%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP327-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VZ84MC6KLO true
% Computer : n020.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 04:36:14 PM UTC 2025
% Result : Unsatisfiable 0.54s 0.94s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : GRP327-1 : TPTP v9.2.0. Released v2.5.0.
% 0.03/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.VZ84MC6KLO true
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 1 14:22:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.53/0.60 % Total configuration time : 435
% 0.53/0.60 % Estimated wc time : 1092
% 0.53/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.53/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.94 % Solved by fo/fo7.sh.
% 0.54/0.94 % done 531 iterations in 0.200s
% 0.54/0.94 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.54/0.94 % SZS output start Refutation
% 0.54/0.94 thf(sk_c3_type, type, sk_c3: $i).
% 0.54/0.94 thf(sk_c6_type, type, sk_c6: $i).
% 0.54/0.94 thf(sk_c5_type, type, sk_c5: $i).
% 0.54/0.94 thf(sk_c4_type, type, sk_c4: $i).
% 0.54/0.94 thf(identity_type, type, identity: $i).
% 0.54/0.94 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.54/0.94 thf(sk_c8_type, type, sk_c8: $i).
% 0.54/0.94 thf(inverse_type, type, inverse: $i > $i).
% 0.54/0.94 thf(sk_c1_type, type, sk_c1: $i).
% 0.54/0.94 thf(sk_c2_type, type, sk_c2: $i).
% 0.54/0.94 thf(sk_c7_type, type, sk_c7: $i).
% 0.54/0.94 thf(prove_this_32, conjecture,
% 0.54/0.94 (~( ( ( multiply @ X2 @ sk_c6 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c6 @ sk_c8 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.94 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ X5 @ sk_c8 ) != ( X4 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ X4 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ) ) ))).
% 0.54/0.94 thf(zf_stmt_0, negated_conjecture,
% 0.54/0.94 (( ( multiply @ X2 @ sk_c6 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c6 @ sk_c8 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c7 ) != ( sk_c6 ) ) |
% 0.54/0.94 ( ( inverse @ X5 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ X5 @ sk_c8 ) != ( X4 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ X4 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ X3 ) != ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ X3 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 0.54/0.94 thf(zip_derived_cl34, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X0 @ sk_c6) != (sk_c7))
% 0.54/0.94 | ((inverse @ X0) != (sk_c7))
% 0.54/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X1) != (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c6 @ sk_c8) != (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c7) != (sk_c6))
% 0.54/0.94 | ((inverse @ X2) != (sk_c8))
% 0.54/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.94 | ((inverse @ X4) != (sk_c7))
% 0.54/0.94 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c7 @ sk_c8) != (sk_c6)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.54/0.94 thf(zip_derived_cl35, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X0 @ (multiply @ sk_c7 @ sk_c8)) != (sk_c7))
% 0.54/0.94 | ((inverse @ X0) != (sk_c7))
% 0.54/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X1) != (sk_c8))
% 0.54/0.94 | ((multiply @ (multiply @ sk_c7 @ sk_c8) @ sk_c8) != (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c7) != (sk_c6))
% 0.54/0.94 | ((inverse @ X2) != (sk_c8))
% 0.54/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.94 | ((inverse @ X4) != (sk_c7))
% 0.54/0.94 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c7 @ sk_c8) != (sk_c6)))),
% 0.54/0.94 inference('local_rewriting', [status(thm)], [zip_derived_cl34])).
% 0.54/0.94 thf(prove_this_1, conjecture, (( multiply @ sk_c7 @ sk_c8 ) != ( sk_c6 ))).
% 0.54/0.94 thf(zf_stmt_1, negated_conjecture,
% 0.54/0.94 (( multiply @ sk_c7 @ sk_c8 ) = ( sk_c6 )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl36, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X0 @ (multiply @ sk_c7 @ sk_c8)) != (sk_c7))
% 0.54/0.94 | ((inverse @ X0) != (sk_c7))
% 0.54/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X1) != (sk_c8))
% 0.54/0.94 | ((multiply @ (multiply @ sk_c7 @ sk_c8) @ sk_c8) != (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c7) != (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ X2) != (sk_c8))
% 0.54/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.94 | ((inverse @ X4) != (sk_c7))
% 0.54/0.94 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c7 @ sk_c8) != (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl35, zip_derived_cl3, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl37, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X4) != (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.94 | ((inverse @ X2) != (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) != (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((multiply @ (multiply @ sk_c7 @ sk_c8) @ sk_c8) != (sk_c7))
% 0.54/0.94 | ((inverse @ X1) != (sk_c8))
% 0.54/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X0) != (sk_c7))
% 0.54/0.94 | ((multiply @ X0 @ (multiply @ sk_c7 @ sk_c8)) != (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl36])).
% 0.54/0.94 thf(zip_derived_cl38, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X4 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X4) != (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c8 @ X3) != (sk_c7))
% 0.54/0.94 | ((multiply @ X2 @ sk_c8) != (X3))
% 0.54/0.94 | ((inverse @ X2) != (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) != (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c7) @ sk_c8) != (sk_c7))
% 0.54/0.94 | ((inverse @ X1) != (sk_c8))
% 0.54/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 0.54/0.94 | ((inverse @ X0) != (sk_c7))
% 0.54/0.94 | ((multiply @ X0 @ (inverse @ sk_c7)) != (sk_c7)))),
% 0.54/0.94 inference('local_rewriting', [status(thm)], [zip_derived_cl37])).
% 0.54/0.94 thf(prove_this_26, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_2, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 0.54/0.94 thf(zip_derived_cl28, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl41, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl28, zip_derived_cl3])).
% 0.54/0.94 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(associativity, axiom,
% 0.54/0.94 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.54/0.94 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.54/0.94 thf(zip_derived_cl2, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.94 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.94 thf(zip_derived_cl65, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((multiply @ identity @ X0)
% 0.54/0.94 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.54/0.94 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl91, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl88, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl91, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl425, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl91])).
% 0.54/0.94 thf(zip_derived_cl445, plain,
% 0.54/0.94 ((((sk_c2) = (inverse @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl41, zip_derived_cl425])).
% 0.54/0.94 thf(prove_this_20, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 0.54/0.94 thf(zf_stmt_3, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 0.54/0.94 thf(zip_derived_cl22, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl56, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl22, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl702, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c3))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl445, zip_derived_cl56])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl715, plain,
% 0.54/0.94 ((((identity) = (sk_c3))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl702, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl716, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((identity) = (sk_c3)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl715])).
% 0.54/0.94 thf(prove_this_14, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_4, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 0.54/0.94 thf(zip_derived_cl16, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl55, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl724, plain,
% 0.54/0.94 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl55])).
% 0.54/0.94 thf(zip_derived_cl734, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl724])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl2532, plain,
% 0.54/0.94 ((((sk_c7) = (sk_c8)) | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl734, zip_derived_cl392])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl2547, plain,
% 0.54/0.94 ((((sk_c8) = (multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)))
% 0.54/0.94 | ((sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl2532, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl2659, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)) != (sk_c7))
% 0.54/0.94 | ((sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('eq_fact', [status(thm)], [zip_derived_cl2547])).
% 0.54/0.94 thf(prove_this_8, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_5, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 0.54/0.94 thf(zip_derived_cl10, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl39, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl10, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl425, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl91])).
% 0.54/0.94 thf(zip_derived_cl435, plain,
% 0.54/0.94 ((((sk_c1) = (inverse @ sk_c7))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl425])).
% 0.54/0.94 thf(prove_this_2, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_6, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 0.54/0.94 thf(zip_derived_cl4, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (sk_c6)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl53, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl4, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl622, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl435, zip_derived_cl53])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl629, plain,
% 0.54/0.94 ((((identity) = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl622, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl630, plain,
% 0.54/0.94 ((((inverse @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 0.54/0.94 | ((identity) = (sk_c8)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl629])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl778, plain,
% 0.54/0.94 ((((sk_c8) = (multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)))
% 0.54/0.94 | ((identity) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl630, zip_derived_cl80])).
% 0.54/0.94 thf(prove_this_12, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_7, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 0.54/0.94 thf(zip_derived_cl14, plain,
% 0.54/0.94 ((((inverse @ sk_c5) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl44, plain,
% 0.54/0.94 ((((multiply @ sk_c7 @ sk_c5) = (identity))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl93, plain,
% 0.54/0.94 ((((sk_c5) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl44, zip_derived_cl80])).
% 0.54/0.94 thf(prove_this_13, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_8, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 0.54/0.94 thf(zip_derived_cl15, plain,
% 0.54/0.94 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl54, plain,
% 0.54/0.94 ((((multiply @ sk_c5 @ (multiply @ sk_c7 @ sk_c8)) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl15, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl123, plain,
% 0.54/0.94 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @
% 0.54/0.94 (multiply @ sk_c7 @ sk_c8)) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl54])).
% 0.54/0.94 thf(zip_derived_cl2, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.94 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl126, plain,
% 0.54/0.94 ((((sk_c8) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl123, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.94 zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl127, plain,
% 0.54/0.94 ((((inverse @ sk_c1) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl126])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl128, plain,
% 0.54/0.94 ((((multiply @ sk_c7 @ sk_c1) = (identity)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl127, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl147, plain,
% 0.54/0.94 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.94 | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl128, zip_derived_cl80])).
% 0.54/0.94 thf(prove_this_30, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_9, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 0.54/0.94 thf(zip_derived_cl32, plain,
% 0.54/0.94 ((((inverse @ sk_c5) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.54/0.94 thf(prove_this_24, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 0.54/0.94 thf(zf_stmt_10, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 0.54/0.94 thf(zip_derived_cl26, plain,
% 0.54/0.94 ((((inverse @ sk_c5) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl104, plain,
% 0.54/0.94 ((((sk_c8) = (multiply @ (inverse @ sk_c2) @ sk_c3))
% 0.54/0.94 | ((inverse @ sk_c5) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl311, plain,
% 0.54/0.94 ((((sk_c8) = (multiply @ sk_c8 @ sk_c3))
% 0.54/0.94 | ((inverse @ sk_c5) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c5) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl104])).
% 0.54/0.94 thf(zip_derived_cl318, plain,
% 0.54/0.94 ((((inverse @ sk_c5) = (sk_c7)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c3)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl311])).
% 0.54/0.94 thf(prove_this_18, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_11, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c5 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 0.54/0.94 thf(zip_derived_cl20, plain,
% 0.54/0.94 ((((inverse @ sk_c5) = (sk_c7)) | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.54/0.94 thf(zip_derived_cl324, plain,
% 0.54/0.94 ((((sk_c8) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c5) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c5) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl318, zip_derived_cl20])).
% 0.54/0.94 thf(zip_derived_cl336, plain,
% 0.54/0.94 ((((inverse @ sk_c5) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl324])).
% 0.54/0.94 thf(zip_derived_cl91, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl338, plain,
% 0.54/0.94 ((((sk_c5) = (multiply @ (inverse @ sk_c7) @ identity))
% 0.54/0.94 | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl336, zip_derived_cl91])).
% 0.54/0.94 thf(prove_this_7, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_12, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 0.54/0.94 thf(zip_derived_cl9, plain,
% 0.54/0.94 ((((multiply @ sk_c5 @ sk_c6) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_12])).
% 0.54/0.94 thf(zip_derived_cl3, plain, (((multiply @ sk_c7 @ sk_c8) = (sk_c6))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.54/0.94 thf(zip_derived_cl264, plain,
% 0.54/0.94 ((((multiply @ sk_c5 @ (multiply @ sk_c7 @ sk_c8)) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl3])).
% 0.54/0.94 thf(zip_derived_cl346, plain,
% 0.54/0.94 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @
% 0.54/0.94 (multiply @ sk_c7 @ sk_c8)) = (sk_c7))
% 0.54/0.94 | ((sk_c8) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl338, zip_derived_cl264])).
% 0.54/0.94 thf(zip_derived_cl2, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.94 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl350, plain,
% 0.54/0.94 ((((sk_c8) = (sk_c7))
% 0.54/0.94 | ((sk_c8) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl346, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.94 zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl351, plain,
% 0.54/0.94 ((((multiply @ sk_c1 @ sk_c7) = (sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl350])).
% 0.54/0.94 thf(zip_derived_cl366, plain,
% 0.54/0.94 ((((multiply @ (multiply @ (inverse @ sk_c7) @ identity) @ sk_c7)
% 0.54/0.94 = (sk_c8))
% 0.54/0.94 | ((sk_c8) = (sk_c7))
% 0.54/0.94 | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl147, zip_derived_cl351])).
% 0.54/0.94 thf(zip_derived_cl2, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.94 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl367, plain,
% 0.54/0.94 ((((identity) = (sk_c8)) | ((sk_c8) = (sk_c7)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl366, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.94 zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl368, plain,
% 0.54/0.94 ((((sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl367])).
% 0.54/0.94 thf(zip_derived_cl860, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)) = (sk_c7))
% 0.54/0.94 | ((identity) = (sk_c8))
% 0.54/0.94 | ((identity) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl778, zip_derived_cl368])).
% 0.54/0.94 thf(zip_derived_cl869, plain,
% 0.54/0.94 ((((identity) = (sk_c8))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl860])).
% 0.54/0.94 thf(prove_this_28, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_13, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 0.54/0.94 thf(zip_derived_cl30, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_13])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl45, plain,
% 0.54/0.94 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl98, plain,
% 0.54/0.94 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl45, zip_derived_cl80])).
% 0.54/0.94 thf(prove_this_22, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 0.54/0.94 thf(zf_stmt_14, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 0.54/0.94 thf(zip_derived_cl24, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_14])).
% 0.54/0.94 thf(zip_derived_cl193, plain,
% 0.54/0.94 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.54/0.94 = (sk_c3))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl98, zip_derived_cl24])).
% 0.54/0.94 thf(zip_derived_cl2, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.94 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl203, plain,
% 0.54/0.94 ((((identity) = (sk_c3))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl193, zip_derived_cl2, zip_derived_cl0,
% 0.54/0.94 zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl204, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((identity) = (sk_c3)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl203])).
% 0.54/0.94 thf(prove_this_16, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_15, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 0.54/0.94 thf(zip_derived_cl18, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_15])).
% 0.54/0.94 thf(zip_derived_cl209, plain,
% 0.54/0.94 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c4) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl204, zip_derived_cl18])).
% 0.54/0.94 thf(zip_derived_cl214, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c8 @ identity) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl209])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl418, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl214, zip_derived_cl392])).
% 0.54/0.94 thf(zip_derived_cl425, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl91])).
% 0.54/0.94 thf(zip_derived_cl498, plain,
% 0.54/0.94 ((((sk_c4) = (inverse @ sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl418, zip_derived_cl425])).
% 0.54/0.94 thf(prove_this_29, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_16, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 0.54/0.94 thf(zip_derived_cl31, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_16])).
% 0.54/0.94 thf(zip_derived_cl425, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl91])).
% 0.54/0.94 thf(zip_derived_cl443, plain,
% 0.54/0.94 ((((sk_c2) = (inverse @ sk_c8)) | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl31, zip_derived_cl425])).
% 0.54/0.94 thf(prove_this_23, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) ) ))).
% 0.54/0.94 thf(zf_stmt_17, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c3 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 0.54/0.94 thf(zip_derived_cl25, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c2 @ sk_c8) = (sk_c3)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_17])).
% 0.54/0.94 thf(zip_derived_cl1265, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c8) @ sk_c8) = (sk_c3))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl443, zip_derived_cl25])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl1270, plain,
% 0.54/0.94 ((((identity) = (sk_c3))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl1265, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl1271, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((identity) = (sk_c3)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl1270])).
% 0.54/0.94 thf(prove_this_17, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_18, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c8 @ sk_c3 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 0.54/0.94 thf(zip_derived_cl19, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c8 @ sk_c3) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_18])).
% 0.54/0.94 thf(zip_derived_cl1275, plain,
% 0.54/0.94 ((((multiply @ sk_c8 @ identity) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl1271, zip_derived_cl19])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl1287, plain,
% 0.54/0.94 ((((sk_c8) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c4 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl1275, zip_derived_cl392])).
% 0.54/0.94 thf(zip_derived_cl1288, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl1287])).
% 0.54/0.94 thf(zip_derived_cl1327, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((sk_c8) = (sk_c7))
% 0.54/0.94 | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl498, zip_derived_cl1288])).
% 0.54/0.94 thf(zip_derived_cl1329, plain,
% 0.54/0.94 ((((sk_c8) = (sk_c7))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl1327])).
% 0.54/0.94 thf(zip_derived_cl1616, plain,
% 0.54/0.94 ((((multiply @ (inverse @ identity) @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)) = (sk_c7))
% 0.54/0.94 | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl869, zip_derived_cl1329])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl90, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl118, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl90, zip_derived_cl80])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl255, plain, (((inverse @ identity) = (identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl118, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl1621, plain,
% 0.54/0.94 ((((sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)) = (sk_c7))
% 0.54/0.94 | ((sk_c8) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl1616, zip_derived_cl255, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl1622, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c7) @ (inverse @ sk_c7)) = (sk_c7))
% 0.54/0.94 | ((sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl1621])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2694, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X4 @ sk_c7) != (sk_c7))
% 0.54/0.94 | ((inverse @ X4) != (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c7 @ X3) != (sk_c7))
% 0.54/0.94 | ((multiply @ X2 @ sk_c7) != (X3))
% 0.54/0.94 | ((inverse @ X2) != (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c7) != (multiply @ sk_c7 @ sk_c7))
% 0.54/0.94 | ((identity) != (sk_c7))
% 0.54/0.94 | ((inverse @ X1) != (sk_c7))
% 0.54/0.94 | ((multiply @ X1 @ sk_c7) != (sk_c7))
% 0.54/0.94 | ((inverse @ X0) != (sk_c7))
% 0.54/0.94 | ((multiply @ X0 @ (inverse @ sk_c7)) != (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl38, zip_derived_cl2678, zip_derived_cl2678,
% 0.54/0.94 zip_derived_cl2678, zip_derived_cl2678, zip_derived_cl2678,
% 0.54/0.94 zip_derived_cl2678, zip_derived_cl1, zip_derived_cl2678,
% 0.54/0.94 zip_derived_cl2678])).
% 0.54/0.94 thf(zip_derived_cl2695, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((multiply @ X4 @ identity) != (identity))
% 0.54/0.94 | ((inverse @ X4) != (identity))
% 0.54/0.94 | ((multiply @ identity @ X3) != (identity))
% 0.54/0.94 | ((multiply @ X2 @ identity) != (X3))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((inverse @ identity) != (multiply @ identity @ identity))
% 0.54/0.94 | ((identity) != (sk_c7))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((multiply @ X1 @ identity) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((multiply @ X0 @ (multiply @ identity @ identity)) != (identity)))),
% 0.54/0.94 inference('local_rewriting', [status(thm)], [zip_derived_cl2694])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl255, plain, (((inverse @ identity) = (identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl118, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl392, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl91, zip_derived_cl88])).
% 0.54/0.94 thf(zip_derived_cl2696, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((X4) != (identity))
% 0.54/0.94 | ((inverse @ X4) != (identity))
% 0.54/0.94 | ((X3) != (identity))
% 0.54/0.94 | ((X2) != (X3))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((identity) != (identity))
% 0.54/0.94 | ((identity) != (sk_c7))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X0) != (identity)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl2695, zip_derived_cl392, zip_derived_cl0,
% 0.54/0.94 zip_derived_cl392, zip_derived_cl255, zip_derived_cl0,
% 0.54/0.94 zip_derived_cl392, zip_derived_cl0, zip_derived_cl392])).
% 0.54/0.94 thf(zip_derived_cl2697, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((identity) != (sk_c7))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((X2) != (X3))
% 0.54/0.94 | ((X3) != (identity))
% 0.54/0.94 | ((inverse @ X4) != (identity))
% 0.54/0.94 | ((X4) != (identity)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl2696])).
% 0.54/0.94 thf(zip_derived_cl2801, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((identity) != (sk_c7))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((X2) != (identity))
% 0.54/0.94 | ((inverse @ X3) != (identity))
% 0.54/0.94 | ((X3) != (identity)))),
% 0.54/0.94 inference('eq_res', [status(thm)], [zip_derived_cl2697])).
% 0.54/0.94 thf(prove_this_10, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_19, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 0.54/0.94 thf(zip_derived_cl12, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_19])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl43, plain,
% 0.54/0.94 ((((multiply @ sk_c8 @ sk_c4) = (identity))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl80, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl94, plain,
% 0.54/0.94 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl43, zip_derived_cl80])).
% 0.54/0.94 thf(prove_this_11, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 0.54/0.94 thf(zf_stmt_20, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 0.54/0.94 thf(zip_derived_cl13, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_20])).
% 0.54/0.94 thf(zip_derived_cl132, plain,
% 0.54/0.94 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c7)
% 0.54/0.94 = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl94, zip_derived_cl13])).
% 0.54/0.94 thf(zip_derived_cl2, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.54/0.94 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.54/0.94 inference('cnf', [status(esa)], [associativity])).
% 0.54/0.94 thf(zip_derived_cl0, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_identity])).
% 0.54/0.94 thf(zip_derived_cl135, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7))
% 0.54/0.94 | ((inverse @ sk_c1) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl132, zip_derived_cl2, zip_derived_cl0])).
% 0.54/0.94 thf(zip_derived_cl136, plain,
% 0.54/0.94 ((((inverse @ sk_c1) = (sk_c7))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl135])).
% 0.54/0.94 thf(zip_derived_cl425, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl91])).
% 0.54/0.94 thf(zip_derived_cl937, plain,
% 0.54/0.94 ((((sk_c1) = (inverse @ sk_c7))
% 0.54/0.94 | ((multiply @ (inverse @ sk_c8) @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl136, zip_derived_cl425])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2763, plain,
% 0.54/0.94 ((((sk_c1) = (inverse @ sk_c7)) | ((identity) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl937, zip_derived_cl2678, zip_derived_cl1,
% 0.54/0.94 zip_derived_cl2678])).
% 0.54/0.94 thf(prove_this_4, conjecture,
% 0.54/0.94 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_21, negated_conjecture,
% 0.54/0.94 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 0.54/0.94 thf(zip_derived_cl6, plain,
% 0.54/0.94 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_21])).
% 0.54/0.94 thf(zip_derived_cl425, plain,
% 0.54/0.94 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl392, zip_derived_cl91])).
% 0.54/0.94 thf(zip_derived_cl437, plain,
% 0.54/0.94 ((((sk_c4) = (inverse @ sk_c8)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl425])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2745, plain,
% 0.54/0.94 ((((sk_c4) = (inverse @ sk_c7)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl437, zip_derived_cl2678, zip_derived_cl2678])).
% 0.54/0.94 thf(prove_this_5, conjecture,
% 0.54/0.94 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 0.54/0.94 thf(zf_stmt_22, negated_conjecture,
% 0.54/0.94 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 0.54/0.94 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c8 ) )),
% 0.54/0.94 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 0.54/0.94 thf(zip_derived_cl7, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c8)))),
% 0.54/0.94 inference('cnf', [status(esa)], [zf_stmt_22])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2678, plain, (((sk_c7) = (sk_c8))),
% 0.54/0.94 inference('clc', [status(thm)], [zip_derived_cl2659, zip_derived_cl1622])).
% 0.54/0.94 thf(zip_derived_cl2681, plain,
% 0.54/0.94 ((((multiply @ sk_c4 @ sk_c7) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl7, zip_derived_cl2678, zip_derived_cl2678])).
% 0.54/0.94 thf(zip_derived_cl3170, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl2745, zip_derived_cl2681])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl3172, plain,
% 0.54/0.94 ((((identity) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7))
% 0.54/0.94 | ((multiply @ sk_c1 @ sk_c7) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl3170, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl3173, plain,
% 0.54/0.94 ((((multiply @ sk_c1 @ sk_c7) = (sk_c7)) | ((identity) = (sk_c7)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3172])).
% 0.54/0.94 thf(zip_derived_cl3178, plain,
% 0.54/0.94 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c7))
% 0.54/0.94 | ((identity) = (sk_c7))
% 0.54/0.94 | ((identity) = (sk_c7)))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl2763, zip_derived_cl3173])).
% 0.54/0.94 thf(zip_derived_cl1, plain,
% 0.54/0.94 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.54/0.94 inference('cnf', [status(esa)], [left_inverse])).
% 0.54/0.94 thf(zip_derived_cl3183, plain,
% 0.54/0.94 ((((identity) = (sk_c7))
% 0.54/0.94 | ((identity) = (sk_c7))
% 0.54/0.94 | ((identity) = (sk_c7)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl3178, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl3184, plain, (((identity) = (sk_c7))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3183])).
% 0.54/0.94 thf(zip_derived_cl3244, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((identity) != (identity))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((X2) != (identity))
% 0.54/0.94 | ((inverse @ X3) != (identity))
% 0.54/0.94 | ((X3) != (identity)))),
% 0.54/0.94 inference('demod', [status(thm)],
% 0.54/0.94 [zip_derived_cl2801, zip_derived_cl3184])).
% 0.54/0.94 thf(zip_derived_cl3245, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.54/0.94 (((X3) != (identity))
% 0.54/0.94 | ((inverse @ X3) != (identity))
% 0.54/0.94 | ((X2) != (identity))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X0) != (identity)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3244])).
% 0.54/0.94 thf(zip_derived_cl3249, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((X2) != (identity))
% 0.54/0.94 | ((inverse @ identity) != (identity)))),
% 0.54/0.94 inference('eq_res', [status(thm)], [zip_derived_cl3245])).
% 0.54/0.94 thf(zip_derived_cl255, plain, (((inverse @ identity) = (identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl118, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl3250, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((X2) != (identity))
% 0.54/0.94 | ((identity) != (identity)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl3249, zip_derived_cl255])).
% 0.54/0.94 thf(zip_derived_cl3251, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.54/0.94 (((X2) != (identity))
% 0.54/0.94 | ((inverse @ X2) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X0) != (identity)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3250])).
% 0.54/0.94 thf(zip_derived_cl3252, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((inverse @ identity) != (identity)))),
% 0.54/0.94 inference('eq_res', [status(thm)], [zip_derived_cl3251])).
% 0.54/0.94 thf(zip_derived_cl255, plain, (((inverse @ identity) = (identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl118, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl3253, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X1) != (identity))
% 0.54/0.94 | ((identity) != (identity)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl3252, zip_derived_cl255])).
% 0.54/0.94 thf(zip_derived_cl3254, plain,
% 0.54/0.94 (![X0 : $i, X1 : $i]:
% 0.54/0.94 (((inverse @ X1) != (identity))
% 0.54/0.94 | ((X1) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((X0) != (identity)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3253])).
% 0.54/0.94 thf(zip_derived_cl3255, plain,
% 0.54/0.94 (![X0 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((inverse @ identity) != (identity)))),
% 0.54/0.94 inference('eq_res', [status(thm)], [zip_derived_cl3254])).
% 0.54/0.94 thf(zip_derived_cl255, plain, (((inverse @ identity) = (identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl118, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl3256, plain,
% 0.54/0.94 (![X0 : $i]:
% 0.54/0.94 (((X0) != (identity))
% 0.54/0.94 | ((inverse @ X0) != (identity))
% 0.54/0.94 | ((identity) != (identity)))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl3255, zip_derived_cl255])).
% 0.54/0.94 thf(zip_derived_cl3257, plain,
% 0.54/0.94 (![X0 : $i]: (((inverse @ X0) != (identity)) | ((X0) != (identity)))),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3256])).
% 0.54/0.94 thf(zip_derived_cl3258, plain, (((inverse @ identity) != (identity))),
% 0.54/0.94 inference('eq_res', [status(thm)], [zip_derived_cl3257])).
% 0.54/0.94 thf(zip_derived_cl255, plain, (((inverse @ identity) = (identity))),
% 0.54/0.94 inference('sup+', [status(thm)], [zip_derived_cl118, zip_derived_cl1])).
% 0.54/0.94 thf(zip_derived_cl3259, plain, (((identity) != (identity))),
% 0.54/0.94 inference('demod', [status(thm)], [zip_derived_cl3258, zip_derived_cl255])).
% 0.54/0.94 thf(zip_derived_cl3260, plain, ($false),
% 0.54/0.94 inference('simplify', [status(thm)], [zip_derived_cl3259])).
% 0.54/0.94
% 0.54/0.94 % SZS output end Refutation
% 0.54/0.94
% 0.54/0.94
% 0.54/0.94 % Terminating...
% 0.56/1.01 % Runner terminated.
% 1.69/1.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------