%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP391-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.kZdOJTg2c2 true
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:36:21 PM UTC 2025
% Result : Unsatisfiable 4.02s 1.61s
% Output : Refutation 4.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.19 % Problem : GRP391-1 : TPTP v9.2.0. Released v2.5.0.
% 0.05/0.20 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.kZdOJTg2c2 true
% 0.09/0.40 % Computer : n019.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8042.1875MB
% 0.09/0.40 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.40 % CPULimit : 300
% 0.09/0.40 % WCLimit : 300
% 0.09/0.40 % DateTime : Wed Oct 1 14:17:38 EDT 2025
% 0.09/0.40 % CPUTime :
% 0.09/0.40 % Running portfolio for 300 s
% 0.09/0.40 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.40 % Number of cores: 8
% 0.09/0.40 % Python version: Python 3.6.8
% 0.09/0.41 % Running in FO mode
% 0.42/0.67 % Total configuration time : 435
% 0.42/0.67 % Estimated wc time : 1092
% 0.42/0.67 % Estimated cpu time (7 cpus) : 156.0
% 0.42/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.43/0.85 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.43/0.89 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.43/0.89 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.44/0.94 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.44/0.96 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.44/0.97 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 4.02/1.61 % Solved by fo/fo7.sh.
% 4.02/1.61 % done 1060 iterations in 0.653s
% 4.02/1.61 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.02/1.61 % SZS output start Refutation
% 4.02/1.61 thf(sk_c1_type, type, sk_c1: $i).
% 4.02/1.61 thf(sk_c3_type, type, sk_c3: $i).
% 4.02/1.61 thf(sk_c5_type, type, sk_c5: $i).
% 4.02/1.61 thf(sk_c4_type, type, sk_c4: $i).
% 4.02/1.61 thf(identity_type, type, identity: $i).
% 4.02/1.61 thf(multiply_type, type, multiply: $i > $i > $i).
% 4.02/1.61 thf(sk_c8_type, type, sk_c8: $i).
% 4.02/1.61 thf(inverse_type, type, inverse: $i > $i).
% 4.02/1.61 thf(sk_c7_type, type, sk_c7: $i).
% 4.02/1.61 thf(sk_c2_type, type, sk_c2: $i).
% 4.02/1.61 thf(sk_c6_type, type, sk_c6: $i).
% 4.02/1.61 thf(prove_this_31, conjecture,
% 4.02/1.61 (~( ( ( multiply @ X5 @ sk_c8 ) != ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ X5 ) != ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( multiply @ X4 @ sk_c7 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( inverse @ X3 ) != ( X4 ) ) |
% 4.02/1.61 ( ( multiply @ X3 @ X4 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) != ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_0, negated_conjecture,
% 4.02/1.61 (( ( multiply @ X5 @ sk_c8 ) != ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ X5 ) != ( sk_c6 ) ) | ( ( inverse @ X2 ) != ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ X2 @ sk_c7 ) != ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c6 @ sk_c7 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( multiply @ X4 @ sk_c7 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( inverse @ X3 ) != ( X4 ) ) |
% 4.02/1.61 ( ( multiply @ X3 @ X4 ) != ( sk_c8 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) != ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_31])).
% 4.02/1.61 thf(zip_derived_cl33, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((multiply @ X0 @ sk_c8) != (sk_c6))
% 4.02/1.61 | ((inverse @ X0) != (sk_c6))
% 4.02/1.61 | ((inverse @ X1) != (sk_c7))
% 4.02/1.61 | ((multiply @ X1 @ sk_c7) != (sk_c6))
% 4.02/1.61 | ((inverse @ X2) != (sk_c8))
% 4.02/1.61 | ((multiply @ X2 @ sk_c8) != (sk_c7))
% 4.02/1.61 | ((multiply @ sk_c6 @ sk_c7) != (sk_c8))
% 4.02/1.61 | ((multiply @ X3 @ sk_c7) != (sk_c8))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (sk_c8))
% 4.02/1.61 | ((inverse @ sk_c6) != (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_0])).
% 4.02/1.61 thf(zip_derived_cl34, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((multiply @ X0 @ (inverse @ sk_c6)) != (sk_c6))
% 4.02/1.61 | ((inverse @ X0) != (sk_c6))
% 4.02/1.61 | ((inverse @ X1) != (sk_c7))
% 4.02/1.61 | ((multiply @ X1 @ sk_c7) != (sk_c6))
% 4.02/1.61 | ((inverse @ X2) != (inverse @ sk_c6))
% 4.02/1.61 | ((multiply @ X2 @ (inverse @ sk_c6)) != (sk_c7))
% 4.02/1.61 | ((multiply @ sk_c6 @ sk_c7) != (inverse @ sk_c6))
% 4.02/1.61 | ((multiply @ X3 @ sk_c7) != (inverse @ sk_c6))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (inverse @ sk_c6))
% 4.02/1.61 | ((inverse @ sk_c6) != (sk_c8)))),
% 4.02/1.61 inference('local_rewriting', [status(thm)], [zip_derived_cl33])).
% 4.02/1.61 thf(prove_this_16, conjecture,
% 4.02/1.61 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 4.02/1.61 thf(zf_stmt_1, negated_conjecture,
% 4.02/1.61 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_16])).
% 4.02/1.61 thf(zip_derived_cl18, plain,
% 4.02/1.61 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c2)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_1])).
% 4.02/1.61 thf(prove_this_10, conjecture,
% 4.02/1.61 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_2, negated_conjecture,
% 4.02/1.61 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 4.02/1.61 thf(zip_derived_cl12, plain,
% 4.02/1.61 ((((inverse @ sk_c4) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_2])).
% 4.02/1.61 thf(zip_derived_cl52, plain,
% 4.02/1.61 ((((multiply @ sk_c1 @ (inverse @ sk_c1)) = (sk_c8))
% 4.02/1.61 | ((inverse @ sk_c4) = (sk_c7))
% 4.02/1.61 | ((inverse @ sk_c4) = (sk_c7)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl18, zip_derived_cl12])).
% 4.02/1.61 thf(zip_derived_cl55, plain,
% 4.02/1.61 ((((inverse @ sk_c4) = (sk_c7))
% 4.02/1.61 | ((multiply @ sk_c1 @ (inverse @ sk_c1)) = (sk_c8)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl52])).
% 4.02/1.61 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(associativity, axiom,
% 4.02/1.61 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 4.02/1.61 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 4.02/1.61 thf(zip_derived_cl2, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 4.02/1.61 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 4.02/1.61 inference('cnf', [status(esa)], [associativity])).
% 4.02/1.61 thf(zip_derived_cl109, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((multiply @ identity @ X0)
% 4.02/1.61 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 4.02/1.61 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl135, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl132, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl126, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl135, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl538, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl135])).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(zip_derived_cl543, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl613, plain,
% 4.02/1.61 ((((inverse @ sk_c4) = (sk_c7)) | ((identity) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl543])).
% 4.02/1.61 thf(zip_derived_cl538, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl135])).
% 4.02/1.61 thf(zip_derived_cl641, plain,
% 4.02/1.61 ((((sk_c4) = (inverse @ sk_c7)) | ((identity) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl613, zip_derived_cl538])).
% 4.02/1.61 thf(prove_this_15, conjecture,
% 4.02/1.61 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c1 ) = ( sk_c2 ) ) ))).
% 4.02/1.61 thf(zf_stmt_3, negated_conjecture,
% 4.02/1.61 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c1 ) = ( sk_c2 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_15])).
% 4.02/1.61 thf(zip_derived_cl17, plain,
% 4.02/1.61 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c2)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_3])).
% 4.02/1.61 thf(prove_this_9, conjecture,
% 4.02/1.61 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_4, negated_conjecture,
% 4.02/1.61 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c1 @ sk_c2 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 4.02/1.61 thf(zip_derived_cl11, plain,
% 4.02/1.61 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 4.02/1.61 | ((multiply @ sk_c1 @ sk_c2) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_4])).
% 4.02/1.61 thf(zip_derived_cl188, plain,
% 4.02/1.61 ((((multiply @ sk_c1 @ (inverse @ sk_c1)) = (sk_c8))
% 4.02/1.61 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 4.02/1.61 | ((multiply @ sk_c4 @ sk_c7) = (sk_c6)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl17, zip_derived_cl11])).
% 4.02/1.61 thf(zip_derived_cl192, plain,
% 4.02/1.61 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6))
% 4.02/1.61 | ((multiply @ sk_c1 @ (inverse @ sk_c1)) = (sk_c8)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl188])).
% 4.02/1.61 thf(zip_derived_cl543, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl538, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4011, plain,
% 4.02/1.61 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((identity) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl192, zip_derived_cl543])).
% 4.02/1.61 thf(zip_derived_cl4033, plain,
% 4.02/1.61 ((((multiply @ (inverse @ sk_c7) @ sk_c7) = (sk_c6))
% 4.02/1.61 | ((identity) = (sk_c8))
% 4.02/1.61 | ((identity) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl641, zip_derived_cl4011])).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(zip_derived_cl4041, plain,
% 4.02/1.61 ((((identity) = (sk_c6))
% 4.02/1.61 | ((identity) = (sk_c8))
% 4.02/1.61 | ((identity) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl4033, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4042, plain,
% 4.02/1.61 ((((identity) = (sk_c8)) | ((identity) = (sk_c6)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4041])).
% 4.02/1.61 thf(prove_this_4, conjecture,
% 4.02/1.61 (~( ( ( inverse @ sk_c4 ) = ( sk_c7 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_5, negated_conjecture,
% 4.02/1.61 (( ( inverse @ sk_c4 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c6 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 4.02/1.61 thf(zip_derived_cl6, plain,
% 4.02/1.61 ((((inverse @ sk_c4) = (sk_c7)) | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_5])).
% 4.02/1.61 thf(prove_this_3, conjecture,
% 4.02/1.61 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_6, negated_conjecture,
% 4.02/1.61 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 4.02/1.61 thf(zip_derived_cl5, plain,
% 4.02/1.61 ((((multiply @ sk_c4 @ sk_c7) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_6])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl142, plain,
% 4.02/1.61 ((((sk_c7) = (multiply @ (inverse @ sk_c4) @ sk_c6))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl429, plain,
% 4.02/1.61 ((((sk_c7) = (multiply @ sk_c7 @ sk_c6))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl142])).
% 4.02/1.61 thf(zip_derived_cl432, plain,
% 4.02/1.61 ((((inverse @ sk_c6) = (sk_c8)) | ((sk_c7) = (multiply @ sk_c7 @ sk_c6)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl429])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl462, plain,
% 4.02/1.61 ((((sk_c6) = (multiply @ (inverse @ sk_c7) @ sk_c7))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl432, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(zip_derived_cl470, plain,
% 4.02/1.61 ((((sk_c6) = (identity)) | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl462, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4086, plain,
% 4.02/1.61 ((((inverse @ sk_c6) = (identity))
% 4.02/1.61 | ((identity) = (sk_c6))
% 4.02/1.61 | ((sk_c6) = (identity)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl4042, zip_derived_cl470])).
% 4.02/1.61 thf(zip_derived_cl4124, plain,
% 4.02/1.61 ((((identity) = (sk_c6)) | ((inverse @ sk_c6) = (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4086])).
% 4.02/1.61 thf(zip_derived_cl538, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl135])).
% 4.02/1.61 thf(zip_derived_cl4142, plain,
% 4.02/1.61 ((((sk_c6) = (inverse @ identity)) | ((identity) = (sk_c6)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl4124, zip_derived_cl538])).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl134, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl159, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4184, plain,
% 4.02/1.61 ((((sk_c6) = (identity)) | ((identity) = (sk_c6)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl4142, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4250, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (sk_c7))
% 4.02/1.61 | ((multiply @ X1 @ sk_c7) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (sk_c7))
% 4.02/1.61 | ((sk_c7) != (identity))
% 4.02/1.61 | ((multiply @ X3 @ sk_c7) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((identity) != (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl34, zip_derived_cl4185, zip_derived_cl393,
% 4.02/1.61 zip_derived_cl518, zip_derived_cl4185, zip_derived_cl4185,
% 4.02/1.61 zip_derived_cl4185, zip_derived_cl4185, zip_derived_cl393,
% 4.02/1.61 zip_derived_cl4185, zip_derived_cl393, zip_derived_cl518,
% 4.02/1.61 zip_derived_cl4185, zip_derived_cl0, zip_derived_cl4185,
% 4.02/1.61 zip_derived_cl393, zip_derived_cl4185, zip_derived_cl393,
% 4.02/1.61 zip_derived_cl4185, zip_derived_cl393, zip_derived_cl4185,
% 4.02/1.61 zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl4251, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((multiply @ X1 @ identity) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((sk_c7) != (identity))
% 4.02/1.61 | ((multiply @ X3 @ identity) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((identity) != (sk_c8)))),
% 4.02/1.61 inference('local_rewriting', [status(thm)], [zip_derived_cl4250])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl4252, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((sk_c7) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((identity) != (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl4251, zip_derived_cl518, zip_derived_cl518])).
% 4.02/1.61 thf(prove_this_5, conjecture,
% 4.02/1.61 (~( ( ( inverse @ sk_c5 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_7, negated_conjecture,
% 4.02/1.61 (( ( inverse @ sk_c5 ) = ( sk_c6 ) ) | ( ( inverse @ sk_c6 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 4.02/1.61 thf(zip_derived_cl7, plain,
% 4.02/1.61 ((((inverse @ sk_c5) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_7])).
% 4.02/1.61 thf(zip_derived_cl1, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_inverse])).
% 4.02/1.61 thf(zip_derived_cl37, plain,
% 4.02/1.61 ((((multiply @ sk_c6 @ sk_c5) = (identity))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl7, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl139, plain,
% 4.02/1.61 ((((sk_c5) = (multiply @ (inverse @ sk_c6) @ identity))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl527, plain,
% 4.02/1.61 ((((sk_c5) = (inverse @ sk_c6)) | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl139, zip_derived_cl518])).
% 4.02/1.61 thf(prove_this_6, conjecture,
% 4.02/1.61 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_8, negated_conjecture,
% 4.02/1.61 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 4.02/1.61 ( ( inverse @ sk_c6 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 4.02/1.61 thf(zip_derived_cl8, plain,
% 4.02/1.61 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_8])).
% 4.02/1.61 thf(zip_derived_cl554, plain,
% 4.02/1.61 ((((multiply @ (inverse @ sk_c6) @ sk_c8) = (sk_c6))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8))
% 4.02/1.61 | ((inverse @ sk_c6) = (sk_c8)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl527, zip_derived_cl8])).
% 4.02/1.61 thf(zip_derived_cl561, plain,
% 4.02/1.61 ((((inverse @ sk_c6) = (sk_c8))
% 4.02/1.61 | ((multiply @ (inverse @ sk_c6) @ sk_c8) = (sk_c6)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl554])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl4278, plain,
% 4.02/1.61 ((((identity) = (sk_c8)) | ((sk_c8) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl561, zip_derived_cl4185, zip_derived_cl393,
% 4.02/1.61 zip_derived_cl4185, zip_derived_cl393, zip_derived_cl0,
% 4.02/1.61 zip_derived_cl4185])).
% 4.02/1.61 thf(zip_derived_cl4279, plain, (((identity) = (sk_c8))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4278])).
% 4.02/1.61 thf(zip_derived_cl4436, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((sk_c7) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((identity) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl4252, zip_derived_cl4279])).
% 4.02/1.61 thf(zip_derived_cl4437, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((sk_c7) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4436])).
% 4.02/1.61 thf(prove_this_25, conjecture,
% 4.02/1.61 (~( ( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_9, negated_conjecture,
% 4.02/1.61 (( ( multiply @ sk_c3 @ sk_c8 ) = ( sk_c7 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 4.02/1.61 thf(zip_derived_cl27, plain,
% 4.02/1.61 ((((multiply @ sk_c3 @ sk_c8) = (sk_c7))
% 4.02/1.61 | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_9])).
% 4.02/1.61 thf(zip_derived_cl126, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl109, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl137, plain,
% 4.02/1.61 ((((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c8))
% 4.02/1.61 | ((multiply @ sk_c3 @ sk_c8) = (sk_c7)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl27, zip_derived_cl126])).
% 4.02/1.61 thf(zip_derived_cl169, plain,
% 4.02/1.61 ((((multiply @ sk_c3 @ sk_c8) != (multiply @ (inverse @ sk_c6) @ sk_c8))
% 4.02/1.61 | ((sk_c7) = (multiply @ (inverse @ sk_c6) @ sk_c8)))),
% 4.02/1.61 inference('eq_fact', [status(thm)], [zip_derived_cl137])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl4266, plain,
% 4.02/1.61 ((((multiply @ sk_c3 @ sk_c8) != (sk_c8)) | ((sk_c7) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl169, zip_derived_cl4185, zip_derived_cl393,
% 4.02/1.61 zip_derived_cl0, zip_derived_cl4185, zip_derived_cl393,
% 4.02/1.61 zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl4279, plain, (((identity) = (sk_c8))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4278])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl4279, plain, (((identity) = (sk_c8))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4278])).
% 4.02/1.61 thf(zip_derived_cl4279, plain, (((identity) = (sk_c8))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4278])).
% 4.02/1.61 thf(zip_derived_cl4443, plain,
% 4.02/1.61 ((((sk_c3) != (identity)) | ((sk_c7) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl4266, zip_derived_cl4279, zip_derived_cl518,
% 4.02/1.61 zip_derived_cl4279, zip_derived_cl4279])).
% 4.02/1.61 thf(prove_this_26, conjecture,
% 4.02/1.61 (~( ( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) ) ))).
% 4.02/1.61 thf(zf_stmt_10, negated_conjecture,
% 4.02/1.61 (( ( inverse @ sk_c3 ) = ( sk_c8 ) ) |
% 4.02/1.61 ( ( multiply @ sk_c6 @ sk_c7 ) = ( sk_c8 ) )),
% 4.02/1.61 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 4.02/1.61 thf(zip_derived_cl28, plain,
% 4.02/1.61 ((((inverse @ sk_c3) = (sk_c8)) | ((multiply @ sk_c6 @ sk_c7) = (sk_c8)))),
% 4.02/1.61 inference('cnf', [status(esa)], [zf_stmt_10])).
% 4.02/1.61 thf(zip_derived_cl4185, plain, (((sk_c6) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4184])).
% 4.02/1.61 thf(zip_derived_cl0, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 4.02/1.61 inference('cnf', [status(esa)], [left_identity])).
% 4.02/1.61 thf(zip_derived_cl4245, plain,
% 4.02/1.61 ((((inverse @ sk_c3) = (sk_c8)) | ((sk_c7) = (sk_c8)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl28, zip_derived_cl4185, zip_derived_cl0])).
% 4.02/1.61 thf(zip_derived_cl4279, plain, (((identity) = (sk_c8))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4278])).
% 4.02/1.61 thf(zip_derived_cl4279, plain, (((identity) = (sk_c8))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4278])).
% 4.02/1.61 thf(zip_derived_cl4561, plain,
% 4.02/1.61 ((((inverse @ sk_c3) = (identity)) | ((sk_c7) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl4245, zip_derived_cl4279, zip_derived_cl4279])).
% 4.02/1.61 thf(zip_derived_cl4437, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((sk_c7) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4436])).
% 4.02/1.61 thf(zip_derived_cl4562, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (identity)))),
% 4.02/1.61 inference('sup-', [status(thm)], [zip_derived_cl4561, zip_derived_cl4437])).
% 4.02/1.61 thf(zip_derived_cl4563, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl4562])).
% 4.02/1.61 thf(zip_derived_cl5042, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.02/1.61 (((inverse @ sk_c3) = (identity))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X3) != (identity))
% 4.02/1.61 | ((multiply @ X3 @ identity) != (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl4563])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl5043, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.02/1.61 (((inverse @ sk_c3) = (identity))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X3) != (identity))
% 4.02/1.61 | ((X3) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5042, zip_derived_cl518])).
% 4.02/1.61 thf(zip_derived_cl5147, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((inverse @ identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5043])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5148, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5147, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5149, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 (((inverse @ sk_c3) = (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5148])).
% 4.02/1.61 thf(zip_derived_cl5150, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((inverse @ identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5149])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5151, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5150, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5152, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 (((inverse @ sk_c3) = (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5151])).
% 4.02/1.61 thf(zip_derived_cl5153, plain,
% 4.02/1.61 (![X0 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5152])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5154, plain,
% 4.02/1.61 (![X0 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((identity) != (identity))
% 4.02/1.61 | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5153, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5155, plain,
% 4.02/1.61 (![X0 : $i]:
% 4.02/1.61 (((inverse @ sk_c3) = (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5154])).
% 4.02/1.61 thf(zip_derived_cl5156, plain,
% 4.02/1.61 ((((inverse @ identity) != (identity)) | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5155])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5157, plain,
% 4.02/1.61 ((((identity) != (identity)) | ((inverse @ sk_c3) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5156, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5158, plain, (((inverse @ sk_c3) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5157])).
% 4.02/1.61 thf(zip_derived_cl538, plain,
% 4.02/1.61 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl518, zip_derived_cl135])).
% 4.02/1.61 thf(zip_derived_cl5161, plain, (((sk_c3) = (inverse @ identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl5158, zip_derived_cl538])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5165, plain, (((sk_c3) = (identity))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5161, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5173, plain,
% 4.02/1.61 ((((identity) != (identity)) | ((sk_c7) = (identity)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl4443, zip_derived_cl5165])).
% 4.02/1.61 thf(zip_derived_cl5174, plain, (((sk_c7) = (identity))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5173])).
% 4.02/1.61 thf(zip_derived_cl5191, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((multiply @ X4 @ X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((identity) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((X0) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)],
% 4.02/1.61 [zip_derived_cl4437, zip_derived_cl5174])).
% 4.02/1.61 thf(zip_derived_cl5192, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (identity))
% 4.02/1.61 | ((X1) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X4) != (X3))
% 4.02/1.61 | ((multiply @ X4 @ X3) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5191])).
% 4.02/1.61 thf(zip_derived_cl5214, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.02/1.61 (((multiply @ X1 @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X3) != (identity))
% 4.02/1.61 | ((inverse @ identity) != (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5192])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5215, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.02/1.61 (((multiply @ X1 @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X3) != (identity))
% 4.02/1.61 | ((identity) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5214, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5216, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 4.02/1.61 (((inverse @ X3) != (identity))
% 4.02/1.61 | ((X3) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((multiply @ X1 @ X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5215])).
% 4.02/1.61 thf(zip_derived_cl5217, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 (((multiply @ X1 @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((inverse @ identity) != (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5216])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5218, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 (((multiply @ X1 @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((inverse @ X2) != (identity))
% 4.02/1.61 | ((identity) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5217, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5219, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i, X2 : $i]:
% 4.02/1.61 (((inverse @ X2) != (identity))
% 4.02/1.61 | ((X2) != (identity))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((multiply @ X1 @ X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5218])).
% 4.02/1.61 thf(zip_derived_cl5220, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 (((multiply @ X1 @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((inverse @ identity) != (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5219])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5221, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 (((multiply @ X1 @ X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((X0) != (identity))
% 4.02/1.61 | ((identity) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5220, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5222, plain,
% 4.02/1.61 (![X0 : $i, X1 : $i]:
% 4.02/1.61 (((X0) != (identity))
% 4.02/1.61 | ((inverse @ X1) != (X0))
% 4.02/1.61 | ((multiply @ X1 @ X0) != (identity)))),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5221])).
% 4.02/1.61 thf(zip_derived_cl5223, plain,
% 4.02/1.61 (![X0 : $i]:
% 4.02/1.61 (((multiply @ X0 @ identity) != (identity))
% 4.02/1.61 | ((inverse @ X0) != (identity)))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5222])).
% 4.02/1.61 thf(zip_derived_cl518, plain,
% 4.02/1.61 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl135, zip_derived_cl132])).
% 4.02/1.61 thf(zip_derived_cl5224, plain,
% 4.02/1.61 (![X0 : $i]: (((X0) != (identity)) | ((inverse @ X0) != (identity)))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5223, zip_derived_cl518])).
% 4.02/1.61 thf(zip_derived_cl5225, plain, (((inverse @ identity) != (identity))),
% 4.02/1.61 inference('eq_res', [status(thm)], [zip_derived_cl5224])).
% 4.02/1.61 thf(zip_derived_cl393, plain, (((inverse @ identity) = (identity))),
% 4.02/1.61 inference('sup+', [status(thm)], [zip_derived_cl159, zip_derived_cl1])).
% 4.02/1.61 thf(zip_derived_cl5226, plain, (((identity) != (identity))),
% 4.02/1.61 inference('demod', [status(thm)], [zip_derived_cl5225, zip_derived_cl393])).
% 4.02/1.61 thf(zip_derived_cl5227, plain, ($false),
% 4.02/1.61 inference('simplify', [status(thm)], [zip_derived_cl5226])).
% 4.02/1.61
% 4.02/1.61 % SZS output end Refutation
% 4.02/1.61
% 4.02/1.61
% 4.02/1.61 % Terminating...
% 4.62/1.77 % Runner terminated.
% 4.64/1.81 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------