TSTP Solution File: GRP340-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRP340-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YIPDnxce2M true
% Computer : n001.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 01:51:16 EDT 2023
% Result : Unsatisfiable 2.53s 1.59s
% Output : Refutation 6.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP340-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.YIPDnxce2M true
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 03:09:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % 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
% 0.21/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 2.53/1.59 % Solved by fo/fo7.sh.
% 2.53/1.59 % done 2138 iterations in 0.823s
% 2.53/1.59 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.53/1.59 % SZS output start Refutation
% 2.53/1.59 thf(sk_c8_type, type, sk_c8: $i).
% 2.53/1.59 thf(sk_c9_type, type, sk_c9: $i).
% 2.53/1.59 thf(sk_c6_type, type, sk_c6: $i).
% 2.53/1.59 thf(sk_c5_type, type, sk_c5: $i).
% 2.53/1.59 thf(sk_c4_type, type, sk_c4: $i).
% 2.53/1.59 thf(identity_type, type, identity: $i).
% 2.53/1.59 thf(multiply_type, type, multiply: $i > $i > $i).
% 2.53/1.59 thf(sk_c11_type, type, sk_c11: $i).
% 2.53/1.59 thf(sk_c2_type, type, sk_c2: $i).
% 2.53/1.59 thf(inverse_type, type, inverse: $i > $i).
% 2.53/1.59 thf(sk_c3_type, type, sk_c3: $i).
% 2.53/1.59 thf(sk_c1_type, type, sk_c1: $i).
% 2.53/1.59 thf(sk_c7_type, type, sk_c7: $i).
% 2.53/1.59 thf(sk_c10_type, type, sk_c10: $i).
% 2.53/1.59 thf(left_identity, axiom, (( multiply @ identity @ X ) = ( X ))).
% 2.53/1.59 thf(zip_derived_cl0, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.53/1.59 inference('cnf', [status(esa)], [left_identity])).
% 2.53/1.59 thf(left_inverse, axiom, (( multiply @ ( inverse @ X ) @ X ) = ( identity ))).
% 2.53/1.59 thf(zip_derived_cl1, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.53/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 2.53/1.59 thf(associativity, axiom,
% 2.53/1.59 (( multiply @ ( multiply @ X @ Y ) @ Z ) =
% 2.53/1.59 ( multiply @ X @ ( multiply @ Y @ Z ) ))).
% 2.53/1.59 thf(zip_derived_cl2, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 2.53/1.59 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 2.53/1.59 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 2.53/1.59 inference('cnf', [status(esa)], [associativity])).
% 2.53/1.59 thf(zip_derived_cl101, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((multiply @ identity @ X0)
% 2.53/1.59 = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl2])).
% 2.53/1.59 thf(zip_derived_cl0, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 2.53/1.59 inference('cnf', [status(esa)], [left_identity])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl180, plain,
% 2.53/1.59 (![X0 : $i]: ((X0) = (multiply @ (inverse @ identity) @ X0))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl0, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl254, plain,
% 2.53/1.59 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ identity)) @ X0))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl180, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl1, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.53/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 2.53/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 2.53/1.59 thf(prove_this_51, conjecture,
% 2.53/1.59 (~( ( ( multiply @ X7 @ X6 ) != ( X8 ) ) |
% 2.53/1.59 ( ( inverse @ X8 ) != ( X6 ) ) | ( ( inverse @ X7 ) != ( X8 ) ) |
% 2.53/1.59 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ X5 ) != ( X6 ) ) |
% 2.53/1.59 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 2.53/1.59 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( multiply @ X3 @ sk_c10 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) != ( sk_c9 ) ) ))).
% 2.53/1.59 thf(zf_stmt_0, negated_conjecture,
% 2.53/1.59 (( ( multiply @ X7 @ X6 ) != ( X8 ) ) | ( ( inverse @ X8 ) != ( X6 ) ) |
% 2.53/1.59 ( ( inverse @ X7 ) != ( X8 ) ) |
% 2.53/1.59 ( ( multiply @ X6 @ sk_c10 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ X5 ) != ( X6 ) ) |
% 2.53/1.59 ( ( multiply @ X5 @ X6 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ X2 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( multiply @ X2 @ sk_c10 ) != ( sk_c9 ) ) |
% 2.53/1.59 ( ( inverse @ X1 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( multiply @ X1 @ sk_c11 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( multiply @ X4 @ sk_c9 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( inverse @ X4 ) != ( sk_c10 ) ) |
% 2.53/1.59 ( ( multiply @ X3 @ sk_c10 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ X3 ) != ( sk_c11 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) != ( sk_c9 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_51])).
% 2.53/1.59 thf(zip_derived_cl53, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 2.53/1.59 (((multiply @ X1 @ X2) != (X0))
% 2.53/1.59 | ((inverse @ X0) != (X2))
% 2.53/1.59 | ((inverse @ X1) != (X0))
% 2.53/1.59 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 2.53/1.59 | ((inverse @ X3) != (X2))
% 2.53/1.59 | ((multiply @ X3 @ X2) != (sk_c11))
% 2.53/1.59 | ((inverse @ X4) != (sk_c10))
% 2.53/1.59 | ((multiply @ X4 @ sk_c10) != (sk_c9))
% 2.53/1.59 | ((inverse @ X5) != (sk_c11))
% 2.53/1.59 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 2.53/1.59 | ((multiply @ X6 @ sk_c9) != (sk_c10))
% 2.53/1.59 | ((inverse @ X6) != (sk_c10))
% 2.53/1.59 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 2.53/1.59 | ((inverse @ X7) != (sk_c11))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) != (sk_c9)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_0])).
% 2.53/1.59 thf(zip_derived_cl54, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 2.53/1.59 (((multiply @ X1 @ X2) != (X0))
% 2.53/1.59 | ((inverse @ X0) != (X2))
% 2.53/1.59 | ((inverse @ X1) != (X0))
% 2.53/1.59 | ((multiply @ X2 @ sk_c10) != (sk_c11))
% 2.53/1.59 | ((inverse @ X3) != (X2))
% 2.53/1.59 | ((multiply @ X3 @ X2) != (sk_c11))
% 2.53/1.59 | ((inverse @ X4) != (sk_c10))
% 2.53/1.59 | ((multiply @ X4 @ sk_c10) != (multiply @ sk_c10 @ sk_c11))
% 2.53/1.59 | ((inverse @ X5) != (sk_c11))
% 2.53/1.59 | ((multiply @ X5 @ sk_c11) != (sk_c10))
% 2.53/1.59 | ((multiply @ X6 @ (multiply @ sk_c10 @ sk_c11)) != (sk_c10))
% 2.53/1.59 | ((inverse @ X6) != (sk_c10))
% 2.53/1.59 | ((multiply @ X7 @ sk_c10) != (sk_c11))
% 2.53/1.59 | ((inverse @ X7) != (sk_c11))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) != (sk_c9)))),
% 2.53/1.59 inference('local_rewriting', [status(thm)], [zip_derived_cl53])).
% 2.53/1.59 thf(prove_this_36, conjecture,
% 2.53/1.59 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.53/1.59 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 2.53/1.59 thf(zf_stmt_1, negated_conjecture,
% 2.53/1.59 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) | ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_36])).
% 2.53/1.59 thf(zip_derived_cl38, plain,
% 2.53/1.59 ((((inverse @ sk_c5) = (sk_c8)) | ((inverse @ sk_c2) = (sk_c10)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_1])).
% 2.53/1.59 thf(prove_this_46, conjecture,
% 2.53/1.59 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 2.53/1.59 thf(zf_stmt_2, negated_conjecture,
% 2.53/1.59 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_46])).
% 2.53/1.59 thf(zip_derived_cl48, plain,
% 2.53/1.59 ((((inverse @ sk_c5) = (sk_c8)) | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_2])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl222, plain,
% 2.53/1.59 ((((sk_c9) = (multiply @ (inverse @ sk_c2) @ sk_c10))
% 2.53/1.59 | ((inverse @ sk_c5) = (sk_c8)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl48, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl2886, plain,
% 2.53/1.59 ((((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 2.53/1.59 | ((inverse @ sk_c5) = (sk_c8))
% 2.53/1.59 | ((inverse @ sk_c5) = (sk_c8)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl222])).
% 2.53/1.59 thf(zip_derived_cl2901, plain,
% 2.53/1.59 ((((inverse @ sk_c5) = (sk_c8))
% 2.53/1.59 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 2.53/1.59 inference('simplify', [status(thm)], [zip_derived_cl2886])).
% 2.53/1.59 thf(prove_this_35, conjecture,
% 2.53/1.59 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ sk_c2 ) = ( sk_c10 ) ) ))).
% 2.53/1.59 thf(zf_stmt_3, negated_conjecture,
% 2.53/1.59 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 2.53/1.59 ( ( inverse @ sk_c2 ) = ( sk_c10 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_35])).
% 2.53/1.59 thf(zip_derived_cl37, plain,
% 2.53/1.59 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 2.53/1.59 | ((inverse @ sk_c2) = (sk_c10)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 2.53/1.59 thf(prove_this_45, conjecture,
% 2.53/1.59 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) ) ))).
% 2.53/1.59 thf(zf_stmt_4, negated_conjecture,
% 2.53/1.59 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c2 @ sk_c9 ) = ( sk_c10 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_45])).
% 2.53/1.59 thf(zip_derived_cl47, plain,
% 2.53/1.59 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 2.53/1.59 | ((multiply @ sk_c2 @ sk_c9) = (sk_c10)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_4])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl221, plain,
% 2.53/1.59 ((((sk_c9) = (multiply @ (inverse @ sk_c2) @ sk_c10))
% 2.53/1.59 | ((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl47, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl5360, plain,
% 2.53/1.59 ((((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 2.53/1.59 | ((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 2.53/1.59 | ((multiply @ sk_c5 @ sk_c8) = (sk_c11)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl37, zip_derived_cl221])).
% 2.53/1.59 thf(zip_derived_cl5376, plain,
% 2.53/1.59 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 2.53/1.59 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 2.53/1.59 inference('simplify', [status(thm)], [zip_derived_cl5360])).
% 2.53/1.59 thf(zip_derived_cl5486, plain,
% 2.53/1.59 ((((multiply @ sk_c5 @ (inverse @ sk_c5)) = (sk_c11))
% 2.53/1.59 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 2.53/1.59 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl2901, zip_derived_cl5376])).
% 2.53/1.59 thf(zip_derived_cl1, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.53/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl181, plain,
% 2.53/1.59 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl134, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 2.53/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 2.53/1.59 thf(zip_derived_cl178, plain,
% 2.53/1.59 (![X0 : $i, X1 : $i]:
% 2.53/1.59 ((multiply @ X1 @ X0) = (multiply @ (inverse @ (inverse @ X1)) @ X0))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl134, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl1231, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 2.53/1.59 thf(zip_derived_cl181, plain,
% 2.53/1.59 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl1291, plain,
% 2.53/1.59 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl181])).
% 2.53/1.59 thf(zip_derived_cl1, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 2.53/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 2.53/1.59 thf(zip_derived_cl1296, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ X0 @ (inverse @ X0)) = (identity))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl1291, zip_derived_cl1])).
% 2.53/1.59 thf(zip_derived_cl5492, plain,
% 2.53/1.59 ((((identity) = (sk_c11))
% 2.53/1.59 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10))
% 2.53/1.59 | ((sk_c9) = (multiply @ sk_c10 @ sk_c10)))),
% 2.53/1.59 inference('demod', [status(thm)],
% 2.53/1.59 [zip_derived_cl5486, zip_derived_cl1296])).
% 2.53/1.59 thf(zip_derived_cl5493, plain,
% 2.53/1.59 ((((sk_c9) = (multiply @ sk_c10 @ sk_c10)) | ((identity) = (sk_c11)))),
% 2.53/1.59 inference('simplify', [status(thm)], [zip_derived_cl5492])).
% 2.53/1.59 thf(prove_this_8, conjecture,
% 2.53/1.59 (~( ( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 2.53/1.59 thf(zf_stmt_5, negated_conjecture,
% 2.53/1.59 (( ( inverse @ sk_c7 ) = ( sk_c6 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_8])).
% 2.53/1.59 thf(zip_derived_cl10, plain,
% 2.53/1.59 ((((inverse @ sk_c7) = (sk_c6))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_5])).
% 2.53/1.59 thf(prove_this_9, conjecture,
% 2.53/1.59 (~( ( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 2.53/1.59 thf(zf_stmt_6, negated_conjecture,
% 2.53/1.59 (( ( inverse @ sk_c6 ) = ( sk_c8 ) ) |
% 2.53/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 2.53/1.59 inference('cnf.neg', [status(esa)], [prove_this_9])).
% 2.53/1.59 thf(zip_derived_cl11, plain,
% 2.53/1.59 ((((inverse @ sk_c6) = (sk_c8))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 2.53/1.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 2.53/1.59 thf(zip_derived_cl62, plain,
% 2.53/1.59 ((((inverse @ (inverse @ sk_c7)) = (sk_c8))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl10, zip_derived_cl11])).
% 2.53/1.59 thf(zip_derived_cl63, plain,
% 2.53/1.59 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 2.53/1.59 | ((inverse @ (inverse @ sk_c7)) = (sk_c8)))),
% 2.53/1.59 inference('simplify', [status(thm)], [zip_derived_cl62])).
% 2.53/1.59 thf(zip_derived_cl181, plain,
% 2.53/1.59 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl134])).
% 2.53/1.59 thf(zip_derived_cl868, plain,
% 2.53/1.59 ((((sk_c7) = (multiply @ sk_c8 @ identity))
% 2.53/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl63, zip_derived_cl181])).
% 2.53/1.59 thf(zip_derived_cl1231, plain,
% 2.53/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 2.53/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl1284, plain,
% 6.54/1.59 ((((sk_c7) = (sk_c8)) | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl868, zip_derived_cl1231])).
% 6.54/1.59 thf(prove_this_6, conjecture,
% 6.54/1.59 (~( ( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 6.54/1.59 thf(zf_stmt_7, negated_conjecture,
% 6.54/1.59 (( ( inverse @ sk_c5 ) = ( sk_c8 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_6])).
% 6.54/1.59 thf(zip_derived_cl8, plain,
% 6.54/1.59 ((((inverse @ sk_c5) = (sk_c8))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_7])).
% 6.54/1.59 thf(zip_derived_cl11, plain,
% 6.54/1.59 ((((inverse @ sk_c6) = (sk_c8))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl61, plain,
% 6.54/1.59 ((((multiply @ sk_c8 @ sk_c6) = (identity))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl11, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl90, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c5) @ sk_c6) = (identity))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl8, zip_derived_cl61])).
% 6.54/1.59 thf(zip_derived_cl93, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c5) @ sk_c6) = (identity)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl90])).
% 6.54/1.59 thf(zip_derived_cl134, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl183, plain,
% 6.54/1.59 ((((sk_c6) = (multiply @ (inverse @ (inverse @ sk_c5)) @ identity))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl93, zip_derived_cl134])).
% 6.54/1.59 thf(zip_derived_cl181, plain,
% 6.54/1.59 (![X0 : $i]: ((X0) = (multiply @ (inverse @ (inverse @ X0)) @ identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl1, zip_derived_cl134])).
% 6.54/1.59 thf(zip_derived_cl1040, plain,
% 6.54/1.59 ((((sk_c6) = (sk_c5)) | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl183, zip_derived_cl181])).
% 6.54/1.59 thf(zip_derived_cl10, plain,
% 6.54/1.59 ((((inverse @ sk_c7) = (sk_c6))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_5])).
% 6.54/1.59 thf(zip_derived_cl1041, plain,
% 6.54/1.59 ((((inverse @ sk_c7) = (sk_c5))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl1040, zip_derived_cl10])).
% 6.54/1.59 thf(zip_derived_cl1051, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((inverse @ sk_c7) = (sk_c5)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl1041])).
% 6.54/1.59 thf(zip_derived_cl1334, plain,
% 6.54/1.59 ((((inverse @ sk_c8) = (sk_c5))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl1284, zip_derived_cl1051])).
% 6.54/1.59 thf(zip_derived_cl1338, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((inverse @ sk_c8) = (sk_c5)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl1334])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl2288, plain,
% 6.54/1.59 ((((multiply @ sk_c5 @ sk_c8) = (identity))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl1338, zip_derived_cl1])).
% 6.54/1.59 thf(prove_this_5, conjecture,
% 6.54/1.59 (~( ( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 6.54/1.59 thf(zf_stmt_8, negated_conjecture,
% 6.54/1.59 (( ( multiply @ sk_c5 @ sk_c8 ) = ( sk_c11 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_5])).
% 6.54/1.59 thf(zip_derived_cl7, plain,
% 6.54/1.59 ((((multiply @ sk_c5 @ sk_c8) = (sk_c11))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_8])).
% 6.54/1.59 thf(zip_derived_cl3779, plain,
% 6.54/1.59 ((((identity) = (sk_c11))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl2288, zip_derived_cl7])).
% 6.54/1.59 thf(zip_derived_cl3790, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9)) | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl3779])).
% 6.54/1.59 thf(zip_derived_cl5507, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) = (multiply @ sk_c10 @ sk_c10))
% 6.54/1.59 | ((identity) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl5493, zip_derived_cl3790])).
% 6.54/1.59 thf(zip_derived_cl5509, plain,
% 6.54/1.59 ((((identity) = (sk_c11))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (multiply @ sk_c10 @ sk_c10)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl5507])).
% 6.54/1.59 thf(zip_derived_cl134, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl5630, plain,
% 6.54/1.59 ((((sk_c11)
% 6.54/1.59 = (multiply @ (inverse @ sk_c10) @ (multiply @ sk_c10 @ sk_c10)))
% 6.54/1.59 | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl5509, zip_derived_cl134])).
% 6.54/1.59 thf(zip_derived_cl134, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl5633, plain,
% 6.54/1.59 ((((sk_c11) = (sk_c10)) | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl5630, zip_derived_cl134])).
% 6.54/1.59 thf(prove_this_12, conjecture,
% 6.54/1.59 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 6.54/1.59 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 6.54/1.59 thf(zf_stmt_9, negated_conjecture,
% 6.54/1.59 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 6.54/1.59 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_12])).
% 6.54/1.59 thf(zip_derived_cl14, plain,
% 6.54/1.59 ((((inverse @ sk_c3) = (sk_c11)) | ((inverse @ sk_c1) = (sk_c11)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_9])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl68, plain,
% 6.54/1.59 ((((multiply @ sk_c11 @ sk_c1) = (identity))
% 6.54/1.59 | ((inverse @ sk_c3) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl14, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl134, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl194, plain,
% 6.54/1.59 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity))
% 6.54/1.59 | ((inverse @ sk_c3) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl68, zip_derived_cl134])).
% 6.54/1.59 thf(prove_this_22, conjecture,
% 6.54/1.59 (~( ( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 6.54/1.59 thf(zf_stmt_10, negated_conjecture,
% 6.54/1.59 (( ( inverse @ sk_c3 ) = ( sk_c11 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_22])).
% 6.54/1.59 thf(zip_derived_cl24, plain,
% 6.54/1.59 ((((inverse @ sk_c3) = (sk_c11))
% 6.54/1.59 | ((multiply @ sk_c1 @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_10])).
% 6.54/1.59 thf(zip_derived_cl708, plain,
% 6.54/1.59 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c10)
% 6.54/1.59 = (sk_c11))
% 6.54/1.59 | ((inverse @ sk_c3) = (sk_c11))
% 6.54/1.59 | ((inverse @ sk_c3) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl24])).
% 6.54/1.59 thf(zip_derived_cl2, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.54/1.59 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.54/1.59 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.54/1.59 inference('cnf', [status(esa)], [associativity])).
% 6.54/1.59 thf(zip_derived_cl0, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_identity])).
% 6.54/1.59 thf(zip_derived_cl729, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((inverse @ sk_c3) = (sk_c11))
% 6.54/1.59 | ((inverse @ sk_c3) = (sk_c11)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl708, zip_derived_cl2, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl730, plain,
% 6.54/1.59 ((((inverse @ sk_c3) = (sk_c11))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl729])).
% 6.54/1.59 thf(zip_derived_cl1291, plain,
% 6.54/1.59 (![X0 : $i]: ((X0) = (inverse @ (inverse @ X0)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl1231, zip_derived_cl181])).
% 6.54/1.59 thf(zip_derived_cl3161, plain,
% 6.54/1.59 ((((sk_c3) = (inverse @ sk_c11))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl730, zip_derived_cl1291])).
% 6.54/1.59 thf(prove_this_11, conjecture,
% 6.54/1.59 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 6.54/1.59 ( ( inverse @ sk_c1 ) = ( sk_c11 ) ) ))).
% 6.54/1.59 thf(zf_stmt_11, negated_conjecture,
% 6.54/1.59 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 6.54/1.59 ( ( inverse @ sk_c1 ) = ( sk_c11 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_11])).
% 6.54/1.59 thf(zip_derived_cl13, plain,
% 6.54/1.59 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 6.54/1.59 | ((inverse @ sk_c1) = (sk_c11)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_11])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl74, plain,
% 6.54/1.59 ((((multiply @ sk_c11 @ sk_c1) = (identity))
% 6.54/1.59 | ((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl13, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl134, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl197, plain,
% 6.54/1.59 ((((sk_c1) = (multiply @ (inverse @ sk_c11) @ identity))
% 6.54/1.59 | ((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl74, zip_derived_cl134])).
% 6.54/1.59 thf(prove_this_21, conjecture,
% 6.54/1.59 (~( ( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) ) ))).
% 6.54/1.59 thf(zf_stmt_12, negated_conjecture,
% 6.54/1.59 (( ( multiply @ sk_c3 @ sk_c11 ) = ( sk_c10 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c1 @ sk_c10 ) = ( sk_c11 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_21])).
% 6.54/1.59 thf(zip_derived_cl23, plain,
% 6.54/1.59 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 6.54/1.59 | ((multiply @ sk_c1 @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_12])).
% 6.54/1.59 thf(zip_derived_cl1088, plain,
% 6.54/1.59 ((((multiply @ (multiply @ (inverse @ sk_c11) @ identity) @ sk_c10)
% 6.54/1.59 = (sk_c11))
% 6.54/1.59 | ((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 6.54/1.59 | ((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl197, zip_derived_cl23])).
% 6.54/1.59 thf(zip_derived_cl2, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.54/1.59 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.54/1.59 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.54/1.59 inference('cnf', [status(esa)], [associativity])).
% 6.54/1.59 thf(zip_derived_cl0, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_identity])).
% 6.54/1.59 thf(zip_derived_cl1114, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 6.54/1.59 | ((multiply @ sk_c3 @ sk_c11) = (sk_c10)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl1088, zip_derived_cl2, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl1115, plain,
% 6.54/1.59 ((((multiply @ sk_c3 @ sk_c11) = (sk_c10))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl1114])).
% 6.54/1.59 thf(zip_derived_cl14908, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c11) @ sk_c11) = (sk_c10))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl3161, zip_derived_cl1115])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl14915, plain,
% 6.54/1.59 ((((identity) = (sk_c10))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl14908, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl14916, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c10)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl14915])).
% 6.54/1.59 thf(zip_derived_cl14922, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c10) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c10)))),
% 6.54/1.59 inference('sup+', [status(thm)],
% 6.54/1.59 [zip_derived_cl5633, zip_derived_cl14916])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl14923, plain,
% 6.54/1.59 ((((identity) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c10)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl14922, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl14924, plain,
% 6.54/1.59 ((((identity) = (sk_c10)) | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl14923])).
% 6.54/1.59 thf(zip_derived_cl5633, plain,
% 6.54/1.59 ((((sk_c11) = (sk_c10)) | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl5630, zip_derived_cl134])).
% 6.54/1.59 thf(zip_derived_cl5669, plain,
% 6.54/1.59 ((((sk_c10) != (identity)) | ((identity) = (sk_c11)))),
% 6.54/1.59 inference('eq_fact', [status(thm)], [zip_derived_cl5633])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl14966, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X1) != (X0))
% 6.54/1.59 | ((multiply @ X2 @ sk_c10) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X2))
% 6.54/1.59 | ((multiply @ X3 @ X2) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (sk_c10))
% 6.54/1.59 | ((multiply @ X4 @ sk_c10) != (sk_c10))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X5) != (sk_c10))
% 6.54/1.59 | ((multiply @ X6 @ sk_c10) != (sk_c10))
% 6.54/1.59 | ((inverse @ X6) != (sk_c10))
% 6.54/1.59 | ((multiply @ X7 @ sk_c10) != (identity))
% 6.54/1.59 | ((inverse @ X7) != (identity))
% 6.54/1.59 | ((sk_c10) != (sk_c9)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl54, zip_derived_cl14927, zip_derived_cl14927,
% 6.54/1.59 zip_derived_cl14927, zip_derived_cl1231, zip_derived_cl14927,
% 6.54/1.59 zip_derived_cl14927, zip_derived_cl1231, zip_derived_cl14927,
% 6.54/1.59 zip_derived_cl1231, zip_derived_cl14927, zip_derived_cl14927,
% 6.54/1.59 zip_derived_cl14927, zip_derived_cl1231])).
% 6.54/1.59 thf(zip_derived_cl14916, plain,
% 6.54/1.59 ((((multiply @ (inverse @ sk_c11) @ sk_c10) = (sk_c11))
% 6.54/1.59 | ((identity) = (sk_c10)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl14915])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl0, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_identity])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl15131, plain,
% 6.54/1.59 ((((sk_c10) = (identity)) | ((identity) = (sk_c10)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl14916, zip_derived_cl14927, zip_derived_cl976,
% 6.54/1.59 zip_derived_cl0, zip_derived_cl14927])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(prove_this_4, conjecture,
% 6.54/1.59 (~( ( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 6.54/1.59 thf(zf_stmt_13, negated_conjecture,
% 6.54/1.59 (( ( inverse @ sk_c4 ) = ( sk_c10 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_4])).
% 6.54/1.59 thf(zip_derived_cl6, plain,
% 6.54/1.59 ((((inverse @ sk_c4) = (sk_c10))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_13])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl60, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c4) = (identity))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl6, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl134, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 ((X0) = (multiply @ (inverse @ X1) @ (multiply @ X1 @ X0)))),
% 6.54/1.59 inference('demod', [status(thm)], [zip_derived_cl101, zip_derived_cl0])).
% 6.54/1.59 thf(zip_derived_cl184, plain,
% 6.54/1.59 ((((sk_c4) = (multiply @ (inverse @ sk_c10) @ identity))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl60, zip_derived_cl134])).
% 6.54/1.59 thf(prove_this_3, conjecture,
% 6.54/1.59 (~( ( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) ) ))).
% 6.54/1.59 thf(zf_stmt_14, negated_conjecture,
% 6.54/1.59 (( ( multiply @ sk_c4 @ sk_c10 ) = ( sk_c9 ) ) |
% 6.54/1.59 ( ( multiply @ sk_c10 @ sk_c11 ) = ( sk_c9 ) )),
% 6.54/1.59 inference('cnf.neg', [status(esa)], [prove_this_3])).
% 6.54/1.59 thf(zip_derived_cl5, plain,
% 6.54/1.59 ((((multiply @ sk_c4 @ sk_c10) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('cnf', [status(esa)], [zf_stmt_14])).
% 6.54/1.59 thf(zip_derived_cl418, plain,
% 6.54/1.59 ((((multiply @ (multiply @ (inverse @ sk_c10) @ identity) @ sk_c10)
% 6.54/1.59 = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl184, zip_derived_cl5])).
% 6.54/1.59 thf(zip_derived_cl2, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.54/1.59 ((multiply @ (multiply @ X0 @ X1) @ X2)
% 6.54/1.59 = (multiply @ X0 @ (multiply @ X1 @ X2)))),
% 6.54/1.59 inference('cnf', [status(esa)], [associativity])).
% 6.54/1.59 thf(zip_derived_cl0, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ identity @ X0) = (X0))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_identity])).
% 6.54/1.59 thf(zip_derived_cl1, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ (inverse @ X0) @ X0) = (identity))),
% 6.54/1.59 inference('cnf', [status(esa)], [left_inverse])).
% 6.54/1.59 thf(zip_derived_cl421, plain,
% 6.54/1.59 ((((identity) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9))
% 6.54/1.59 | ((multiply @ sk_c10 @ sk_c11) = (sk_c9)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl418, zip_derived_cl2, zip_derived_cl0,
% 6.54/1.59 zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl422, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) = (sk_c9)) | ((identity) = (sk_c9)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl421])).
% 6.54/1.59 thf(zip_derived_cl436, plain,
% 6.54/1.59 ((((multiply @ sk_c10 @ sk_c11) != (identity)) | ((identity) = (sk_c9)))),
% 6.54/1.59 inference('eq_fact', [status(thm)], [zip_derived_cl422])).
% 6.54/1.59 thf(zip_derived_cl14927, plain, (((identity) = (sk_c11))),
% 6.54/1.59 inference('clc', [status(thm)], [zip_derived_cl14924, zip_derived_cl5669])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl15007, plain,
% 6.54/1.59 ((((sk_c10) != (identity)) | ((identity) = (sk_c9)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl436, zip_derived_cl14927, zip_derived_cl1231])).
% 6.54/1.59 thf(zip_derived_cl15132, plain, (((sk_c10) = (identity))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15131])).
% 6.54/1.59 thf(zip_derived_cl15221, plain,
% 6.54/1.59 ((((identity) != (identity)) | ((identity) = (sk_c9)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15007, zip_derived_cl15132])).
% 6.54/1.59 thf(zip_derived_cl15222, plain, (((identity) = (sk_c9))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15221])).
% 6.54/1.59 thf(zip_derived_cl15253, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X1) != (X0))
% 6.54/1.59 | ((X2) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X2))
% 6.54/1.59 | ((multiply @ X3 @ X2) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((X6) != (identity))
% 6.54/1.59 | ((inverse @ X6) != (identity))
% 6.54/1.59 | ((X7) != (identity))
% 6.54/1.59 | ((inverse @ X7) != (identity))
% 6.54/1.59 | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl14966, zip_derived_cl15132, zip_derived_cl1231,
% 6.54/1.59 zip_derived_cl15132, zip_derived_cl15132, zip_derived_cl1231,
% 6.54/1.59 zip_derived_cl15132, zip_derived_cl15132,
% 6.54/1.59 zip_derived_cl15132, zip_derived_cl1231, zip_derived_cl15132,
% 6.54/1.59 zip_derived_cl15132, zip_derived_cl15132, zip_derived_cl1231,
% 6.54/1.59 zip_derived_cl15132, zip_derived_cl15222])).
% 6.54/1.59 thf(zip_derived_cl15254, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i, X7 : $i]:
% 6.54/1.59 (((inverse @ X7) != (identity))
% 6.54/1.59 | ((X7) != (identity))
% 6.54/1.59 | ((inverse @ X6) != (identity))
% 6.54/1.59 | ((X6) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((multiply @ X3 @ X2) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X2))
% 6.54/1.59 | ((X2) != (identity))
% 6.54/1.59 | ((inverse @ X1) != (X0))
% 6.54/1.59 | ((inverse @ X0) != (X2))
% 6.54/1.59 | ((multiply @ X1 @ X2) != (X0)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15253])).
% 6.54/1.59 thf(zip_derived_cl15255, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((X6) != (identity))
% 6.54/1.59 | ((inverse @ X6) != (identity))
% 6.54/1.59 | ((inverse @ identity) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15254])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl15256, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((X6) != (identity))
% 6.54/1.59 | ((inverse @ X6) != (identity))
% 6.54/1.59 | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15255, zip_derived_cl976])).
% 6.54/1.59 thf(zip_derived_cl15257, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i, X6 : $i]:
% 6.54/1.59 (((inverse @ X6) != (identity))
% 6.54/1.59 | ((X6) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((multiply @ X1 @ X0) != (X2)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15256])).
% 6.54/1.59 thf(zip_derived_cl15258, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((inverse @ identity) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15257])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl15259, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X5) != (identity))
% 6.54/1.59 | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15258, zip_derived_cl976])).
% 6.54/1.59 thf(zip_derived_cl15260, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 6.54/1.59 (((X5) != (identity))
% 6.54/1.59 | ((inverse @ X5) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((multiply @ X1 @ X0) != (X2)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15259])).
% 6.54/1.59 thf(zip_derived_cl15261, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((inverse @ identity) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15260])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl15262, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((X4) != (identity))
% 6.54/1.59 | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15261, zip_derived_cl976])).
% 6.54/1.59 thf(zip_derived_cl15263, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 6.54/1.59 (((X4) != (identity))
% 6.54/1.59 | ((inverse @ X4) != (identity))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((multiply @ X1 @ X0) != (X2)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15262])).
% 6.54/1.59 thf(zip_derived_cl15264, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ identity) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15263])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl15265, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.54/1.59 (((multiply @ X1 @ X0) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15264, zip_derived_cl976])).
% 6.54/1.59 thf(zip_derived_cl15266, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 6.54/1.59 (((multiply @ X3 @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X3) != (X0))
% 6.54/1.59 | ((X0) != (identity))
% 6.54/1.59 | ((inverse @ X1) != (X2))
% 6.54/1.59 | ((inverse @ X2) != (X0))
% 6.54/1.59 | ((multiply @ X1 @ X0) != (X2)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15265])).
% 6.54/1.59 thf(zip_derived_cl15267, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.54/1.59 (((multiply @ X0 @ identity) != (X1))
% 6.54/1.59 | ((inverse @ X1) != (identity))
% 6.54/1.59 | ((inverse @ X0) != (X1))
% 6.54/1.59 | ((inverse @ X2) != (identity))
% 6.54/1.59 | ((multiply @ X2 @ identity) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15266])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl1231, plain,
% 6.54/1.59 (![X0 : $i]: ((multiply @ X0 @ identity) = (X0))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl178])).
% 6.54/1.59 thf(zip_derived_cl15268, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 6.54/1.59 (((X0) != (X1))
% 6.54/1.59 | ((inverse @ X1) != (identity))
% 6.54/1.59 | ((inverse @ X0) != (X1))
% 6.54/1.59 | ((inverse @ X2) != (identity))
% 6.54/1.59 | ((X2) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15267, zip_derived_cl1231, zip_derived_cl1231])).
% 6.54/1.59 thf(zip_derived_cl15321, plain,
% 6.54/1.59 (![X0 : $i, X1 : $i]:
% 6.54/1.59 (((X0) != (identity))
% 6.54/1.59 | ((inverse @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X1) != (X1))
% 6.54/1.59 | ((inverse @ X1) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15268])).
% 6.54/1.59 thf(zip_derived_cl15322, plain,
% 6.54/1.59 (![X0 : $i]:
% 6.54/1.59 (((inverse @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X0) != (X0))
% 6.54/1.59 | ((inverse @ identity) != (identity)))),
% 6.54/1.59 inference('eq_res', [status(thm)], [zip_derived_cl15321])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl15323, plain,
% 6.54/1.59 (![X0 : $i]:
% 6.54/1.59 (((inverse @ X0) != (identity))
% 6.54/1.59 | ((inverse @ X0) != (X0))
% 6.54/1.59 | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15322, zip_derived_cl976])).
% 6.54/1.59 thf(zip_derived_cl15324, plain,
% 6.54/1.59 (![X0 : $i]: (((inverse @ X0) != (X0)) | ((inverse @ X0) != (identity)))),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15323])).
% 6.54/1.59 thf(zip_derived_cl15325, plain,
% 6.54/1.59 ((((identity) != (identity)) | ((inverse @ identity) != (identity)))),
% 6.54/1.59 inference('sup-', [status(thm)], [zip_derived_cl976, zip_derived_cl15324])).
% 6.54/1.59 thf(zip_derived_cl976, plain, (((inverse @ identity) = (identity))),
% 6.54/1.59 inference('sup+', [status(thm)], [zip_derived_cl254, zip_derived_cl1])).
% 6.54/1.59 thf(zip_derived_cl15329, plain,
% 6.54/1.59 ((((identity) != (identity)) | ((identity) != (identity)))),
% 6.54/1.59 inference('demod', [status(thm)],
% 6.54/1.59 [zip_derived_cl15325, zip_derived_cl976])).
% 6.54/1.59 thf(zip_derived_cl15330, plain, ($false),
% 6.54/1.59 inference('simplify', [status(thm)], [zip_derived_cl15329])).
% 6.54/1.59
% 6.54/1.59 % SZS output end Refutation
% 6.54/1.59
% 6.54/1.59
% 6.54/1.59 % Terminating...
% 7.45/1.69 % Runner terminated.
% 7.45/1.70 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------