%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP213-1 : TPTP v9.2.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WmkFkkTfxY true
% Computer : n005.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 04:36:00 PM UTC 2025
% Result : Unsatisfiable 1.04s 1.06s
% Output : Refutation 1.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP213-1 : TPTP v9.2.0. Released v2.5.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WmkFkkTfxY true
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 14:18:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.54/0.61 % Total configuration time : 435
% 0.54/0.61 % Estimated wc time : 1092
% 0.54/0.61 % Estimated cpu time (7 cpus) : 156.0
% 0.68/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.68/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.68/0.71 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.68/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.68/0.72 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.68/0.73 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.68/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.04/1.06 % Solved by fo/fo7.sh.
% 1.04/1.06 % done 651 iterations in 0.303s
% 1.04/1.06 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.04/1.06 % SZS output start Refutation
% 1.04/1.06 thf(sk_c2_type, type, sk_c2: $i).
% 1.04/1.06 thf(sk_c7_type, type, sk_c7: $i).
% 1.04/1.06 thf(sk_c5_type, type, sk_c5: $i).
% 1.04/1.06 thf(sk_c6_type, type, sk_c6: $i).
% 1.04/1.06 thf(identity_type, type, identity: $i).
% 1.04/1.06 thf(multiply_type, type, multiply: $i > $i > $i).
% 1.04/1.06 thf(sk_c8_type, type, sk_c8: $i).
% 1.04/1.06 thf(inverse_type, type, inverse: $i > $i).
% 1.04/1.06 thf(sk_c4_type, type, sk_c4: $i).
% 1.04/1.06 thf(sk_c3_type, type, sk_c3: $i).
% 1.04/1.06 thf(sk_c1_type, type, sk_c1: $i).
% 1.04/1.06 thf(prove_this_25, conjecture,
% 1.04/1.06 (~( ( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ X3 @ sk_c8 ) != ( X2 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 1.04/1.06 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 1.04/1.06 ( ( inverse @ X5 ) != ( X6 ) ) |
% 1.04/1.06 ( ( multiply @ X5 @ X6 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c7 ) ) ))).
% 1.04/1.06 thf(zf_stmt_0, negated_conjecture,
% 1.04/1.06 (( ( inverse @ X3 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ X3 @ sk_c8 ) != ( X2 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c8 @ X2 ) != ( sk_c7 ) ) |
% 1.04/1.06 ( ( multiply @ X1 @ sk_c7 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) | ( ( inverse @ X5 ) != ( X6 ) ) |
% 1.04/1.06 ( ( multiply @ X5 @ X6 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c7 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_25])).
% 1.04/1.06 thf(zip_derived_cl27, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.04/1.06 (((inverse @ X0) != (sk_c8))
% 1.04/1.06 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.04/1.06 | ((multiply @ sk_c8 @ X1) != (sk_c7))
% 1.04/1.06 | ((multiply @ X2 @ sk_c7) != (sk_c8))
% 1.04/1.06 | ((inverse @ X2) != (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c8) != (sk_c7))
% 1.04/1.06 | ((inverse @ X4) != (X3))
% 1.04/1.06 | ((multiply @ X4 @ X3) != (sk_c8))
% 1.04/1.06 | ((inverse @ X5) != (sk_c8))
% 1.04/1.06 | ((multiply @ X5 @ sk_c8) != (sk_c7)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_0])).
% 1.04/1.06 thf(zip_derived_cl28, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.04/1.06 (((inverse @ X0) != (sk_c8))
% 1.04/1.06 | ((multiply @ X0 @ sk_c8) != (X1))
% 1.04/1.06 | ((multiply @ sk_c8 @ X1) != (inverse @ sk_c8))
% 1.04/1.06 | ((multiply @ X2 @ (inverse @ sk_c8)) != (sk_c8))
% 1.04/1.06 | ((inverse @ X2) != (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c8) != (sk_c7))
% 1.04/1.06 | ((inverse @ X4) != (X3))
% 1.04/1.06 | ((multiply @ X4 @ X3) != (sk_c8))
% 1.04/1.06 | ((inverse @ X5) != (sk_c8))
% 1.04/1.06 | ((multiply @ X5 @ sk_c8) != (inverse @ sk_c8)))),
% 1.04/1.06 inference('local_rewriting', [status(thm)], [zip_derived_cl27])).
% 1.04/1.06 thf(prove_this_12, conjecture,
% 1.04/1.06 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.04/1.06 thf(zf_stmt_1, negated_conjecture,
% 1.04/1.06 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 1.04/1.06 thf(zip_derived_cl14, plain,
% 1.04/1.06 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_1])).
% 1.04/1.06 thf(prove_this_11, conjecture,
% 1.04/1.06 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.04/1.06 thf(zf_stmt_2, negated_conjecture,
% 1.04/1.06 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 1.04/1.06 thf(zip_derived_cl13, plain,
% 1.04/1.06 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_2])).
% 1.04/1.06 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(associativity, axiom,
% 1.04/1.06 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 1.04/1.06 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 1.04/1.06 thf(zip_derived_cl2, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.06 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.04/1.06 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.04/1.06 inference('cnf', [status(esa)], [associativity])).
% 1.04/1.06 thf(zip_derived_cl68, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((multiply @ identity @ X0)
% 1.04/1.06 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 1.04/1.06 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 1.04/1.06 thf(zip_derived_cl0, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_identity])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl104, plain,
% 1.04/1.06 ((((sk_c8) = (multiply @ (inverse @ sk_c5) @ sk_c6))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl346, plain,
% 1.04/1.06 ((((sk_c8) = (multiply @ sk_c8 @ sk_c6))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl104])).
% 1.04/1.06 thf(zip_derived_cl351, plain,
% 1.04/1.06 ((((inverse @ sk_c1) = (sk_c8)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c6)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl346])).
% 1.04/1.06 thf(prove_this_10, conjecture,
% 1.04/1.06 (~( ( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.04/1.06 thf(zf_stmt_3, negated_conjecture,
% 1.04/1.06 (( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_10])).
% 1.04/1.06 thf(zip_derived_cl12, plain,
% 1.04/1.06 ((((multiply @ sk_c8 @ sk_c6) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_3])).
% 1.04/1.06 thf(zip_derived_cl364, plain,
% 1.04/1.06 ((((sk_c8) = (sk_c7))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl351, zip_derived_cl12])).
% 1.04/1.06 thf(zip_derived_cl372, plain,
% 1.04/1.06 ((((inverse @ sk_c1) = (sk_c8)) | ((sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl364])).
% 1.04/1.06 thf(prove_this_8, conjecture,
% 1.04/1.06 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.04/1.06 thf(zf_stmt_4, negated_conjecture,
% 1.04/1.06 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 1.04/1.06 thf(zip_derived_cl10, plain,
% 1.04/1.06 ((((inverse @ sk_c4) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_4])).
% 1.04/1.06 thf(prove_this_9, conjecture,
% 1.04/1.06 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.04/1.06 thf(zf_stmt_5, negated_conjecture,
% 1.04/1.06 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 1.04/1.06 thf(zip_derived_cl11, plain,
% 1.04/1.06 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_5])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl102, plain,
% 1.04/1.06 ((((sk_c7) = (multiply @ (inverse @ sk_c4) @ sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl308, plain,
% 1.04/1.06 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl102])).
% 1.04/1.06 thf(zip_derived_cl311, plain,
% 1.04/1.06 ((((inverse @ sk_c1) = (sk_c8)) | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl308])).
% 1.04/1.06 thf(zip_derived_cl381, plain,
% 1.04/1.06 ((((sk_c8) = (multiply @ sk_c8 @ sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl372, zip_derived_cl311])).
% 1.04/1.06 thf(zip_derived_cl386, plain,
% 1.04/1.06 ((((inverse @ sk_c1) = (sk_c8)) | ((sk_c8) = (multiply @ sk_c8 @ sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl381])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl413, plain,
% 1.04/1.06 ((((sk_c8) = (multiply @ (inverse @ sk_c8) @ sk_c8))
% 1.04/1.06 | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl386, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl415, plain,
% 1.04/1.06 ((((sk_c8) = (identity)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl413, zip_derived_cl1])).
% 1.04/1.06 thf(prove_this_2, conjecture,
% 1.04/1.06 (~( ( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.04/1.06 thf(zf_stmt_6, negated_conjecture,
% 1.04/1.06 (( ( inverse @ sk_c4 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_2])).
% 1.04/1.06 thf(zip_derived_cl4, plain,
% 1.04/1.06 ((((inverse @ sk_c4) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_6])).
% 1.04/1.06 thf(prove_this_3, conjecture,
% 1.04/1.06 (~( ( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.04/1.06 thf(zf_stmt_7, negated_conjecture,
% 1.04/1.06 (( ( multiply @ sk_c4 @ sk_c7 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 1.04/1.06 thf(zip_derived_cl5, plain,
% 1.04/1.06 ((((multiply @ sk_c4 @ sk_c7) = (sk_c8))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_7])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl101, plain,
% 1.04/1.06 ((((sk_c7) = (multiply @ (inverse @ sk_c4) @ sk_c8))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl5, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl1658, plain,
% 1.04/1.06 ((((sk_c7) = (multiply @ sk_c8 @ sk_c8))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl4, zip_derived_cl101])).
% 1.04/1.06 thf(zip_derived_cl1665, plain,
% 1.04/1.06 ((((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((sk_c7) = (multiply @ sk_c8 @ sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1658])).
% 1.04/1.06 thf(prove_this_6, conjecture,
% 1.04/1.06 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.04/1.06 thf(zf_stmt_8, negated_conjecture,
% 1.04/1.06 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 1.04/1.06 thf(zip_derived_cl8, plain,
% 1.04/1.06 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_8])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl37, plain,
% 1.04/1.06 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl1])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl100, plain,
% 1.04/1.06 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl83])).
% 1.04/1.06 thf(prove_this_5, conjecture,
% 1.04/1.06 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.04/1.06 thf(zf_stmt_9, negated_conjecture,
% 1.04/1.06 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c6 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 1.04/1.06 thf(zip_derived_cl7, plain,
% 1.04/1.06 ((((multiply @ sk_c5 @ sk_c8) = (sk_c6))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_9])).
% 1.04/1.06 thf(zip_derived_cl213, plain,
% 1.04/1.06 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 1.04/1.06 = (sk_c6))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl7])).
% 1.04/1.06 thf(zip_derived_cl2, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.06 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 1.04/1.06 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 1.04/1.06 inference('cnf', [status(esa)], [associativity])).
% 1.04/1.06 thf(zip_derived_cl0, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_identity])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl219, plain,
% 1.04/1.06 ((((identity) = (sk_c6))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('demod', [status(thm)],
% 1.04/1.06 [zip_derived_cl213, zip_derived_cl2, zip_derived_cl0,
% 1.04/1.06 zip_derived_cl1])).
% 1.04/1.06 thf(zip_derived_cl220, plain,
% 1.04/1.06 ((((multiply @ sk_c1 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c6)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl219])).
% 1.04/1.06 thf(prove_this_4, conjecture,
% 1.04/1.06 (~( ( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.04/1.06 thf(zf_stmt_10, negated_conjecture,
% 1.04/1.06 (( ( multiply @ sk_c8 @ sk_c6 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 1.04/1.06 thf(zip_derived_cl6, plain,
% 1.04/1.06 ((((multiply @ sk_c8 @ sk_c6) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_10])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl97, plain,
% 1.04/1.06 ((((sk_c6) = (multiply @ (inverse @ sk_c8) @ sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl256, plain,
% 1.04/1.06 ((((identity) = (multiply @ (inverse @ sk_c8) @ sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl220, zip_derived_cl97])).
% 1.04/1.06 thf(zip_derived_cl257, plain,
% 1.04/1.06 ((((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((identity) = (multiply @ (inverse @ sk_c8) @ sk_c7)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl256])).
% 1.04/1.06 thf(zip_derived_cl1700, plain,
% 1.04/1.06 ((((identity)
% 1.04/1.06 = (multiply @ (inverse @ sk_c8) @ (multiply @ sk_c8 @ sk_c8)))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl1665, zip_derived_cl257])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl1712, plain,
% 1.04/1.06 ((((identity) = (sk_c8))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl1700, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl1713, plain,
% 1.04/1.06 ((((multiply @ sk_c1 @ sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1712])).
% 1.04/1.06 thf(prove_this_13, conjecture,
% 1.04/1.06 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c8 ) ) ))).
% 1.04/1.06 thf(zf_stmt_11, negated_conjecture,
% 1.04/1.06 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( multiply @ sk_c2 @ sk_c3 ) = ( sk_c8 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_13])).
% 1.04/1.06 thf(zip_derived_cl15, plain,
% 1.04/1.06 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c3) = (sk_c8)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_11])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl105, plain,
% 1.04/1.06 ((((sk_c3) = (multiply @ (inverse @ sk_c2) @ sk_c8))
% 1.04/1.06 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl15, zip_derived_cl83])).
% 1.04/1.06 thf(prove_this_19, conjecture,
% 1.04/1.06 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.04/1.06 ( ( inverse @ sk_c2 ) = ( sk_c3 ) ) ))).
% 1.04/1.06 thf(zf_stmt_12, negated_conjecture,
% 1.04/1.06 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c3 ) )),
% 1.04/1.06 inference('cnf.neg', [status(esa)], [prove_this_19])).
% 1.04/1.06 thf(zip_derived_cl21, plain,
% 1.04/1.06 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c3)))),
% 1.04/1.06 inference('cnf', [status(esa)], [zf_stmt_12])).
% 1.04/1.06 thf(zip_derived_cl155, plain,
% 1.04/1.06 ((((inverse @ sk_c2) = (multiply @ (inverse @ sk_c2) @ sk_c8))
% 1.04/1.06 | ((inverse @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl105, zip_derived_cl21])).
% 1.04/1.06 thf(zip_derived_cl162, plain,
% 1.04/1.06 ((((inverse @ sk_c8) = (sk_c7))
% 1.04/1.06 | ((inverse @ sk_c2) = (multiply @ (inverse @ sk_c2) @ sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl155])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl523, plain,
% 1.04/1.06 ((((sk_c8)
% 1.04/1.06 = (multiply @ (inverse @ (inverse @ sk_c2)) @ (inverse @ sk_c2)))
% 1.04/1.06 | ((inverse @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl162, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl525, plain,
% 1.04/1.06 ((((sk_c8) = (identity)) | ((inverse @ sk_c8) = (sk_c7)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl523, zip_derived_cl1])).
% 1.04/1.06 thf(zip_derived_cl1724, plain,
% 1.04/1.06 ((((inverse @ sk_c8) = (multiply @ sk_c1 @ sk_c8))
% 1.04/1.06 | ((identity) = (sk_c8))
% 1.04/1.06 | ((sk_c8) = (identity)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl1713, zip_derived_cl525])).
% 1.04/1.06 thf(zip_derived_cl1728, plain,
% 1.04/1.06 ((((identity) = (sk_c8))
% 1.04/1.06 | ((inverse @ sk_c8) = (multiply @ sk_c1 @ sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1724])).
% 1.04/1.06 thf(zip_derived_cl1769, plain,
% 1.04/1.06 ((((inverse @ (inverse @ sk_c1)) = (multiply @ sk_c1 @ sk_c8))
% 1.04/1.06 | ((sk_c8) = (identity))
% 1.04/1.06 | ((identity) = (sk_c8)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl415, zip_derived_cl1728])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl93, plain,
% 1.04/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl90, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl83, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl737, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl90])).
% 1.04/1.06 thf(zip_derived_cl93, plain,
% 1.04/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl769, plain,
% 1.04/1.06 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl737, zip_derived_cl93])).
% 1.04/1.06 thf(zip_derived_cl1770, plain,
% 1.04/1.06 ((((sk_c1) = (multiply @ sk_c1 @ sk_c8))
% 1.04/1.06 | ((sk_c8) = (identity))
% 1.04/1.06 | ((identity) = (sk_c8)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl1769, zip_derived_cl769])).
% 1.04/1.06 thf(zip_derived_cl1771, plain,
% 1.04/1.06 ((((sk_c8) = (identity)) | ((sk_c1) = (multiply @ sk_c1 @ sk_c8)))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1770])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl1778, plain,
% 1.04/1.06 ((((sk_c8) = (multiply @ (inverse @ sk_c1) @ sk_c1))
% 1.04/1.06 | ((sk_c8) = (identity)))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl1771, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl1787, plain,
% 1.04/1.06 ((((sk_c8) = (identity)) | ((sk_c8) = (identity)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl1778, zip_derived_cl1])).
% 1.04/1.06 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.06 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.06 thf(zip_derived_cl737, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl90])).
% 1.04/1.06 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.06 thf(zip_derived_cl0, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_identity])).
% 1.04/1.06 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.06 thf(zip_derived_cl0, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_identity])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl92, plain,
% 1.04/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl83, plain,
% 1.04/1.06 (![X0 : $i, X1 : $i]:
% 1.04/1.06 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 1.04/1.06 inference('demod', [status(thm)], [zip_derived_cl68, zip_derived_cl0])).
% 1.04/1.06 thf(zip_derived_cl114, plain,
% 1.04/1.06 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl92, zip_derived_cl83])).
% 1.04/1.06 thf(zip_derived_cl1, plain,
% 1.04/1.06 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.06 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.06 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.06 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.06 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.06 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.06 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.06 thf(zip_derived_cl737, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl90])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl737, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl90])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl1819, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 1.04/1.07 (((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (X1))
% 1.04/1.07 | ((X1) != (identity))
% 1.04/1.07 | ((X2) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (identity))
% 1.04/1.07 | ((identity) != (sk_c7))
% 1.04/1.07 | ((inverse @ X4) != (X3))
% 1.04/1.07 | ((multiply @ X4 @ X3) != (identity))
% 1.04/1.07 | ((inverse @ X5) != (identity))
% 1.04/1.07 | ((X5) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)],
% 1.04/1.07 [zip_derived_cl28, zip_derived_cl1788, zip_derived_cl1788,
% 1.04/1.07 zip_derived_cl737, zip_derived_cl1788, zip_derived_cl0,
% 1.04/1.07 zip_derived_cl1788, zip_derived_cl292, zip_derived_cl1788,
% 1.04/1.07 zip_derived_cl292, zip_derived_cl737, zip_derived_cl1788,
% 1.04/1.07 zip_derived_cl1788, zip_derived_cl1788, zip_derived_cl292,
% 1.04/1.07 zip_derived_cl1788, zip_derived_cl1788, zip_derived_cl1788,
% 1.04/1.07 zip_derived_cl737, zip_derived_cl1788, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl1902, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((identity) != (sk_c7))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((X3) != (identity))
% 1.04/1.07 | ((X4) != (identity))
% 1.04/1.07 | ((inverse @ X4) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl1819])).
% 1.04/1.07 thf(prove_this_1, conjecture,
% 1.04/1.07 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.04/1.07 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) ) ))).
% 1.04/1.07 thf(zf_stmt_13, negated_conjecture,
% 1.04/1.07 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.04/1.07 ( ( multiply @ sk_c1 @ sk_c8 ) = ( sk_c7 ) )),
% 1.04/1.07 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 1.04/1.07 thf(zip_derived_cl3, plain,
% 1.04/1.07 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c8) = (sk_c7)))),
% 1.04/1.07 inference('cnf', [status(esa)], [zf_stmt_13])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl737, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl90])).
% 1.04/1.07 thf(zip_derived_cl1795, plain,
% 1.04/1.07 ((((identity) = (sk_c7)) | ((sk_c1) = (sk_c7)))),
% 1.04/1.07 inference('demod', [status(thm)],
% 1.04/1.07 [zip_derived_cl3, zip_derived_cl1788, zip_derived_cl292,
% 1.04/1.07 zip_derived_cl1788, zip_derived_cl737])).
% 1.04/1.07 thf(prove_this_7, conjecture,
% 1.04/1.07 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 1.04/1.07 ( ( inverse @ sk_c1 ) = ( sk_c8 ) ) ))).
% 1.04/1.07 thf(zf_stmt_14, negated_conjecture,
% 1.04/1.07 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c8 ) )),
% 1.04/1.07 inference('cnf.neg', [status(esa)], [prove_this_7])).
% 1.04/1.07 thf(zip_derived_cl9, plain,
% 1.04/1.07 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c8)))),
% 1.04/1.07 inference('cnf', [status(esa)], [zf_stmt_14])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl1788, plain, (((sk_c8) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1787])).
% 1.04/1.07 thf(zip_derived_cl1801, plain,
% 1.04/1.07 ((((identity) = (sk_c7)) | ((inverse @ sk_c1) = (identity)))),
% 1.04/1.07 inference('demod', [status(thm)],
% 1.04/1.07 [zip_derived_cl9, zip_derived_cl1788, zip_derived_cl292,
% 1.04/1.07 zip_derived_cl1788])).
% 1.04/1.07 thf(zip_derived_cl1902, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((identity) != (sk_c7))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((X3) != (identity))
% 1.04/1.07 | ((X4) != (identity))
% 1.04/1.07 | ((inverse @ X4) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl1819])).
% 1.04/1.07 thf(zip_derived_cl1930, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/1.07 (((identity) != (identity))
% 1.04/1.07 | ((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((X1) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X3))
% 1.04/1.07 | ((multiply @ X2 @ X3) != (identity))
% 1.04/1.07 | ((inverse @ X4) != (identity))
% 1.04/1.07 | ((X4) != (identity)))),
% 1.04/1.07 inference('sup-', [status(thm)], [zip_derived_cl1801, zip_derived_cl1902])).
% 1.04/1.07 thf(zip_derived_cl1932, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/1.07 (((X4) != (identity))
% 1.04/1.07 | ((inverse @ X4) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X3) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X3))
% 1.04/1.07 | ((inverse @ X1) != (identity))
% 1.04/1.07 | ((X1) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((inverse @ sk_c1) = (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl1930])).
% 1.04/1.07 thf(zip_derived_cl2357, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((X1) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X3))
% 1.04/1.07 | ((multiply @ X2 @ X3) != (identity))
% 1.04/1.07 | ((inverse @ identity) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl1932])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2358, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((X1) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X3))
% 1.04/1.07 | ((multiply @ X2 @ X3) != (identity))
% 1.04/1.07 | ((identity) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2357, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2359, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/1.07 (((multiply @ X2 @ X3) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X3))
% 1.04/1.07 | ((inverse @ X1) != (identity))
% 1.04/1.07 | ((X1) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((inverse @ sk_c1) = (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2358])).
% 1.04/1.07 thf(zip_derived_cl2433, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((inverse @ identity) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (X2))
% 1.04/1.07 | ((multiply @ X1 @ X2) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2359])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2434, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((identity) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (X2))
% 1.04/1.07 | ((multiply @ X1 @ X2) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2433, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2435, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.07 (((multiply @ X1 @ X2) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (X2))
% 1.04/1.07 | ((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((inverse @ sk_c1) = (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2434])).
% 1.04/1.07 thf(zip_derived_cl2436, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((inverse @ identity) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (X1))
% 1.04/1.07 | ((multiply @ X0 @ X1) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2435])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2437, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((identity) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (X1))
% 1.04/1.07 | ((multiply @ X0 @ X1) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2436, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2438, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i]:
% 1.04/1.07 (((multiply @ X0 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (X1))
% 1.04/1.07 | ((inverse @ sk_c1) = (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2437])).
% 1.04/1.07 thf(zip_derived_cl2452, plain,
% 1.04/1.07 (![X0 : $i]:
% 1.04/1.07 (((inverse @ sk_c1) = (identity))
% 1.04/1.07 | ((multiply @ X0 @ (inverse @ X0)) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2438])).
% 1.04/1.07 thf(zip_derived_cl769, plain,
% 1.04/1.07 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl737, zip_derived_cl93])).
% 1.04/1.07 thf(zip_derived_cl1, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 1.04/1.07 inference('cnf', [status(esa)], [left_inverse])).
% 1.04/1.07 thf(zip_derived_cl777, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl769, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2453, plain,
% 1.04/1.07 ((((inverse @ sk_c1) = (identity)) | ((identity) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2452, zip_derived_cl777])).
% 1.04/1.07 thf(zip_derived_cl2454, plain, (((inverse @ sk_c1) = (identity))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2453])).
% 1.04/1.07 thf(zip_derived_cl769, plain,
% 1.04/1.07 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl737, zip_derived_cl93])).
% 1.04/1.07 thf(zip_derived_cl2466, plain, (((sk_c1) = (inverse @ identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl2454, zip_derived_cl769])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2470, plain, (((sk_c1) = (identity))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2466, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2472, plain,
% 1.04/1.07 ((((identity) = (sk_c7)) | ((identity) = (sk_c7)))),
% 1.04/1.07 inference('demod', [status(thm)],
% 1.04/1.07 [zip_derived_cl1795, zip_derived_cl2470])).
% 1.04/1.07 thf(zip_derived_cl2473, plain, (((identity) = (sk_c7))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2472])).
% 1.04/1.07 thf(zip_derived_cl2508, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((identity) != (identity))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((X3) != (identity))
% 1.04/1.07 | ((X4) != (identity))
% 1.04/1.07 | ((inverse @ X4) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)],
% 1.04/1.07 [zip_derived_cl1902, zip_derived_cl2473])).
% 1.04/1.07 thf(zip_derived_cl2509, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 1.04/1.07 (((inverse @ X4) != (identity))
% 1.04/1.07 | ((X4) != (identity))
% 1.04/1.07 | ((X3) != (identity))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2508])).
% 1.04/1.07 thf(zip_derived_cl2520, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((X3) != (identity))
% 1.04/1.07 | ((inverse @ identity) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2509])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2521, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((X3) != (identity))
% 1.04/1.07 | ((identity) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2520, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2522, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 1.04/1.07 (((X3) != (identity))
% 1.04/1.07 | ((inverse @ X3) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2521])).
% 1.04/1.07 thf(zip_derived_cl2523, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((inverse @ identity) != (identity)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2522])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2524, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.07 (((X0) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X2) != (X1))
% 1.04/1.07 | ((identity) != (identity)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2523, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2525, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i, X2 : $i]:
% 1.04/1.07 (((inverse @ X2) != (X1))
% 1.04/1.07 | ((multiply @ X2 @ X1) != (identity))
% 1.04/1.07 | ((inverse @ X0) != (identity))
% 1.04/1.07 | ((X0) != (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2524])).
% 1.04/1.07 thf(zip_derived_cl2526, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i]:
% 1.04/1.07 (((inverse @ identity) != (identity))
% 1.04/1.07 | ((multiply @ X1 @ X0) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (X0)))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2525])).
% 1.04/1.07 thf(zip_derived_cl292, plain, (((inverse @ identity) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl114, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2527, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i]:
% 1.04/1.07 (((identity) != (identity))
% 1.04/1.07 | ((multiply @ X1 @ X0) != (identity))
% 1.04/1.07 | ((inverse @ X1) != (X0)))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2526, zip_derived_cl292])).
% 1.04/1.07 thf(zip_derived_cl2528, plain,
% 1.04/1.07 (![X0 : $i, X1 : $i]:
% 1.04/1.07 (((inverse @ X1) != (X0)) | ((multiply @ X1 @ X0) != (identity)))),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2527])).
% 1.04/1.07 thf(zip_derived_cl2531, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) != (identity))),
% 1.04/1.07 inference('eq_res', [status(thm)], [zip_derived_cl2528])).
% 1.04/1.07 thf(zip_derived_cl777, plain,
% 1.04/1.07 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 1.04/1.07 inference('sup+', [status(thm)], [zip_derived_cl769, zip_derived_cl1])).
% 1.04/1.07 thf(zip_derived_cl2532, plain, (((identity) != (identity))),
% 1.04/1.07 inference('demod', [status(thm)], [zip_derived_cl2531, zip_derived_cl777])).
% 1.04/1.07 thf(zip_derived_cl2533, plain, ($false),
% 1.04/1.07 inference('simplify', [status(thm)], [zip_derived_cl2532])).
% 1.04/1.07
% 1.04/1.07 % SZS output end Refutation
% 1.04/1.07
% 1.04/1.07
% 1.04/1.07 % Terminating...
% 1.71/1.19 % Runner terminated.
% 1.71/1.20 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------