TSTP Solution File: GRP212-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP212-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ryWjjtWLoO true
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:44 EDT 2023
% Result : Unsatisfiable 161.14s 23.66s
% Output : Refutation 161.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP212-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ryWjjtWLoO true
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Mon Aug 28 23:43:25 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.18/0.35 % Running portfolio for 300 s
% 0.18/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.35 % Number of cores: 8
% 0.18/0.35 % Python version: Python 3.6.8
% 0.18/0.35 % Running in FO mode
% 0.22/0.62 % Total configuration time : 435
% 0.22/0.62 % Estimated wc time : 1092
% 0.22/0.62 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 161.14/23.66 % Solved by fo/fo3_bce.sh.
% 161.14/23.66 % BCE start: 34
% 161.14/23.66 % BCE eliminated: 0
% 161.14/23.66 % PE start: 34
% 161.14/23.66 logic: eq
% 161.14/23.66 % PE eliminated: 0
% 161.14/23.66 % done 11758 iterations in 22.902s
% 161.14/23.66 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 161.14/23.66 % SZS output start Refutation
% 161.14/23.66 thf(sk_c5_type, type, sk_c5: $i).
% 161.14/23.66 thf(sk_c8_type, type, sk_c8: $i).
% 161.14/23.66 thf(sk_c6_type, type, sk_c6: $i).
% 161.14/23.66 thf(sk_c4_type, type, sk_c4: $i).
% 161.14/23.66 thf(identity_type, type, identity: $i).
% 161.14/23.66 thf(multiply_type, type, multiply: $i > $i > $i).
% 161.14/23.66 thf(sk_c2_type, type, sk_c2: $i).
% 161.14/23.66 thf(inverse_type, type, inverse: $i > $i).
% 161.14/23.66 thf(sk_c7_type, type, sk_c7: $i).
% 161.14/23.66 thf(sk_c3_type, type, sk_c3: $i).
% 161.14/23.66 thf(sk_c1_type, type, sk_c1: $i).
% 161.14/23.66 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(associativity, axiom,
% 161.14/23.66 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 161.14/23.66 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl43, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((multiply @ identity @ X0)
% 161.14/23.66 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 161.14/23.66 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl716, plain,
% 161.14/23.66 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl711, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl53, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl74814, plain, (((inverse @ identity) = (identity))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl74814, plain, (((inverse @ identity) = (identity))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(prove_this_31, conjecture,
% 161.14/23.66 (~( ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ X3 @ sk_c8 ) != ( X2 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ X6 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ X5 @ sk_c7 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ X4 ) != ( X5 ) ) |
% 161.14/23.66 ( ( multiply @ X4 @ X5 ) != ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_0, negated_conjecture,
% 161.14/23.66 (( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ X3 @ sk_c8 ) != ( X2 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ X6 @ sk_c7 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ X6 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ X5 @ sk_c7 ) != ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ X4 ) != ( X5 ) ) | ( ( multiply @ X4 @ X5 ) != ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 161.14/23.66 thf(zip_derived_cl33, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 161.14/23.66 (((inverse @ X0) != (sk_c8))
% 161.14/23.66 | ((multiply @ X0 @ sk_c8) != (X1))
% 161.14/23.66 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X2) != (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) != (sk_c7))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X3) != (sk_c8))
% 161.14/23.66 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X5) != (X4))
% 161.14/23.66 | ((multiply @ X5 @ X4) != (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_0])).
% 161.14/23.66 thf(zip_derived_cl82, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 161.14/23.66 (((sk_c8) != (X0))
% 161.14/23.66 | ((multiply @ X2 @ X1) != (sk_c8))
% 161.14/23.66 | ((inverse @ X2) != (X1))
% 161.14/23.66 | ((multiply @ X1 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X3) != (sk_c8))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) != (sk_c7))
% 161.14/23.66 | ((inverse @ X4) != (sk_c8))
% 161.14/23.66 | ((multiply @ X4 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c8 @ X0) != (sk_c7))
% 161.14/23.66 | ((inverse @ identity) != (sk_c8)))),
% 161.14/23.66 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl33])).
% 161.14/23.66 thf(zip_derived_cl2659, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((X0) != (sk_c8))
% 161.14/23.66 | ((inverse @ identity) != (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X2) != (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) != (sk_c7))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X3) != (sk_c8))
% 161.14/23.66 | ((multiply @ X0 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ identity) != (X0))
% 161.14/23.66 | ((sk_c8) != (X1)))),
% 161.14/23.66 inference('sup-', [status(thm)], [zip_derived_cl0, zip_derived_cl82])).
% 161.14/23.66 thf(zip_derived_cl2865, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((X0) != (sk_c8))
% 161.14/23.66 | ((inverse @ identity) != (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X2) != (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) != (sk_c7))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X3) != (sk_c8))
% 161.14/23.66 | ((multiply @ X0 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((sk_c8) != (X0))
% 161.14/23.66 | ((sk_c8) != (X1)))),
% 161.14/23.66 inference('local_rewriting', [status(thm)], [zip_derived_cl2659])).
% 161.14/23.66 thf(zip_derived_cl2866, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((sk_c8) != (X1))
% 161.14/23.66 | ((multiply @ X0 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X3) != (sk_c8))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) != (sk_c7))
% 161.14/23.66 | ((inverse @ X2) != (sk_c8))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 161.14/23.66 | ((inverse @ identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl2865])).
% 161.14/23.66 thf(zip_derived_cl74814, plain, (((inverse @ identity) = (identity))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl237709, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((sk_c8) != (X1))
% 161.14/23.66 | ((multiply @ X0 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ X3) != (sk_c8))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) != (sk_c7))
% 161.14/23.66 | ((inverse @ X2) != (sk_c8))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (sk_c8)))),
% 161.14/23.66 inference('demod', [status(thm)],
% 161.14/23.66 [zip_derived_cl2866, zip_derived_cl74814])).
% 161.14/23.66 thf(zip_derived_cl237710, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((identity) != (X1))
% 161.14/23.66 | ((multiply @ X0 @ sk_c7) != (identity))
% 161.14/23.66 | ((inverse @ X3) != (identity))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (identity))
% 161.14/23.66 | ((inverse @ identity) != (sk_c7))
% 161.14/23.66 | ((inverse @ X2) != (identity))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (identity))
% 161.14/23.66 | ((multiply @ identity @ X1) != (sk_c7))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (identity)))),
% 161.14/23.66 inference('local_rewriting', [status(thm)], [zip_derived_cl237709])).
% 161.14/23.66 thf(zip_derived_cl74814, plain, (((inverse @ identity) = (identity))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl237711, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((identity) != (X1))
% 161.14/23.66 | ((multiply @ X0 @ sk_c7) != (identity))
% 161.14/23.66 | ((inverse @ X3) != (identity))
% 161.14/23.66 | ((multiply @ X3 @ sk_c7) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((inverse @ X2) != (identity))
% 161.14/23.66 | ((multiply @ X2 @ sk_c7) != (identity))
% 161.14/23.66 | ((X1) != (sk_c7))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (identity)))),
% 161.14/23.66 inference('demod', [status(thm)],
% 161.14/23.66 [zip_derived_cl237710, zip_derived_cl74814, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl237712, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((identity) != (X1))
% 161.14/23.66 | ((multiply @ X0 @ identity) != (identity))
% 161.14/23.66 | ((inverse @ X3) != (identity))
% 161.14/23.66 | ((multiply @ X3 @ identity) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((inverse @ X2) != (identity))
% 161.14/23.66 | ((multiply @ X2 @ identity) != (identity))
% 161.14/23.66 | ((X1) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (identity)))),
% 161.14/23.66 inference('local_rewriting', [status(thm)], [zip_derived_cl237711])).
% 161.14/23.66 thf(zip_derived_cl237713, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((X0) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((multiply @ X2 @ identity) != (identity))
% 161.14/23.66 | ((inverse @ X2) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((multiply @ X3 @ identity) != (identity))
% 161.14/23.66 | ((inverse @ X3) != (identity))
% 161.14/23.66 | ((multiply @ X0 @ identity) != (identity))
% 161.14/23.66 | ((identity) != (X1)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl237712])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl237714, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((X0) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X2) != (identity))
% 161.14/23.66 | ((inverse @ X2) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((X3) != (identity))
% 161.14/23.66 | ((inverse @ X3) != (identity))
% 161.14/23.66 | ((X0) != (identity))
% 161.14/23.66 | ((identity) != (X1)))),
% 161.14/23.66 inference('demod', [status(thm)],
% 161.14/23.66 [zip_derived_cl237713, zip_derived_cl66414,
% 161.14/23.66 zip_derived_cl66414, zip_derived_cl66414])).
% 161.14/23.66 thf(zip_derived_cl237715, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 161.14/23.66 (((identity) != (X1))
% 161.14/23.66 | ((inverse @ X3) != (identity))
% 161.14/23.66 | ((X3) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((inverse @ X2) != (identity))
% 161.14/23.66 | ((X2) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl237714])).
% 161.14/23.66 thf(zip_derived_cl237716, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 (((identity) != (identity))
% 161.14/23.66 | ((X0) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X1) != (identity))
% 161.14/23.66 | ((inverse @ X1) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((identity) != (identity))
% 161.14/23.66 | ((identity) != (X2)))),
% 161.14/23.66 inference('sup-', [status(thm)],
% 161.14/23.66 [zip_derived_cl74814, zip_derived_cl237715])).
% 161.14/23.66 thf(zip_derived_cl237894, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 (((identity) != (X2))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((inverse @ X1) != (identity))
% 161.14/23.66 | ((X1) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl237716])).
% 161.14/23.66 thf(zip_derived_cl243046, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 (((identity) != (identity))
% 161.14/23.66 | ((X0) != (identity))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((identity) != (identity))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((identity) != (X1)))),
% 161.14/23.66 inference('sup-', [status(thm)],
% 161.14/23.66 [zip_derived_cl74814, zip_derived_cl237894])).
% 161.14/23.66 thf(zip_derived_cl243224, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 (((identity) != (X1))
% 161.14/23.66 | ((identity) != (sk_c7))
% 161.14/23.66 | ((identity) != (sk_c8))
% 161.14/23.66 | ((X0) != (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl243046])).
% 161.14/23.66 thf(prove_this_8, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 161.14/23.66 thf(zf_stmt_1, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 161.14/23.66 thf(zip_derived_cl10, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_1])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl35, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c4) = (identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl1])).
% 161.14/23.66 thf(prove_this_7, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 161.14/23.66 thf(zf_stmt_2, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 161.14/23.66 thf(zip_derived_cl9, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_2])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl34, plain,
% 161.14/23.66 ((((multiply @ sk_c7 @ sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl67, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ identity @ X0)
% 161.14/23.66 = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl68, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl134, plain,
% 161.14/23.66 ((((sk_c4) = (multiply @ sk_c7 @ identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl35, zip_derived_cl68])).
% 161.14/23.66 thf(zip_derived_cl143, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((sk_c4) = (multiply @ sk_c7 @ identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl134])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl152, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c4 @ X0)
% 161.14/23.66 = (multiply @ sk_c7 @ (multiply @ identity @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl143, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl153, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c4 @ X0) = (multiply @ sk_c7 @ X0))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl152, zip_derived_cl0])).
% 161.14/23.66 thf(prove_this_9, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 161.14/23.66 thf(zf_stmt_3, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 161.14/23.66 thf(zip_derived_cl11, plain,
% 161.14/23.66 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_3])).
% 161.14/23.66 thf(zip_derived_cl164, plain,
% 161.14/23.66 ((((multiply @ sk_c7 @ sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl153, zip_derived_cl11])).
% 161.14/23.66 thf(zip_derived_cl168, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c7 @ sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl164])).
% 161.14/23.66 thf(zip_derived_cl11, plain,
% 161.14/23.66 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_3])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl50, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c8 @ X0)
% 161.14/23.66 = (multiply @ sk_c4 @ (multiply @ sk_c7 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl298, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c7) = (multiply @ sk_c4 @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl168, zip_derived_cl50])).
% 161.14/23.66 thf(zip_derived_cl306, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c7) = (multiply @ sk_c4 @ sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl298])).
% 161.14/23.66 thf(zip_derived_cl153, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c4 @ X0) = (multiply @ sk_c7 @ X0))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl152, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl344, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c7) = (multiply @ sk_c7 @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl306, zip_derived_cl153])).
% 161.14/23.66 thf(zip_derived_cl347, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c7) = (multiply @ sk_c7 @ sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl344])).
% 161.14/23.66 thf(prove_this_12, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 161.14/23.66 thf(zf_stmt_4, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 161.14/23.66 thf(zip_derived_cl14, plain,
% 161.14/23.66 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_4])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl36, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl68, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl139, plain,
% 161.14/23.66 ((((sk_c5) = (multiply @ sk_c7 @ identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl36, zip_derived_cl68])).
% 161.14/23.66 thf(zip_derived_cl145, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((sk_c5) = (multiply @ sk_c7 @ identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl139])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl154, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c5 @ X0)
% 161.14/23.66 = (multiply @ sk_c7 @ (multiply @ identity @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl145, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl156, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c5 @ X0) = (multiply @ sk_c7 @ X0))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl154, zip_derived_cl0])).
% 161.14/23.66 thf(prove_this_11, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 161.14/23.66 thf(zf_stmt_5, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 161.14/23.66 thf(zip_derived_cl13, plain,
% 161.14/23.66 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_5])).
% 161.14/23.66 thf(zip_derived_cl189, plain,
% 161.14/23.66 ((((multiply @ sk_c7 @ sk_c8) = (sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl13])).
% 161.14/23.66 thf(zip_derived_cl193, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 161.14/23.66 thf(zip_derived_cl402, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c7) = (sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl347, zip_derived_cl193])).
% 161.14/23.66 thf(zip_derived_cl406, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl402])).
% 161.14/23.66 thf(prove_this_10, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 161.14/23.66 thf(zf_stmt_6, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 161.14/23.66 thf(zip_derived_cl12, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_6])).
% 161.14/23.66 thf(zip_derived_cl68, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl136, plain,
% 161.14/23.66 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl12, zip_derived_cl68])).
% 161.14/23.66 thf(zip_derived_cl144, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl136])).
% 161.14/23.66 thf(zip_derived_cl50, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c8 @ X0)
% 161.14/23.66 = (multiply @ sk_c4 @ (multiply @ sk_c7 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl297, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c7) = (multiply @ sk_c4 @ sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl144, zip_derived_cl50])).
% 161.14/23.66 thf(zip_derived_cl305, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c7) = (multiply @ sk_c4 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl297])).
% 161.14/23.66 thf(zip_derived_cl193, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 161.14/23.66 thf(zip_derived_cl50, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c8 @ X0)
% 161.14/23.66 = (multiply @ sk_c4 @ (multiply @ sk_c7 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl296, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c4 @ sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl50])).
% 161.14/23.66 thf(zip_derived_cl304, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c4 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl296])).
% 161.14/23.66 thf(zip_derived_cl336, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c8 @ sk_c7))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl305, zip_derived_cl304])).
% 161.14/23.66 thf(zip_derived_cl340, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c8 @ sk_c7)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl336])).
% 161.14/23.66 thf(zip_derived_cl424, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c8) = (sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl406, zip_derived_cl340])).
% 161.14/23.66 thf(zip_derived_cl428, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c8 @ sk_c8) = (sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl424])).
% 161.14/23.66 thf(zip_derived_cl68, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl457, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ sk_c7 @ sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl428, zip_derived_cl68])).
% 161.14/23.66 thf(zip_derived_cl460, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c8) = (multiply @ sk_c7 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl457])).
% 161.14/23.66 thf(zip_derived_cl304, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c4 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl296])).
% 161.14/23.66 thf(zip_derived_cl153, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c4 @ X0) = (multiply @ sk_c7 @ X0))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl152, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl311, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c7 @ sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl304, zip_derived_cl153])).
% 161.14/23.66 thf(zip_derived_cl314, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((multiply @ sk_c8 @ sk_c8) = (multiply @ sk_c7 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl311])).
% 161.14/23.66 thf(zip_derived_cl701, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c8) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl460, zip_derived_cl314])).
% 161.14/23.66 thf(zip_derived_cl706, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c8 @ sk_c8) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl701])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl864, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ sk_c8) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl875, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl864, zip_derived_cl1])).
% 161.14/23.66 thf(prove_this_1, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_7, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 161.14/23.66 thf(zip_derived_cl3, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_7])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl719, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ (inverse @ sk_c1) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl984, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ (inverse @ sk_c1)) @ sk_c2))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl719, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl10830, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ sk_c2) @ sk_c2))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl875, zip_derived_cl984])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl10843, plain,
% 161.14/23.66 ((((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl10830, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl10844, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl10843])).
% 161.14/23.66 thf(zip_derived_cl875, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl864, zip_derived_cl1])).
% 161.14/23.66 thf(prove_this_2, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_8, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 161.14/23.66 thf(zip_derived_cl4, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_8])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl720, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ (inverse @ sk_c1) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl999, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ (inverse @ sk_c1)) @ sk_c2))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl720, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl10948, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ sk_c2) @ sk_c2))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl875, zip_derived_cl999])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl10961, plain,
% 161.14/23.66 ((((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl10948, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl10962, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl10961])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl11078, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c4) = (identity)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl10962, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl11100, plain,
% 161.14/23.66 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11078, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl12114, plain,
% 161.14/23.66 ((((sk_c4) = (multiply @ sk_c7 @ identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl10844, zip_derived_cl11100])).
% 161.14/23.66 thf(zip_derived_cl12121, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((sk_c4) = (multiply @ sk_c7 @ identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl12114])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl74764, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((sk_c4) = (sk_c7)))),
% 161.14/23.66 inference('demod', [status(thm)],
% 161.14/23.66 [zip_derived_cl12121, zip_derived_cl66414])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl11100, plain,
% 161.14/23.66 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11078, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl74863, plain,
% 161.14/23.66 ((((sk_c4) = (inverse @ sk_c8)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl66414, zip_derived_cl11100])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(prove_this_24, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_9, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 161.14/23.66 thf(zip_derived_cl26, plain,
% 161.14/23.66 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_9])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl39, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c3) = (identity))
% 161.14/23.66 | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl765, plain,
% 161.14/23.66 ((((sk_c3) = (multiply @ (inverse @ sk_c8) @ identity))
% 161.14/23.66 | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl39, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl74862, plain,
% 161.14/23.66 ((((sk_c3) = (inverse @ sk_c8)) | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl765])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl716, plain,
% 161.14/23.66 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl74832, plain,
% 161.14/23.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl716])).
% 161.14/23.66 thf(zip_derived_cl80834, plain,
% 161.14/23.66 ((((sk_c5) = (inverse @ sk_c8)) | ((sk_c3) = (inverse @ sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl74862, zip_derived_cl74832])).
% 161.14/23.66 thf(zip_derived_cl83891, plain,
% 161.14/23.66 ((((sk_c3) != (sk_c5)) | ((sk_c5) = (inverse @ sk_c8)))),
% 161.14/23.66 inference('eq_fact', [status(thm)], [zip_derived_cl80834])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl83894, plain,
% 161.14/23.66 ((((multiply @ sk_c5 @ sk_c8) = (identity)) | ((sk_c3) != (sk_c5)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl83891, zip_derived_cl1])).
% 161.14/23.66 thf(prove_this_5, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_10, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 161.14/23.66 thf(zip_derived_cl7, plain,
% 161.14/23.66 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_10])).
% 161.14/23.66 thf(zip_derived_cl84179, plain,
% 161.14/23.66 ((((identity) = (sk_c6))
% 161.14/23.66 | ((sk_c3) != (sk_c5))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl83894, zip_derived_cl7])).
% 161.14/23.66 thf(zip_derived_cl193, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c7 @ sk_c8) = (sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl189])).
% 161.14/23.66 thf(zip_derived_cl34, plain,
% 161.14/23.66 ((((multiply @ sk_c7 @ sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl9, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl197, plain,
% 161.14/23.66 ((((sk_c6) = (identity))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl34])).
% 161.14/23.66 thf(zip_derived_cl198, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl197])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl199, plain,
% 161.14/23.66 ((((multiply @ sk_c2 @ sk_c1) = (identity)) | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl198, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl200, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ identity @ X0)
% 161.14/23.66 = (multiply @ sk_c2 @ (multiply @ sk_c1 @ X0)))
% 161.14/23.66 | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl199, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl201, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c2 @ (multiply @ sk_c1 @ X0)))
% 161.14/23.66 | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl200, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl726, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c2) @ X0))
% 161.14/23.66 | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl201, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl13996, plain,
% 161.14/23.66 ((((multiply @ sk_c1 @ sk_c2) = (identity)) | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl726, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl120706, plain,
% 161.14/23.66 ((((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c3) != (sk_c5))
% 161.14/23.66 | ((identity) = (sk_c6))
% 161.14/23.66 | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl84179, zip_derived_cl13996])).
% 161.14/23.66 thf(zip_derived_cl120777, plain,
% 161.14/23.66 ((((identity) = (sk_c6)) | ((sk_c3) != (sk_c5)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl120706])).
% 161.14/23.66 thf(zip_derived_cl875, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl864, zip_derived_cl1])).
% 161.14/23.66 thf(prove_this_6, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_11, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 161.14/23.66 thf(zip_derived_cl8, plain,
% 161.14/23.66 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_11])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl721, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ (inverse @ sk_c1) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl1013, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ (inverse @ sk_c1)) @ sk_c2))
% 161.14/23.66 | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl721, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl10996, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ sk_c2) @ sk_c2))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl875, zip_derived_cl1013])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl11009, plain,
% 161.14/23.66 ((((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c5) = (sk_c8)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl10996, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl11010, plain,
% 161.14/23.66 ((((inverse @ sk_c5) = (sk_c8)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl11009])).
% 161.14/23.66 thf(prove_this_23, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_12, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 161.14/23.66 thf(zip_derived_cl25, plain,
% 161.14/23.66 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_12])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl794, plain,
% 161.14/23.66 ((((sk_c8) = (multiply @ (inverse @ sk_c5) @ sk_c6))
% 161.14/23.66 | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl1412, plain,
% 161.14/23.66 ((((sk_c6) = (multiply @ (inverse @ (inverse @ sk_c5)) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl794, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl11585, plain,
% 161.14/23.66 ((((sk_c6) = (multiply @ (inverse @ sk_c8) @ sk_c8))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl11010, zip_derived_cl1412])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl11587, plain,
% 161.14/23.66 ((((sk_c6) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl11585, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl74832, plain,
% 161.14/23.66 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl716])).
% 161.14/23.66 thf(zip_derived_cl80838, plain,
% 161.14/23.66 ((((sk_c3) = (inverse @ sk_c8))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c6) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl11587, zip_derived_cl74832])).
% 161.14/23.66 thf(zip_derived_cl66414, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.66 thf(zip_derived_cl11010, plain,
% 161.14/23.66 ((((inverse @ sk_c5) = (sk_c8)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl11009])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl11084, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c5) = (identity)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11010, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl11130, plain,
% 161.14/23.66 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11084, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl74864, plain,
% 161.14/23.66 ((((sk_c5) = (inverse @ sk_c8)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl66414, zip_derived_cl11130])).
% 161.14/23.66 thf(zip_derived_cl103055, plain,
% 161.14/23.66 ((((sk_c5) = (sk_c3))
% 161.14/23.66 | ((sk_c6) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl80838, zip_derived_cl74864])).
% 161.14/23.66 thf(zip_derived_cl103100, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((sk_c6) = (identity)) | ((sk_c5) = (sk_c3)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl103055])).
% 161.14/23.66 thf(zip_derived_cl120779, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((identity) = (sk_c6)))),
% 161.14/23.66 inference('clc', [status(thm)],
% 161.14/23.66 [zip_derived_cl120777, zip_derived_cl103100])).
% 161.14/23.66 thf(zip_derived_cl460, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c8) = (multiply @ sk_c7 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl457])).
% 161.14/23.66 thf(zip_derived_cl406, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c8 @ sk_c7) = (sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl402])).
% 161.14/23.66 thf(zip_derived_cl68, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c7 @ (multiply @ sk_c8 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl67, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl423, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c7 @ sk_c6))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl406, zip_derived_cl68])).
% 161.14/23.66 thf(zip_derived_cl427, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c7) = (multiply @ sk_c7 @ sk_c6)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl423])).
% 161.14/23.66 thf(zip_derived_cl703, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl460, zip_derived_cl427])).
% 161.14/23.66 thf(zip_derived_cl708, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl703])).
% 161.14/23.66 thf(zip_derived_cl719, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ (inverse @ sk_c1) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl993, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ sk_c2 @ sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl708, zip_derived_cl719])).
% 161.14/23.66 thf(prove_this_19, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_13, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 161.14/23.66 thf(zip_derived_cl21, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_13])).
% 161.14/23.66 thf(prove_this_25, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_14, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 161.14/23.66 thf(zip_derived_cl27, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_14])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl795, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ (inverse @ sk_c3) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl1422, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl795])).
% 161.14/23.66 thf(zip_derived_cl1425, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl1422])).
% 161.14/23.66 thf(zip_derived_cl3, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_7])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl44, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c8 @ X0)
% 161.14/23.66 = (multiply @ sk_c1 @ (multiply @ sk_c2 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl3, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl1432, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c1 @ (multiply @ sk_c2 @ sk_c8)))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl1425, zip_derived_cl44])).
% 161.14/23.66 thf(zip_derived_cl1442, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7))
% 161.14/23.66 | ((sk_c7) = (multiply @ sk_c1 @ (multiply @ sk_c2 @ sk_c8))))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl1432])).
% 161.14/23.66 thf(zip_derived_cl11657, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c1 @ sk_c2))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl993, zip_derived_cl1442])).
% 161.14/23.66 thf(zip_derived_cl11684, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7))
% 161.14/23.66 | ((sk_c7) = (multiply @ sk_c1 @ sk_c2)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl11657])).
% 161.14/23.66 thf(zip_derived_cl3, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_7])).
% 161.14/23.66 thf(zip_derived_cl12228, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c8) = (sk_c7)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl11684, zip_derived_cl3])).
% 161.14/23.66 thf(zip_derived_cl12249, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl12228])).
% 161.14/23.66 thf(zip_derived_cl708, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl703])).
% 161.14/23.66 thf(zip_derived_cl720, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ (inverse @ sk_c1) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl1008, plain,
% 161.14/23.66 ((((sk_c2) = (multiply @ sk_c2 @ sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl708, zip_derived_cl720])).
% 161.14/23.66 thf(prove_this_20, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_15, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c3 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 161.14/23.66 thf(zip_derived_cl22, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c3) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_15])).
% 161.14/23.66 thf(prove_this_26, conjecture,
% 161.14/23.66 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_16, negated_conjecture,
% 161.14/23.66 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c3 @ sk_c7 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 161.14/23.66 thf(zip_derived_cl28, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c3 @ sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_16])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl796, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ (inverse @ sk_c3) @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl1506, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl796])).
% 161.14/23.66 thf(zip_derived_cl1508, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl1506])).
% 161.14/23.66 thf(zip_derived_cl4, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_8])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl45, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c8 @ X0)
% 161.14/23.66 = (multiply @ sk_c1 @ (multiply @ sk_c2 @ X0)))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl1515, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c1 @ (multiply @ sk_c2 @ sk_c8)))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl1508, zip_derived_cl45])).
% 161.14/23.66 thf(zip_derived_cl1523, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (multiply @ sk_c1 @ (multiply @ sk_c2 @ sk_c8))))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl1515])).
% 161.14/23.66 thf(zip_derived_cl15396, plain,
% 161.14/23.66 ((((sk_c7) = (multiply @ sk_c1 @ sk_c2))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl1008, zip_derived_cl1523])).
% 161.14/23.66 thf(zip_derived_cl15419, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (multiply @ sk_c1 @ sk_c2)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl15396])).
% 161.14/23.66 thf(zip_derived_cl4, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_8])).
% 161.14/23.66 thf(zip_derived_cl15750, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c4) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl15419, zip_derived_cl4])).
% 161.14/23.66 thf(zip_derived_cl15771, plain,
% 161.14/23.66 ((((inverse @ sk_c4) = (sk_c8)) | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl15750])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl15773, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c4) = (identity)) | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl15771, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl15795, plain,
% 161.14/23.66 ((((sk_c4) = (multiply @ (inverse @ sk_c8) @ identity))
% 161.14/23.66 | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl15773, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl15833, plain,
% 161.14/23.66 ((((sk_c4) = (multiply @ sk_c7 @ identity))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl12249, zip_derived_cl15795])).
% 161.14/23.66 thf(zip_derived_cl15842, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8)) | ((sk_c4) = (multiply @ sk_c7 @ identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl15833])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl15874, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c4 @ X0)
% 161.14/23.66 = (multiply @ sk_c7 @ (multiply @ identity @ X0)))
% 161.14/23.66 | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl15842, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl15905, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c4 @ X0) = (multiply @ sk_c7 @ X0))
% 161.14/23.66 | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl15874, zip_derived_cl0])).
% 161.14/23.66 thf(prove_this_3, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_17, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 161.14/23.66 thf(zip_derived_cl5, plain,
% 161.14/23.66 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_17])).
% 161.14/23.66 thf(zip_derived_cl16007, plain,
% 161.14/23.66 ((((multiply @ sk_c7 @ sk_c7) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl15905, zip_derived_cl5])).
% 161.14/23.66 thf(zip_derived_cl12249, plain,
% 161.14/23.66 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl12228])).
% 161.14/23.66 thf(prove_this_4, conjecture,
% 161.14/23.66 (~( ( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 161.14/23.66 thf(zf_stmt_18, negated_conjecture,
% 161.14/23.66 (( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 161.14/23.66 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 161.14/23.66 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 161.14/23.66 thf(zip_derived_cl6, plain,
% 161.14/23.66 ((((multiply @ sk_c8 @ sk_c6) = (sk_c7))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_18])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl758, plain,
% 161.14/23.66 ((((sk_c6) = (multiply @ (inverse @ sk_c8) @ sk_c7))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl12258, plain,
% 161.14/23.66 ((((sk_c6) = (multiply @ sk_c7 @ sk_c7))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl12249, zip_derived_cl758])).
% 161.14/23.66 thf(zip_derived_cl22618, plain,
% 161.14/23.66 ((((sk_c6) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl16007, zip_derived_cl12258])).
% 161.14/23.66 thf(zip_derived_cl22637, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8))
% 161.14/23.66 | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl22618])).
% 161.14/23.66 thf(zip_derived_cl168, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((multiply @ sk_c7 @ sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl164])).
% 161.14/23.66 thf(zip_derived_cl144, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c6) = (multiply @ sk_c7 @ sk_c7)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl136])).
% 161.14/23.66 thf(zip_derived_cl170, plain,
% 161.14/23.66 ((((sk_c6) = (sk_c8))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2))
% 161.14/23.66 | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl168, zip_derived_cl144])).
% 161.14/23.66 thf(zip_derived_cl171, plain,
% 161.14/23.66 ((((inverse @ sk_c1) = (sk_c2)) | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl170])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl172, plain,
% 161.14/23.66 ((((multiply @ sk_c2 @ sk_c1) = (identity)) | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl171, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl2, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i, X2 : $i]:
% 161.14/23.66 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 161.14/23.66 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 161.14/23.66 inference('cnf', [status(esa)], [associativity])).
% 161.14/23.66 thf(zip_derived_cl184, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ identity @ X0)
% 161.14/23.66 = (multiply @ sk_c2 @ (multiply @ sk_c1 @ X0)))
% 161.14/23.66 | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl172, zip_derived_cl2])).
% 161.14/23.66 thf(zip_derived_cl0, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.66 thf(zip_derived_cl185, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((X0) = (multiply @ sk_c2 @ (multiply @ sk_c1 @ X0)))
% 161.14/23.66 | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl184, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl725, plain,
% 161.14/23.66 (![X0 : $i]:
% 161.14/23.66 (((multiply @ sk_c1 @ X0) = (multiply @ (inverse @ sk_c2) @ X0))
% 161.14/23.66 | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl185, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl1, plain,
% 161.14/23.66 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.66 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.66 thf(zip_derived_cl9237, plain,
% 161.14/23.66 ((((multiply @ sk_c1 @ sk_c2) = (identity)) | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl725, zip_derived_cl1])).
% 161.14/23.66 thf(zip_derived_cl22667, plain,
% 161.14/23.66 ((((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c6) = (sk_c8))
% 161.14/23.66 | ((sk_c7) = (sk_c8))
% 161.14/23.66 | ((sk_c6) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl22637, zip_derived_cl9237])).
% 161.14/23.66 thf(zip_derived_cl22705, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8)) | ((sk_c6) = (sk_c8)) | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl22667])).
% 161.14/23.66 thf(zip_derived_cl120828, plain,
% 161.14/23.66 ((((identity) = (sk_c8))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c7) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl120779, zip_derived_cl22705])).
% 161.14/23.66 thf(zip_derived_cl120941, plain,
% 161.14/23.66 ((((sk_c7) = (sk_c8)) | ((identity) = (sk_c8)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl120828])).
% 161.14/23.66 thf(zip_derived_cl12121, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((sk_c4) = (multiply @ sk_c7 @ identity)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl12114])).
% 161.14/23.66 thf(zip_derived_cl53, plain,
% 161.14/23.66 (![X0 : $i, X1 : $i]:
% 161.14/23.66 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.66 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.66 thf(zip_derived_cl12287, plain,
% 161.14/23.66 ((((identity) = (multiply @ (inverse @ sk_c7) @ sk_c4))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)], [zip_derived_cl12121, zip_derived_cl53])).
% 161.14/23.66 thf(zip_derived_cl121102, plain,
% 161.14/23.66 ((((identity) = (multiply @ (inverse @ sk_c8) @ sk_c4))
% 161.14/23.66 | ((identity) = (sk_c8))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl120941, zip_derived_cl12287])).
% 161.14/23.66 thf(zip_derived_cl121280, plain,
% 161.14/23.66 ((((identity) = (sk_c8))
% 161.14/23.66 | ((identity) = (multiply @ (inverse @ sk_c8) @ sk_c4)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl121102])).
% 161.14/23.66 thf(zip_derived_cl233228, plain,
% 161.14/23.66 ((((identity) = (multiply @ sk_c4 @ sk_c4))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((identity) = (sk_c8)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl74863, zip_derived_cl121280])).
% 161.14/23.66 thf(zip_derived_cl233273, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((identity) = (multiply @ sk_c4 @ sk_c4)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl233228])).
% 161.14/23.66 thf(zip_derived_cl234094, plain,
% 161.14/23.66 ((((identity) = (multiply @ sk_c4 @ sk_c7))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((sk_c8) = (identity)))),
% 161.14/23.66 inference('sup+', [status(thm)],
% 161.14/23.66 [zip_derived_cl74764, zip_derived_cl233273])).
% 161.14/23.66 thf(zip_derived_cl234104, plain,
% 161.14/23.66 ((((sk_c8) = (identity)) | ((identity) = (multiply @ sk_c4 @ sk_c7)))),
% 161.14/23.66 inference('simplify', [status(thm)], [zip_derived_cl234094])).
% 161.14/23.66 thf(zip_derived_cl5, plain,
% 161.14/23.66 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.66 inference('cnf', [status(esa)], [zf_stmt_17])).
% 161.14/23.66 thf(zip_derived_cl236070, plain,
% 161.14/23.66 ((((identity) = (sk_c8))
% 161.14/23.66 | ((sk_c8) = (identity))
% 161.14/23.66 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl234104, zip_derived_cl5])).
% 161.14/23.67 thf(zip_derived_cl236164, plain,
% 161.14/23.67 ((((multiply @ sk_c1 @ sk_c2) = (sk_c8)) | ((identity) = (sk_c8)))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl236070])).
% 161.14/23.67 thf(zip_derived_cl66414, plain,
% 161.14/23.67 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl716, zip_derived_cl711])).
% 161.14/23.67 thf(zip_derived_cl875, plain,
% 161.14/23.67 ((((sk_c8) = (identity)) | ((inverse @ sk_c1) = (sk_c2)))),
% 161.14/23.67 inference('demod', [status(thm)], [zip_derived_cl864, zip_derived_cl1])).
% 161.14/23.67 thf(zip_derived_cl1, plain,
% 161.14/23.67 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.67 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.67 thf(zip_derived_cl919, plain,
% 161.14/23.67 ((((multiply @ sk_c2 @ sk_c1) = (identity)) | ((sk_c8) = (identity)))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl875, zip_derived_cl1])).
% 161.14/23.67 thf(zip_derived_cl53, plain,
% 161.14/23.67 (![X0 : $i, X1 : $i]:
% 161.14/23.67 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 161.14/23.67 inference('demod', [status(thm)], [zip_derived_cl43, zip_derived_cl0])).
% 161.14/23.67 thf(zip_derived_cl977, plain,
% 161.14/23.67 ((((sk_c1) = (multiply @ (inverse @ sk_c2) @ identity))
% 161.14/23.67 | ((sk_c8) = (identity)))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl919, zip_derived_cl53])).
% 161.14/23.67 thf(zip_derived_cl74849, plain,
% 161.14/23.67 ((((sk_c1) = (inverse @ sk_c2)) | ((sk_c8) = (identity)))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl977])).
% 161.14/23.67 thf(zip_derived_cl1, plain,
% 161.14/23.67 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 161.14/23.67 inference('cnf', [status(esa)], [left_inverse])).
% 161.14/23.67 thf(zip_derived_cl76142, plain,
% 161.14/23.67 ((((multiply @ sk_c1 @ sk_c2) = (identity)) | ((sk_c8) = (identity)))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl74849, zip_derived_cl1])).
% 161.14/23.67 thf(zip_derived_cl243746, plain,
% 161.14/23.67 ((((sk_c8) = (identity))
% 161.14/23.67 | ((identity) = (sk_c8))
% 161.14/23.67 | ((sk_c8) = (identity)))),
% 161.14/23.67 inference('sup+', [status(thm)],
% 161.14/23.67 [zip_derived_cl236164, zip_derived_cl76142])).
% 161.14/23.67 thf(zip_derived_cl243818, plain, (((sk_c8) = (identity))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl243746])).
% 161.14/23.67 thf(zip_derived_cl245734, plain,
% 161.14/23.67 (![X0 : $i, X1 : $i]:
% 161.14/23.67 (((identity) != (X1))
% 161.14/23.67 | ((identity) != (sk_c7))
% 161.14/23.67 | ((identity) != (identity))
% 161.14/23.67 | ((X0) != (identity)))),
% 161.14/23.67 inference('demod', [status(thm)],
% 161.14/23.67 [zip_derived_cl243224, zip_derived_cl243818])).
% 161.14/23.67 thf(zip_derived_cl245735, plain,
% 161.14/23.67 (![X0 : $i, X1 : $i]:
% 161.14/23.67 (((X0) != (identity)) | ((identity) != (sk_c7)) | ((identity) != (X1)))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl245734])).
% 161.14/23.67 thf(zip_derived_cl1425, plain,
% 161.14/23.67 ((((inverse @ sk_c8) = (sk_c7)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl1422])).
% 161.14/23.67 thf(zip_derived_cl243818, plain, (((sk_c8) = (identity))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl243746])).
% 161.14/23.67 thf(zip_derived_cl74814, plain, (((inverse @ identity) = (identity))),
% 161.14/23.67 inference('sup+', [status(thm)], [zip_derived_cl66414, zip_derived_cl1])).
% 161.14/23.67 thf(zip_derived_cl243818, plain, (((sk_c8) = (identity))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl243746])).
% 161.14/23.67 thf(zip_derived_cl243818, plain, (((sk_c8) = (identity))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl243746])).
% 161.14/23.67 thf(zip_derived_cl0, plain,
% 161.14/23.67 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 161.14/23.67 inference('cnf', [status(esa)], [left_identity])).
% 161.14/23.67 thf(zip_derived_cl244716, plain,
% 161.14/23.67 ((((identity) = (sk_c7)) | ((sk_c7) = (identity)))),
% 161.14/23.67 inference('demod', [status(thm)],
% 161.14/23.67 [zip_derived_cl1425, zip_derived_cl243818,
% 161.14/23.67 zip_derived_cl74814, zip_derived_cl243818,
% 161.14/23.67 zip_derived_cl243818, zip_derived_cl0])).
% 161.14/23.67 thf(zip_derived_cl244717, plain, (((identity) = (sk_c7))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl244716])).
% 161.14/23.67 thf(zip_derived_cl246178, plain,
% 161.14/23.67 (![X0 : $i, X1 : $i]:
% 161.14/23.67 (((X0) != (identity))
% 161.14/23.67 | ((identity) != (identity))
% 161.14/23.67 | ((identity) != (X1)))),
% 161.14/23.67 inference('demod', [status(thm)],
% 161.14/23.67 [zip_derived_cl245735, zip_derived_cl244717])).
% 161.14/23.67 thf(zip_derived_cl246179, plain,
% 161.14/23.67 (![X0 : $i, X1 : $i]: (((identity) != (X1)) | ((X0) != (identity)))),
% 161.14/23.67 inference('simplify', [status(thm)], [zip_derived_cl246178])).
% 161.14/23.67 thf(zip_derived_cl246180, plain, (![X0 : $i]: ((X0) != (identity))),
% 161.14/23.67 inference('condensation', [status(thm)], [zip_derived_cl246179])).
% 161.14/23.67 thf(zip_derived_cl246181, plain, ($false),
% 161.14/23.67 inference('eq_res', [status(thm)], [zip_derived_cl246180])).
% 161.14/23.67
% 161.14/23.67 % SZS output end Refutation
% 161.14/23.67
% 161.14/23.67
% 161.14/23.67 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 161.14/23.67 % Terminating...
% 161.65/23.73 % Runner terminated.
% 161.65/23.74 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------