%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP277-1 : 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.f3A8LXRiSi 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 04:36:08 PM UTC 2025
% Result : Unsatisfiable 28.21s 4.65s
% Output : Refutation 28.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP277-1 : TPTP v9.2.0. Released v2.5.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.f3A8LXRiSi true
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 1 14:10:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.57/0.69 % Total configuration time : 435
% 0.57/0.69 % Estimated wc time : 1092
% 0.57/0.69 % Estimated cpu time (7 cpus) : 156.0
% 0.60/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.62/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.62/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 28.21/4.65 % Solved by fo/fo3_bce.sh.
% 28.21/4.65 % BCE start: 28
% 28.21/4.65 % BCE eliminated: 0
% 28.21/4.65 % PE start: 28
% 28.21/4.65 logic: eq
% 28.21/4.65 % PE eliminated: 0
% 28.21/4.65 % done 5013 iterations in 3.830s
% 28.21/4.65 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 28.21/4.65 % SZS output start Refutation
% 28.21/4.65 thf(sk_c4_type, type, sk_c4: $i).
% 28.21/4.65 thf(sk_c6_type, type, sk_c6: $i).
% 28.21/4.65 thf(sk_c3_type, type, sk_c3: $i).
% 28.21/4.65 thf(sk_c2_type, type, sk_c2: $i).
% 28.21/4.65 thf(identity_type, type, identity: $i).
% 28.21/4.65 thf(multiply_type, type, multiply: $i > $i > $i).
% 28.21/4.65 thf(sk_c7_type, type, sk_c7: $i).
% 28.21/4.65 thf(inverse_type, type, inverse: $i > $i).
% 28.21/4.65 thf(sk_c5_type, type, sk_c5: $i).
% 28.21/4.65 thf(sk_c1_type, type, sk_c1: $i).
% 28.21/4.65 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 28.21/4.65 thf(zip_derived_cl1, plain,
% 28.21/4.65 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.65 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.65 thf(zip_derived_cl1, plain,
% 28.21/4.65 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.65 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.65 thf(associativity, axiom,
% 28.21/4.65 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 28.21/4.65 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 28.21/4.65 thf(zip_derived_cl2, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.65 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.65 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.65 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.65 thf(zip_derived_cl33, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i]:
% 28.21/4.65 ((multiply @ identity @ X0)
% 28.21/4.65 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 28.21/4.65 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 28.21/4.65 thf(zip_derived_cl0, plain,
% 28.21/4.65 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.65 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.65 thf(zip_derived_cl47, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i]:
% 28.21/4.65 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.65 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.65 thf(zip_derived_cl606, plain,
% 28.21/4.65 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl47])).
% 28.21/4.65 thf(zip_derived_cl47, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i]:
% 28.21/4.65 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.65 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.65 thf(zip_derived_cl47, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i]:
% 28.21/4.65 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.65 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.65 thf(zip_derived_cl601, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i]:
% 28.21/4.65 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl47])).
% 28.21/4.65 thf(zip_derived_cl15292, plain,
% 28.21/4.65 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl606, zip_derived_cl601])).
% 28.21/4.65 thf(prove_this_14, conjecture,
% 28.21/4.65 (~( ( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.65 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 28.21/4.65 thf(zf_stmt_0, negated_conjecture,
% 28.21/4.65 (( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.65 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 28.21/4.65 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 28.21/4.65 thf(zip_derived_cl16, plain,
% 28.21/4.65 ((((inverse @ sk_c2) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 28.21/4.65 inference('cnf', [status(esa)], [zf_stmt_0])).
% 28.21/4.65 thf(zip_derived_cl47, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i]:
% 28.21/4.65 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.65 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.65 thf(zip_derived_cl627, plain,
% 28.21/4.65 ((((sk_c5) = (multiply @ (inverse @ sk_c7) @ sk_c6))
% 28.21/4.65 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl47])).
% 28.21/4.65 thf(prove_this_10, conjecture,
% 28.21/4.65 (~( ( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 28.21/4.65 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 28.21/4.65 thf(zf_stmt_1, negated_conjecture,
% 28.21/4.65 (( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 28.21/4.65 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 28.21/4.65 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 28.21/4.65 thf(zip_derived_cl12, plain,
% 28.21/4.65 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 28.21/4.65 thf(prove_this_11, conjecture,
% 28.21/4.65 (~( ( ( inverse @ sk_c3 ) = ( sk_c4 ) ) |
% 28.21/4.65 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 28.21/4.65 thf(zf_stmt_2, negated_conjecture,
% 28.21/4.65 (( ( inverse @ sk_c3 ) = ( sk_c4 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 28.21/4.65 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 28.21/4.65 thf(zip_derived_cl13, plain,
% 28.21/4.65 ((((inverse @ sk_c3) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('cnf', [status(esa)], [zf_stmt_2])).
% 28.21/4.65 thf(zip_derived_cl1, plain,
% 28.21/4.65 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.65 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.65 thf(zip_derived_cl29, plain,
% 28.21/4.65 ((((multiply @ sk_c4 @ sk_c3) = (identity))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 28.21/4.65 thf(zip_derived_cl2, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.65 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.65 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.65 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.65 thf(zip_derived_cl52, plain,
% 28.21/4.65 (![X0 : $i]:
% 28.21/4.65 (((multiply @ identity @ X0)
% 28.21/4.65 = (multiply @ sk_c4 @ (multiply @ sk_c3 @ X0)))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl2])).
% 28.21/4.65 thf(zip_derived_cl0, plain,
% 28.21/4.65 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.65 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.65 thf(zip_derived_cl53, plain,
% 28.21/4.65 (![X0 : $i]:
% 28.21/4.65 (((X0) = (multiply @ sk_c4 @ (multiply @ sk_c3 @ X0)))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('demod', [status(thm)], [zip_derived_cl52, zip_derived_cl0])).
% 28.21/4.65 thf(zip_derived_cl97, plain,
% 28.21/4.65 ((((sk_c4) = (multiply @ sk_c4 @ sk_c6))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl53])).
% 28.21/4.65 thf(zip_derived_cl100, plain,
% 28.21/4.65 ((((inverse @ sk_c1) = (sk_c7)) | ((sk_c4) = (multiply @ sk_c4 @ sk_c6)))),
% 28.21/4.65 inference('simplify', [status(thm)], [zip_derived_cl97])).
% 28.21/4.65 thf(zip_derived_cl12, plain,
% 28.21/4.65 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('cnf', [status(esa)], [zf_stmt_1])).
% 28.21/4.65 thf(zip_derived_cl2, plain,
% 28.21/4.65 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.65 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.65 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.65 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.65 thf(zip_derived_cl44, plain,
% 28.21/4.65 (![X0 : $i]:
% 28.21/4.65 (((multiply @ sk_c6 @ X0)
% 28.21/4.65 = (multiply @ sk_c3 @ (multiply @ sk_c4 @ X0)))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl2])).
% 28.21/4.65 thf(zip_derived_cl263, plain,
% 28.21/4.65 ((((multiply @ sk_c6 @ sk_c6) = (multiply @ sk_c3 @ sk_c4))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.65 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.65 inference('sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl44])).
% 28.21/4.66 thf(zip_derived_cl267, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c6 @ sk_c6) = (multiply @ sk_c3 @ sk_c4)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl263])).
% 28.21/4.66 thf(zip_derived_cl12, plain,
% 28.21/4.66 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_1])).
% 28.21/4.66 thf(zip_derived_cl278, plain,
% 28.21/4.66 ((((multiply @ sk_c6 @ sk_c6) = (sk_c6))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl267, zip_derived_cl12])).
% 28.21/4.66 thf(zip_derived_cl283, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((multiply @ sk_c6 @ sk_c6) = (sk_c6)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl278])).
% 28.21/4.66 thf(prove_this_9, conjecture,
% 28.21/4.66 (~( ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 28.21/4.66 thf(zf_stmt_3, negated_conjecture,
% 28.21/4.66 (( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 28.21/4.66 thf(zip_derived_cl11, plain,
% 28.21/4.66 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_3])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl43, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c7 @ X0)
% 28.21/4.66 = (multiply @ sk_c2 @ (multiply @ sk_c6 @ X0)))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl290, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c6) = (multiply @ sk_c2 @ sk_c6))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl283, zip_derived_cl43])).
% 28.21/4.66 thf(zip_derived_cl294, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c6) = (multiply @ sk_c2 @ sk_c6)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl290])).
% 28.21/4.66 thf(zip_derived_cl11, plain,
% 28.21/4.66 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_3])).
% 28.21/4.66 thf(zip_derived_cl299, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c6) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl294, zip_derived_cl11])).
% 28.21/4.66 thf(zip_derived_cl304, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl299])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl622, plain,
% 28.21/4.66 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl304, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl681, plain,
% 28.21/4.66 ((((sk_c6) = (identity)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl622, zip_derived_cl1])).
% 28.21/4.66 thf(prove_this_5, conjecture,
% 28.21/4.66 (~( ( ( inverse @ sk_c3 ) = ( sk_c4 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 28.21/4.66 thf(zf_stmt_4, negated_conjecture,
% 28.21/4.66 (( ( inverse @ sk_c3 ) = ( sk_c4 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 28.21/4.66 thf(zip_derived_cl7, plain,
% 28.21/4.66 ((((inverse @ sk_c3) = (sk_c4)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_4])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl611, plain,
% 28.21/4.66 ((((sk_c7) = (multiply @ (inverse @ sk_c1) @ sk_c6))
% 28.21/4.66 | ((inverse @ sk_c3) = (sk_c4)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl714, plain,
% 28.21/4.66 ((((sk_c7) = (multiply @ sk_c7 @ sk_c6))
% 28.21/4.66 | ((sk_c6) = (identity))
% 28.21/4.66 | ((inverse @ sk_c3) = (sk_c4)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl681, zip_derived_cl611])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl1328, plain,
% 28.21/4.66 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ sk_c7))
% 28.21/4.66 | ((inverse @ sk_c3) = (sk_c4))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl714, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl1337, plain,
% 28.21/4.66 ((((sk_c6) = (identity))
% 28.21/4.66 | ((inverse @ sk_c3) = (sk_c4))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl1328, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl1338, plain,
% 28.21/4.66 ((((inverse @ sk_c3) = (sk_c4)) | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl1337])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl1359, plain,
% 28.21/4.66 ((((multiply @ sk_c4 @ sk_c3) = (identity)) | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl1338, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl1367, plain,
% 28.21/4.66 ((((sk_c3) = (multiply @ (inverse @ sk_c4) @ identity))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl1359, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl1374, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c3 @ X0)
% 28.21/4.66 = (multiply @ (inverse @ sk_c4) @ (multiply @ identity @ X0)))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl1367, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl1377, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c3 @ X0) = (multiply @ (inverse @ sk_c4) @ X0))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl1374, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl3307, plain,
% 28.21/4.66 ((((multiply @ sk_c3 @ sk_c4) = (identity)) | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl1377, zip_derived_cl1])).
% 28.21/4.66 thf(prove_this_4, conjecture,
% 28.21/4.66 (~( ( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 28.21/4.66 thf(zf_stmt_5, negated_conjecture,
% 28.21/4.66 (( ( multiply @ sk_c3 @ sk_c4 ) = ( sk_c6 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 28.21/4.66 thf(zip_derived_cl6, plain,
% 28.21/4.66 ((((multiply @ sk_c3 @ sk_c4) = (sk_c6))
% 28.21/4.66 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_5])).
% 28.21/4.66 thf(zip_derived_cl3326, plain,
% 28.21/4.66 ((((identity) = (sk_c6))
% 28.21/4.66 | ((sk_c6) = (identity))
% 28.21/4.66 | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl3307, zip_derived_cl6])).
% 28.21/4.66 thf(zip_derived_cl3334, plain,
% 28.21/4.66 ((((multiply @ sk_c1 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c6)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3326])).
% 28.21/4.66 thf(zip_derived_cl681, plain,
% 28.21/4.66 ((((sk_c6) = (identity)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl622, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl690, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c1) = (identity)) | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl681, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl694, plain,
% 28.21/4.66 ((((sk_c1) = (multiply @ (inverse @ sk_c7) @ identity))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl690, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl738, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c1 @ X0)
% 28.21/4.66 = (multiply @ (inverse @ sk_c7) @ (multiply @ identity @ X0)))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl694, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl741, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c7) @ X0))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl738, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl1832, plain,
% 28.21/4.66 ((((multiply @ sk_c1 @ sk_c7) = (identity)) | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl3355, plain,
% 28.21/4.66 ((((sk_c6) = (identity))
% 28.21/4.66 | ((identity) = (sk_c6))
% 28.21/4.66 | ((sk_c6) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl3334, zip_derived_cl1832])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3445, plain,
% 28.21/4.66 ((((sk_c5) = (multiply @ (inverse @ sk_c7) @ identity))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl627, zip_derived_cl3359])).
% 28.21/4.66 thf(prove_this_13, conjecture,
% 28.21/4.66 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 28.21/4.66 thf(zf_stmt_6, negated_conjecture,
% 28.21/4.66 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 28.21/4.66 thf(zip_derived_cl15, plain,
% 28.21/4.66 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_6])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3371, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((multiply @ sk_c7 @ sk_c5) = (identity)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl15, zip_derived_cl3359, zip_derived_cl0,
% 28.21/4.66 zip_derived_cl3359])).
% 28.21/4.66 thf(zip_derived_cl304, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl299])).
% 28.21/4.66 thf(zip_derived_cl11, plain,
% 28.21/4.66 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_3])).
% 28.21/4.66 thf(prove_this_8, conjecture,
% 28.21/4.66 (~( ( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 28.21/4.66 thf(zf_stmt_7, negated_conjecture,
% 28.21/4.66 (( ( inverse @ sk_c2 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 28.21/4.66 thf(zip_derived_cl10, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_7])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl28, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c2) = (identity))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl50, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ identity @ X0)
% 28.21/4.66 = (multiply @ sk_c7 @ (multiply @ sk_c2 @ X0)))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl51, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c2 @ X0)))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl50, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl77, plain,
% 28.21/4.66 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl51])).
% 28.21/4.66 thf(zip_derived_cl80, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl77])).
% 28.21/4.66 thf(zip_derived_cl80, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl77])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl82, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c6 @ X0)
% 28.21/4.66 = (multiply @ sk_c7 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl2])).
% 28.21/4.66 thf(prove_this_7, conjecture,
% 28.21/4.66 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 28.21/4.66 ( ( inverse @ sk_c1 ) = ( sk_c7 ) ) ))).
% 28.21/4.66 thf(zf_stmt_8, negated_conjecture,
% 28.21/4.66 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 28.21/4.66 ( ( inverse @ sk_c1 ) = ( sk_c7 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 28.21/4.66 thf(zip_derived_cl9, plain,
% 28.21/4.66 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_8])).
% 28.21/4.66 thf(zip_derived_cl107, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ (multiply @ sk_c7 @ sk_c7)) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl82, zip_derived_cl9])).
% 28.21/4.66 thf(zip_derived_cl109, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ (multiply @ sk_c7 @ sk_c7)) = (sk_c5)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl107])).
% 28.21/4.66 thf(zip_derived_cl111, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c6) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl109])).
% 28.21/4.66 thf(zip_derived_cl112, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c6) = (sk_c5)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl111])).
% 28.21/4.66 thf(zip_derived_cl306, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c1) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl304, zip_derived_cl112])).
% 28.21/4.66 thf(zip_derived_cl309, plain,
% 28.21/4.66 ((((inverse @ sk_c1) = (sk_c7)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl306])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl310, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c1) = (identity)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl309, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl332, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ identity @ X0)
% 28.21/4.66 = (multiply @ sk_c7 @ (multiply @ sk_c1 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl310, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl334, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c1 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl332, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl616, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c7) @ X0))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl334, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl869, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl3626, plain,
% 28.21/4.66 ((((sk_c5) = (multiply @ sk_c1 @ identity))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl3371, zip_derived_cl869])).
% 28.21/4.66 thf(zip_derived_cl3633, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((sk_c5) = (multiply @ sk_c1 @ identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3626])).
% 28.21/4.66 thf(zip_derived_cl869, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl47])).
% 28.21/4.66 thf(prove_this_20, conjecture,
% 28.21/4.66 (~( ( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 28.21/4.66 thf(zf_stmt_9, negated_conjecture,
% 28.21/4.66 (( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 28.21/4.66 thf(zip_derived_cl22, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7)) | ((multiply @ sk_c5 @ sk_c6) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_9])).
% 28.21/4.66 thf(zip_derived_cl16, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_0])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl36, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c6 @ X0)
% 28.21/4.66 = (multiply @ sk_c7 @ (multiply @ sk_c5 @ X0)))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl147, plain,
% 28.21/4.66 ((((multiply @ sk_c6 @ sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl36])).
% 28.21/4.66 thf(zip_derived_cl149, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c6 @ sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl147])).
% 28.21/4.66 thf(prove_this_2, conjecture,
% 28.21/4.66 (~( ( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) ) ))).
% 28.21/4.66 thf(zf_stmt_10, negated_conjecture,
% 28.21/4.66 (( ( inverse @ sk_c2 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c1 @ sk_c7 ) = ( sk_c6 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 28.21/4.66 thf(zip_derived_cl4, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c7) = (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_10])).
% 28.21/4.66 thf(zip_derived_cl2, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 28.21/4.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 28.21/4.66 inference('cnf', [status(esa)], [associativity])).
% 28.21/4.66 thf(zip_derived_cl34, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c6 @ X0)
% 28.21/4.66 = (multiply @ sk_c1 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 28.21/4.66 thf(zip_derived_cl152, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c7)
% 28.21/4.66 = (multiply @ sk_c1 @ (multiply @ sk_c7 @ sk_c6)))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl149, zip_derived_cl34])).
% 28.21/4.66 thf(zip_derived_cl156, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c7)
% 28.21/4.66 = (multiply @ sk_c1 @ (multiply @ sk_c7 @ sk_c6))))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl152])).
% 28.21/4.66 thf(zip_derived_cl2292, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c7) = (sk_c6))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl869, zip_derived_cl156])).
% 28.21/4.66 thf(zip_derived_cl869, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl2342, plain,
% 28.21/4.66 ((((sk_c7) = (multiply @ sk_c1 @ sk_c6))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl2292, zip_derived_cl869])).
% 28.21/4.66 thf(zip_derived_cl2345, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((sk_c7) = (multiply @ sk_c1 @ sk_c6)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl2342])).
% 28.21/4.66 thf(zip_derived_cl627, plain,
% 28.21/4.66 ((((sk_c5) = (multiply @ (inverse @ sk_c7) @ sk_c6))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl616, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c7) @ X0))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl334, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl874, plain,
% 28.21/4.66 ((((multiply @ sk_c1 @ sk_c6) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl627, zip_derived_cl616])).
% 28.21/4.66 thf(zip_derived_cl2429, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl2345, zip_derived_cl874])).
% 28.21/4.66 thf(zip_derived_cl2435, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl2429])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl2439, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c2) = (identity)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl2435, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl869, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl2467, plain,
% 28.21/4.66 ((((sk_c2) = (multiply @ sk_c1 @ identity))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl2439, zip_derived_cl869])).
% 28.21/4.66 thf(zip_derived_cl2472, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((sk_c2) = (multiply @ sk_c1 @ identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl2467])).
% 28.21/4.66 thf(zip_derived_cl3647, plain,
% 28.21/4.66 ((((sk_c2) = (sk_c5)) | ((sk_c7) = (sk_c5)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl3633, zip_derived_cl2472])).
% 28.21/4.66 thf(zip_derived_cl3652, plain, ((((sk_c7) = (sk_c5)) | ((sk_c2) = (sk_c5)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3647])).
% 28.21/4.66 thf(zip_derived_cl2435, plain,
% 28.21/4.66 ((((inverse @ sk_c2) = (sk_c7)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl2429])).
% 28.21/4.66 thf(zip_derived_cl3666, plain,
% 28.21/4.66 ((((inverse @ sk_c5) = (sk_c7))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl3652, zip_derived_cl2435])).
% 28.21/4.66 thf(zip_derived_cl3670, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((inverse @ sk_c5) = (sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3666])).
% 28.21/4.66 thf(prove_this_19, conjecture,
% 28.21/4.66 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) ) ))).
% 28.21/4.66 thf(zf_stmt_11, negated_conjecture,
% 28.21/4.66 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c5 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c5 @ sk_c6 ) = ( sk_c7 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 28.21/4.66 thf(zip_derived_cl21, plain,
% 28.21/4.66 ((((multiply @ sk_c6 @ sk_c7) = (sk_c5))
% 28.21/4.66 | ((multiply @ sk_c5 @ sk_c6) = (sk_c7)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_11])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl646, plain,
% 28.21/4.66 ((((sk_c6) = (multiply @ (inverse @ sk_c5) @ sk_c7))
% 28.21/4.66 | ((multiply @ sk_c6 @ sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl3451, plain,
% 28.21/4.66 ((((identity) = (multiply @ (inverse @ sk_c5) @ sk_c7))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl646, zip_derived_cl3359, zip_derived_cl3359,
% 28.21/4.66 zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl4868, plain,
% 28.21/4.66 ((((identity) = (multiply @ sk_c7 @ sk_c7))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl3670, zip_derived_cl3451])).
% 28.21/4.66 thf(zip_derived_cl4871, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((identity) = (multiply @ sk_c7 @ sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl4868])).
% 28.21/4.66 thf(zip_derived_cl869, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((X0) = (multiply @ sk_c1 @ (multiply @ sk_c7 @ X0)))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl616, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl4888, plain,
% 28.21/4.66 ((((sk_c7) = (multiply @ sk_c1 @ identity))
% 28.21/4.66 | ((sk_c7) = (sk_c5))
% 28.21/4.66 | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl4871, zip_derived_cl869])).
% 28.21/4.66 thf(zip_derived_cl4904, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((sk_c7) = (multiply @ sk_c1 @ identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl4888])).
% 28.21/4.66 thf(zip_derived_cl3633, plain,
% 28.21/4.66 ((((sk_c7) = (sk_c5)) | ((sk_c5) = (multiply @ sk_c1 @ identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3626])).
% 28.21/4.66 thf(zip_derived_cl4914, plain,
% 28.21/4.66 ((((sk_c5) = (sk_c7)) | ((sk_c7) = (sk_c5)) | ((sk_c7) = (sk_c5)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl4904, zip_derived_cl3633])).
% 28.21/4.66 thf(zip_derived_cl4920, plain, (((sk_c5) = (sk_c7))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl4914])).
% 28.21/4.66 thf(zip_derived_cl11592, plain,
% 28.21/4.66 ((((sk_c7) = (multiply @ (inverse @ sk_c7) @ identity))
% 28.21/4.66 | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl3445, zip_derived_cl4920])).
% 28.21/4.66 thf(zip_derived_cl15371, plain,
% 28.21/4.66 ((((sk_c7) = (inverse @ sk_c7)) | ((inverse @ sk_c2) = (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl15292, zip_derived_cl11592])).
% 28.21/4.66 thf(zip_derived_cl15292, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl606, zip_derived_cl601])).
% 28.21/4.66 thf(zip_derived_cl606, plain,
% 28.21/4.66 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl15356, plain,
% 28.21/4.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl15292, zip_derived_cl606])).
% 28.21/4.66 thf(zip_derived_cl17627, plain,
% 28.21/4.66 ((((sk_c2) = (inverse @ sk_c7)) | ((sk_c7) = (inverse @ sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl15371, zip_derived_cl15356])).
% 28.21/4.66 thf(zip_derived_cl17667, plain,
% 28.21/4.66 ((((sk_c2) != (sk_c7)) | ((sk_c7) = (inverse @ sk_c7)))),
% 28.21/4.66 inference('eq_fact', [status(thm)], [zip_derived_cl17627])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(zip_derived_cl17668, plain,
% 28.21/4.66 ((((multiply @ sk_c7 @ sk_c7) = (identity)) | ((sk_c2) != (sk_c7)))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl17667, zip_derived_cl1])).
% 28.21/4.66 thf(zip_derived_cl15292, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl606, zip_derived_cl601])).
% 28.21/4.66 thf(prove_this_15, conjecture,
% 28.21/4.66 (~( ( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) ) ))).
% 28.21/4.66 thf(zf_stmt_12, negated_conjecture,
% 28.21/4.66 (( ( multiply @ sk_c2 @ sk_c6 ) = ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c7 @ sk_c5 ) = ( sk_c6 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 28.21/4.66 thf(zip_derived_cl17, plain,
% 28.21/4.66 ((((multiply @ sk_c2 @ sk_c6) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c5) = (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_12])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3373, plain,
% 28.21/4.66 ((((multiply @ sk_c2 @ identity) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c5) = (identity)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl17, zip_derived_cl3359, zip_derived_cl3359])).
% 28.21/4.66 thf(zip_derived_cl4920, plain, (((sk_c5) = (sk_c7))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl4914])).
% 28.21/4.66 thf(zip_derived_cl6498, plain,
% 28.21/4.66 ((((multiply @ sk_c2 @ identity) = (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c7) = (identity)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl3373, zip_derived_cl4920])).
% 28.21/4.66 thf(zip_derived_cl15401, plain,
% 28.21/4.66 ((((sk_c2) = (sk_c7)) | ((multiply @ sk_c7 @ sk_c7) = (identity)))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl15292, zip_derived_cl6498])).
% 28.21/4.66 thf(zip_derived_cl17789, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 28.21/4.66 inference('clc', [status(thm)],
% 28.21/4.66 [zip_derived_cl17668, zip_derived_cl15401])).
% 28.21/4.66 thf(zip_derived_cl47, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i]:
% 28.21/4.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 28.21/4.66 inference('demod', [status(thm)], [zip_derived_cl33, zip_derived_cl0])).
% 28.21/4.66 thf(zip_derived_cl17815, plain,
% 28.21/4.66 (((sk_c7) = (multiply @ (inverse @ sk_c7) @ identity))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl17789, zip_derived_cl47])).
% 28.21/4.66 thf(zip_derived_cl15292, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl606, zip_derived_cl601])).
% 28.21/4.66 thf(zip_derived_cl18801, plain, (((sk_c7) = (inverse @ sk_c7))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl17815, zip_derived_cl15292])).
% 28.21/4.66 thf(zip_derived_cl17789, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 28.21/4.66 inference('clc', [status(thm)],
% 28.21/4.66 [zip_derived_cl17668, zip_derived_cl15401])).
% 28.21/4.66 thf(zip_derived_cl1, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_inverse])).
% 28.21/4.66 thf(prove_this_25, conjecture,
% 28.21/4.66 (~( ( ( multiply @ X4 @ sk_c7 ) != ( sk_c6 ) ) |
% 28.21/4.66 ( ( inverse @ X3 ) != ( X4 ) ) |
% 28.21/4.66 ( ( multiply @ X3 @ X4 ) != ( sk_c6 ) ) |
% 28.21/4.66 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c5 @ sk_c6 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c7 @ sk_c5 ) != ( sk_c6 ) ) |
% 28.21/4.66 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) ))).
% 28.21/4.66 thf(zf_stmt_13, negated_conjecture,
% 28.21/4.66 (( ( multiply @ X4 @ sk_c7 ) != ( sk_c6 ) ) |
% 28.21/4.66 ( ( inverse @ X3 ) != ( X4 ) ) |
% 28.21/4.66 ( ( multiply @ X3 @ X4 ) != ( sk_c6 ) ) |
% 28.21/4.66 ( ( multiply @ X1 @ sk_c6 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( inverse @ X1 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c5 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c5 @ sk_c6 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ sk_c7 @ sk_c5 ) != ( sk_c6 ) ) |
% 28.21/4.66 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 28.21/4.66 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) )),
% 28.21/4.66 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 28.21/4.66 thf(zip_derived_cl27, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 28.21/4.66 (((multiply @ X0 @ sk_c7) != (sk_c6))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (sk_c6))
% 28.21/4.66 | ((multiply @ X2 @ sk_c6) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c6 @ sk_c7) != (sk_c5))
% 28.21/4.66 | ((multiply @ sk_c5 @ sk_c6) != (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c5) != (sk_c6))
% 28.21/4.66 | ((inverse @ X3) != (sk_c7))
% 28.21/4.66 | ((multiply @ X3 @ sk_c7) != (sk_c6)))),
% 28.21/4.66 inference('cnf', [status(esa)], [zf_stmt_13])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl0, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 28.21/4.66 inference('cnf', [status(esa)], [left_identity])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3359, plain, (((sk_c6) = (identity))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl3355])).
% 28.21/4.66 thf(zip_derived_cl3383, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 28.21/4.66 (((multiply @ X0 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((multiply @ X2 @ identity) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((sk_c7) != (sk_c5))
% 28.21/4.66 | ((multiply @ sk_c5 @ identity) != (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c5) != (identity))
% 28.21/4.66 | ((inverse @ X3) != (sk_c7))
% 28.21/4.66 | ((multiply @ X3 @ sk_c7) != (identity)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl27, zip_derived_cl3359, zip_derived_cl3359,
% 28.21/4.66 zip_derived_cl3359, zip_derived_cl3359, zip_derived_cl0,
% 28.21/4.66 zip_derived_cl3359, zip_derived_cl3359, zip_derived_cl3359])).
% 28.21/4.66 thf(zip_derived_cl3384, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 28.21/4.66 (((multiply @ X0 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((multiply @ X2 @ identity) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((sk_c7) != (sk_c5))
% 28.21/4.66 | ((multiply @ sk_c7 @ identity) != (sk_c7))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X3) != (sk_c7))
% 28.21/4.66 | ((multiply @ X3 @ sk_c7) != (identity)))),
% 28.21/4.66 inference('local_rewriting', [status(thm)], [zip_derived_cl3383])).
% 28.21/4.66 thf(zip_derived_cl15292, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl606, zip_derived_cl601])).
% 28.21/4.66 thf(zip_derived_cl4920, plain, (((sk_c5) = (sk_c7))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl4914])).
% 28.21/4.66 thf(zip_derived_cl15292, plain,
% 28.21/4.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 28.21/4.66 inference('sup+', [status(thm)], [zip_derived_cl606, zip_derived_cl601])).
% 28.21/4.66 thf(zip_derived_cl17789, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 28.21/4.66 inference('clc', [status(thm)],
% 28.21/4.66 [zip_derived_cl17668, zip_derived_cl15401])).
% 28.21/4.66 thf(zip_derived_cl33765, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 28.21/4.66 (((multiply @ X0 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((X2) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((sk_c7) != (sk_c7))
% 28.21/4.66 | ((sk_c7) != (sk_c7))
% 28.21/4.66 | ((identity) != (identity))
% 28.21/4.66 | ((inverse @ X3) != (sk_c7))
% 28.21/4.66 | ((multiply @ X3 @ sk_c7) != (identity)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl3384, zip_derived_cl15292, zip_derived_cl4920,
% 28.21/4.66 zip_derived_cl15292, zip_derived_cl17789])).
% 28.21/4.66 thf(zip_derived_cl33766, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 28.21/4.66 (((multiply @ X3 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X3) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((X2) != (sk_c7))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl33765])).
% 28.21/4.66 thf(zip_derived_cl33777, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 (((identity) != (identity))
% 28.21/4.66 | ((multiply @ X0 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((X2) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((inverse @ (inverse @ sk_c7)) != (sk_c7)))),
% 28.21/4.66 inference('sup-', [status(thm)], [zip_derived_cl1, zip_derived_cl33766])).
% 28.21/4.66 thf(zip_derived_cl18801, plain, (((sk_c7) = (inverse @ sk_c7))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl17815, zip_derived_cl15292])).
% 28.21/4.66 thf(zip_derived_cl18801, plain, (((sk_c7) = (inverse @ sk_c7))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl17815, zip_derived_cl15292])).
% 28.21/4.66 thf(zip_derived_cl33830, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 (((identity) != (identity))
% 28.21/4.66 | ((multiply @ X0 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((X2) != (sk_c7))
% 28.21/4.66 | ((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((sk_c7) != (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl33777, zip_derived_cl18801, zip_derived_cl18801])).
% 28.21/4.66 thf(zip_derived_cl33831, plain,
% 28.21/4.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 28.21/4.66 (((inverse @ X2) != (sk_c7))
% 28.21/4.66 | ((X2) != (sk_c7))
% 28.21/4.66 | ((multiply @ X1 @ X0) != (identity))
% 28.21/4.66 | ((inverse @ X1) != (X0))
% 28.21/4.66 | ((multiply @ X0 @ sk_c7) != (identity)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl33830])).
% 28.21/4.66 thf(zip_derived_cl34071, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((identity) != (identity))
% 28.21/4.66 | ((multiply @ sk_c7 @ sk_c7) != (identity))
% 28.21/4.66 | ((inverse @ sk_c7) != (sk_c7))
% 28.21/4.66 | ((X0) != (sk_c7))
% 28.21/4.66 | ((inverse @ X0) != (sk_c7)))),
% 28.21/4.66 inference('sup-', [status(thm)],
% 28.21/4.66 [zip_derived_cl17789, zip_derived_cl33831])).
% 28.21/4.66 thf(zip_derived_cl17789, plain, (((multiply @ sk_c7 @ sk_c7) = (identity))),
% 28.21/4.66 inference('clc', [status(thm)],
% 28.21/4.66 [zip_derived_cl17668, zip_derived_cl15401])).
% 28.21/4.66 thf(zip_derived_cl18801, plain, (((sk_c7) = (inverse @ sk_c7))),
% 28.21/4.66 inference('sup+', [status(thm)],
% 28.21/4.66 [zip_derived_cl17815, zip_derived_cl15292])).
% 28.21/4.66 thf(zip_derived_cl34587, plain,
% 28.21/4.66 (![X0 : $i]:
% 28.21/4.66 (((identity) != (identity))
% 28.21/4.66 | ((identity) != (identity))
% 28.21/4.66 | ((sk_c7) != (sk_c7))
% 28.21/4.66 | ((X0) != (sk_c7))
% 28.21/4.66 | ((inverse @ X0) != (sk_c7)))),
% 28.21/4.66 inference('demod', [status(thm)],
% 28.21/4.66 [zip_derived_cl34071, zip_derived_cl17789, zip_derived_cl18801])).
% 28.21/4.66 thf(zip_derived_cl34588, plain,
% 28.21/4.66 (![X0 : $i]: (((inverse @ X0) != (sk_c7)) | ((X0) != (sk_c7)))),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl34587])).
% 28.21/4.66 thf(zip_derived_cl34855, plain,
% 28.21/4.66 ((((sk_c7) != (sk_c7)) | ((sk_c7) != (sk_c7)))),
% 28.21/4.66 inference('sup-', [status(thm)],
% 28.21/4.66 [zip_derived_cl18801, zip_derived_cl34588])).
% 28.21/4.66 thf(zip_derived_cl34905, plain, ($false),
% 28.21/4.66 inference('simplify', [status(thm)], [zip_derived_cl34855])).
% 28.21/4.66
% 28.21/4.66 % SZS output end Refutation
% 28.21/4.66
% 28.21/4.66
% 28.21/4.66 % Terminating...
% 28.21/4.73 % Runner terminated.
% 28.21/4.75 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------