TSTP Solution File: GRP317-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP317-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Ui0NdFn8IR true
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:51:10 EDT 2023
% Result : Unsatisfiable 0.57s 0.92s
% Output : Refutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP317-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Ui0NdFn8IR true
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 00:19:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.64 % Total configuration time : 435
% 0.21/0.64 % Estimated wc time : 1092
% 0.21/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.57/0.92 % Solved by fo/fo7.sh.
% 0.57/0.92 % done 336 iterations in 0.152s
% 0.57/0.92 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/0.92 % SZS output start Refutation
% 0.57/0.92 thf(sk_c2_type, type, sk_c2: $i).
% 0.57/0.92 thf(sk_c7_type, type, sk_c7: $i).
% 0.57/0.92 thf(sk_c1_type, type, sk_c1: $i).
% 0.57/0.92 thf(sk_c6_type, type, sk_c6: $i).
% 0.57/0.92 thf(identity_type, type, identity: $i).
% 0.57/0.92 thf(multiply_type, type, multiply: $i > $i > $i).
% 0.57/0.92 thf(sk_c9_type, type, sk_c9: $i).
% 0.57/0.92 thf(inverse_type, type, inverse: $i > $i).
% 0.57/0.92 thf(sk_c5_type, type, sk_c5: $i).
% 0.57/0.92 thf(sk_c8_type, type, sk_c8: $i).
% 0.57/0.92 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(associativity, axiom,
% 0.57/0.92 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 0.57/0.92 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 0.57/0.92 thf(zip_derived_cl2, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.57/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.57/0.92 thf(zip_derived_cl290, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((multiply @ identity @ X0)
% 0.57/0.92 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl339, plain,
% 0.57/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl321])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl403, plain,
% 0.57/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl339, zip_derived_cl321])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(prove_this_55, conjecture,
% 0.57/0.92 (~( ( ( inverse @ X2 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ X2 @ sk_c9 ) != ( sk_c7 ) ) |
% 0.57/0.92 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ X5 @ sk_c9 ) != ( X6 ) ) |
% 0.57/0.92 ( ( inverse @ X6 ) != ( sk_c9 ) ) | ( ( inverse @ X5 ) != ( X6 ) ) |
% 0.57/0.92 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c9 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( inverse @ X3 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ X3 @ sk_c9 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) != ( sk_c7 ) ) ))).
% 0.57/0.92 thf(zf_stmt_0, negated_conjecture,
% 0.57/0.92 (( ( inverse @ X2 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ X2 @ sk_c9 ) != ( sk_c7 ) ) |
% 0.57/0.92 ( ( inverse @ X1 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ X1 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c8 ) != ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c7 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ X5 @ sk_c9 ) != ( X6 ) ) |
% 0.57/0.92 ( ( inverse @ X6 ) != ( sk_c9 ) ) | ( ( inverse @ X5 ) != ( X6 ) ) |
% 0.57/0.92 ( ( inverse @ X4 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ X4 @ sk_c8 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c9 @ sk_c7 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( inverse @ X3 ) != ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ X3 @ sk_c9 ) != ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) != ( sk_c7 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_55])).
% 0.57/0.92 thf(zip_derived_cl57, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (sk_c9))
% 0.57/0.92 | ((multiply @ X0 @ sk_c9) != (sk_c7))
% 0.57/0.92 | ((inverse @ X1) != (sk_c8))
% 0.57/0.92 | ((multiply @ X1 @ sk_c8) != (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c8) != (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c7) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ sk_c9) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (sk_c9))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (sk_c8))
% 0.57/0.92 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c9 @ sk_c7) != (sk_c8))
% 0.57/0.92 | ((inverse @ X5) != (sk_c9))
% 0.57/0.92 | ((multiply @ X5 @ sk_c9) != (sk_c8))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) != (sk_c7)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_0])).
% 0.57/0.92 thf(zip_derived_cl58, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (sk_c9))
% 0.57/0.92 | ((multiply @ X0 @ sk_c9) != (multiply @ sk_c8 @ sk_c9))
% 0.57/0.92 | ((inverse @ X1) != (sk_c8))
% 0.57/0.92 | ((multiply @ X1 @ sk_c8) != (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c8) != (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c8 @ (multiply @ sk_c8 @ sk_c9)) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ sk_c9) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (sk_c9))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (sk_c8))
% 0.57/0.92 | ((multiply @ X4 @ sk_c8) != (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c9 @ (multiply @ sk_c8 @ sk_c9)) != (sk_c8))
% 0.57/0.92 | ((inverse @ X5) != (sk_c9))
% 0.57/0.92 | ((multiply @ X5 @ sk_c9) != (sk_c8))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) != (sk_c7)))),
% 0.57/0.92 inference('local_rewriting', [status(thm)], [zip_derived_cl57])).
% 0.57/0.92 thf(prove_this_18, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 0.57/0.92 thf(zf_stmt_1, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_18])).
% 0.57/0.92 thf(zip_derived_cl20, plain,
% 0.57/0.92 ((((inverse @ sk_c6) = (sk_c9)) | ((inverse @ sk_c1) = (sk_c9)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_1])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl79, plain,
% 0.57/0.92 ((((multiply @ sk_c9 @ sk_c1) = (identity))
% 0.57/0.92 | ((inverse @ sk_c6) = (sk_c9)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl20, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl354, plain,
% 0.57/0.92 ((((sk_c1) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.57/0.92 | ((inverse @ sk_c6) = (sk_c9)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl79, zip_derived_cl321])).
% 0.57/0.92 thf(prove_this_12, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.57/0.92 thf(zf_stmt_2, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c6 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 0.57/0.92 thf(zip_derived_cl14, plain,
% 0.57/0.92 ((((inverse @ sk_c6) = (sk_c9)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_2])).
% 0.57/0.92 thf(zip_derived_cl666, plain,
% 0.57/0.92 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.57/0.92 = (sk_c8))
% 0.57/0.92 | ((inverse @ sk_c6) = (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c6) = (sk_c9)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl354, zip_derived_cl14])).
% 0.57/0.92 thf(zip_derived_cl2, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.57/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl681, plain,
% 0.57/0.92 ((((identity) = (sk_c8))
% 0.57/0.92 | ((inverse @ sk_c6) = (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c6) = (sk_c9)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl666, zip_derived_cl2, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl682, plain,
% 0.57/0.92 ((((inverse @ sk_c6) = (sk_c9)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl681])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl685, plain,
% 0.57/0.92 ((((multiply @ sk_c9 @ sk_c6) = (identity)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl682, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl806, plain,
% 0.57/0.92 ((((sk_c6) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.57/0.92 | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl685, zip_derived_cl321])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl340, plain,
% 0.57/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl321])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl337, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl321, zip_derived_cl321])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl1149, plain,
% 0.57/0.92 ((((sk_c6) = (inverse @ sk_c9)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl806, zip_derived_cl1091])).
% 0.57/0.92 thf(prove_this_17, conjecture,
% 0.57/0.92 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 0.57/0.92 thf(zf_stmt_3, negated_conjecture,
% 0.57/0.92 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_17])).
% 0.57/0.92 thf(zip_derived_cl19, plain,
% 0.57/0.92 ((((multiply @ sk_c6 @ sk_c9) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_3])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl340, plain,
% 0.57/0.92 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl321])).
% 0.57/0.92 thf(zip_derived_cl1163, plain,
% 0.57/0.92 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1091, zip_derived_cl340])).
% 0.57/0.92 thf(zip_derived_cl1354, plain,
% 0.57/0.92 ((((sk_c1) = (inverse @ sk_c9)) | ((multiply @ sk_c6 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl19, zip_derived_cl1163])).
% 0.57/0.92 thf(prove_this_11, conjecture,
% 0.57/0.92 (~( ( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.57/0.92 thf(zf_stmt_4, negated_conjecture,
% 0.57/0.92 (( ( multiply @ sk_c6 @ sk_c9 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 0.57/0.92 thf(zip_derived_cl13, plain,
% 0.57/0.92 ((((multiply @ sk_c6 @ sk_c9) = (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_4])).
% 0.57/0.92 thf(zip_derived_cl1860, plain,
% 0.57/0.92 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c8))
% 0.57/0.92 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1354, zip_derived_cl13])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl1877, plain,
% 0.57/0.92 ((((identity) = (sk_c8))
% 0.57/0.92 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c6 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl1860, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl1878, plain,
% 0.57/0.92 ((((multiply @ sk_c6 @ sk_c9) = (sk_c7)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl1877])).
% 0.57/0.92 thf(zip_derived_cl2113, plain,
% 0.57/0.92 ((((multiply @ (inverse @ sk_c9) @ sk_c9) = (sk_c7))
% 0.57/0.92 | ((identity) = (sk_c8))
% 0.57/0.92 | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1149, zip_derived_cl1878])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl2117, plain,
% 0.57/0.92 ((((identity) = (sk_c7))
% 0.57/0.92 | ((identity) = (sk_c8))
% 0.57/0.92 | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl2113, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2118, plain,
% 0.57/0.92 ((((identity) = (sk_c8)) | ((identity) = (sk_c7)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2117])).
% 0.57/0.92 thf(prove_this_14, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c1 ) = ( sk_c9 ) ) ))).
% 0.57/0.92 thf(zf_stmt_5, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c1 ) = ( sk_c9 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_14])).
% 0.57/0.92 thf(zip_derived_cl16, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c1) = (sk_c9)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_5])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl63, plain,
% 0.57/0.92 ((((multiply @ sk_c9 @ sk_c1) = (identity))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl16, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl352, plain,
% 0.57/0.92 ((((sk_c1) = (multiply @ (inverse @ sk_c9) @ identity))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl63, zip_derived_cl321])).
% 0.57/0.92 thf(prove_this_8, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) ) ))).
% 0.57/0.92 thf(zf_stmt_6, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c1 @ sk_c9 ) = ( sk_c8 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 0.57/0.92 thf(zip_derived_cl10, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c1 @ sk_c9) = (sk_c8)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_6])).
% 0.57/0.92 thf(zip_derived_cl442, plain,
% 0.57/0.92 ((((multiply @ (multiply @ (inverse @ sk_c9) @ identity) @ sk_c9)
% 0.57/0.92 = (sk_c8))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl352, zip_derived_cl10])).
% 0.57/0.92 thf(zip_derived_cl2, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.57/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl457, plain,
% 0.57/0.92 ((((identity) = (sk_c8))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl442, zip_derived_cl2, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl458, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (sk_c7)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl457])).
% 0.57/0.92 thf(zip_derived_cl2159, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (identity))
% 0.57/0.92 | ((identity) = (sk_c8))
% 0.57/0.92 | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl2118, zip_derived_cl458])).
% 0.57/0.92 thf(zip_derived_cl2169, plain,
% 0.57/0.92 ((((identity) = (sk_c8)) | ((inverse @ sk_c8) = (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2159])).
% 0.57/0.92 thf(zip_derived_cl1163, plain,
% 0.57/0.92 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl1091, zip_derived_cl340])).
% 0.57/0.92 thf(zip_derived_cl2173, plain,
% 0.57/0.92 ((((sk_c8) = (inverse @ identity)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl2169, zip_derived_cl1163])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2183, plain,
% 0.57/0.92 ((((sk_c8) = (identity)) | ((identity) = (sk_c8)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2173, zip_derived_cl1078])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2239, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (sk_c9))
% 0.57/0.92 | ((multiply @ X0 @ sk_c9) != (sk_c9))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (sk_c9))
% 0.57/0.92 | ((identity) != (sk_c7))
% 0.57/0.92 | ((sk_c9) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ sk_c9) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (sk_c9))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((X4) != (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c9 @ sk_c9) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (sk_c9))
% 0.57/0.92 | ((multiply @ X5 @ sk_c9) != (identity))
% 0.57/0.92 | ((sk_c9) != (sk_c7)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl58, zip_derived_cl2184, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl2184, zip_derived_cl1091,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl1078, zip_derived_cl2184,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl0, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl2184, zip_derived_cl1091,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl0, zip_derived_cl2184,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl2184, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl2240, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((sk_c9) != (sk_c7))
% 0.57/0.92 | ((multiply @ X5 @ sk_c9) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c9 @ sk_c9) != (identity))
% 0.57/0.92 | ((X4) != (sk_c9))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ sk_c9) != (X2))
% 0.57/0.92 | ((identity) != (sk_c7))
% 0.57/0.92 | ((X1) != (sk_c9))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((multiply @ X0 @ sk_c9) != (sk_c9))
% 0.57/0.92 | ((inverse @ X0) != (sk_c9)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2239])).
% 0.57/0.92 thf(prove_this_1, conjecture,
% 0.57/0.92 (~( ( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) ))).
% 0.57/0.92 thf(zf_stmt_7, negated_conjecture,
% 0.57/0.92 (( ( multiply @ sk_c8 @ sk_c7 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_1])).
% 0.57/0.92 thf(zip_derived_cl3, plain,
% 0.57/0.92 ((((multiply @ sk_c8 @ sk_c7) = (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_7])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2194, plain, ((((sk_c7) = (sk_c9)) | ((sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl3, zip_derived_cl2184, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl2195, plain, (((sk_c7) = (sk_c9))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2194])).
% 0.57/0.92 thf(zip_derived_cl2195, plain, (((sk_c7) = (sk_c9))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2194])).
% 0.57/0.92 thf(zip_derived_cl2319, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((sk_c9) != (sk_c9))
% 0.57/0.92 | ((multiply @ X5 @ sk_c9) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c9 @ sk_c9) != (identity))
% 0.57/0.92 | ((X4) != (sk_c9))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ sk_c9) != (X2))
% 0.57/0.92 | ((identity) != (sk_c9))
% 0.57/0.92 | ((X1) != (sk_c9))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((multiply @ X0 @ sk_c9) != (sk_c9))
% 0.57/0.92 | ((inverse @ X0) != (sk_c9)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2240, zip_derived_cl2195, zip_derived_cl2195])).
% 0.57/0.92 thf(zip_derived_cl2320, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (sk_c9))
% 0.57/0.92 | ((multiply @ X0 @ sk_c9) != (sk_c9))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (sk_c9))
% 0.57/0.92 | ((identity) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ sk_c9) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (sk_c9))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((X4) != (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c9 @ sk_c9) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (sk_c9))
% 0.57/0.92 | ((multiply @ X5 @ sk_c9) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2319])).
% 0.57/0.92 thf(zip_derived_cl2321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((multiply @ X0 @ identity) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((identity) != (sk_c9))
% 0.57/0.92 | ((multiply @ X3 @ identity) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((X4) != (identity))
% 0.57/0.92 | ((multiply @ identity @ identity) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (identity))
% 0.57/0.92 | ((multiply @ X5 @ identity) != (identity)))),
% 0.57/0.92 inference('local_rewriting', [status(thm)], [zip_derived_cl2320])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl1091, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl340, zip_derived_cl337])).
% 0.57/0.92 thf(zip_derived_cl2322, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((identity) != (sk_c9))
% 0.57/0.92 | ((X3) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((X4) != (identity))
% 0.57/0.92 | ((identity) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (identity))
% 0.57/0.92 | ((X5) != (identity)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2321, zip_derived_cl1091, zip_derived_cl1091,
% 0.57/0.92 zip_derived_cl0, zip_derived_cl1091])).
% 0.57/0.92 thf(zip_derived_cl2323, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((X5) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (identity))
% 0.57/0.92 | ((X4) != (identity))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((X3) != (X2))
% 0.57/0.92 | ((identity) != (sk_c9))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2322])).
% 0.57/0.92 thf(prove_this_4, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) ))).
% 0.57/0.92 thf(zf_stmt_8, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 0.57/0.92 thf(zip_derived_cl6, plain,
% 0.57/0.92 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_8])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl76, plain,
% 0.57/0.92 ((((multiply @ sk_c8 @ sk_c5) = (identity))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl343, plain,
% 0.57/0.92 ((((sk_c5) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl76, zip_derived_cl321])).
% 0.57/0.92 thf(prove_this_3, conjecture,
% 0.57/0.92 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) ) ))).
% 0.57/0.92 thf(zf_stmt_9, negated_conjecture,
% 0.57/0.92 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c9 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c8 @ sk_c9 ) = ( sk_c7 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 0.57/0.92 thf(zip_derived_cl5, plain,
% 0.57/0.92 ((((multiply @ sk_c5 @ sk_c8) = (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_9])).
% 0.57/0.92 thf(zip_derived_cl591, plain,
% 0.57/0.92 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.57/0.92 = (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl343, zip_derived_cl5])).
% 0.57/0.92 thf(zip_derived_cl2, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.57/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl597, plain,
% 0.57/0.92 ((((identity) = (sk_c9))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7))
% 0.57/0.92 | ((multiply @ sk_c8 @ sk_c9) = (sk_c7)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl591, zip_derived_cl2, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl598, plain,
% 0.57/0.92 ((((multiply @ sk_c8 @ sk_c9) = (sk_c7)) | ((identity) = (sk_c9)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl597])).
% 0.57/0.92 thf(prove_this_32, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( inverse @ sk_c2 ) = ( sk_c8 ) ) ))).
% 0.57/0.92 thf(zf_stmt_10, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c8 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_32])).
% 0.57/0.92 thf(zip_derived_cl34, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (sk_c7)) | ((inverse @ sk_c2) = (sk_c8)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_10])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl64, plain,
% 0.57/0.92 ((((multiply @ sk_c8 @ sk_c2) = (identity))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl34, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl321, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 0.57/0.92 inference('demod', [status(thm)], [zip_derived_cl290, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl344, plain,
% 0.57/0.92 ((((sk_c2) = (multiply @ (inverse @ sk_c8) @ identity))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl64, zip_derived_cl321])).
% 0.57/0.92 thf(prove_this_26, conjecture,
% 0.57/0.92 (~( ( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c9 ) ) ))).
% 0.57/0.92 thf(zf_stmt_11, negated_conjecture,
% 0.57/0.92 (( ( inverse @ sk_c8 ) = ( sk_c7 ) ) |
% 0.57/0.92 ( ( multiply @ sk_c2 @ sk_c8 ) = ( sk_c9 ) )),
% 0.57/0.92 inference('cnf.neg', [status(esa)], [prove_this_26])).
% 0.57/0.92 thf(zip_derived_cl28, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (sk_c7)) | ((multiply @ sk_c2 @ sk_c8) = (sk_c9)))),
% 0.57/0.92 inference('cnf', [status(esa)], [zf_stmt_11])).
% 0.57/0.92 thf(zip_derived_cl405, plain,
% 0.57/0.92 ((((multiply @ (multiply @ (inverse @ sk_c8) @ identity) @ sk_c8)
% 0.57/0.92 = (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl28])).
% 0.57/0.92 thf(zip_derived_cl2, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 0.57/0.92 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 0.57/0.92 inference('cnf', [status(esa)], [associativity])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl1, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_inverse])).
% 0.57/0.92 thf(zip_derived_cl418, plain,
% 0.57/0.92 ((((identity) = (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7))
% 0.57/0.92 | ((inverse @ sk_c8) = (sk_c7)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl405, zip_derived_cl2, zip_derived_cl0,
% 0.57/0.92 zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl419, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (sk_c7)) | ((identity) = (sk_c9)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl418])).
% 0.57/0.92 thf(zip_derived_cl609, plain,
% 0.57/0.92 ((((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c9))
% 0.57/0.92 | ((identity) = (sk_c9))
% 0.57/0.92 | ((identity) = (sk_c9)))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl598, zip_derived_cl419])).
% 0.57/0.92 thf(zip_derived_cl613, plain,
% 0.57/0.92 ((((identity) = (sk_c9))
% 0.57/0.92 | ((inverse @ sk_c8) = (multiply @ sk_c8 @ sk_c9)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl609])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2184, plain, (((sk_c8) = (identity))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2183])).
% 0.57/0.92 thf(zip_derived_cl0, plain,
% 0.57/0.92 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 0.57/0.92 inference('cnf', [status(esa)], [left_identity])).
% 0.57/0.92 thf(zip_derived_cl2268, plain,
% 0.57/0.92 ((((identity) = (sk_c9)) | ((identity) = (sk_c9)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl613, zip_derived_cl2184, zip_derived_cl1078,
% 0.57/0.92 zip_derived_cl2184, zip_derived_cl0])).
% 0.57/0.92 thf(zip_derived_cl2269, plain, (((identity) = (sk_c9))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2268])).
% 0.57/0.92 thf(zip_derived_cl2353, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((X5) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (identity))
% 0.57/0.92 | ((X4) != (identity))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((X3) != (X2))
% 0.57/0.92 | ((identity) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2323, zip_derived_cl2269])).
% 0.57/0.92 thf(zip_derived_cl2354, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((X3) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (X2))
% 0.57/0.92 | ((inverse @ X4) != (identity))
% 0.57/0.92 | ((X4) != (identity))
% 0.57/0.92 | ((inverse @ X5) != (identity))
% 0.57/0.92 | ((X5) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2353])).
% 0.57/0.92 thf(zip_derived_cl2355, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 0.57/0.92 (((X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((X3) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (identity))
% 0.57/0.92 | ((X4) != (identity))
% 0.57/0.92 | ((inverse @ X4) != (identity)))),
% 0.57/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2354])).
% 0.57/0.92 thf(zip_derived_cl2356, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (X2))
% 0.57/0.92 | ((inverse @ X3) != (identity))
% 0.57/0.92 | ((X3) != (identity))
% 0.57/0.92 | ((inverse @ identity) != (identity)))),
% 0.57/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2355])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2357, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (X2))
% 0.57/0.92 | ((inverse @ X3) != (identity))
% 0.57/0.92 | ((X3) != (identity))
% 0.57/0.92 | ((identity) != (identity)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2356, zip_derived_cl1078])).
% 0.57/0.92 thf(zip_derived_cl2358, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 0.57/0.92 (((X3) != (identity))
% 0.57/0.92 | ((inverse @ X3) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2357])).
% 0.57/0.92 thf(zip_derived_cl2359, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (X2))
% 0.57/0.92 | ((inverse @ identity) != (identity)))),
% 0.57/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2358])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2360, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((inverse @ X2) != (X2))
% 0.57/0.92 | ((identity) != (identity)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2359, zip_derived_cl1078])).
% 0.57/0.92 thf(zip_derived_cl2361, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i, X2 : $i]:
% 0.57/0.92 (((inverse @ X2) != (X2))
% 0.57/0.92 | ((inverse @ X2) != (identity))
% 0.57/0.92 | ((X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2360])).
% 0.57/0.92 thf(zip_derived_cl2362, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ identity) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (X1)))),
% 0.57/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2361])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2363, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 (((inverse @ X0) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((identity) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((inverse @ X1) != (X1)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2362, zip_derived_cl1078])).
% 0.57/0.92 thf(zip_derived_cl2364, plain,
% 0.57/0.92 (![X0 : $i, X1 : $i]:
% 0.57/0.92 (((inverse @ X1) != (X1))
% 0.57/0.92 | ((inverse @ X1) != (identity))
% 0.57/0.92 | ((X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2363])).
% 0.57/0.92 thf(zip_derived_cl2365, plain,
% 0.57/0.92 (![X0 : $i]:
% 0.57/0.92 (((inverse @ identity) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (X0)))),
% 0.57/0.92 inference('eq_res', [status(thm)], [zip_derived_cl2364])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2366, plain,
% 0.57/0.92 (![X0 : $i]:
% 0.57/0.92 (((identity) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (identity))
% 0.57/0.92 | ((inverse @ X0) != (X0)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2365, zip_derived_cl1078])).
% 0.57/0.92 thf(zip_derived_cl2367, plain,
% 0.57/0.92 (![X0 : $i]: (((inverse @ X0) != (X0)) | ((inverse @ X0) != (identity)))),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2366])).
% 0.57/0.92 thf(zip_derived_cl2412, plain,
% 0.57/0.92 ((((identity) != (identity)) | ((inverse @ identity) != (identity)))),
% 0.57/0.92 inference('sup-', [status(thm)], [zip_derived_cl1078, zip_derived_cl2367])).
% 0.57/0.92 thf(zip_derived_cl1078, plain, (((inverse @ identity) = (identity))),
% 0.57/0.92 inference('sup+', [status(thm)], [zip_derived_cl403, zip_derived_cl1])).
% 0.57/0.92 thf(zip_derived_cl2415, plain,
% 0.57/0.92 ((((identity) != (identity)) | ((identity) != (identity)))),
% 0.57/0.92 inference('demod', [status(thm)],
% 0.57/0.92 [zip_derived_cl2412, zip_derived_cl1078])).
% 0.57/0.92 thf(zip_derived_cl2416, plain, ($false),
% 0.57/0.92 inference('simplify', [status(thm)], [zip_derived_cl2415])).
% 0.57/0.92
% 0.57/0.92 % SZS output end Refutation
% 0.57/0.92
% 0.57/0.92
% 0.57/0.92 % Terminating...
% 0.57/0.96 % Runner terminated.
% 1.61/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------