%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP251-1 : 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.eZwGDBKEoD true
% Computer : n027.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 04:36:05 PM UTC 2025
% Result : Unsatisfiable 6.25s 1.42s
% Output : Refutation 6.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : GRP251-1 : TPTP v9.2.0. Released v2.5.0.
% 0.08/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.eZwGDBKEoD true
% 0.10/0.30 % Computer : n027.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Oct 1 14:18:23 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.10/0.31 % Python version: Python 3.6.8
% 0.15/0.31 % Running in FO mode
% 0.39/0.55 % Total configuration time : 435
% 0.39/0.55 % Estimated wc time : 1092
% 0.39/0.55 % Estimated cpu time (7 cpus) : 156.0
% 0.43/0.66 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.43/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.43/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.43/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.43/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.43/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.43/0.67 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 6.25/1.42 % Solved by fo/fo7.sh.
% 6.25/1.42 % done 1300 iterations in 0.717s
% 6.25/1.42 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.25/1.42 % SZS output start Refutation
% 6.25/1.42 thf(sk_c7_type, type, sk_c7: $i).
% 6.25/1.42 thf(sk_c9_type, type, sk_c9: $i).
% 6.25/1.42 thf(sk_c2_type, type, sk_c2: $i).
% 6.25/1.42 thf(sk_c8_type, type, sk_c8: $i).
% 6.25/1.42 thf(sk_c5_type, type, sk_c5: $i).
% 6.25/1.42 thf(identity_type, type, identity: $i).
% 6.25/1.42 thf(multiply_type, type, multiply: $i > $i > $i).
% 6.25/1.42 thf(sk_c10_type, type, sk_c10: $i).
% 6.25/1.42 thf(inverse_type, type, inverse: $i > $i).
% 6.25/1.42 thf(sk_c4_type, type, sk_c4: $i).
% 6.25/1.42 thf(sk_c6_type, type, sk_c6: $i).
% 6.25/1.42 thf(sk_c1_type, type, sk_c1: $i).
% 6.25/1.42 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(associativity, axiom,
% 6.25/1.42 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 6.25/1.42 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 6.25/1.42 thf(zip_derived_cl2, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.25/1.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.25/1.42 inference('cnf', [status(esa)], [associativity])).
% 6.25/1.42 thf(zip_derived_cl117, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((multiply @ identity @ X0)
% 6.25/1.42 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 6.25/1.42 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 6.25/1.42 thf(zip_derived_cl0, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_identity])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl165, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl149])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl162, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl149, zip_derived_cl149])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl165, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl149])).
% 6.25/1.42 thf(zip_derived_cl1770, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1712, zip_derived_cl165])).
% 6.25/1.42 thf(prove_this_43, conjecture,
% 6.25/1.42 (~( ( ( inverse @ X7 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ X7 @ sk_c9 ) != ( X3 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c9 @ X3 ) != ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 6.25/1.42 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 6.25/1.42 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ X6 @ sk_c8 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ X6 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ X5 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ X5 @ sk_c9 ) != ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 6.25/1.42 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_0, negated_conjecture,
% 6.25/1.42 (( ( inverse @ X7 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ X7 @ sk_c9 ) != ( X3 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c9 @ X3 ) != ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ X2 ) != ( sk_c8 ) ) |
% 6.25/1.42 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 6.25/1.42 ( ( multiply @ X1 @ sk_c10 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ X6 @ sk_c8 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ X6 ) != ( sk_c9 ) ) | ( ( inverse @ X5 ) != ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ X5 @ sk_c9 ) != ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 6.25/1.42 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 6.25/1.42 thf(zip_derived_cl45, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.25/1.42 (((inverse @ X0) != (sk_c9))
% 6.25/1.42 | ((multiply @ X0 @ sk_c9) != (X1))
% 6.25/1.42 | ((multiply @ sk_c9 @ X1) != (sk_c8))
% 6.25/1.42 | ((inverse @ X2) != (sk_c8))
% 6.25/1.42 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c9))
% 6.25/1.42 | ((inverse @ X5) != (sk_c9))
% 6.25/1.42 | ((multiply @ X5 @ sk_c9) != (sk_c8))
% 6.25/1.42 | ((inverse @ X6) != (sk_c10))
% 6.25/1.42 | ((multiply @ X6 @ sk_c10) != (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_0])).
% 6.25/1.42 thf(zip_derived_cl1780, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.25/1.42 (((X0) != (sk_c9))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X2 @ sk_c9) != (sk_c8))
% 6.25/1.42 | ((inverse @ X2) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c10))
% 6.25/1.42 | ((multiply @ X5 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X5) != (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c9 @ X6) != (sk_c8))
% 6.25/1.42 | ((multiply @ (inverse @ X0) @ sk_c9) != (X6)))),
% 6.25/1.42 inference('sup-', [status(thm)], [zip_derived_cl1770, zip_derived_cl45])).
% 6.25/1.42 thf(zip_derived_cl1921, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.25/1.42 (((multiply @ (inverse @ sk_c9) @ sk_c9) != (X0))
% 6.25/1.42 | ((multiply @ sk_c9 @ X0) != (sk_c8))
% 6.25/1.42 | ((inverse @ X1) != (sk_c8))
% 6.25/1.42 | ((multiply @ X1 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X2) != (sk_c10))
% 6.25/1.42 | ((multiply @ X2 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c9))
% 6.25/1.42 | ((multiply @ X4 @ sk_c9) != (sk_c8))
% 6.25/1.42 | ((inverse @ X5) != (sk_c10))
% 6.25/1.42 | ((multiply @ X5 @ sk_c10) != (sk_c9)))),
% 6.25/1.42 inference('eq_res', [status(thm)], [zip_derived_cl1780])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl1922, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.25/1.42 (((identity) != (X0))
% 6.25/1.42 | ((multiply @ sk_c9 @ X0) != (sk_c8))
% 6.25/1.42 | ((inverse @ X1) != (sk_c8))
% 6.25/1.42 | ((multiply @ X1 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X2) != (sk_c10))
% 6.25/1.42 | ((multiply @ X2 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c9))
% 6.25/1.42 | ((multiply @ X4 @ sk_c9) != (sk_c8))
% 6.25/1.42 | ((inverse @ X5) != (sk_c10))
% 6.25/1.42 | ((multiply @ X5 @ sk_c10) != (sk_c9)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl1921, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl1923, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 6.25/1.42 | ((inverse @ X1) != (sk_c9))
% 6.25/1.42 | ((inverse @ X2) != (sk_c9))
% 6.25/1.42 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c9 @ identity) != (sk_c8)))),
% 6.25/1.42 inference('eq_res', [status(thm)], [zip_derived_cl1922])).
% 6.25/1.42 thf(zip_derived_cl1924, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c9) != (multiply @ sk_c9 @ identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c9))
% 6.25/1.42 | ((inverse @ X2) != (sk_c9))
% 6.25/1.42 | ((multiply @ X2 @ (multiply @ sk_c9 @ identity)) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X4 @ (multiply @ sk_c9 @ identity)) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (multiply @ sk_c9 @ identity))
% 6.25/1.42 | ((multiply @ sk_c9 @ identity) != (sk_c8)))),
% 6.25/1.42 inference('local_rewriting', [status(thm)], [zip_derived_cl1923])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1925, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c9) != (sk_c9))
% 6.25/1.42 | ((inverse @ X1) != (sk_c9))
% 6.25/1.42 | ((inverse @ X2) != (sk_c9))
% 6.25/1.42 | ((multiply @ X2 @ sk_c9) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X4 @ sk_c9) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c9))
% 6.25/1.42 | ((sk_c9) != (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl1924, zip_derived_cl1712, zip_derived_cl1712,
% 6.25/1.42 zip_derived_cl1712, zip_derived_cl1712, zip_derived_cl1712])).
% 6.25/1.42 thf(prove_this_28, conjecture,
% 6.25/1.42 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_1, negated_conjecture,
% 6.25/1.42 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_28])).
% 6.25/1.42 thf(zip_derived_cl30, plain,
% 6.25/1.42 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_1])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl67, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 6.25/1.42 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl30, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl175, plain,
% 6.25/1.42 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 6.25/1.42 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl67, zip_derived_cl149])).
% 6.25/1.42 thf(prove_this_21, conjecture,
% 6.25/1.42 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.25/1.42 thf(zf_stmt_2, negated_conjecture,
% 6.25/1.42 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 6.25/1.42 thf(zip_derived_cl23, plain,
% 6.25/1.42 ((((inverse @ sk_c6) = (sk_c9)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_2])).
% 6.25/1.42 thf(zip_derived_cl777, plain,
% 6.25/1.42 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 6.25/1.42 = (sk_c8))
% 6.25/1.42 | ((inverse @ sk_c6) = (sk_c9))
% 6.25/1.42 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl175, zip_derived_cl23])).
% 6.25/1.42 thf(zip_derived_cl2, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.25/1.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.25/1.42 inference('cnf', [status(esa)], [associativity])).
% 6.25/1.42 thf(zip_derived_cl0, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_identity])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl794, plain,
% 6.25/1.42 ((((identity) = (sk_c8))
% 6.25/1.42 | ((inverse @ sk_c6) = (sk_c9))
% 6.25/1.42 | ((inverse @ sk_c6) = (sk_c9)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl777, zip_derived_cl2, zip_derived_cl0,
% 6.25/1.42 zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl795, plain,
% 6.25/1.42 ((((inverse @ sk_c6) = (sk_c9)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl794])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl798, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ sk_c6) = (identity)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl795, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl854, plain,
% 6.25/1.42 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity))
% 6.25/1.42 | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl798, zip_derived_cl149])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1760, plain,
% 6.25/1.42 ((((sk_c6) = (inverse @ sk_c9)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl854, zip_derived_cl1712])).
% 6.25/1.42 thf(prove_this_27, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_3, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 6.25/1.42 thf(zip_derived_cl29, plain,
% 6.25/1.42 ((((multiply @ sk_c6 @ sk_c9) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_3])).
% 6.25/1.42 thf(zip_derived_cl1770, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1712, zip_derived_cl165])).
% 6.25/1.42 thf(zip_derived_cl1798, plain,
% 6.25/1.42 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c6 @ sk_c9) = (sk_c7)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl1770])).
% 6.25/1.42 thf(prove_this_20, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.25/1.42 thf(zf_stmt_4, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 6.25/1.42 thf(zip_derived_cl22, plain,
% 6.25/1.42 ((((multiply @ sk_c6 @ sk_c9) = (sk_c7))
% 6.25/1.42 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_4])).
% 6.25/1.42 thf(zip_derived_cl2785, plain,
% 6.25/1.42 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7))
% 6.25/1.42 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1798, zip_derived_cl22])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl2805, plain,
% 6.25/1.42 ((((identity) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7))
% 6.25/1.42 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl2785, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl2806, plain,
% 6.25/1.42 ((((multiply @ sk_c6 @ sk_c9) = (sk_c7)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl2805])).
% 6.25/1.42 thf(zip_derived_cl3252, plain,
% 6.25/1.42 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c7))
% 6.25/1.42 | ((identity) = (sk_c8))
% 6.25/1.42 | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1760, zip_derived_cl2806])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl3257, plain,
% 6.25/1.42 ((((identity) = (sk_c7))
% 6.25/1.42 | ((identity) = (sk_c8))
% 6.25/1.42 | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl3252, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl3258, plain,
% 6.25/1.42 ((((identity) = (sk_c8)) | ((identity) = (sk_c7)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl3257])).
% 6.25/1.42 thf(prove_this_26, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c9 @ sk_c7 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_5, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c9 @ sk_c7 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 6.25/1.42 thf(zip_derived_cl28, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_5])).
% 6.25/1.42 thf(zip_derived_cl1770, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1712, zip_derived_cl165])).
% 6.25/1.42 thf(zip_derived_cl1797, plain,
% 6.25/1.42 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c9 @ sk_c7) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl1770])).
% 6.25/1.42 thf(prove_this_19, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c9 @ sk_c7 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.25/1.42 thf(zf_stmt_6, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c9 @ sk_c7 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 6.25/1.42 thf(zip_derived_cl21, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ sk_c7) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_6])).
% 6.25/1.42 thf(zip_derived_cl2741, plain,
% 6.25/1.42 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c9 @ sk_c7) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c9 @ sk_c7) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1797, zip_derived_cl21])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl2761, plain,
% 6.25/1.42 ((((identity) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c9 @ sk_c7) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c9 @ sk_c7) = (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl2741, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl2762, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ sk_c7) = (sk_c8)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl2761])).
% 6.25/1.42 thf(zip_derived_cl3275, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ identity) = (sk_c8))
% 6.25/1.42 | ((identity) = (sk_c8))
% 6.25/1.42 | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl3258, zip_derived_cl2762])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl3286, plain,
% 6.25/1.42 ((((sk_c9) = (sk_c8)) | ((identity) = (sk_c8)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl3275, zip_derived_cl1712])).
% 6.25/1.42 thf(zip_derived_cl3287, plain,
% 6.25/1.42 ((((identity) = (sk_c8)) | ((sk_c9) = (sk_c8)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl3286])).
% 6.25/1.42 thf(zip_derived_cl3319, plain,
% 6.25/1.42 ((((sk_c9) != (identity)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('eq_fact', [status(thm)], [zip_derived_cl3287])).
% 6.25/1.42 thf(prove_this_25, conjecture,
% 6.25/1.42 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_7, negated_conjecture,
% 6.25/1.42 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 6.25/1.42 thf(zip_derived_cl27, plain,
% 6.25/1.42 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_7])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl52, plain,
% 6.25/1.42 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 6.25/1.42 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl173, plain,
% 6.25/1.42 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 6.25/1.42 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl52, zip_derived_cl149])).
% 6.25/1.42 thf(prove_this_18, conjecture,
% 6.25/1.42 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.25/1.42 thf(zf_stmt_8, negated_conjecture,
% 6.25/1.42 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 6.25/1.42 thf(zip_derived_cl20, plain,
% 6.25/1.42 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_8])).
% 6.25/1.42 thf(zip_derived_cl315, plain,
% 6.25/1.42 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 6.25/1.42 = (sk_c8))
% 6.25/1.42 | ((inverse @ sk_c5) = (sk_c8))
% 6.25/1.42 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl173, zip_derived_cl20])).
% 6.25/1.42 thf(zip_derived_cl2, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.25/1.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.25/1.42 inference('cnf', [status(esa)], [associativity])).
% 6.25/1.42 thf(zip_derived_cl0, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_identity])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl332, plain,
% 6.25/1.42 ((((identity) = (sk_c8))
% 6.25/1.42 | ((inverse @ sk_c5) = (sk_c8))
% 6.25/1.42 | ((inverse @ sk_c5) = (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl315, zip_derived_cl2, zip_derived_cl0,
% 6.25/1.42 zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl333, plain,
% 6.25/1.42 ((((inverse @ sk_c5) = (sk_c8)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl332])).
% 6.25/1.42 thf(prove_this_24, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_9, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 6.25/1.42 thf(zip_derived_cl26, plain,
% 6.25/1.42 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_9])).
% 6.25/1.42 thf(zip_derived_cl1770, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1712, zip_derived_cl165])).
% 6.25/1.42 thf(zip_derived_cl1795, plain,
% 6.25/1.42 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1770])).
% 6.25/1.42 thf(prove_this_17, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 6.25/1.42 thf(zf_stmt_10, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 6.25/1.42 thf(zip_derived_cl19, plain,
% 6.25/1.42 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_10])).
% 6.25/1.42 thf(zip_derived_cl2696, plain,
% 6.25/1.42 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1795, zip_derived_cl19])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl2716, plain,
% 6.25/1.42 ((((identity) = (sk_c8))
% 6.25/1.42 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl2696, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl2717, plain,
% 6.25/1.42 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl2716])).
% 6.25/1.42 thf(zip_derived_cl2830, plain,
% 6.25/1.42 ((((multiply @ sk_c5 @ (inverse @ sk_c5)) = (sk_c9))
% 6.25/1.42 | ((identity) = (sk_c8))
% 6.25/1.42 | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl2717])).
% 6.25/1.42 thf(zip_derived_cl1770, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1712, zip_derived_cl165])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl1779, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1770, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl2847, plain,
% 6.25/1.42 ((((identity) = (sk_c9))
% 6.25/1.42 | ((identity) = (sk_c8))
% 6.25/1.42 | ((identity) = (sk_c8)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl2830, zip_derived_cl1779])).
% 6.25/1.42 thf(zip_derived_cl2848, plain,
% 6.25/1.42 ((((identity) = (sk_c8)) | ((identity) = (sk_c9)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl2847])).
% 6.25/1.42 thf(zip_derived_cl3328, plain, (((identity) = (sk_c8))),
% 6.25/1.42 inference('clc', [status(thm)], [zip_derived_cl3319, zip_derived_cl2848])).
% 6.25/1.42 thf(zip_derived_cl3385, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c9) != (sk_c9))
% 6.25/1.42 | ((inverse @ X1) != (sk_c9))
% 6.25/1.42 | ((inverse @ X2) != (sk_c9))
% 6.25/1.42 | ((multiply @ X2 @ sk_c9) != (sk_c9))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (sk_c9))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X4 @ sk_c9) != (sk_c9))
% 6.25/1.42 | ((inverse @ X4) != (sk_c9))
% 6.25/1.42 | ((sk_c9) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl1925, zip_derived_cl3328])).
% 6.25/1.42 thf(zip_derived_cl3386, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ identity) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((multiply @ X2 @ identity) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X4 @ identity) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (identity))
% 6.25/1.42 | ((sk_c9) != (identity)))),
% 6.25/1.42 inference('local_rewriting', [status(thm)], [zip_derived_cl3385])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl1712, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl162])).
% 6.25/1.42 thf(zip_derived_cl3387, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((X4) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (identity))
% 6.25/1.42 | ((sk_c9) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl3386, zip_derived_cl1712, zip_derived_cl1712,
% 6.25/1.42 zip_derived_cl1712])).
% 6.25/1.42 thf(prove_this_9, conjecture,
% 6.25/1.42 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 6.25/1.42 thf(zf_stmt_11, negated_conjecture,
% 6.25/1.42 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 6.25/1.42 thf(zip_derived_cl11, plain,
% 6.25/1.42 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_11])).
% 6.25/1.42 thf(zip_derived_cl11, plain,
% 6.25/1.42 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_11])).
% 6.25/1.42 thf(zip_derived_cl1779, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1770, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl2400, plain,
% 6.25/1.42 ((((multiply @ sk_c4 @ sk_c10) = (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1779])).
% 6.25/1.42 thf(zip_derived_cl11, plain,
% 6.25/1.42 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_11])).
% 6.25/1.42 thf(zip_derived_cl11, plain,
% 6.25/1.42 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_11])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl48, plain,
% 6.25/1.42 ((((multiply @ sk_c10 @ sk_c4) = (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl167, plain,
% 6.25/1.42 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl149])).
% 6.25/1.42 thf(prove_this_8, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 6.25/1.42 thf(zf_stmt_12, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 6.25/1.42 thf(zip_derived_cl10, plain,
% 6.25/1.42 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_12])).
% 6.25/1.42 thf(zip_derived_cl221, plain,
% 6.25/1.42 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 6.25/1.42 = (sk_c9))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl167, zip_derived_cl10])).
% 6.25/1.42 thf(zip_derived_cl2, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.25/1.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.25/1.42 inference('cnf', [status(esa)], [associativity])).
% 6.25/1.42 thf(zip_derived_cl0, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_identity])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl226, plain,
% 6.25/1.42 ((((identity) = (sk_c9))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl221, zip_derived_cl2, zip_derived_cl0,
% 6.25/1.42 zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl227, plain,
% 6.25/1.42 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl226])).
% 6.25/1.42 thf(zip_derived_cl3387, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((X4) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (identity))
% 6.25/1.42 | ((sk_c9) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl3386, zip_derived_cl1712, zip_derived_cl1712,
% 6.25/1.42 zip_derived_cl1712])).
% 6.25/1.42 thf(zip_derived_cl3397, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((identity) != (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (identity))
% 6.25/1.42 | ((X3) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (sk_c10))
% 6.25/1.42 | ((multiply @ X4 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('sup-', [status(thm)], [zip_derived_cl227, zip_derived_cl3387])).
% 6.25/1.42 thf(zip_derived_cl3399, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X4 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (sk_c10))
% 6.25/1.42 | ((X3) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl3397])).
% 6.25/1.42 thf(zip_derived_cl6800, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.25/1.42 (((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((inverse @ identity) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('eq_res', [status(thm)], [zip_derived_cl3399])).
% 6.25/1.42 thf(zip_derived_cl0, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_identity])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl164, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl149])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl217, plain,
% 6.25/1.42 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl164, zip_derived_cl149])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl1178, plain, (((inverse @ identity) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl6801, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.25/1.42 (((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((identity) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((multiply @ X3 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl6800, zip_derived_cl1178])).
% 6.25/1.42 thf(zip_derived_cl6802, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.25/1.42 (((multiply @ X3 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (sk_c10))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl6801])).
% 6.25/1.42 thf(zip_derived_cl6803, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 (((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ identity) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (sk_c10))
% 6.25/1.42 | ((multiply @ X2 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('eq_res', [status(thm)], [zip_derived_cl6802])).
% 6.25/1.42 thf(zip_derived_cl1178, plain, (((inverse @ identity) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl6804, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 (((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((identity) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (sk_c10))
% 6.25/1.42 | ((multiply @ X2 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl6803, zip_derived_cl1178])).
% 6.25/1.42 thf(zip_derived_cl6805, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 (((multiply @ X2 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((X0) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl6804])).
% 6.25/1.42 thf(zip_derived_cl6806, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 (((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ identity) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('eq_res', [status(thm)], [zip_derived_cl6805])).
% 6.25/1.42 thf(zip_derived_cl1178, plain, (((inverse @ identity) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl6807, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 (((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((identity) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X1 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl6806, zip_derived_cl1178])).
% 6.25/1.42 thf(zip_derived_cl6808, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 (((multiply @ X1 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (sk_c10))
% 6.25/1.42 | ((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl6807])).
% 6.25/1.42 thf(zip_derived_cl6822, plain,
% 6.25/1.42 (![X0 : $i]:
% 6.25/1.42 (((sk_c10) != (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((multiply @ sk_c4 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl6808])).
% 6.25/1.42 thf(zip_derived_cl6869, plain,
% 6.25/1.42 (![X0 : $i]:
% 6.25/1.42 (((multiply @ sk_c4 @ sk_c10) != (identity))
% 6.25/1.42 | ((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl6822])).
% 6.25/1.42 thf(zip_derived_cl6909, plain,
% 6.25/1.42 (![X0 : $i]:
% 6.25/1.42 (((identity) != (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((multiply @ X0 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('sup-', [status(thm)], [zip_derived_cl2400, zip_derived_cl6869])).
% 6.25/1.42 thf(zip_derived_cl6919, plain,
% 6.25/1.42 (![X0 : $i]:
% 6.25/1.42 (((multiply @ X0 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl6909])).
% 6.25/1.42 thf(zip_derived_cl6943, plain,
% 6.25/1.42 ((((sk_c10) != (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10))
% 6.25/1.42 | ((multiply @ sk_c4 @ sk_c10) != (identity)))),
% 6.25/1.42 inference('sup-', [status(thm)], [zip_derived_cl11, zip_derived_cl6919])).
% 6.25/1.42 thf(zip_derived_cl6990, plain,
% 6.25/1.42 ((((multiply @ sk_c4 @ sk_c10) != (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl6943])).
% 6.25/1.42 thf(zip_derived_cl2400, plain,
% 6.25/1.42 ((((multiply @ sk_c4 @ sk_c10) = (identity))
% 6.25/1.42 | ((inverse @ sk_c1) = (sk_c10)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1779])).
% 6.25/1.42 thf(zip_derived_cl7027, plain, (((inverse @ sk_c1) = (sk_c10))),
% 6.25/1.42 inference('clc', [status(thm)], [zip_derived_cl6990, zip_derived_cl2400])).
% 6.25/1.42 thf(zip_derived_cl7027, plain, (((inverse @ sk_c1) = (sk_c10))),
% 6.25/1.42 inference('clc', [status(thm)], [zip_derived_cl6990, zip_derived_cl2400])).
% 6.25/1.42 thf(zip_derived_cl7027, plain, (((inverse @ sk_c1) = (sk_c10))),
% 6.25/1.42 inference('clc', [status(thm)], [zip_derived_cl6990, zip_derived_cl2400])).
% 6.25/1.42 thf(zip_derived_cl7027, plain, (((inverse @ sk_c1) = (sk_c10))),
% 6.25/1.42 inference('clc', [status(thm)], [zip_derived_cl6990, zip_derived_cl2400])).
% 6.25/1.42 thf(zip_derived_cl7077, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (inverse @ sk_c1))
% 6.25/1.42 | ((X4) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (identity))
% 6.25/1.42 | ((sk_c9) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl3387, zip_derived_cl7027, zip_derived_cl7027,
% 6.25/1.42 zip_derived_cl7027, zip_derived_cl7027])).
% 6.25/1.42 thf(prove_this_2, conjecture,
% 6.25/1.42 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_13, negated_conjecture,
% 6.25/1.42 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 6.25/1.42 thf(zip_derived_cl4, plain,
% 6.25/1.42 ((((inverse @ sk_c4) = (sk_c10))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_13])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl58, plain,
% 6.25/1.42 ((((multiply @ sk_c10 @ sk_c4) = (identity))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl149, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i]:
% 6.25/1.42 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.25/1.42 inference('demod', [status(thm)], [zip_derived_cl117, zip_derived_cl0])).
% 6.25/1.42 thf(zip_derived_cl168, plain,
% 6.25/1.42 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl149])).
% 6.25/1.42 thf(prove_this_1, conjecture,
% 6.25/1.42 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 6.25/1.42 thf(zf_stmt_14, negated_conjecture,
% 6.25/1.42 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 6.25/1.42 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) )),
% 6.25/1.42 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 6.25/1.42 thf(zip_derived_cl3, plain,
% 6.25/1.42 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 6.25/1.42 inference('cnf', [status(esa)], [zf_stmt_14])).
% 6.25/1.42 thf(zip_derived_cl430, plain,
% 6.25/1.42 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 6.25/1.42 = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl168, zip_derived_cl3])).
% 6.25/1.42 thf(zip_derived_cl2, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.42 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.25/1.42 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.25/1.42 inference('cnf', [status(esa)], [associativity])).
% 6.25/1.42 thf(zip_derived_cl0, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_identity])).
% 6.25/1.42 thf(zip_derived_cl1, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.25/1.42 inference('cnf', [status(esa)], [left_inverse])).
% 6.25/1.42 thf(zip_derived_cl436, plain,
% 6.25/1.42 ((((identity) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9))
% 6.25/1.42 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl430, zip_derived_cl2, zip_derived_cl0,
% 6.25/1.42 zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl437, plain,
% 6.25/1.42 ((((multiply @ sk_c1 @ sk_c10) = (sk_c9)) | ((identity) = (sk_c9)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl436])).
% 6.25/1.42 thf(zip_derived_cl7027, plain, (((inverse @ sk_c1) = (sk_c10))),
% 6.25/1.42 inference('clc', [status(thm)], [zip_derived_cl6990, zip_derived_cl2400])).
% 6.25/1.42 thf(zip_derived_cl1779, plain,
% 6.25/1.42 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl1770, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl7044, plain,
% 6.25/1.42 ((((identity) = (sk_c9)) | ((identity) = (sk_c9)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl437, zip_derived_cl7027, zip_derived_cl1779])).
% 6.25/1.42 thf(zip_derived_cl7045, plain, (((identity) = (sk_c9))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl7044])).
% 6.25/1.42 thf(zip_derived_cl7176, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (inverse @ sk_c1))
% 6.25/1.42 | ((X4) != (identity))
% 6.25/1.42 | ((inverse @ X4) != (identity))
% 6.25/1.42 | ((identity) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl7077, zip_derived_cl7045])).
% 6.25/1.42 thf(zip_derived_cl7177, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.25/1.42 (((inverse @ X4) != (identity))
% 6.25/1.42 | ((X4) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (inverse @ sk_c1))
% 6.25/1.42 | ((multiply @ X3 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.42 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 6.25/1.42 inference('simplify', [status(thm)], [zip_derived_cl7176])).
% 6.25/1.42 thf(zip_derived_cl7178, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.25/1.42 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (inverse @ sk_c1))
% 6.25/1.42 | ((inverse @ identity) != (identity)))),
% 6.25/1.42 inference('eq_res', [status(thm)], [zip_derived_cl7177])).
% 6.25/1.42 thf(zip_derived_cl1178, plain, (((inverse @ identity) = (identity))),
% 6.25/1.42 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl1])).
% 6.25/1.42 thf(zip_derived_cl7179, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.25/1.42 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.42 | ((X1) != (identity))
% 6.25/1.42 | ((inverse @ X1) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((multiply @ X3 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((inverse @ X3) != (inverse @ sk_c1))
% 6.25/1.42 | ((identity) != (identity)))),
% 6.25/1.42 inference('demod', [status(thm)],
% 6.25/1.42 [zip_derived_cl7178, zip_derived_cl1178])).
% 6.25/1.42 thf(zip_derived_cl7180, plain,
% 6.25/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.25/1.42 (((inverse @ X3) != (inverse @ sk_c1))
% 6.25/1.42 | ((multiply @ X3 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.42 | ((X2) != (identity))
% 6.25/1.42 | ((inverse @ X2) != (identity))
% 6.25/1.43 | ((inverse @ X1) != (identity))
% 6.25/1.43 | ((X1) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 6.25/1.43 inference('simplify', [status(thm)], [zip_derived_cl7179])).
% 6.25/1.43 thf(zip_derived_cl7181, plain,
% 6.25/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.43 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((X1) != (identity))
% 6.25/1.43 | ((inverse @ X1) != (identity))
% 6.25/1.43 | ((inverse @ identity) != (identity))
% 6.25/1.43 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X2) != (inverse @ sk_c1)))),
% 6.25/1.43 inference('eq_res', [status(thm)], [zip_derived_cl7180])).
% 6.25/1.43 thf(zip_derived_cl1178, plain, (((inverse @ identity) = (identity))),
% 6.25/1.43 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl1])).
% 6.25/1.43 thf(zip_derived_cl7182, plain,
% 6.25/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.43 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((X1) != (identity))
% 6.25/1.43 | ((inverse @ X1) != (identity))
% 6.25/1.43 | ((identity) != (identity))
% 6.25/1.43 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X2) != (inverse @ sk_c1)))),
% 6.25/1.43 inference('demod', [status(thm)],
% 6.25/1.43 [zip_derived_cl7181, zip_derived_cl1178])).
% 6.25/1.43 thf(zip_derived_cl7183, plain,
% 6.25/1.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.25/1.43 (((inverse @ X2) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ X2 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X1) != (identity))
% 6.25/1.43 | ((X1) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 6.25/1.43 inference('simplify', [status(thm)], [zip_derived_cl7182])).
% 6.25/1.43 thf(zip_derived_cl7184, plain,
% 6.25/1.43 (![X0 : $i, X1 : $i]:
% 6.25/1.43 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((inverse @ identity) != (identity))
% 6.25/1.43 | ((multiply @ X1 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X1) != (inverse @ sk_c1)))),
% 6.25/1.43 inference('eq_res', [status(thm)], [zip_derived_cl7183])).
% 6.25/1.43 thf(zip_derived_cl1178, plain, (((inverse @ identity) = (identity))),
% 6.25/1.43 inference('sup+', [status(thm)], [zip_derived_cl217, zip_derived_cl1])).
% 6.25/1.43 thf(zip_derived_cl7185, plain,
% 6.25/1.43 (![X0 : $i, X1 : $i]:
% 6.25/1.43 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((identity) != (identity))
% 6.25/1.43 | ((multiply @ X1 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X1) != (inverse @ sk_c1)))),
% 6.25/1.43 inference('demod', [status(thm)],
% 6.25/1.43 [zip_derived_cl7184, zip_derived_cl1178])).
% 6.25/1.43 thf(zip_derived_cl7186, plain,
% 6.25/1.43 (![X0 : $i, X1 : $i]:
% 6.25/1.43 (((inverse @ X1) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ X1 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 6.25/1.43 inference('simplify', [status(thm)], [zip_derived_cl7185])).
% 6.25/1.43 thf(zip_derived_cl7190, plain,
% 6.25/1.43 (![X0 : $i]:
% 6.25/1.43 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ sk_c1 @ (inverse @ sk_c1)) != (identity)))),
% 6.25/1.43 inference('eq_res', [status(thm)], [zip_derived_cl7186])).
% 6.25/1.43 thf(zip_derived_cl1779, plain,
% 6.25/1.43 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.25/1.43 inference('sup+', [status(thm)], [zip_derived_cl1770, zip_derived_cl1])).
% 6.25/1.43 thf(zip_derived_cl7191, plain,
% 6.25/1.43 (![X0 : $i]:
% 6.25/1.43 (((multiply @ X0 @ (inverse @ sk_c1)) != (identity))
% 6.25/1.43 | ((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((identity) != (identity)))),
% 6.25/1.43 inference('demod', [status(thm)],
% 6.25/1.43 [zip_derived_cl7190, zip_derived_cl1779])).
% 6.25/1.43 thf(zip_derived_cl7192, plain,
% 6.25/1.43 (![X0 : $i]:
% 6.25/1.43 (((inverse @ X0) != (inverse @ sk_c1))
% 6.25/1.43 | ((multiply @ X0 @ (inverse @ sk_c1)) != (identity)))),
% 6.25/1.43 inference('simplify', [status(thm)], [zip_derived_cl7191])).
% 6.25/1.43 thf(zip_derived_cl7198, plain,
% 6.25/1.43 (((multiply @ sk_c1 @ (inverse @ sk_c1)) != (identity))),
% 6.25/1.43 inference('eq_res', [status(thm)], [zip_derived_cl7192])).
% 6.25/1.43 thf(zip_derived_cl1779, plain,
% 6.25/1.43 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 6.25/1.43 inference('sup+', [status(thm)], [zip_derived_cl1770, zip_derived_cl1])).
% 6.25/1.43 thf(zip_derived_cl7199, plain, (((identity) != (identity))),
% 6.25/1.43 inference('demod', [status(thm)],
% 6.25/1.43 [zip_derived_cl7198, zip_derived_cl1779])).
% 6.25/1.43 thf(zip_derived_cl7200, plain, ($false),
% 6.25/1.43 inference('simplify', [status(thm)], [zip_derived_cl7199])).
% 6.25/1.43
% 6.25/1.43 % SZS output end Refutation
% 6.25/1.43
% 6.25/1.43
% 6.25/1.43 % Terminating...
% 6.41/1.48 % Runner terminated.
% 6.41/1.49 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------