.34 ((((sk_c10) = (multiply @ sk_c10 @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl1058, zip_derived_cl442])).
% 144.23/21.34 thf(zip_derived_cl2836, plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i]:
% 144.23/21.34 (((multiply @ X1 @ X0) != (sk_c11))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X0 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (X0))
% 144.23/21.34 | ((inverse @ X0) != (X0))))
% 144.23/21.34 <= ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)], [zip_derived_cl496, zip_derived_cl223])).
% 144.23/21.34 thf(zip_derived_cl3497, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c10) != (identity))
% 144.23/21.34 | ((multiply @ identity @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (identity))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('s_sup-', [status(thm)],
% 144.23/21.34 [zip_derived_cl1071, zip_derived_cl2836])).
% 144.23/21.34 thf(zip_derived_cl0, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 144.23/21.34 inference('cnf', [status(esa)], [left_identity])).
% 144.23/21.34 thf(zip_derived_cl3587, plain,
% 144.23/21.34 (((((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ sk_c10) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((inverse @ identity) != (identity))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl3497, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl3588, plain,
% 144.23/21.34 (((((inverse @ identity) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((inverse @ sk_c10) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('simplify', [status(thm)], [zip_derived_cl3587])).
% 144.23/21.34 thf(zip_derived_cl2430, plain,
% 144.23/21.34 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl494, zip_derived_cl1])).
% 144.23/21.34 thf(zip_derived_cl504, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl196, plain,
% 144.23/21.34 (![X0 : $i, X1 : $i]:
% 144.23/21.34 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 144.23/21.34 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 144.23/21.34 thf(zip_derived_cl1059, plain,
% 144.23/21.34 ((![X0 : $i]: ((X0) = (multiply @ sk_c4 @ (multiply @ sk_c10 @ X0))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl72861, plain,
% 144.23/21.34 ((((inverse @ sk_c10) = (multiply @ sk_c4 @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)],
% 144.23/21.34 [zip_derived_cl2430, zip_derived_cl1059])).
% 144.23/21.34 thf(zip_derived_cl505, plain,
% 144.23/21.34 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl179, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl504, plain,
% 144.23/21.34 ((![X0 : $i]:
% 144.23/21.34 ((multiply @ sk_c4 @ X0) = (multiply @ (inverse @ sk_c10) @ X0)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl442, zip_derived_cl196])).
% 144.23/21.34 thf(zip_derived_cl1060, plain,
% 144.23/21.34 ((((multiply @ sk_c4 @ identity) = (sk_c4)))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('s_sup+', [status(thm)], [zip_derived_cl505, zip_derived_cl504])).
% 144.23/21.34 thf(zip_derived_cl73081, plain,
% 144.23/21.34 ((((inverse @ sk_c10) = (sk_c4))) <= ((((inverse @ sk_c4) = (sk_c10))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl72861, zip_derived_cl1060])).
% 144.23/21.34 thf(zip_derived_cl139133, plain,
% 144.23/21.34 (((((inverse @ identity) != (identity))
% 144.23/21.34 | ((inverse @ (inverse @ identity)) != (identity))
% 144.23/21.34 | ((sk_c4) != (identity))
% 144.23/21.34 | ((sk_c10) != (sk_c11))))
% 144.23/21.34 <= ((((inverse @ sk_c4) = (sk_c10))) &
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))))),
% 144.23/21.34 inference('demod', [status(thm)],
% 144.23/21.34 [zip_derived_cl3588, zip_derived_cl73081])).
% 144.23/21.34 thf('46', plain,
% 144.23/21.34 (~
% 144.23/21.34 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 144.23/21.34 ~ (((inverse @ identity) = (identity))) |
% 144.23/21.34 ~ (((inverse @ sk_c4) = (sk_c10))) | ~ (((identity) = (sk_c4))) |
% 144.23/21.34 ~ (((identity) = (inverse @ (inverse @ identity)))) |
% 144.23/21.34 ~ (((sk_c10) = (sk_c11)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl139133])).
% 144.23/21.34 thf('47', plain,
% 144.23/21.34 ((![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 144.23/21.34 (((inverse @ X0) != (X2))
% 144.23/21.34 | ((multiply @ X1 @ X2) != (X0))
% 144.23/21.34 | ((inverse @ X1) != (X0))
% 144.23/21.34 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 144.23/21.34 | ((inverse @ X3) != (X2))
% 144.23/21.34 | ((multiply @ X3 @ X2) != (sk_c11)))) |
% 144.23/21.34 (![X7 : $i]:
% 144.23/21.34 (((inverse @ X7) != (sk_c11))
% 144.23/21.34 | ((multiply @ X7 @ sk_c11) != (sk_c10)))) |
% 144.23/21.34 (![X6 : $i]:
% 144.23/21.34 (((inverse @ X6) != (sk_c10)) | ((multiply @ X6 @ sk_c10) != (sk_c9)))) |
% 144.23/21.34 ~ (((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 144.23/21.34 inference('split', [status(esa)], [zip_derived_cl53])).
% 144.23/21.34 thf(zip_derived_cl139155, plain, ($false),
% 144.23/21.34 inference('sat_resolution*', [status(thm)],
% 144.23/21.34 ['0', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10', '11',
% 144.23/21.34 '12', '13', '14', '15', '16', '17', '18', '19', '20', '21',
% 144.23/21.34 '22', '23', '24', '25', '26', '27', '28', '29', '30', '31',
% 144.23/21.34 '32', '33', '34', '35', '36', '37', '38', '39', '40', '41',
% 144.23/21.34 '42', '43', '44', '45', '46', '47'])).
% 144.23/21.34
% 144.23/21.34 % SZS output end Refutation
% 144.23/21.34
% 144.23/21.34
% 144.23/21.34 % Terminating...
% 144.23/21.38 % Runner terminated.
% 144.23/21.39 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------