TSTP Solution File: GRP248-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP248-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2yKtSt7eEW true
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:50:53 EDT 2023
% Result : Unsatisfiable 0.56s 1.13s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP248-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2yKtSt7eEW true
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:29:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.36 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.51/0.71 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.51/0.73 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.51/0.75 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.51/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.51/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.51/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.56/0.76 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.56/1.13 % Solved by fo/fo7.sh.
% 0.56/1.13 % done 1119 iterations in 0.335s
% 0.56/1.13 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.56/1.13 % SZS output start Refutation
% 0.56/1.13 thf(sk_c6_type, type, sk_c6: $i).
% 0.56/1.13 thf(sk_c9_type, type, sk_c9: $i).
% 0.56/1.13 thf(sk_c2_type, type, sk_c2: $i).
% 0.56/1.13 thf(sk_c8_type, type, sk_c8: $i).
% 0.56/1.13 thf(sk_c5_type, type, sk_c5: $i).
% 0.56/1.13 thf(identity_type, type, identity: $i).
% 0.56/1.13 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.56/1.13 thf(sk_c10_type, type, sk_c10: $i).
% 0.56/1.13 thf(inverse_type, type, inverse: $i > $i).
% 0.56/1.13 thf(sk_c4_type, type, sk_c4: $i).
% 0.56/1.13 thf(sk_c3_type, type, sk_c3: $i).
% 0.56/1.13 thf(sk_c7_type, type, sk_c7: $i).
% 0.56/1.13 thf(sk_c1_type, type, sk_c1: $i).
% 0.56/1.13 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(associativity, axiom,
% 0.56/1.13 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.56/1.13 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.56/1.13 thf(zip_derived_cl2, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.56/1.13 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.56/1.13 inference('cnf', [status(esa)], [associativity])).
% 0.56/1.13 thf(zip_derived_cl134, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((multiply @ identity @ X0)
% 0.56/1.13 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl180, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl232, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl180, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl581, plain, (((inverse @ identity) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl232, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl181, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl178, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl165, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl181, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(prove_this_43, conjecture,
% 0.56/1.13 (~( ( ( multiply @ X3 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ X7 ) != ( X3 ) ) |
% 0.56/1.13 ( ( multiply @ X7 @ X3 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ X2 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ X6 @ sk_c8 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ X6 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ X5 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ X5 @ sk_c9 ) != ( sk_c8 ) ) |
% 0.56/1.13 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_0, negated_conjecture,
% 0.56/1.13 (( ( multiply @ X3 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ X7 ) != ( X3 ) ) |
% 0.56/1.13 ( ( multiply @ X7 @ X3 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ X2 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ X2 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ X1 @ sk_c9 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ X1 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ X6 @ sk_c8 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ X6 ) != ( sk_c10 ) ) | ( ( inverse @ X5 ) != ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ X5 @ sk_c9 ) != ( sk_c8 ) ) |
% 0.56/1.13 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ X4 @ sk_c10 ) != ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_43])).
% 0.56/1.13 thf(zip_derived_cl45, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 0.56/1.13 (((multiply @ X0 @ sk_c8) != (sk_c9))
% 0.56/1.13 | ((inverse @ X1) != (X0))
% 0.56/1.13 | ((multiply @ X1 @ X0) != (sk_c9))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 0.56/1.13 | ((inverse @ X2) != (sk_c9))
% 0.56/1.13 | ((multiply @ X3 @ sk_c9) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (sk_c10))
% 0.56/1.13 | ((multiply @ X4 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X4) != (sk_c10))
% 0.56/1.13 | ((inverse @ X5) != (sk_c9))
% 0.56/1.13 | ((multiply @ X5 @ sk_c9) != (sk_c8))
% 0.56/1.13 | ((inverse @ X6) != (sk_c10))
% 0.56/1.13 | ((multiply @ X6 @ sk_c10) != (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.56/1.13 thf(zip_derived_cl46, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.56/1.13 (((multiply @ X0 @ sk_c10) != (sk_c9))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c9) != (sk_c8))
% 0.56/1.13 | ((inverse @ X1) != (sk_c9))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (sk_c10))
% 0.56/1.13 | ((multiply @ X3 @ sk_c9) != (sk_c10))
% 0.56/1.13 | ((inverse @ X4) != (sk_c9))
% 0.56/1.13 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 0.56/1.13 | ((multiply @ X5 @ (inverse @ X5)) != (sk_c9))
% 0.56/1.13 | ((multiply @ (inverse @ X5) @ sk_c8) != (sk_c9)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl45])).
% 0.56/1.13 thf(zip_derived_cl641, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.56/1.13 (((X0) != (sk_c10))
% 0.56/1.13 | ((multiply @ (inverse @ X1) @ sk_c8) != (sk_c9))
% 0.56/1.13 | ((multiply @ X1 @ (inverse @ X1)) != (sk_c9))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (sk_c9))
% 0.56/1.13 | ((inverse @ X2) != (sk_c9))
% 0.56/1.13 | ((multiply @ X3 @ sk_c9) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (sk_c10))
% 0.56/1.13 | ((multiply @ X4 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X4) != (sk_c10))
% 0.56/1.13 | ((inverse @ X5) != (sk_c9))
% 0.56/1.13 | ((multiply @ X5 @ sk_c9) != (sk_c8))
% 0.56/1.13 | ((multiply @ (inverse @ X0) @ sk_c10) != (sk_c9)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl633, zip_derived_cl46])).
% 0.56/1.13 thf(zip_derived_cl831, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ sk_c10) @ sk_c10) != (sk_c9))
% 0.56/1.13 | ((multiply @ X0 @ sk_c9) != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (sk_c9))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X2 @ sk_c9) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (sk_c9))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (sk_c9))
% 0.56/1.13 | ((multiply @ X4 @ (inverse @ X4)) != (sk_c9))
% 0.56/1.13 | ((multiply @ (inverse @ X4) @ sk_c8) != (sk_c9)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl641])).
% 0.56/1.13 thf(zip_derived_cl832, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ sk_c10) @ sk_c10) != (sk_c9))
% 0.56/1.13 | ((multiply @ X0 @ (multiply @ (inverse @ sk_c10) @ sk_c10))
% 0.56/1.13 != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (multiply @ (inverse @ sk_c10) @ sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X2 @ (multiply @ (inverse @ sk_c10) @ sk_c10))
% 0.56/1.13 != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (multiply @ (inverse @ sk_c10) @ sk_c10))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8)
% 0.56/1.13 != (multiply @ (inverse @ sk_c10) @ sk_c10))
% 0.56/1.13 | ((multiply @ X4 @ (inverse @ X4))
% 0.56/1.13 != (multiply @ (inverse @ sk_c10) @ sk_c10))
% 0.56/1.13 | ((multiply @ (inverse @ X4) @ sk_c8)
% 0.56/1.13 != (multiply @ (inverse @ sk_c10) @ sk_c10)))),
% 0.56/1.13 inference('local_rewriting', [status(thm)], [zip_derived_cl831])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl833, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((identity) != (sk_c9))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X4 @ (inverse @ X4)) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X4) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl832, zip_derived_cl1, zip_derived_cl1,
% 0.56/1.13 zip_derived_cl596, zip_derived_cl1, zip_derived_cl1,
% 0.56/1.13 zip_derived_cl596, zip_derived_cl1, zip_derived_cl1,
% 0.56/1.13 zip_derived_cl1, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1110, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((identity) != (sk_c9))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((identity) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X4) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl833, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl1111, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X4) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((identity) != (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1110])).
% 0.56/1.13 thf(prove_this_10, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c5 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_1, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c5 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 0.56/1.13 thf(zip_derived_cl12, plain,
% 0.56/1.13 ((((inverse @ sk_c5) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.56/1.13 thf(prove_this_13, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_2, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 0.56/1.13 thf(zip_derived_cl15, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.56/1.13 thf(prove_this_12, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_3, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 0.56/1.13 thf(zip_derived_cl14, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c7) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.56/1.13 thf(zip_derived_cl88, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl14])).
% 0.56/1.13 thf(zip_derived_cl89, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl88])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1106, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl640])).
% 0.56/1.13 thf(prove_this_25, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_4, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 0.56/1.13 thf(zip_derived_cl27, plain,
% 0.56/1.13 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl654, plain,
% 0.56/1.13 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl633])).
% 0.56/1.13 thf(prove_this_18, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.56/1.13 thf(zf_stmt_5, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 0.56/1.13 thf(zip_derived_cl20, plain,
% 0.56/1.13 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.56/1.13 thf(zip_derived_cl1073, plain,
% 0.56/1.13 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 0.56/1.13 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl654, zip_derived_cl20])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1090, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c5 @ sk_c8) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl1073, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1091, plain,
% 0.56/1.13 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1090])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl1427, plain,
% 0.56/1.13 ((((sk_c8) = (multiply @ (inverse @ sk_c5) @ sk_c9))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1091, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl1575, plain,
% 0.56/1.13 ((((multiply @ (inverse @ sk_c5) @ sk_c9) != (identity))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('eq_fact', [status(thm)], [zip_derived_cl1427])).
% 0.56/1.13 thf(zip_derived_cl1581, plain,
% 0.56/1.13 ((((multiply @ (inverse @ sk_c5) @ identity) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl1106, zip_derived_cl1575])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl1590, plain,
% 0.56/1.13 ((((inverse @ sk_c5) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl1581, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl1596, plain,
% 0.56/1.13 ((((sk_c9) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((identity) = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl12, zip_derived_cl1590])).
% 0.56/1.13 thf(zip_derived_cl1604, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((sk_c9) != (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1596])).
% 0.56/1.13 thf(prove_this_27, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_6, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_27])).
% 0.56/1.13 thf(zip_derived_cl29, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl55, plain,
% 0.56/1.13 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 0.56/1.13 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl29, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl191, plain,
% 0.56/1.13 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.56/1.13 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl55, zip_derived_cl165])).
% 0.56/1.13 thf(prove_this_20, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.56/1.13 thf(zf_stmt_7, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_20])).
% 0.56/1.13 thf(zip_derived_cl22, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.56/1.13 thf(zip_derived_cl278, plain,
% 0.56/1.13 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.56/1.13 = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c6) = (sk_c7))
% 0.56/1.13 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl191, zip_derived_cl22])).
% 0.56/1.13 thf(zip_derived_cl2, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.56/1.13 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.56/1.13 inference('cnf', [status(esa)], [associativity])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl294, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c6) = (sk_c7))
% 0.56/1.13 | ((inverse @ sk_c6) = (sk_c7)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl278, zip_derived_cl2, zip_derived_cl0,
% 0.56/1.13 zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl295, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl294])).
% 0.56/1.13 thf(prove_this_26, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_8, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 0.56/1.13 thf(zip_derived_cl28, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c7) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl655, plain,
% 0.56/1.13 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c6 @ sk_c7) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl28, zip_derived_cl633])).
% 0.56/1.13 thf(prove_this_19, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.56/1.13 thf(zf_stmt_9, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 0.56/1.13 thf(zip_derived_cl21, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c7) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.56/1.13 thf(zip_derived_cl1159, plain,
% 0.56/1.13 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 0.56/1.13 | ((multiply @ sk_c6 @ sk_c7) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c6 @ sk_c7) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl655, zip_derived_cl21])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1176, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((multiply @ sk_c6 @ sk_c7) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c6 @ sk_c7) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl1159, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1177, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c7) = (sk_c9)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1176])).
% 0.56/1.13 thf(zip_derived_cl1447, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c9))
% 0.56/1.13 | ((identity) = (sk_c8))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl295, zip_derived_cl1177])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1451, plain,
% 0.56/1.13 ((((identity) = (sk_c9))
% 0.56/1.13 | ((identity) = (sk_c8))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl1447, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl1452, plain,
% 0.56/1.13 ((((identity) = (sk_c8)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1451])).
% 0.56/1.13 thf(zip_derived_cl1611, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl1604, zip_derived_cl1452])).
% 0.56/1.13 thf(prove_this_11, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_10, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 0.56/1.13 thf(zip_derived_cl13, plain,
% 0.56/1.13 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.56/1.13 thf(zip_derived_cl1614, plain,
% 0.56/1.13 ((((multiply @ sk_c5 @ identity) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1611, zip_derived_cl13])).
% 0.56/1.13 thf(zip_derived_cl1630, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c5 @ identity) = (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1614])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl1728, plain,
% 0.56/1.13 ((((sk_c9) = (sk_c5)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1630, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl12, plain,
% 0.56/1.13 ((((inverse @ sk_c5) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.56/1.13 thf(zip_derived_cl1737, plain,
% 0.56/1.13 ((((inverse @ sk_c9) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1728, zip_derived_cl12])).
% 0.56/1.13 thf(zip_derived_cl1751, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((inverse @ sk_c9) = (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1737])).
% 0.56/1.13 thf(zip_derived_cl1611, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl1604, zip_derived_cl1452])).
% 0.56/1.13 thf(zip_derived_cl581, plain, (((inverse @ identity) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl232, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1106, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl15, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.56/1.13 thf(prove_this_14, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_11, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c7 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 0.56/1.13 thf(zip_derived_cl16, plain,
% 0.56/1.13 ((((multiply @ sk_c7 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl201, plain,
% 0.56/1.13 ((((sk_c8) = (multiply @ (inverse @ sk_c7) @ sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl165])).
% 0.56/1.13 thf(zip_derived_cl1941, plain,
% 0.56/1.13 ((((sk_c8) = (multiply @ (inverse @ (inverse @ sk_c6)) @ sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl201])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl1950, plain,
% 0.56/1.13 ((((sk_c8) = (multiply @ sk_c6 @ sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl1941, zip_derived_cl633])).
% 0.56/1.13 thf(zip_derived_cl1951, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((sk_c8) = (multiply @ sk_c6 @ sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1950])).
% 0.56/1.13 thf(zip_derived_cl1961, plain,
% 0.56/1.13 ((((sk_c8) = (multiply @ sk_c6 @ identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1106, zip_derived_cl1951])).
% 0.56/1.13 thf(zip_derived_cl1963, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((sk_c8) = (multiply @ sk_c6 @ identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1961])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl2066, plain,
% 0.56/1.13 ((((sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1963, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl1106, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl1611, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl1604, zip_derived_cl1452])).
% 0.56/1.13 thf(zip_derived_cl16, plain,
% 0.56/1.13 ((((multiply @ sk_c7 @ sk_c8) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.56/1.13 thf(zip_derived_cl1615, plain,
% 0.56/1.13 ((((multiply @ sk_c7 @ identity) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1611, zip_derived_cl16])).
% 0.56/1.13 thf(zip_derived_cl1631, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c7 @ identity) = (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1615])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl1779, plain,
% 0.56/1.13 ((((sk_c9) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1631, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl15, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.56/1.13 thf(zip_derived_cl1794, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1779, zip_derived_cl15])).
% 0.56/1.13 thf(zip_derived_cl1805, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((inverse @ sk_c6) = (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1794])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1811, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c9) = (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1805, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl1932, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ identity) = (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1106, zip_derived_cl1811])).
% 0.56/1.13 thf(zip_derived_cl1934, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c6 @ identity) = (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1932])).
% 0.56/1.13 thf(zip_derived_cl2, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.56/1.13 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.56/1.13 inference('cnf', [status(esa)], [associativity])).
% 0.56/1.13 thf(zip_derived_cl2647, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((multiply @ identity @ X0)
% 0.56/1.13 = (multiply @ sk_c6 @ (multiply @ identity @ X0)))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1934, zip_derived_cl2])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl2659, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((X0) = (multiply @ sk_c6 @ X0)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl2647, zip_derived_cl0, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl2664, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (identity)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl2659, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl2692, plain,
% 0.56/1.13 ((((inverse @ sk_c8) = (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl2066, zip_derived_cl2664])).
% 0.56/1.13 thf(zip_derived_cl2695, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((inverse @ sk_c8) = (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl2692])).
% 0.56/1.13 thf(zip_derived_cl1106, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl640])).
% 0.56/1.13 thf(prove_this_9, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_12, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 0.56/1.13 thf(zip_derived_cl11, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_12])).
% 0.56/1.13 thf(zip_derived_cl1138, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ identity) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1106, zip_derived_cl11])).
% 0.56/1.13 thf(zip_derived_cl1152, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c4 @ identity) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1138])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl1900, plain,
% 0.56/1.13 ((((sk_c10) = (sk_c4)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1152, zip_derived_cl596])).
% 0.56/1.13 thf(prove_this_8, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_13, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c1 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 0.56/1.13 thf(zip_derived_cl10, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_13])).
% 0.56/1.13 thf(zip_derived_cl1910, plain,
% 0.56/1.13 ((((inverse @ sk_c10) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1900, zip_derived_cl10])).
% 0.56/1.13 thf(zip_derived_cl1922, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((inverse @ sk_c10) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1910])).
% 0.56/1.13 thf(zip_derived_cl1106, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl1111, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X4) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((identity) != (sk_c9)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1110])).
% 0.56/1.13 thf(zip_derived_cl1363, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((identity) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X4) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl1106, zip_derived_cl1111])).
% 0.56/1.13 thf(zip_derived_cl1364, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X4) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1363])).
% 0.56/1.13 thf(zip_derived_cl3313, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/1.13 (((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (sk_c10))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c10) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (identity))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X3) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl1364])).
% 0.56/1.13 thf(zip_derived_cl3314, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/1.13 (((sk_c10) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ (inverse @ X0) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((X3) != (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl1922, zip_derived_cl3313])).
% 0.56/1.13 thf(zip_derived_cl3315, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/1.13 (((X3) != (sk_c8))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X0) @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3314])).
% 0.56/1.13 thf(zip_derived_cl3328, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 (((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((multiply @ (inverse @ X0) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((multiply @ X2 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X2) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c8) != (identity)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl3315])).
% 0.56/1.13 thf(zip_derived_cl3336, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 (((identity) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((multiply @ X0 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X2) @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl2695, zip_derived_cl3328])).
% 0.56/1.13 thf(zip_derived_cl3350, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X2) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((multiply @ X0 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3336])).
% 0.56/1.13 thf(zip_derived_cl3367, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((identity) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((multiply @ X0 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((multiply @ identity @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X1) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl581, zip_derived_cl3350])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl3401, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((identity) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((multiply @ X0 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X1) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl3367, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl3402, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X1) @ sk_c8) != (identity))
% 0.56/1.13 | ((sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X0 @ sk_c8) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3401])).
% 0.56/1.13 thf(zip_derived_cl3403, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X1) @ identity) != (identity))
% 0.56/1.13 | ((sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X0 @ identity) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('local_rewriting', [status(thm)], [zip_derived_cl3402])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3435, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((inverse @ X1) != (identity))
% 0.56/1.13 | ((sk_c8) != (identity))
% 0.56/1.13 | ((X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl3403, zip_derived_cl596, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl3443, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((identity) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ X1) != (identity)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl1611, zip_derived_cl3435])).
% 0.56/1.13 thf(zip_derived_cl3453, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((inverse @ X1) != (identity))
% 0.56/1.13 | ((X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3443])).
% 0.56/1.13 thf(zip_derived_cl3458, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c10) != (sk_c10))
% 0.56/1.13 | ((inverse @ X0) != (identity)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl3453])).
% 0.56/1.13 thf(zip_derived_cl1922, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((inverse @ sk_c10) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1910])).
% 0.56/1.13 thf(zip_derived_cl3459, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((inverse @ X0) != (identity)) | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3458, zip_derived_cl1922])).
% 0.56/1.13 thf(zip_derived_cl3464, plain,
% 0.56/1.13 ((((sk_c9) != (identity))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c1) = (sk_c10)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl1751, zip_derived_cl3459])).
% 0.56/1.13 thf(zip_derived_cl3498, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((sk_c9) != (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3464])).
% 0.56/1.13 thf(zip_derived_cl1106, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c10)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl89, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3590, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X4) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((identity) != (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl1111, zip_derived_cl3525, zip_derived_cl3525,
% 0.56/1.13 zip_derived_cl3525, zip_derived_cl3525])).
% 0.56/1.13 thf(prove_this_6, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_14, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c6 ) = ( sk_c7 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 0.56/1.13 thf(zip_derived_cl8, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_14])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl3531, plain,
% 0.56/1.13 ((((inverse @ sk_c6) = (sk_c7)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl8, zip_derived_cl3525, zip_derived_cl640])).
% 0.56/1.13 thf(prove_this_5, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_15, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 0.56/1.13 thf(zip_derived_cl7, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c7) = (sk_c9))
% 0.56/1.13 | ((multiply @ sk_c1 @ sk_c10) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_15])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl3530, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ sk_c7) = (sk_c9)) | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl7, zip_derived_cl3525, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl3735, plain,
% 0.56/1.13 ((((multiply @ sk_c6 @ (inverse @ sk_c6)) = (sk_c9))
% 0.56/1.13 | ((identity) = (sk_c9))
% 0.56/1.13 | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl3531, zip_derived_cl3530])).
% 0.56/1.13 thf(zip_derived_cl640, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl633, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl3741, plain,
% 0.56/1.13 ((((identity) = (sk_c9))
% 0.56/1.13 | ((identity) = (sk_c9))
% 0.56/1.13 | ((identity) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl3735, zip_derived_cl640])).
% 0.56/1.13 thf(zip_derived_cl3742, plain, (((identity) = (sk_c9))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3741])).
% 0.56/1.13 thf(zip_derived_cl3785, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X4) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((X0) != (sk_c8))
% 0.56/1.13 | ((identity) != (identity)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl3590, zip_derived_cl3742])).
% 0.56/1.13 thf(zip_derived_cl3786, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.56/1.13 (((X0) != (sk_c8))
% 0.56/1.13 | ((inverse @ X0) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X3) != (identity))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ (inverse @ X4) @ sk_c8) != (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3785])).
% 0.56/1.13 thf(zip_derived_cl3795, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/1.13 (((multiply @ (inverse @ X0) @ sk_c8) != (identity))
% 0.56/1.13 | ((multiply @ X1 @ sk_c8) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((multiply @ X3 @ sk_c8) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X3) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ sk_c8) != (identity)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl3786])).
% 0.56/1.13 thf(prove_this_24, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c5 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_16, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c5 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_24])).
% 0.56/1.13 thf(zip_derived_cl26, plain,
% 0.56/1.13 ((((inverse @ sk_c5) = (sk_c9)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_16])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl75, plain,
% 0.56/1.13 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 0.56/1.13 | ((inverse @ sk_c5) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl26, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl193, plain,
% 0.56/1.13 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.56/1.13 | ((inverse @ sk_c5) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl75, zip_derived_cl165])).
% 0.56/1.13 thf(prove_this_17, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c5 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.56/1.13 thf(zf_stmt_17, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c5 ) = ( sk_c9 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 0.56/1.13 thf(zip_derived_cl19, plain,
% 0.56/1.13 ((((inverse @ sk_c5) = (sk_c9)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_17])).
% 0.56/1.13 thf(zip_derived_cl444, plain,
% 0.56/1.13 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.56/1.13 = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c5) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c5) = (sk_c9)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl193, zip_derived_cl19])).
% 0.56/1.13 thf(zip_derived_cl2, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.56/1.13 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.56/1.13 inference('cnf', [status(esa)], [associativity])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl461, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c5) = (sk_c9))
% 0.56/1.13 | ((inverse @ sk_c5) = (sk_c9)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl444, zip_derived_cl2, zip_derived_cl0,
% 0.56/1.13 zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl462, plain,
% 0.56/1.13 ((((inverse @ sk_c5) = (sk_c9)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl461])).
% 0.56/1.13 thf(zip_derived_cl3742, plain, (((identity) = (sk_c9))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3741])).
% 0.56/1.13 thf(zip_derived_cl3757, plain,
% 0.56/1.13 ((((inverse @ sk_c5) = (identity)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl462, zip_derived_cl3742])).
% 0.56/1.13 thf(zip_derived_cl1575, plain,
% 0.56/1.13 ((((multiply @ (inverse @ sk_c5) @ sk_c9) != (identity))
% 0.56/1.13 | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('eq_fact', [status(thm)], [zip_derived_cl1427])).
% 0.56/1.13 thf(zip_derived_cl3742, plain, (((identity) = (sk_c9))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3741])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3773, plain,
% 0.56/1.13 ((((inverse @ sk_c5) != (identity)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl1575, zip_derived_cl3742, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl3809, plain, (((identity) = (sk_c8))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3757, zip_derived_cl3773])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3809, plain, (((identity) = (sk_c8))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3757, zip_derived_cl3773])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3809, plain, (((identity) = (sk_c8))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3757, zip_derived_cl3773])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3809, plain, (((identity) = (sk_c8))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3757, zip_derived_cl3773])).
% 0.56/1.13 thf(zip_derived_cl581, plain, (((inverse @ identity) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl232, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl3816, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/1.13 (((inverse @ X0) != (identity))
% 0.56/1.13 | ((X1) != (identity))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((X3) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X3) != (inverse @ sk_c1))
% 0.56/1.13 | ((identity) != (identity)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl3795, zip_derived_cl3809, zip_derived_cl596,
% 0.56/1.13 zip_derived_cl3809, zip_derived_cl596, zip_derived_cl3809,
% 0.56/1.13 zip_derived_cl596, zip_derived_cl3809, zip_derived_cl581])).
% 0.56/1.13 thf(zip_derived_cl3817, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.56/1.13 (((inverse @ X3) != (inverse @ sk_c1))
% 0.56/1.13 | ((X3) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (identity))
% 0.56/1.13 | ((X1) != (identity))
% 0.56/1.13 | ((inverse @ X0) != (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3816])).
% 0.56/1.13 thf(zip_derived_cl3842, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 (((inverse @ X0) != (identity))
% 0.56/1.13 | ((inverse @ identity) != (identity))
% 0.56/1.13 | ((X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl3817])).
% 0.56/1.13 thf(zip_derived_cl581, plain, (((inverse @ identity) = (identity))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl232, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl3843, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 (((inverse @ X0) != (identity))
% 0.56/1.13 | ((identity) != (identity))
% 0.56/1.13 | ((X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X2) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl3842, zip_derived_cl581])).
% 0.56/1.13 thf(zip_derived_cl3844, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 (((inverse @ X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((X2) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (identity)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3843])).
% 0.56/1.13 thf(zip_derived_cl3845, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((identity) != (identity))
% 0.56/1.13 | ((X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X1) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('sup-', [status(thm)], [zip_derived_cl581, zip_derived_cl3844])).
% 0.56/1.13 thf(zip_derived_cl3847, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 (((inverse @ X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((X1) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((X0) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3845])).
% 0.56/1.13 thf(zip_derived_cl3848, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ (inverse @ sk_c1)) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl3847])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl3849, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (inverse @ sk_c1))
% 0.56/1.13 | ((sk_c1) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl3848, zip_derived_cl633])).
% 0.56/1.13 thf(zip_derived_cl3850, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((X0) != (sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (sk_c1))
% 0.56/1.13 | ((sk_c1) != (inverse @ sk_c1)))),
% 0.56/1.13 inference('local_rewriting', [status(thm)], [zip_derived_cl3849])).
% 0.56/1.13 thf(prove_this_30, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_18, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_30])).
% 0.56/1.13 thf(zip_derived_cl32, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c3) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_18])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl659, plain,
% 0.56/1.13 ((((sk_c3) = (inverse @ sk_c10))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl32, zip_derived_cl633])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3577, plain,
% 0.56/1.13 ((((sk_c3) = (sk_c1)) | ((multiply @ sk_c4 @ sk_c9) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl659, zip_derived_cl3525, zip_derived_cl633,
% 0.56/1.13 zip_derived_cl3525])).
% 0.56/1.13 thf(zip_derived_cl3742, plain, (((identity) = (sk_c9))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3741])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3937, plain,
% 0.56/1.13 ((((sk_c3) = (sk_c1)) | ((sk_c4) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl3577, zip_derived_cl3742, zip_derived_cl596])).
% 0.56/1.13 thf(prove_this_23, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_19, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_23])).
% 0.56/1.13 thf(zip_derived_cl25, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_19])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl652, plain,
% 0.56/1.13 ((((sk_c2) = (inverse @ sk_c9)) | ((multiply @ sk_c4 @ sk_c9) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl633])).
% 0.56/1.13 thf(prove_this_16, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.56/1.13 thf(zf_stmt_20, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 0.56/1.13 thf(zip_derived_cl18, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_20])).
% 0.56/1.13 thf(zip_derived_cl1020, plain,
% 0.56/1.13 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl652, zip_derived_cl18])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl1037, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl1020, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl1038, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1037])).
% 0.56/1.13 thf(prove_this_37, conjecture,
% 0.56/1.13 (~( ( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_21, negated_conjecture,
% 0.56/1.13 (( ( multiply @ sk_c4 @ sk_c9 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_37])).
% 0.56/1.13 thf(zip_derived_cl39, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c3 @ sk_c8) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_21])).
% 0.56/1.13 thf(zip_derived_cl1057, plain,
% 0.56/1.13 ((((multiply @ sk_c3 @ identity) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c4 @ sk_c9) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl1038, zip_derived_cl39])).
% 0.56/1.13 thf(zip_derived_cl1067, plain,
% 0.56/1.13 ((((multiply @ sk_c4 @ sk_c9) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c3 @ identity) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl1057])).
% 0.56/1.13 thf(zip_derived_cl3742, plain, (((identity) = (sk_c9))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl3741])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl5215, plain,
% 0.56/1.13 ((((sk_c4) = (inverse @ sk_c1))
% 0.56/1.13 | ((multiply @ sk_c3 @ identity) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl1067, zip_derived_cl3742, zip_derived_cl596,
% 0.56/1.13 zip_derived_cl3525, zip_derived_cl3525])).
% 0.56/1.13 thf(zip_derived_cl5227, plain,
% 0.56/1.13 ((((multiply @ sk_c1 @ identity) = (inverse @ sk_c1))
% 0.56/1.13 | ((sk_c4) = (inverse @ sk_c1))
% 0.56/1.13 | ((sk_c4) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl3937, zip_derived_cl5215])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(zip_derived_cl5237, plain,
% 0.56/1.13 ((((sk_c1) = (inverse @ sk_c1))
% 0.56/1.13 | ((sk_c4) = (inverse @ sk_c1))
% 0.56/1.13 | ((sk_c4) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl5227, zip_derived_cl596])).
% 0.56/1.13 thf(zip_derived_cl5238, plain,
% 0.56/1.13 ((((sk_c4) = (inverse @ sk_c1)) | ((sk_c1) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl5237])).
% 0.56/1.13 thf(zip_derived_cl596, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 0.56/1.13 thf(prove_this_22, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c2 ) = ( sk_c9 ) ) ))).
% 0.56/1.13 thf(zf_stmt_22, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c9 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 0.56/1.13 thf(zip_derived_cl24, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c2) = (sk_c9)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_22])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl71, plain,
% 0.56/1.13 ((((multiply @ sk_c9 @ sk_c2) = (identity))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl24, zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl165, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i]:
% 0.56/1.13 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.56/1.13 inference('demod', [status(thm)], [zip_derived_cl134, zip_derived_cl0])).
% 0.56/1.13 thf(zip_derived_cl192, plain,
% 0.56/1.13 ((((sk_c2) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl71, zip_derived_cl165])).
% 0.56/1.13 thf(prove_this_15, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.56/1.13 thf(zf_stmt_23, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c8 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 0.56/1.13 thf(zip_derived_cl17, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c8)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_23])).
% 0.56/1.13 thf(zip_derived_cl352, plain,
% 0.56/1.13 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.56/1.13 = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl192, zip_derived_cl17])).
% 0.56/1.13 thf(zip_derived_cl2, plain,
% 0.56/1.13 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.56/1.13 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.56/1.13 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.56/1.13 inference('cnf', [status(esa)], [associativity])).
% 0.56/1.13 thf(zip_derived_cl0, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_identity])).
% 0.56/1.13 thf(zip_derived_cl1, plain,
% 0.56/1.13 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.56/1.13 inference('cnf', [status(esa)], [left_inverse])).
% 0.56/1.13 thf(zip_derived_cl369, plain,
% 0.56/1.13 ((((identity) = (sk_c8))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl352, zip_derived_cl2, zip_derived_cl0,
% 0.56/1.13 zip_derived_cl1])).
% 0.56/1.13 thf(zip_derived_cl370, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10)) | ((identity) = (sk_c8)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl369])).
% 0.56/1.13 thf(prove_this_36, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_24, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 0.56/1.13 thf(zip_derived_cl38, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c3 @ sk_c8) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_24])).
% 0.56/1.13 thf(zip_derived_cl383, plain,
% 0.56/1.13 ((((multiply @ sk_c3 @ identity) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl370, zip_derived_cl38])).
% 0.56/1.13 thf(zip_derived_cl391, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10))
% 0.56/1.13 | ((multiply @ sk_c3 @ identity) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl383])).
% 0.56/1.13 thf(zip_derived_cl634, plain,
% 0.56/1.13 ((((sk_c3) = (sk_c10)) | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl391])).
% 0.56/1.13 thf(prove_this_29, conjecture,
% 0.56/1.13 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c3 ) = ( sk_c10 ) ) ))).
% 0.56/1.13 thf(zf_stmt_25, negated_conjecture,
% 0.56/1.13 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 0.56/1.13 ( ( inverse @ sk_c3 ) = ( sk_c10 ) )),
% 0.56/1.13 inference('cnf.neg', [status(esa)], [prove_this_29])).
% 0.56/1.13 thf(zip_derived_cl31, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c3) = (sk_c10)))),
% 0.56/1.13 inference('cnf', [status(esa)], [zf_stmt_25])).
% 0.56/1.13 thf(zip_derived_cl665, plain,
% 0.56/1.13 ((((inverse @ sk_c10) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10))
% 0.56/1.13 | ((inverse @ sk_c4) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl634, zip_derived_cl31])).
% 0.56/1.13 thf(zip_derived_cl685, plain,
% 0.56/1.13 ((((inverse @ sk_c4) = (sk_c10)) | ((inverse @ sk_c10) = (sk_c10)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl665])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl1302, plain,
% 0.56/1.13 ((((sk_c4) = (inverse @ sk_c10)) | ((inverse @ sk_c10) = (sk_c10)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl633])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl633, plain,
% 0.56/1.13 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl596, zip_derived_cl181])).
% 0.56/1.13 thf(zip_derived_cl3525, plain, (((inverse @ sk_c1) = (sk_c10))),
% 0.56/1.13 inference('clc', [status(thm)], [zip_derived_cl3498, zip_derived_cl1106])).
% 0.56/1.13 thf(zip_derived_cl3596, plain,
% 0.56/1.13 ((((sk_c4) = (sk_c1)) | ((sk_c1) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl1302, zip_derived_cl3525, zip_derived_cl633,
% 0.56/1.13 zip_derived_cl3525, zip_derived_cl633, zip_derived_cl3525])).
% 0.56/1.13 thf(zip_derived_cl5258, plain,
% 0.56/1.13 ((((inverse @ sk_c1) = (sk_c1))
% 0.56/1.13 | ((sk_c1) = (inverse @ sk_c1))
% 0.56/1.13 | ((sk_c1) = (inverse @ sk_c1)))),
% 0.56/1.13 inference('sup+', [status(thm)], [zip_derived_cl5238, zip_derived_cl3596])).
% 0.56/1.13 thf(zip_derived_cl5260, plain, (((inverse @ sk_c1) = (sk_c1))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl5258])).
% 0.56/1.13 thf(zip_derived_cl5271, plain,
% 0.56/1.13 (![X0 : $i]:
% 0.56/1.13 (((X0) != (sk_c1))
% 0.56/1.13 | ((inverse @ X0) != (sk_c1))
% 0.56/1.13 | ((sk_c1) != (sk_c1)))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl3850, zip_derived_cl5260])).
% 0.56/1.13 thf(zip_derived_cl5272, plain,
% 0.56/1.13 (![X0 : $i]: (((inverse @ X0) != (sk_c1)) | ((X0) != (sk_c1)))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl5271])).
% 0.56/1.13 thf(zip_derived_cl5338, plain, (((inverse @ sk_c1) != (sk_c1))),
% 0.56/1.13 inference('eq_res', [status(thm)], [zip_derived_cl5272])).
% 0.56/1.13 thf(zip_derived_cl5260, plain, (((inverse @ sk_c1) = (sk_c1))),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl5258])).
% 0.56/1.13 thf(zip_derived_cl5339, plain, (((sk_c1) != (sk_c1))),
% 0.56/1.13 inference('demod', [status(thm)],
% 0.56/1.13 [zip_derived_cl5338, zip_derived_cl5260])).
% 0.56/1.13 thf(zip_derived_cl5340, plain, ($false),
% 0.56/1.13 inference('simplify', [status(thm)], [zip_derived_cl5339])).
% 0.56/1.13
% 0.56/1.13 % SZS output end Refutation
% 0.56/1.13
% 0.56/1.13
% 0.56/1.13 % Terminating...
% 0.57/1.20 % Runner terminated.
% 0.57/1.20 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------