%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP350-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lJvqVtqlql true
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:17 PM UTC 2025
% Result : Unsatisfiable 8.54s 1.79s
% Output : Refutation 8.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP350-1 : TPTP v9.2.0. Released v2.5.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lJvqVtqlql true
% 0.13/0.35 % Computer : n024.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 : Wed Oct 1 14:08:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.48/0.60 % Total configuration time : 435
% 0.48/0.60 % Estimated wc time : 1092
% 0.48/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.50/0.70 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.50/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 8.54/1.79 % Solved by fo/fo7.sh.
% 8.54/1.79 % done 1154 iterations in 1.022s
% 8.54/1.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.54/1.79 % SZS output start Refutation
% 8.54/1.79 thf(sk_c8_type, type, sk_c8: $i).
% 8.54/1.79 thf(sk_c9_type, type, sk_c9: $i).
% 8.54/1.79 thf(sk_c6_type, type, sk_c6: $i).
% 8.54/1.79 thf(sk_c5_type, type, sk_c5: $i).
% 8.54/1.79 thf(sk_c4_type, type, sk_c4: $i).
% 8.54/1.79 thf(identity_type, type, identity: $i).
% 8.54/1.79 thf(multiply_type, type, multiply: $i > $i > $i).
% 8.54/1.79 thf(sk_c11_type, type, sk_c11: $i).
% 8.54/1.79 thf(sk_c2_type, type, sk_c2: $i).
% 8.54/1.79 thf(inverse_type, type, inverse: $i > $i).
% 8.54/1.79 thf(sk_c3_type, type, sk_c3: $i).
% 8.54/1.79 thf(sk_c1_type, type, sk_c1: $i).
% 8.54/1.79 thf(sk_c10_type, type, sk_c10: $i).
% 8.54/1.79 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 8.54/1.79 thf(zip_derived_cl0, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.79 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(associativity, axiom,
% 8.54/1.79 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 8.54/1.79 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 8.54/1.79 thf(zip_derived_cl2, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.79 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.54/1.79 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.54/1.79 inference('cnf', [status(esa)], [associativity])).
% 8.54/1.79 thf(zip_derived_cl194, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((multiply @ identity @ X0)
% 8.54/1.79 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 8.54/1.79 thf(zip_derived_cl0, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl257, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl333, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl257, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.79 thf(prove_this_71, conjecture,
% 8.54/1.79 (~( ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 8.54/1.79 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 8.54/1.79 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ X5 ) != ( X6 ) ) |
% 8.54/1.79 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 8.54/1.79 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ X3 @ sk_c10 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c9 @ sk_c11 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c10 ) != ( sk_c9 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) != ( sk_c9 ) ) ))).
% 8.54/1.79 thf(zf_stmt_0, negated_conjecture,
% 8.54/1.79 (( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 8.54/1.79 ( ( inverse @ X7 ) != ( X8 ) ) |
% 8.54/1.79 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ X5 ) != ( X6 ) ) |
% 8.54/1.79 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 8.54/1.79 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ X3 @ sk_c10 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c9 @ sk_c11 ) != ( sk_c10 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c10 ) != ( sk_c9 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) != ( sk_c9 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_71])).
% 8.54/1.79 thf(zip_derived_cl73, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.79 (((multiply @ X1 @ X2) != (X0))
% 8.54/1.79 | ((inverse @ X0) != (X2))
% 8.54/1.79 | ((inverse @ X1) != (X0))
% 8.54/1.79 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 8.54/1.79 | ((inverse @ X3) != (X2))
% 8.54/1.79 | ((multiply @ X3 @ X2) != (sk_c11))
% 8.54/1.79 | ((inverse @ X4) != (sk_c10))
% 8.54/1.79 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 8.54/1.79 | ((inverse @ X5) != (sk_c11))
% 8.54/1.79 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 8.54/1.79 | ((multiply @ X6 @ sk_c9) != (sk_c10))
% 8.54/1.79 | ((inverse @ X6) != (sk_c10))
% 8.54/1.79 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 8.54/1.79 | ((inverse @ X7) != (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) != (sk_c10))
% 8.54/1.79 | ((inverse @ sk_c10) != (sk_c9))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) != (sk_c9)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_0])).
% 8.54/1.79 thf(zip_derived_cl74, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.79 (((multiply @ X1 @ X2) != (X0))
% 8.54/1.79 | ((inverse @ X0) != (X2))
% 8.54/1.79 | ((inverse @ X1) != (X0))
% 8.54/1.79 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 8.54/1.79 | ((inverse @ X3) != (X2))
% 8.54/1.79 | ((multiply @ X3 @ X2) != (sk_c11))
% 8.54/1.79 | ((inverse @ X4) != (sk_c10))
% 8.54/1.79 | ((multiply @ X4 @ sk_c10) != (multiply @ sk_c10 @ sk_c11))
% 8.54/1.79 | ((inverse @ X5) != (sk_c11))
% 8.54/1.79 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 8.54/1.79 | ((multiply @ X6 @ (multiply @ sk_c10 @ sk_c11)) != (sk_c10))
% 8.54/1.79 | ((inverse @ X6) != (sk_c10))
% 8.54/1.79 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 8.54/1.79 | ((inverse @ X7) != (sk_c11))
% 8.54/1.79 | ((multiply @ (multiply @ sk_c10 @ sk_c11) @ sk_c11) != (sk_c10))
% 8.54/1.79 | ((inverse @ sk_c10) != (sk_c9))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) != (sk_c9)))),
% 8.54/1.79 inference('local_rewriting', [status(thm)], [zip_derived_cl73])).
% 8.54/1.79 thf(zip_derived_cl2, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.79 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.54/1.79 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.54/1.79 inference('cnf', [status(esa)], [associativity])).
% 8.54/1.79 thf(zip_derived_cl190, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.79 (((multiply @ X1 @ X2) != (X0))
% 8.54/1.79 | ((inverse @ X0) != (X2))
% 8.54/1.79 | ((inverse @ X1) != (X0))
% 8.54/1.79 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 8.54/1.79 | ((inverse @ X3) != (X2))
% 8.54/1.79 | ((multiply @ X3 @ X2) != (sk_c11))
% 8.54/1.79 | ((inverse @ X4) != (sk_c10))
% 8.54/1.79 | ((multiply @ X4 @ sk_c10) != (multiply @ sk_c10 @ sk_c11))
% 8.54/1.79 | ((inverse @ X5) != (sk_c11))
% 8.54/1.79 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 8.54/1.79 | ((multiply @ X6 @ (multiply @ sk_c10 @ sk_c11)) != (sk_c10))
% 8.54/1.79 | ((inverse @ X6) != (sk_c10))
% 8.54/1.79 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 8.54/1.79 | ((inverse @ X7) != (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c10 @ (multiply @ sk_c11 @ sk_c11)) != (sk_c10))
% 8.54/1.79 | ((inverse @ sk_c10) != (sk_c9))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) != (sk_c9)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl74, zip_derived_cl2])).
% 8.54/1.79 thf(prove_this_56, conjecture,
% 8.54/1.79 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 8.54/1.79 thf(zf_stmt_1, negated_conjecture,
% 8.54/1.79 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_56])).
% 8.54/1.79 thf(zip_derived_cl58, plain,
% 8.54/1.79 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c10)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_1])).
% 8.54/1.79 thf(prove_this_66, conjecture,
% 8.54/1.79 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 8.54/1.79 thf(zf_stmt_2, negated_conjecture,
% 8.54/1.79 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_66])).
% 8.54/1.79 thf(zip_derived_cl68, plain,
% 8.54/1.79 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_2])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl294, plain,
% 8.54/1.79 ((((sk_c9) = (multiply @ (inverse @ sk_c2) @ sk_c10))
% 8.54/1.79 | ((inverse @ sk_c5) = (sk_c8)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl68, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl3729, plain,
% 8.54/1.79 ((((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 8.54/1.79 | ((inverse @ sk_c5) = (sk_c8))
% 8.54/1.79 | ((inverse @ sk_c5) = (sk_c8)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl294])).
% 8.54/1.79 thf(zip_derived_cl3744, plain,
% 8.54/1.79 ((((inverse @ sk_c5) = (sk_c8))
% 8.54/1.79 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl3729])).
% 8.54/1.79 thf(prove_this_55, conjecture,
% 8.54/1.79 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 8.54/1.79 thf(zf_stmt_3, negated_conjecture,
% 8.54/1.79 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_55])).
% 8.54/1.79 thf(zip_derived_cl57, plain,
% 8.54/1.79 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 8.54/1.79 | ((inverse @ sk_c2) = (sk_c10)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_3])).
% 8.54/1.79 thf(prove_this_65, conjecture,
% 8.54/1.79 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 8.54/1.79 thf(zf_stmt_4, negated_conjecture,
% 8.54/1.79 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_65])).
% 8.54/1.79 thf(zip_derived_cl67, plain,
% 8.54/1.79 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_4])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl1083, plain,
% 8.54/1.79 ((((sk_c9) = (multiply @ (inverse @ sk_c2) @ sk_c10))
% 8.54/1.79 | ((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl7540, plain,
% 8.54/1.79 ((((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 8.54/1.79 | ((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl57, zip_derived_cl1083])).
% 8.54/1.79 thf(zip_derived_cl7556, plain,
% 8.54/1.79 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 8.54/1.79 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl7540])).
% 8.54/1.79 thf(zip_derived_cl7621, plain,
% 8.54/1.79 ((((multiply @ sk_c5 @ (inverse @ sk_c5)) = (sk_c11))
% 8.54/1.79 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 8.54/1.79 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl3744, zip_derived_cl7556])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl258, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl255, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl234, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl258, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl1550, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1477, zip_derived_cl258])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl1575, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl7630, plain,
% 8.54/1.79 ((((identity) = (sk_c11))
% 8.54/1.79 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 8.54/1.79 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 8.54/1.79 inference('demod', [status(thm)],
% 8.54/1.79 [zip_derived_cl7621, zip_derived_cl1575])).
% 8.54/1.79 thf(zip_derived_cl7631, plain,
% 8.54/1.79 ((((sk_c9) = (multiply @ sk_c10 @ sk_c10)) | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl7630])).
% 8.54/1.79 thf(prove_this_9, conjecture,
% 8.54/1.79 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 8.54/1.79 thf(zf_stmt_5, negated_conjecture,
% 8.54/1.79 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 8.54/1.79 thf(zip_derived_cl11, plain,
% 8.54/1.79 ((((inverse @ sk_c6) = (sk_c8))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_5])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl95, plain,
% 8.54/1.79 ((((multiply @ sk_c8 @ sk_c6) = (identity))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl285, plain,
% 8.54/1.79 ((((sk_c6) = (multiply @ (inverse @ sk_c8) @ identity))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl95, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl1539, plain,
% 8.54/1.79 ((((sk_c6) = (inverse @ sk_c8))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl285, zip_derived_cl1477])).
% 8.54/1.79 thf(prove_this_6, conjecture,
% 8.54/1.79 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 8.54/1.79 thf(zf_stmt_6, negated_conjecture,
% 8.54/1.79 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 8.54/1.79 thf(zip_derived_cl8, plain,
% 8.54/1.79 ((((inverse @ sk_c5) = (sk_c8))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_6])).
% 8.54/1.79 thf(zip_derived_cl95, plain,
% 8.54/1.79 ((((multiply @ sk_c8 @ sk_c6) = (identity))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl178, plain,
% 8.54/1.79 ((((multiply @ (inverse @ sk_c5) @ sk_c6) = (identity))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl95])).
% 8.54/1.79 thf(zip_derived_cl183, plain,
% 8.54/1.79 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 8.54/1.79 | ((multiply @ (inverse @ sk_c5) @ sk_c6) = (identity)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl178])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl1372, plain,
% 8.54/1.79 ((((sk_c6) = (multiply @ (inverse @ (inverse @ sk_c5)) @ identity))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl183, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl258, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl1388, plain,
% 8.54/1.79 ((((sk_c6) = (sk_c5)) | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl1372, zip_derived_cl258])).
% 8.54/1.79 thf(zip_derived_cl1773, plain,
% 8.54/1.79 ((((inverse @ sk_c8) = (sk_c5))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1539, zip_derived_cl1388])).
% 8.54/1.79 thf(zip_derived_cl1779, plain,
% 8.54/1.79 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 8.54/1.79 | ((inverse @ sk_c8) = (sk_c5)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl1773])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl2360, plain,
% 8.54/1.79 ((((multiply @ sk_c5 @ sk_c8) = (identity))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1779, zip_derived_cl1])).
% 8.54/1.79 thf(prove_this_5, conjecture,
% 8.54/1.79 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 8.54/1.79 thf(zf_stmt_7, negated_conjecture,
% 8.54/1.79 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 8.54/1.79 thf(zip_derived_cl7, plain,
% 8.54/1.79 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_7])).
% 8.54/1.79 thf(zip_derived_cl4958, plain,
% 8.54/1.79 ((((identity) = (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl2360, zip_derived_cl7])).
% 8.54/1.79 thf(zip_derived_cl4976, plain,
% 8.54/1.79 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9)) | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl4958])).
% 8.54/1.79 thf(zip_derived_cl7660, plain,
% 8.54/1.79 ((((multiply @ sk_c10 @ sk_c11) = (multiply @ sk_c10 @ sk_c10))
% 8.54/1.79 | ((identity) = (sk_c11))
% 8.54/1.79 | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl7631, zip_derived_cl4976])).
% 8.54/1.79 thf(zip_derived_cl7663, plain,
% 8.54/1.79 ((((identity) = (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c10 @ sk_c11) = (multiply @ sk_c10 @ sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl7660])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl7853, plain,
% 8.54/1.79 ((((sk_c11)
% 8.54/1.79 = (multiply @ (inverse @ sk_c10) @ (multiply @ sk_c10 @ sk_c10)))
% 8.54/1.79 | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl7663, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl7870, plain,
% 8.54/1.79 ((((sk_c11) = (sk_c10)) | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl7853, zip_derived_cl234])).
% 8.54/1.79 thf(prove_this_12, conjecture,
% 8.54/1.79 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) ))).
% 8.54/1.79 thf(zf_stmt_8, negated_conjecture,
% 8.54/1.79 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c10 ) = ( sk_c9 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 8.54/1.79 thf(zip_derived_cl14, plain,
% 8.54/1.79 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_8])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl75, plain,
% 8.54/1.79 ((((multiply @ sk_c11 @ sk_c3) = (identity))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl234, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i]:
% 8.54/1.79 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.79 thf(zip_derived_cl268, plain,
% 8.54/1.79 ((((sk_c3) = (multiply @ (inverse @ sk_c11) @ identity))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl234])).
% 8.54/1.79 thf(prove_this_11, conjecture,
% 8.54/1.79 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) ))).
% 8.54/1.79 thf(zf_stmt_9, negated_conjecture,
% 8.54/1.79 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.79 ( ( inverse @ sk_c10 ) = ( sk_c9 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 8.54/1.79 thf(zip_derived_cl13, plain,
% 8.54/1.79 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_9])).
% 8.54/1.79 thf(zip_derived_cl503, plain,
% 8.54/1.79 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c11)
% 8.54/1.79 = (sk_c10))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl268, zip_derived_cl13])).
% 8.54/1.79 thf(zip_derived_cl2, plain,
% 8.54/1.79 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.79 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.54/1.79 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.54/1.79 inference('cnf', [status(esa)], [associativity])).
% 8.54/1.79 thf(zip_derived_cl0, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl510, plain,
% 8.54/1.79 ((((identity) = (sk_c10))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9))
% 8.54/1.79 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.79 inference('demod', [status(thm)],
% 8.54/1.79 [zip_derived_cl503, zip_derived_cl2, zip_derived_cl0,
% 8.54/1.79 zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl511, plain,
% 8.54/1.79 ((((inverse @ sk_c10) = (sk_c9)) | ((identity) = (sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl510])).
% 8.54/1.79 thf(prove_this_22, conjecture,
% 8.54/1.79 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 8.54/1.79 thf(zf_stmt_10, negated_conjecture,
% 8.54/1.79 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 8.54/1.79 thf(zip_derived_cl24, plain,
% 8.54/1.79 ((((inverse @ sk_c3) = (sk_c11))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_10])).
% 8.54/1.79 thf(zip_derived_cl1550, plain,
% 8.54/1.79 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1477, zip_derived_cl258])).
% 8.54/1.79 thf(zip_derived_cl1589, plain,
% 8.54/1.79 ((((sk_c3) = (inverse @ sk_c11))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl1550])).
% 8.54/1.79 thf(prove_this_21, conjecture,
% 8.54/1.79 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) ) ))).
% 8.54/1.79 thf(zf_stmt_11, negated_conjecture,
% 8.54/1.79 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.79 ( ( multiply @ sk_c9 @ sk_c11 ) = ( sk_c10 ) )),
% 8.54/1.79 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 8.54/1.79 thf(zip_derived_cl23, plain,
% 8.54/1.79 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 8.54/1.79 inference('cnf', [status(esa)], [zf_stmt_11])).
% 8.54/1.79 thf(zip_derived_cl2377, plain,
% 8.54/1.79 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c10))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl1589, zip_derived_cl23])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl2386, plain,
% 8.54/1.79 ((((identity) = (sk_c10))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10))
% 8.54/1.79 | ((multiply @ sk_c9 @ sk_c11) = (sk_c10)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl2377, zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl2387, plain,
% 8.54/1.79 ((((multiply @ sk_c9 @ sk_c11) = (sk_c10)) | ((identity) = (sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl2386])).
% 8.54/1.79 thf(zip_derived_cl2529, plain,
% 8.54/1.79 ((((multiply @ (inverse @ sk_c10) @ sk_c11) = (sk_c10))
% 8.54/1.79 | ((identity) = (sk_c10))
% 8.54/1.79 | ((identity) = (sk_c10)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl511, zip_derived_cl2387])).
% 8.54/1.79 thf(zip_derived_cl2534, plain,
% 8.54/1.79 ((((identity) = (sk_c10))
% 8.54/1.79 | ((multiply @ (inverse @ sk_c10) @ sk_c11) = (sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl2529])).
% 8.54/1.79 thf(zip_derived_cl7912, plain,
% 8.54/1.79 ((((multiply @ (inverse @ sk_c10) @ sk_c10) = (sk_c10))
% 8.54/1.79 | ((identity) = (sk_c11))
% 8.54/1.79 | ((identity) = (sk_c10)))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl7870, zip_derived_cl2534])).
% 8.54/1.79 thf(zip_derived_cl1, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.79 thf(zip_derived_cl7923, plain,
% 8.54/1.79 ((((identity) = (sk_c10))
% 8.54/1.79 | ((identity) = (sk_c11))
% 8.54/1.79 | ((identity) = (sk_c10)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl7912, zip_derived_cl1])).
% 8.54/1.79 thf(zip_derived_cl7924, plain,
% 8.54/1.79 ((((identity) = (sk_c11)) | ((identity) = (sk_c10)))),
% 8.54/1.79 inference('simplify', [status(thm)], [zip_derived_cl7923])).
% 8.54/1.79 thf(zip_derived_cl7870, plain,
% 8.54/1.79 ((((sk_c11) = (sk_c10)) | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('demod', [status(thm)], [zip_derived_cl7853, zip_derived_cl234])).
% 8.54/1.79 thf(zip_derived_cl7922, plain,
% 8.54/1.79 ((((sk_c10) != (identity)) | ((identity) = (sk_c11)))),
% 8.54/1.79 inference('eq_fact', [status(thm)], [zip_derived_cl7870])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl0, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.79 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.79 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.79 thf(zip_derived_cl1477, plain,
% 8.54/1.79 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.79 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.79 thf(zip_derived_cl8011, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X1) != (X0))
% 8.54/1.80 | ((multiply @ X2 @ sk_c10) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X2))
% 8.54/1.80 | ((multiply @ X3 @ X2) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (sk_c10))
% 8.54/1.80 | ((multiply @ X4 @ sk_c10) != (sk_c10))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (sk_c10))
% 8.54/1.80 | ((multiply @ X6 @ sk_c10) != (sk_c10))
% 8.54/1.80 | ((inverse @ X6) != (sk_c10))
% 8.54/1.80 | ((multiply @ X7 @ sk_c10) != (identity))
% 8.54/1.80 | ((inverse @ X7) != (identity))
% 8.54/1.80 | ((sk_c10) != (sk_c10))
% 8.54/1.80 | ((inverse @ sk_c10) != (sk_c9))
% 8.54/1.80 | ((sk_c10) != (sk_c9)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl190, zip_derived_cl7929, zip_derived_cl7929,
% 8.54/1.80 zip_derived_cl7929, zip_derived_cl1477, zip_derived_cl7929,
% 8.54/1.80 zip_derived_cl7929, zip_derived_cl1477, zip_derived_cl7929,
% 8.54/1.80 zip_derived_cl1477, zip_derived_cl7929, zip_derived_cl7929,
% 8.54/1.80 zip_derived_cl7929, zip_derived_cl7929, zip_derived_cl0,
% 8.54/1.80 zip_derived_cl1477, zip_derived_cl7929, zip_derived_cl1477])).
% 8.54/1.80 thf(zip_derived_cl8012, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.80 (((sk_c10) != (sk_c9))
% 8.54/1.80 | ((inverse @ sk_c10) != (sk_c9))
% 8.54/1.80 | ((inverse @ X7) != (identity))
% 8.54/1.80 | ((multiply @ X7 @ sk_c10) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (sk_c10))
% 8.54/1.80 | ((multiply @ X6 @ sk_c10) != (sk_c10))
% 8.54/1.80 | ((X5) != (sk_c10))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((multiply @ X4 @ sk_c10) != (sk_c10))
% 8.54/1.80 | ((inverse @ X4) != (sk_c10))
% 8.54/1.80 | ((multiply @ X3 @ X2) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X2))
% 8.54/1.80 | ((multiply @ X2 @ sk_c10) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X0))
% 8.54/1.80 | ((inverse @ X0) != (X2))
% 8.54/1.80 | ((multiply @ X1 @ X2) != (X0)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl8011])).
% 8.54/1.80 thf(prove_this_31, conjecture,
% 8.54/1.80 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 8.54/1.80 thf(zf_stmt_12, negated_conjecture,
% 8.54/1.80 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 8.54/1.80 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 8.54/1.80 thf(zip_derived_cl33, plain,
% 8.54/1.80 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 8.54/1.80 | ((inverse @ sk_c1) = (sk_c11)))),
% 8.54/1.80 inference('cnf', [status(esa)], [zf_stmt_12])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl7954, plain,
% 8.54/1.80 ((((sk_c3) = (sk_c10)) | ((inverse @ sk_c1) = (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl33, zip_derived_cl7929, zip_derived_cl1477,
% 8.54/1.80 zip_derived_cl7929])).
% 8.54/1.80 thf(zip_derived_cl1550, plain,
% 8.54/1.80 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl1477, zip_derived_cl258])).
% 8.54/1.80 thf(zip_derived_cl234, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i]:
% 8.54/1.80 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.80 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.80 thf(zip_derived_cl1577, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i]:
% 8.54/1.80 ((X1) = (multiply @ X0 @ (multiply @ (inverse @ X0) @ X1)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl1550, zip_derived_cl234])).
% 8.54/1.80 thf(zip_derived_cl8363, plain,
% 8.54/1.80 (![X0 : $i]:
% 8.54/1.80 (((X0) = (multiply @ sk_c1 @ (multiply @ identity @ X0)))
% 8.54/1.80 | ((sk_c3) = (sk_c10)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl7954, zip_derived_cl1577])).
% 8.54/1.80 thf(zip_derived_cl0, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.80 thf(zip_derived_cl8373, plain,
% 8.54/1.80 (![X0 : $i]: (((X0) = (multiply @ sk_c1 @ X0)) | ((sk_c3) = (sk_c10)))),
% 8.54/1.80 inference('demod', [status(thm)], [zip_derived_cl8363, zip_derived_cl0])).
% 8.54/1.80 thf(prove_this_41, conjecture,
% 8.54/1.80 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.80 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 8.54/1.80 thf(zf_stmt_13, negated_conjecture,
% 8.54/1.80 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 8.54/1.80 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) )),
% 8.54/1.80 inference('cnf.neg', [status(esa)], [prove_this_41])).
% 8.54/1.80 thf(zip_derived_cl43, plain,
% 8.54/1.80 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 8.54/1.80 | ((multiply @ sk_c1 @ sk_c10) = (sk_c11)))),
% 8.54/1.80 inference('cnf', [status(esa)], [zf_stmt_13])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl7964, plain,
% 8.54/1.80 ((((sk_c3) = (sk_c10)) | ((multiply @ sk_c1 @ sk_c10) = (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl43, zip_derived_cl7929, zip_derived_cl1477,
% 8.54/1.80 zip_derived_cl7929])).
% 8.54/1.80 thf(zip_derived_cl9817, plain,
% 8.54/1.80 ((((sk_c10) = (identity)) | ((sk_c3) = (sk_c10)) | ((sk_c3) = (sk_c10)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl8373, zip_derived_cl7964])).
% 8.54/1.80 thf(zip_derived_cl9831, plain,
% 8.54/1.80 ((((sk_c3) = (sk_c10)) | ((sk_c10) = (identity)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9817])).
% 8.54/1.80 thf(prove_this_32, conjecture,
% 8.54/1.80 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 8.54/1.80 thf(zf_stmt_14, negated_conjecture,
% 8.54/1.80 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 8.54/1.80 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 8.54/1.80 thf(zip_derived_cl34, plain,
% 8.54/1.80 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c11)))),
% 8.54/1.80 inference('cnf', [status(esa)], [zf_stmt_14])).
% 8.54/1.80 thf(zip_derived_cl1, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.80 thf(zip_derived_cl90, plain,
% 8.54/1.80 ((((multiply @ sk_c11 @ sk_c1) = (identity))
% 8.54/1.80 | ((inverse @ sk_c3) = (sk_c11)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl234, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i]:
% 8.54/1.80 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.80 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.80 thf(zip_derived_cl272, plain,
% 8.54/1.80 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity))
% 8.54/1.80 | ((inverse @ sk_c3) = (sk_c11)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl90, zip_derived_cl234])).
% 8.54/1.80 thf(prove_this_42, conjecture,
% 8.54/1.80 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.80 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 8.54/1.80 thf(zf_stmt_15, negated_conjecture,
% 8.54/1.80 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 8.54/1.80 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) )),
% 8.54/1.80 inference('cnf.neg', [status(esa)], [prove_this_42])).
% 8.54/1.80 thf(zip_derived_cl44, plain,
% 8.54/1.80 ((((inverse @ sk_c3) = (sk_c11))
% 8.54/1.80 | ((multiply @ sk_c1 @ sk_c10) = (sk_c11)))),
% 8.54/1.80 inference('cnf', [status(esa)], [zf_stmt_15])).
% 8.54/1.80 thf(zip_derived_cl910, plain,
% 8.54/1.80 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c10)
% 8.54/1.80 = (sk_c11))
% 8.54/1.80 | ((inverse @ sk_c3) = (sk_c11))
% 8.54/1.80 | ((inverse @ sk_c3) = (sk_c11)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl272, zip_derived_cl44])).
% 8.54/1.80 thf(zip_derived_cl2, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.80 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.54/1.80 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.54/1.80 inference('cnf', [status(esa)], [associativity])).
% 8.54/1.80 thf(zip_derived_cl0, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.80 thf(zip_derived_cl927, plain,
% 8.54/1.80 ((((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 8.54/1.80 | ((inverse @ sk_c3) = (sk_c11))
% 8.54/1.80 | ((inverse @ sk_c3) = (sk_c11)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl910, zip_derived_cl2, zip_derived_cl0])).
% 8.54/1.80 thf(zip_derived_cl928, plain,
% 8.54/1.80 ((((inverse @ sk_c3) = (sk_c11))
% 8.54/1.80 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl927])).
% 8.54/1.80 thf(zip_derived_cl1550, plain,
% 8.54/1.80 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl1477, zip_derived_cl258])).
% 8.54/1.80 thf(zip_derived_cl4316, plain,
% 8.54/1.80 ((((sk_c3) = (inverse @ sk_c11))
% 8.54/1.80 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl928, zip_derived_cl1550])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl0, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.80 thf(zip_derived_cl7929, plain, (((identity) = (sk_c11))),
% 8.54/1.80 inference('clc', [status(thm)], [zip_derived_cl7924, zip_derived_cl7922])).
% 8.54/1.80 thf(zip_derived_cl8113, plain,
% 8.54/1.80 ((((sk_c3) = (identity)) | ((sk_c10) = (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl4316, zip_derived_cl7929, zip_derived_cl1257,
% 8.54/1.80 zip_derived_cl7929, zip_derived_cl1257, zip_derived_cl0,
% 8.54/1.80 zip_derived_cl7929])).
% 8.54/1.80 thf(zip_derived_cl9852, plain,
% 8.54/1.80 ((((sk_c10) = (identity))
% 8.54/1.80 | ((sk_c10) = (identity))
% 8.54/1.80 | ((sk_c10) = (identity)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl9831, zip_derived_cl8113])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl10001, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.80 (((identity) != (sk_c9))
% 8.54/1.80 | ((identity) != (sk_c9))
% 8.54/1.80 | ((inverse @ X7) != (identity))
% 8.54/1.80 | ((X7) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((multiply @ X3 @ X2) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X2))
% 8.54/1.80 | ((X2) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X0))
% 8.54/1.80 | ((inverse @ X0) != (X2))
% 8.54/1.80 | ((multiply @ X1 @ X2) != (X0)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl8012, zip_derived_cl9859, zip_derived_cl9859,
% 8.54/1.80 zip_derived_cl1257, zip_derived_cl9859, zip_derived_cl1477,
% 8.54/1.80 zip_derived_cl9859, zip_derived_cl9859, zip_derived_cl1477,
% 8.54/1.80 zip_derived_cl9859, zip_derived_cl9859, zip_derived_cl9859,
% 8.54/1.80 zip_derived_cl1477, zip_derived_cl9859, zip_derived_cl9859,
% 8.54/1.80 zip_derived_cl9859, zip_derived_cl1477])).
% 8.54/1.80 thf(zip_derived_cl10002, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X1) != (X0))
% 8.54/1.80 | ((X2) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X2))
% 8.54/1.80 | ((multiply @ X3 @ X2) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (identity))
% 8.54/1.80 | ((X7) != (identity))
% 8.54/1.80 | ((inverse @ X7) != (identity))
% 8.54/1.80 | ((identity) != (sk_c9)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10001])).
% 8.54/1.80 thf(prove_this_14, conjecture,
% 8.54/1.80 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) ))).
% 8.54/1.80 thf(zf_stmt_16, negated_conjecture,
% 8.54/1.80 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c10 ) = ( sk_c9 ) )),
% 8.54/1.80 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 8.54/1.80 thf(zip_derived_cl16, plain,
% 8.54/1.80 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.80 inference('cnf', [status(esa)], [zf_stmt_16])).
% 8.54/1.80 thf(zip_derived_cl1, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.80 thf(zip_derived_cl76, plain,
% 8.54/1.80 ((((multiply @ sk_c10 @ sk_c4) = (identity))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl234, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i]:
% 8.54/1.80 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 8.54/1.80 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl0])).
% 8.54/1.80 thf(zip_derived_cl260, plain,
% 8.54/1.80 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl234])).
% 8.54/1.80 thf(prove_this_13, conjecture,
% 8.54/1.80 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c10 ) = ( sk_c9 ) ) ))).
% 8.54/1.80 thf(zf_stmt_17, negated_conjecture,
% 8.54/1.80 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 8.54/1.80 ( ( inverse @ sk_c10 ) = ( sk_c9 ) )),
% 8.54/1.80 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 8.54/1.80 thf(zip_derived_cl15, plain,
% 8.54/1.80 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.80 inference('cnf', [status(esa)], [zf_stmt_17])).
% 8.54/1.80 thf(zip_derived_cl479, plain,
% 8.54/1.80 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 8.54/1.80 = (sk_c9))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl260, zip_derived_cl15])).
% 8.54/1.80 thf(zip_derived_cl2, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.80 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 8.54/1.80 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 8.54/1.80 inference('cnf', [status(esa)], [associativity])).
% 8.54/1.80 thf(zip_derived_cl0, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_identity])).
% 8.54/1.80 thf(zip_derived_cl1, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 8.54/1.80 inference('cnf', [status(esa)], [left_inverse])).
% 8.54/1.80 thf(zip_derived_cl486, plain,
% 8.54/1.80 ((((identity) = (sk_c9))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9))
% 8.54/1.80 | ((inverse @ sk_c10) = (sk_c9)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl479, zip_derived_cl2, zip_derived_cl0,
% 8.54/1.80 zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl487, plain,
% 8.54/1.80 ((((inverse @ sk_c10) = (sk_c9)) | ((identity) = (sk_c9)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl486])).
% 8.54/1.80 thf(zip_derived_cl9859, plain, (((sk_c10) = (identity))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9852])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl9902, plain,
% 8.54/1.80 ((((identity) = (sk_c9)) | ((identity) = (sk_c9)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl487, zip_derived_cl9859, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl9903, plain, (((identity) = (sk_c9))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl9902])).
% 8.54/1.80 thf(zip_derived_cl10037, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X1) != (X0))
% 8.54/1.80 | ((X2) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X2))
% 8.54/1.80 | ((multiply @ X3 @ X2) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (identity))
% 8.54/1.80 | ((X7) != (identity))
% 8.54/1.80 | ((inverse @ X7) != (identity))
% 8.54/1.80 | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10002, zip_derived_cl9903])).
% 8.54/1.80 thf(zip_derived_cl10038, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 8.54/1.80 (((inverse @ X7) != (identity))
% 8.54/1.80 | ((X7) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((multiply @ X3 @ X2) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X2))
% 8.54/1.80 | ((X2) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X0))
% 8.54/1.80 | ((inverse @ X0) != (X2))
% 8.54/1.80 | ((multiply @ X1 @ X2) != (X0)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10037])).
% 8.54/1.80 thf(zip_derived_cl10039, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (identity))
% 8.54/1.80 | ((inverse @ identity) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10038])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl10040, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((inverse @ X6) != (identity))
% 8.54/1.80 | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10039, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl10041, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 8.54/1.80 (((inverse @ X6) != (identity))
% 8.54/1.80 | ((X6) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((multiply @ X1 @ X0) != (X2)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10040])).
% 8.54/1.80 thf(zip_derived_cl10042, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((inverse @ identity) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10041])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl10043, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X5) != (identity))
% 8.54/1.80 | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10042, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl10044, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 8.54/1.80 (((X5) != (identity))
% 8.54/1.80 | ((inverse @ X5) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((multiply @ X1 @ X0) != (X2)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10043])).
% 8.54/1.80 thf(zip_derived_cl10045, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((inverse @ identity) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10044])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl10046, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((X4) != (identity))
% 8.54/1.80 | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10045, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl10047, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 8.54/1.80 (((X4) != (identity))
% 8.54/1.80 | ((inverse @ X4) != (identity))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((multiply @ X1 @ X0) != (X2)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10046])).
% 8.54/1.80 thf(zip_derived_cl10048, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ identity) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10047])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl10049, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.54/1.80 (((multiply @ X1 @ X0) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10048, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl10050, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 8.54/1.80 (((multiply @ X3 @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X3) != (X0))
% 8.54/1.80 | ((X0) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X2))
% 8.54/1.80 | ((inverse @ X2) != (X0))
% 8.54/1.80 | ((multiply @ X1 @ X0) != (X2)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10049])).
% 8.54/1.80 thf(zip_derived_cl10051, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.80 (((multiply @ X0 @ identity) != (X1))
% 8.54/1.80 | ((inverse @ X1) != (identity))
% 8.54/1.80 | ((inverse @ X0) != (X1))
% 8.54/1.80 | ((inverse @ X2) != (identity))
% 8.54/1.80 | ((multiply @ X2 @ identity) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10050])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl1477, plain,
% 8.54/1.80 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl258, zip_derived_cl255])).
% 8.54/1.80 thf(zip_derived_cl10052, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i, X2 : $i]:
% 8.54/1.80 (((X0) != (X1))
% 8.54/1.80 | ((inverse @ X1) != (identity))
% 8.54/1.80 | ((inverse @ X0) != (X1))
% 8.54/1.80 | ((inverse @ X2) != (identity))
% 8.54/1.80 | ((X2) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10051, zip_derived_cl1477, zip_derived_cl1477])).
% 8.54/1.80 thf(zip_derived_cl10083, plain,
% 8.54/1.80 (![X0 : $i, X1 : $i]:
% 8.54/1.80 (((X0) != (identity))
% 8.54/1.80 | ((inverse @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X1) != (X1))
% 8.54/1.80 | ((inverse @ X1) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10052])).
% 8.54/1.80 thf(zip_derived_cl10084, plain,
% 8.54/1.80 (![X0 : $i]:
% 8.54/1.80 (((inverse @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X0) != (X0))
% 8.54/1.80 | ((inverse @ identity) != (identity)))),
% 8.54/1.80 inference('eq_res', [status(thm)], [zip_derived_cl10083])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl10085, plain,
% 8.54/1.80 (![X0 : $i]:
% 8.54/1.80 (((inverse @ X0) != (identity))
% 8.54/1.80 | ((inverse @ X0) != (X0))
% 8.54/1.80 | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10084, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl10086, plain,
% 8.54/1.80 (![X0 : $i]: (((inverse @ X0) != (X0)) | ((inverse @ X0) != (identity)))),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10085])).
% 8.54/1.80 thf(zip_derived_cl10087, plain,
% 8.54/1.80 ((((identity) != (identity)) | ((inverse @ identity) != (identity)))),
% 8.54/1.80 inference('sup-', [status(thm)],
% 8.54/1.80 [zip_derived_cl1257, zip_derived_cl10086])).
% 8.54/1.80 thf(zip_derived_cl1257, plain, (((inverse @ identity) = (identity))),
% 8.54/1.80 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl1])).
% 8.54/1.80 thf(zip_derived_cl10094, plain,
% 8.54/1.80 ((((identity) != (identity)) | ((identity) != (identity)))),
% 8.54/1.80 inference('demod', [status(thm)],
% 8.54/1.80 [zip_derived_cl10087, zip_derived_cl1257])).
% 8.54/1.80 thf(zip_derived_cl10095, plain, ($false),
% 8.54/1.80 inference('simplify', [status(thm)], [zip_derived_cl10094])).
% 8.54/1.80
% 8.54/1.80 % SZS output end Refutation
% 8.54/1.80
% 8.54/1.80
% 8.54/1.80 % Terminating...
% 8.54/1.85 % Runner terminated.
% 8.54/1.86 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------